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B. Coins
<div class="problem-statement"><div class="header"><div class="title">B. Coins</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>In Berland a money reform is being prepared. New coins are being introduced. After long economic calculations was decided that the most expensive coin should possess the denomination of exactly <span class="tex-span"><i>n</i></span> Berland dollars. Also the following restriction has been introduced for comfort: the denomination of each coin <span class="tex-font-style-bf">should be divisible</span> by the denomination of any cheaper coin. It is known that among all the possible variants the variant with the largest number of new coins will be chosen. Find this variant. Print in the order of decreasing of the coins' denominations.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first and only line contains an integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">6</sup></span>) which represents the denomination of the most expensive coin. </p></div><div class="output-specification"><div class="section-title">Output</div><p>Print the denominations of all the coins in the order of decreasing. The number of coins must be the largest possible (with the given denomination <span class="tex-span"><i>n</i></span> of the most expensive coin). Also, the denomination of every coin must be divisible by the denomination of any cheaper coin. Naturally, the denominations of all the coins should be different. If there are several solutins to that problem, print any of them.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>10<br/></pre></div><div class="output"><div class="title">Output</div><pre>10 5 1<br/></pre></div><div class="input"><div class="title">Input</div><pre>4<br/></pre></div><div class="output"><div class="title">Output</div><pre>4 2 1<br/></pre></div><div class="input"><div class="title">Input</div><pre>3<br/></pre></div><div class="output"><div class="title">Output</div><pre>3 1<br/></pre></div></div></div></div>
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Coins</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>In Berland a money reform is being prepared. New coins are being introduced. After long economic calculations was decided that the most expensive coin should possess the denomination of exactly <span class="tex-span"><i>n</i></span> Berland dollars. Also the following restriction has been introduced for comfort: the denomination of each coin <span class="tex-font-style-bf">should be divisible</span> by the denomination of any cheaper coin. It is known that among all the possible variants the variant with the largest number of new coins will be chosen. Find this variant. Print in the order of decreasing of the coins' denominations.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first and only line contains an integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">6</sup></span>) which represents the denomination of the most expensive coin. </p></div><div class="output-specification"><div class="section-title">Output</div><p>Print the denominations of all the coins in the order of decreasing. The number of coins must be the largest possible (with the given denomination <span class="tex-span"><i>n</i></span> of the most expensive coin). Also, the denomination of every coin must be divisible by the denomination of any cheaper coin. Naturally, the denominations of all the coins should be different. 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["Greedy algorithms"]
["greedy", "*1300"]
https://codeforces.com/blog/entry/1771
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Chat room<br /></b><div align="left">Solution is greedy algorithm. The first thing we do is find in our string the first letter 'h'. Then we find letter 'e' which is righter that found 'h'. If we find the whole word 'hello' in such way, obliviously, answer is YES.<br />Now let's prove that if answer exists, we find it. Let see on position of the 'h' in right answer. If we move it to the first 'h' in our string, nothing changes. But now we can say that our greedy algorithm correctly Now let's do such with the second letter, and so on.<br />We have greedy algorithm with work time O(n), where n - length of the input.<br /></div><br /><div align="left"><div align="center"><b>Problem B. Coins<br /></b><div align="left">This problem also have greedy solution: we run down all number from 2 and greater and while denomination of the last added to answer coin is divisible by current number, we divide and increase answer.<br />You can prove correctness, if you take a look at prime factorizations of coins' denominations. In each next denomination each prime have less or equal power than the current one (it's equivalent to '<span class="tex-span"><i>a</i></span> divide <span class="tex-span"><i>b</i></span>'). Obliviously, if summary degree of primes decreases at least two (for example, we had number<span class="tex-span"><i>a</i> = <i>x</i>· <i>y</i>· <i>z</i></span> (where <span class="tex-span"><i>y</i>, <i>z</i> &gt; 1</span>, and the current number is <span class="tex-span"><i>b</i> = <i>x</i></span>), then we can add one more coin with demonitaion <span class="tex-span"><i>a</i> &gt; <i>c</i> = <i>x</i>· <i>y</i> &gt; <i>b</i></span>. So, in the optimal answer sum of degrees decreasing at exactly one. Our greedy algorithm do exactly what it need.<br /><br /><div align="center"><b>Problem C. Trees.</b><br /><div align="left">The first thing we notice - beautiful sequence is can be determined with any member. The next thing - at least one tree will remain the same height. Prove: let's fix height of the first tree, and correct heights of all other ones. Obliviously, they all remain positive.<br />Solution with work time <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">2</sup>)</span>: we run down which tree we will fix, determine required height of the first tree and then relax answer.<br />This solution can be optimized to linear solution: if we don't touch some tree, we know the first element of sequence. Let's count for each possible element amount of trees, which have required height. It can be done with linear loop and the 'increment' operation on array. After that we just find value of the first element, for which amount of 'good' trees is maximal and output <span class="tex-span"><i>n</i> - <i>x</i></span>, where <span class="tex-span"><i>x</i></span> is this amount.<br /><div align="center"><b><br />Problem D. Calendar</b><br /><div align="left">We know, that all lines of calendar should have equal length, so we can find this length. It's just <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/8cef3c7e80f6e681d72233b1fd7d682f2480a9a7.png" style="max-width: 100.0%;max-height: 100.0%;" />, where <span class="tex-span"><i>suml</i></span> - summary length of all strings. Now let take a look at string, which will be the first one in our calendar. Obliviously, it's profitably to take string with maximal <span class="tex-span"><i>s</i> + <i>d</i></span> (where <span class="tex-span"><i>s</i></span> is our string and <span class="tex-span"><i>d</i></span> - is character from input). Such string is unique otherwise we have two equal strings in input (as <span class="tex-span"><i>d</i></span> is not contained in any string); Of cause, you should remember that if you fix the first string in a line, you fix length of the second one - it's required to have at least one such. Great, now we know the first string in our calendar. Now let's determine the second one. We know it's length, so we need just to take minimal string with such length.<br />We know one line, let's do similary with the second line and so on.<br /></div><div align="left"><br /><div align="center"><b>Problem E. Expression</b><br /><div align="left">Under construction. The main idea is 3D dynamic with O(<span class="tex-span">10<sup class="upper-index">2</sup></span>) transition.<br /></div></div></div></div></div></div></div></div></div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/58" class="notice" style="text-decoration: none;">Codeforces Beta Round 54 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-1484-1771").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "1484", blogEntryId: "1771", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=beta+round+%2354" class="tag notice" style="text-decoration: none;">beta round #54</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=tutorial" class="tag notice" style="text-decoration: none;">tutorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1771"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+25</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1771"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/yeputons"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/yeputons"> yeputons </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Apr/20/2011 14:44">12 years ago</span> </li> <li> <a href="/blog/entry/1771#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1771#comments"> 25 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1781"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (6)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="34253" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/iman_MC" style="position: relative;"> <img src='https://userpic.codeforces.org/2447/avatar/b2ab3e48d7eb8c6.jpg'/> </a> <div><a href="/profile/iman_MC" title="Pupil iman_MC" class="rated-user user-green">iman_MC</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/23/2011 19:32">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34253" href="?#comment-34253" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34253" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="2447" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34253"> <div class="moveup"> <div class="ttypography">Really thanks for your Problem analysis .<br />I hope you complete this with write part E , good luck man :D</div> </div> </div> <div class="reply info"> <a class="comment-34253 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34253 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34253"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="322835" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/1005032.maa2" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/1005032.maa2" title="Unrated, 1005032.maa2" class="rated-user user-black">1005032.maa2</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Oct/28/2016 08:13">7 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-322835" href="?#comment-322835" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="322835" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="483783" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-322835"> <div class="moveup"> <div class="ttypography"><p>Good Job Man</p></div> </div> </div> <div class="reply info"> <a class="comment-322835 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-322835 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-322835"> <li> <div class="comment"> <table class="comment-table" commentId="322890" commentParentId="322835"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Krktv" style="position: relative;"> <img src='https://userpic.codeforces.org/282980/avatar/a606aa5c5f801b89.jpg'/> </a> <div><a href="/profile/Krktv" title="Candidate Master Krktv" class="rated-user user-violet">Krktv</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Oct/29/2016 01:56">7 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-322890" href="?#comment-322890" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-322835" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="322890" class="CommentVoteFrame" data-commentRating="13" data-commentUserId="282980" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+13</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-322890"> <div class="moveup"> <div class="ttypography"><p>And necroposting is not a good job</p></div> </div> </div> <div class="reply info"> <a class="comment-322890 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-322890 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-322890"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="442334" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/berserker" style="position: relative;"> <img src='https://userpic.codeforces.org/492227/avatar/94b128dc6f18638b.jpg'/> </a> <div><a href="/profile/berserker" title="Expert berserker" class="rated-user user-blue">berserker</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jul/03/2018 20:57">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-442334" href="?#comment-442334" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="442334" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="492227" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-442334"> <div class="moveup"> <div class="ttypography"><p>Can anyone give ideas about the DP solution for E.</p></div> </div> </div> <div class="reply info"> <a class="comment-442334 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-442334 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-442334"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="498855" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Bekh" style="position: relative;"> <img src='https://userpic.codeforces.org/617670/avatar/3bb275557d131f6c.jpg'/> </a> <div><a href="/profile/Bekh" title="Master Bekh" class="rated-user user-orange">Bekh</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/13/2019 07:15">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-498855" href="?#comment-498855" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="498855" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="617670" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-498855"> <div class="moveup"> <div class="ttypography"><p>I'm 8 years late, but <a href="/contest/58/problem/C" title="Codeforces Beta Round 54 (Div. 2)">58C - Trees</a> has weak testcases. some solutions pass although they allow some tree heights to become non positive. </p><p>Case:<br /><code>10</code><br /><code>1 1 1 2 3 3 2 1 1 1</code> </p><p>Answer should be 8, (correct sequence: <code>1 2 3 4 5 5 4 3 2 1</code>) </p><p>Wrong answer is 4, (Assumes the correct sequence is: <code>-1 0 1 2 3 3 2 1 0 -1</code>)</p><p>Wrong submission: <a href="/contest/58/submission/51244937" title="Submission 51244937 by Bekh">51244937</a><br />Correct submission: <a href="/contest/58/submission/51245002" title="Submission 51245002 by Bekh">51245002</a></p></div> </div> </div> <div class="reply info"> <a class="comment-498855 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-498855 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-498855"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="556210" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Kylin_" style="position: relative;"> <img src='https://userpic.codeforces.org/1193717/avatar/2296672a2c313067.jpg'/> </a> <div><a href="/profile/Kylin_" title="Expert Kylin_" class="rated-user user-blue">Kylin_</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Nov/05/2019 09:12">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-556210" href="?#comment-556210" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="556210" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1193717" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-556210"> <div class="moveup"> <div class="ttypography"><p>So when we can get the solution of E?</p></div> </div> </div> <div class="reply info"> <a class="comment-556210 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-556210 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-556210"> </ul> </div> <br/> <div id="editBox-1781" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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58C
58
C
en
C. Trees
<div class="problem-statement"><div class="header"><div class="title">C. Trees</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>On Bertown's main street <span class="tex-span"><i>n</i></span> trees are growing, the tree number <span class="tex-span"><i>i</i></span> has the height of <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> meters (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>n</i></span>). By the arrival of the President of Berland these trees were decided to be changed so that their heights formed a <span class="tex-font-style-underline">beautiful</span> sequence. This means that the heights of trees on ends (the <span class="tex-span">1</span>st one and the <span class="tex-span"><i>n</i></span>-th one) should be equal to each other, the heights of the <span class="tex-span">2</span>-nd and the <span class="tex-span">(<i>n</i> - 1)</span>-th tree must also be equal to each other, at that the height of the <span class="tex-span">2</span>-nd tree should be larger than the height of the first tree by <span class="tex-span">1</span>, and so on. In other words, the heights of the trees, standing at equal distance from the edge (of one end of the sequence) must be equal to each other, and with the increasing of the distance from the edge by <span class="tex-span">1</span> the tree height must also increase by <span class="tex-span">1</span>. For example, the sequences "<span class="tex-font-style-tt">2 3 4 5 5 4 3 2</span>" and "<span class="tex-font-style-tt">1 2 3 2 1</span>" are beautiful, and '<span class="tex-font-style-tt">1 3 3 1</span>" and "<span class="tex-font-style-tt">1 2 3 1</span>" are not. </p><p>Changing the height of a tree is a very expensive operation, using advanced technologies invented by Berland scientists. In one operation you can choose any tree and change its height to any number, either increase or decrease. Note that even after the change the height should remain a positive integer, i. e, it can't be less than or equal to zero. Identify the smallest number of changes of the trees' height needed for the sequence of their heights to become beautiful.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup></span>) which is the number of trees. The second line contains integers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">5</sup></span>) which are the heights of the trees.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single number which is the minimal number of trees whose heights will have to be changed for the sequence to become beautiful.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br/>2 2 2<br/></pre></div><div class="output"><div class="title">Output</div><pre>1<br/></pre></div><div class="input"><div class="title">Input</div><pre>4<br/>1 2 2 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>0<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="C" data-uuid="ps_fd0137d5e765ab69d20a28b4e805683b937f537d"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. Trees</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>On Bertown's main street <span class="tex-span"><i>n</i></span> trees are growing, the tree number <span class="tex-span"><i>i</i></span> has the height of <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> meters (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>n</i></span>). By the arrival of the President of Berland these trees were decided to be changed so that their heights formed a <span class="tex-font-style-underline">beautiful</span> sequence. This means that the heights of trees on ends (the <span class="tex-span">1</span>st one and the <span class="tex-span"><i>n</i></span>-th one) should be equal to each other, the heights of the <span class="tex-span">2</span>-nd and the <span class="tex-span">(<i>n</i> - 1)</span>-th tree must also be equal to each other, at that the height of the <span class="tex-span">2</span>-nd tree should be larger than the height of the first tree by <span class="tex-span">1</span>, and so on. In other words, the heights of the trees, standing at equal distance from the edge (of one end of the sequence) must be equal to each other, and with the increasing of the distance from the edge by <span class="tex-span">1</span> the tree height must also increase by <span class="tex-span">1</span>. For example, the sequences &quot;<span class="tex-font-style-tt">2 3 4 5 5 4 3 2</span>&quot; and &quot;<span class="tex-font-style-tt">1 2 3 2 1</span>&quot; are beautiful, and '<span class="tex-font-style-tt">1 3 3 1</span>&quot; and &quot;<span class="tex-font-style-tt">1 2 3 1</span>&quot; are not. </p><p>Changing the height of a tree is a very expensive operation, using advanced technologies invented by Berland scientists. In one operation you can choose any tree and change its height to any number, either increase or decrease. Note that even after the change the height should remain a positive integer, i. e, it can't be less than or equal to zero. Identify the smallest number of changes of the trees' height needed for the sequence of their heights to become beautiful.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup></span>) which is the number of trees. The second line contains integers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">5</sup></span>) which are the heights of the trees.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single number which is the minimal number of trees whose heights will have to be changed for the sequence to become beautiful.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br />2 2 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>1<br /></pre></div><div class="input"><div class="title">Input</div><pre>4<br />1 2 2 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>0<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=C]"); 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["Brute force"]
["brute force", "*1800"]
https://codeforces.com/blog/entry/1771
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Chat room<br /></b><div align="left">Solution is greedy algorithm. The first thing we do is find in our string the first letter 'h'. Then we find letter 'e' which is righter that found 'h'. If we find the whole word 'hello' in such way, obliviously, answer is YES.<br />Now let's prove that if answer exists, we find it. Let see on position of the 'h' in right answer. If we move it to the first 'h' in our string, nothing changes. But now we can say that our greedy algorithm correctly Now let's do such with the second letter, and so on.<br />We have greedy algorithm with work time O(n), where n - length of the input.<br /></div><br /><div align="left"><div align="center"><b>Problem B. Coins<br /></b><div align="left">This problem also have greedy solution: we run down all number from 2 and greater and while denomination of the last added to answer coin is divisible by current number, we divide and increase answer.<br />You can prove correctness, if you take a look at prime factorizations of coins' denominations. In each next denomination each prime have less or equal power than the current one (it's equivalent to '<span class="tex-span"><i>a</i></span> divide <span class="tex-span"><i>b</i></span>'). Obliviously, if summary degree of primes decreases at least two (for example, we had number<span class="tex-span"><i>a</i> = <i>x</i>· <i>y</i>· <i>z</i></span> (where <span class="tex-span"><i>y</i>, <i>z</i> &gt; 1</span>, and the current number is <span class="tex-span"><i>b</i> = <i>x</i></span>), then we can add one more coin with demonitaion <span class="tex-span"><i>a</i> &gt; <i>c</i> = <i>x</i>· <i>y</i> &gt; <i>b</i></span>. So, in the optimal answer sum of degrees decreasing at exactly one. Our greedy algorithm do exactly what it need.<br /><br /><div align="center"><b>Problem C. Trees.</b><br /><div align="left">The first thing we notice - beautiful sequence is can be determined with any member. The next thing - at least one tree will remain the same height. Prove: let's fix height of the first tree, and correct heights of all other ones. Obliviously, they all remain positive.<br />Solution with work time <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">2</sup>)</span>: we run down which tree we will fix, determine required height of the first tree and then relax answer.<br />This solution can be optimized to linear solution: if we don't touch some tree, we know the first element of sequence. Let's count for each possible element amount of trees, which have required height. It can be done with linear loop and the 'increment' operation on array. After that we just find value of the first element, for which amount of 'good' trees is maximal and output <span class="tex-span"><i>n</i> - <i>x</i></span>, where <span class="tex-span"><i>x</i></span> is this amount.<br /><div align="center"><b><br />Problem D. Calendar</b><br /><div align="left">We know, that all lines of calendar should have equal length, so we can find this length. It's just <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/8cef3c7e80f6e681d72233b1fd7d682f2480a9a7.png" style="max-width: 100.0%;max-height: 100.0%;" />, where <span class="tex-span"><i>suml</i></span> - summary length of all strings. Now let take a look at string, which will be the first one in our calendar. Obliviously, it's profitably to take string with maximal <span class="tex-span"><i>s</i> + <i>d</i></span> (where <span class="tex-span"><i>s</i></span> is our string and <span class="tex-span"><i>d</i></span> - is character from input). Such string is unique otherwise we have two equal strings in input (as <span class="tex-span"><i>d</i></span> is not contained in any string); Of cause, you should remember that if you fix the first string in a line, you fix length of the second one - it's required to have at least one such. Great, now we know the first string in our calendar. Now let's determine the second one. We know it's length, so we need just to take minimal string with such length.<br />We know one line, let's do similary with the second line and so on.<br /></div><div align="left"><br /><div align="center"><b>Problem E. Expression</b><br /><div align="left">Under construction. The main idea is 3D dynamic with O(<span class="tex-span">10<sup class="upper-index">2</sup></span>) transition.<br /></div></div></div></div></div></div></div></div></div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/58" class="notice" style="text-decoration: none;">Codeforces Beta Round 54 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-1484-1771").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "1484", blogEntryId: "1771", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=beta+round+%2354" class="tag notice" style="text-decoration: none;">beta round #54</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=tutorial" class="tag notice" style="text-decoration: none;">tutorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1771"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+25</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1771"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/yeputons"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/yeputons"> yeputons </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Apr/20/2011 14:44">12 years ago</span> </li> <li> <a href="/blog/entry/1771#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1771#comments"> 25 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1781"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (6)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="34253" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/iman_MC" style="position: relative;"> <img src='https://userpic.codeforces.org/2447/avatar/b2ab3e48d7eb8c6.jpg'/> </a> <div><a href="/profile/iman_MC" title="Pupil iman_MC" class="rated-user user-green">iman_MC</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/23/2011 19:32">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34253" href="?#comment-34253" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34253" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="2447" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34253"> <div class="moveup"> <div class="ttypography">Really thanks for your Problem analysis .<br />I hope you complete this with write part E , good luck man :D</div> </div> </div> <div class="reply info"> <a class="comment-34253 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34253 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34253"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="322835" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/1005032.maa2" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/1005032.maa2" title="Unrated, 1005032.maa2" class="rated-user user-black">1005032.maa2</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Oct/28/2016 08:13">7 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-322835" href="?#comment-322835" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="322835" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="483783" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-322835"> <div class="moveup"> <div class="ttypography"><p>Good Job Man</p></div> </div> </div> <div class="reply info"> <a class="comment-322835 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-322835 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-322835"> <li> <div class="comment"> <table class="comment-table" commentId="322890" commentParentId="322835"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Krktv" style="position: relative;"> <img src='https://userpic.codeforces.org/282980/avatar/a606aa5c5f801b89.jpg'/> </a> <div><a href="/profile/Krktv" title="Candidate Master Krktv" class="rated-user user-violet">Krktv</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Oct/29/2016 01:56">7 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-322890" href="?#comment-322890" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-322835" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="322890" class="CommentVoteFrame" data-commentRating="13" data-commentUserId="282980" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+13</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-322890"> <div class="moveup"> <div class="ttypography"><p>And necroposting is not a good job</p></div> </div> </div> <div class="reply info"> <a class="comment-322890 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-322890 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-322890"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="442334" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/berserker" style="position: relative;"> <img src='https://userpic.codeforces.org/492227/avatar/94b128dc6f18638b.jpg'/> </a> <div><a href="/profile/berserker" title="Expert berserker" class="rated-user user-blue">berserker</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jul/03/2018 20:57">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-442334" href="?#comment-442334" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="442334" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="492227" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-442334"> <div class="moveup"> <div class="ttypography"><p>Can anyone give ideas about the DP solution for E.</p></div> </div> </div> <div class="reply info"> <a class="comment-442334 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-442334 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-442334"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="498855" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Bekh" style="position: relative;"> <img src='https://userpic.codeforces.org/617670/avatar/3bb275557d131f6c.jpg'/> </a> <div><a href="/profile/Bekh" title="Master Bekh" class="rated-user user-orange">Bekh</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/13/2019 07:15">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-498855" href="?#comment-498855" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="498855" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="617670" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-498855"> <div class="moveup"> <div class="ttypography"><p>I'm 8 years late, but <a href="/contest/58/problem/C" title="Codeforces Beta Round 54 (Div. 2)">58C - Trees</a> has weak testcases. some solutions pass although they allow some tree heights to become non positive. </p><p>Case:<br /><code>10</code><br /><code>1 1 1 2 3 3 2 1 1 1</code> </p><p>Answer should be 8, (correct sequence: <code>1 2 3 4 5 5 4 3 2 1</code>) </p><p>Wrong answer is 4, (Assumes the correct sequence is: <code>-1 0 1 2 3 3 2 1 0 -1</code>)</p><p>Wrong submission: <a href="/contest/58/submission/51244937" title="Submission 51244937 by Bekh">51244937</a><br />Correct submission: <a href="/contest/58/submission/51245002" title="Submission 51245002 by Bekh">51245002</a></p></div> </div> </div> <div class="reply info"> <a class="comment-498855 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-498855 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-498855"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="556210" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Kylin_" style="position: relative;"> <img src='https://userpic.codeforces.org/1193717/avatar/2296672a2c313067.jpg'/> </a> <div><a href="/profile/Kylin_" title="Expert Kylin_" class="rated-user user-blue">Kylin_</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Nov/05/2019 09:12">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-556210" href="?#comment-556210" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="556210" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1193717" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-556210"> <div class="moveup"> <div class="ttypography"><p>So when we can get the solution of E?</p></div> </div> </div> <div class="reply info"> <a class="comment-556210 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-556210 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-556210"> </ul> </div> <br/> <div id="editBox-1781" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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58D
58
D
en
D. Calendar
<div class="problem-statement"><div class="header"><div class="title">D. Calendar</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>BerOilGasDiamondBank has branches in <span class="tex-span"><i>n</i></span> cities, at that <span class="tex-span"><i>n</i></span> is an even number. The bank management wants to publish a calendar with the names of all those cities written in two columns: the calendar should consist of exactly <span class="tex-span"><i>n</i> / 2</span> lines of strictly equal length, each of which contains exactly two names and exactly one separator character between them. The name of every city should be used in the calendar exactly once. For historical reasons the symbol <span class="tex-span"><i>d</i></span> is used as the separator of words in the calendar. </p><p>The BerOilGasDiamondBank management wants to show that all its branches are equally important to it, that's why the order of their appearance in the calendar should be following: if we "glue"(concatinate) all the <span class="tex-span"><i>n</i> / 2</span> calendar lines (from top to bottom) to make a single line, then the lexicographically minimal line is obtained. No separator character will be used to separate calendar lines. For example, if the lines are "bertown!berville", "newberville!bera", then the resulting line is "bertown!bervillenewberville!bera". In some sense one has to find the lexicographically minimal calendar, where the comparison of calendars happens line by line.</p><p>Help BerOilGasDiamondBank and construct the required calendar.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains an integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">4</sup></span>, <span class="tex-span"><i>n</i></span> is even) which is the number of branches. Then follow <span class="tex-span"><i>n</i></span> lines which are the names of the cities. All the names consist of lowercase Latin letters; their lengths are no less than 1 and no more than 10 symbols. The next line contains a single symbol <span class="tex-span"><i>d</i></span> (<span class="tex-span"><i>d</i></span> has an ASCII-code from 33 to 126 inclusively, excluding lowercase Latin letters) which is the separator between words in the calendar lines. It is guaranteed that the calendar is possible to be constructed and all the names are different.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span"><i>n</i> / 2</span> lines of similar length which are the required calendar. Every line should contain exactly two words and exactly one separator between them. If there are several solutions, print the lexicographically minimal one. The lexicographical comparison of lines is realized by the "<span class="tex-font-style-tt">&lt;</span>" operator in the modern programming languages.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>4<br/>b<br/>aa<br/>hg<br/>c<br/>.<br/></pre></div><div class="output"><div class="title">Output</div><pre>aa.b<br/>c.hg<br/></pre></div><div class="input"><div class="title">Input</div><pre>2<br/>aa<br/>a<br/>!<br/></pre></div><div class="output"><div class="title">Output</div><pre>a!aa<br/></pre></div><div class="input"><div class="title">Input</div><pre>2<br/>aa<br/>a<br/>|<br/></pre></div><div class="output"><div class="title">Output</div><pre>aa|a<br/></pre></div></div></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/58">Codeforces Beta Round 54 (Div. 2)</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? Just register for practice and you will be able to submit solutions. </div> <div style="text-align:center;margin:1em;"> <form action="" method="post"><input type='hidden' name='csrf_token' value='740eed375527cd875dfcc8f13e53abba'/> <input type="hidden" name="action" value="registerForPractice"/> <input type="submit" name="submit" value="Register for practice" style="padding:0 0.5em;"> </form> </div> </div> </div> <div class="roundbox sidebox ContestVirtualFrame borderTopRound " style=""> <div class="caption titled">&rarr; Virtual participation <i class="sidebar-caption-icon las la-angle-down"></i> <div class="top-links"> </div> </div> <div style=" " data-page-url="/data/sidebarFrames" > <div style="margin:1em;font-size:0.8em;"> Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests. If you've seen these problems, a virtual contest is not for you - solve these problems in the archive. If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="D" data-uuid="ps_d779985297566ee9ba0857e9d77865c19294becd"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">D. Calendar</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>BerOilGasDiamondBank has branches in <span class="tex-span"><i>n</i></span> cities, at that <span class="tex-span"><i>n</i></span> is an even number. The bank management wants to publish a calendar with the names of all those cities written in two columns: the calendar should consist of exactly <span class="tex-span"><i>n</i> / 2</span> lines of strictly equal length, each of which contains exactly two names and exactly one separator character between them. The name of every city should be used in the calendar exactly once. For historical reasons the symbol <span class="tex-span"><i>d</i></span> is used as the separator of words in the calendar. </p><p>The BerOilGasDiamondBank management wants to show that all its branches are equally important to it, that's why the order of their appearance in the calendar should be following: if we &quot;glue&quot;(concatinate) all the <span class="tex-span"><i>n</i> / 2</span> calendar lines (from top to bottom) to make a single line, then the lexicographically minimal line is obtained. No separator character will be used to separate calendar lines. For example, if the lines are &quot;bertown!berville&quot;, &quot;newberville!bera&quot;, then the resulting line is &quot;bertown!bervillenewberville!bera&quot;. In some sense one has to find the lexicographically minimal calendar, where the comparison of calendars happens line by line.</p><p>Help BerOilGasDiamondBank and construct the required calendar.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains an integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">4</sup></span>, <span class="tex-span"><i>n</i></span> is even) which is the number of branches. Then follow <span class="tex-span"><i>n</i></span> lines which are the names of the cities. All the names consist of lowercase Latin letters; their lengths are no less than 1 and no more than 10 symbols. The next line contains a single symbol <span class="tex-span"><i>d</i></span> (<span class="tex-span"><i>d</i></span> has an ASCII-code from 33 to 126 inclusively, excluding lowercase Latin letters) which is the separator between words in the calendar lines. It is guaranteed that the calendar is possible to be constructed and all the names are different.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span"><i>n</i> / 2</span> lines of similar length which are the required calendar. Every line should contain exactly two words and exactly one separator between them. If there are several solutions, print the lexicographically minimal one. The lexicographical comparison of lines is realized by the &quot;<span class="tex-font-style-tt">&lt;</span>&quot; operator in the modern programming languages.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>4<br />b<br />aa<br />hg<br />c<br />.<br /></pre></div><div class="output"><div class="title">Output</div><pre>aa.b<br />c.hg<br /></pre></div><div class="input"><div class="title">Input</div><pre>2<br />aa<br />a<br />!<br /></pre></div><div class="output"><div class="title">Output</div><pre>a!aa<br /></pre></div><div class="input"><div class="title">Input</div><pre>2<br />aa<br />a<br />|<br /></pre></div><div class="output"><div class="title">Output</div><pre>aa|a<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=D]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); 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["Greedy algorithms", "Prefix- and Z-functions, suffix structures, Knuth\u2013Morris\u2013Pratt algorithm, etc"]
["greedy", "strings", "*2000"]
https://codeforces.com/blog/entry/1771
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Chat room<br /></b><div align="left">Solution is greedy algorithm. The first thing we do is find in our string the first letter 'h'. Then we find letter 'e' which is righter that found 'h'. If we find the whole word 'hello' in such way, obliviously, answer is YES.<br />Now let's prove that if answer exists, we find it. Let see on position of the 'h' in right answer. If we move it to the first 'h' in our string, nothing changes. But now we can say that our greedy algorithm correctly Now let's do such with the second letter, and so on.<br />We have greedy algorithm with work time O(n), where n - length of the input.<br /></div><br /><div align="left"><div align="center"><b>Problem B. Coins<br /></b><div align="left">This problem also have greedy solution: we run down all number from 2 and greater and while denomination of the last added to answer coin is divisible by current number, we divide and increase answer.<br />You can prove correctness, if you take a look at prime factorizations of coins' denominations. In each next denomination each prime have less or equal power than the current one (it's equivalent to '<span class="tex-span"><i>a</i></span> divide <span class="tex-span"><i>b</i></span>'). Obliviously, if summary degree of primes decreases at least two (for example, we had number<span class="tex-span"><i>a</i> = <i>x</i>· <i>y</i>· <i>z</i></span> (where <span class="tex-span"><i>y</i>, <i>z</i> &gt; 1</span>, and the current number is <span class="tex-span"><i>b</i> = <i>x</i></span>), then we can add one more coin with demonitaion <span class="tex-span"><i>a</i> &gt; <i>c</i> = <i>x</i>· <i>y</i> &gt; <i>b</i></span>. So, in the optimal answer sum of degrees decreasing at exactly one. Our greedy algorithm do exactly what it need.<br /><br /><div align="center"><b>Problem C. Trees.</b><br /><div align="left">The first thing we notice - beautiful sequence is can be determined with any member. The next thing - at least one tree will remain the same height. Prove: let's fix height of the first tree, and correct heights of all other ones. Obliviously, they all remain positive.<br />Solution with work time <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">2</sup>)</span>: we run down which tree we will fix, determine required height of the first tree and then relax answer.<br />This solution can be optimized to linear solution: if we don't touch some tree, we know the first element of sequence. Let's count for each possible element amount of trees, which have required height. It can be done with linear loop and the 'increment' operation on array. After that we just find value of the first element, for which amount of 'good' trees is maximal and output <span class="tex-span"><i>n</i> - <i>x</i></span>, where <span class="tex-span"><i>x</i></span> is this amount.<br /><div align="center"><b><br />Problem D. Calendar</b><br /><div align="left">We know, that all lines of calendar should have equal length, so we can find this length. It's just <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/8cef3c7e80f6e681d72233b1fd7d682f2480a9a7.png" style="max-width: 100.0%;max-height: 100.0%;" />, where <span class="tex-span"><i>suml</i></span> - summary length of all strings. Now let take a look at string, which will be the first one in our calendar. Obliviously, it's profitably to take string with maximal <span class="tex-span"><i>s</i> + <i>d</i></span> (where <span class="tex-span"><i>s</i></span> is our string and <span class="tex-span"><i>d</i></span> - is character from input). Such string is unique otherwise we have two equal strings in input (as <span class="tex-span"><i>d</i></span> is not contained in any string); Of cause, you should remember that if you fix the first string in a line, you fix length of the second one - it's required to have at least one such. Great, now we know the first string in our calendar. Now let's determine the second one. We know it's length, so we need just to take minimal string with such length.<br />We know one line, let's do similary with the second line and so on.<br /></div><div align="left"><br /><div align="center"><b>Problem E. Expression</b><br /><div align="left">Under construction. The main idea is 3D dynamic with O(<span class="tex-span">10<sup class="upper-index">2</sup></span>) transition.<br /></div></div></div></div></div></div></div></div></div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/58" class="notice" style="text-decoration: none;">Codeforces Beta Round 54 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-1484-1771").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "1484", blogEntryId: "1771", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=beta+round+%2354" class="tag notice" style="text-decoration: none;">beta round #54</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=tutorial" class="tag notice" style="text-decoration: none;">tutorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1771"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+25</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1771"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/yeputons"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/yeputons"> yeputons </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Apr/20/2011 14:44">12 years ago</span> </li> <li> <a href="/blog/entry/1771#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1771#comments"> 25 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1781"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (6)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="34253" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/iman_MC" style="position: relative;"> <img src='https://userpic.codeforces.org/2447/avatar/b2ab3e48d7eb8c6.jpg'/> </a> <div><a href="/profile/iman_MC" title="Pupil iman_MC" class="rated-user user-green">iman_MC</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/23/2011 19:32">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34253" href="?#comment-34253" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34253" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="2447" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34253"> <div class="moveup"> <div class="ttypography">Really thanks for your Problem analysis .<br />I hope you complete this with write part E , good luck man :D</div> </div> </div> <div class="reply info"> <a class="comment-34253 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34253 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34253"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="322835" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/1005032.maa2" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/1005032.maa2" title="Unrated, 1005032.maa2" class="rated-user user-black">1005032.maa2</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Oct/28/2016 08:13">7 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-322835" href="?#comment-322835" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="322835" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="483783" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-322835"> <div class="moveup"> <div class="ttypography"><p>Good Job Man</p></div> </div> </div> <div class="reply info"> <a class="comment-322835 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-322835 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-322835"> <li> <div class="comment"> <table class="comment-table" commentId="322890" commentParentId="322835"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Krktv" style="position: relative;"> <img src='https://userpic.codeforces.org/282980/avatar/a606aa5c5f801b89.jpg'/> </a> <div><a href="/profile/Krktv" title="Candidate Master Krktv" class="rated-user user-violet">Krktv</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Oct/29/2016 01:56">7 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-322890" href="?#comment-322890" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-322835" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="322890" class="CommentVoteFrame" data-commentRating="13" data-commentUserId="282980" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+13</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-322890"> <div class="moveup"> <div class="ttypography"><p>And necroposting is not a good job</p></div> </div> </div> <div class="reply info"> <a class="comment-322890 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-322890 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-322890"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="442334" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/berserker" style="position: relative;"> <img src='https://userpic.codeforces.org/492227/avatar/94b128dc6f18638b.jpg'/> </a> <div><a href="/profile/berserker" title="Expert berserker" class="rated-user user-blue">berserker</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jul/03/2018 20:57">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-442334" href="?#comment-442334" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="442334" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="492227" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-442334"> <div class="moveup"> <div class="ttypography"><p>Can anyone give ideas about the DP solution for E.</p></div> </div> </div> <div class="reply info"> <a class="comment-442334 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-442334 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-442334"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="498855" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Bekh" style="position: relative;"> <img src='https://userpic.codeforces.org/617670/avatar/3bb275557d131f6c.jpg'/> </a> <div><a href="/profile/Bekh" title="Master Bekh" class="rated-user user-orange">Bekh</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/13/2019 07:15">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-498855" href="?#comment-498855" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="498855" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="617670" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-498855"> <div class="moveup"> <div class="ttypography"><p>I'm 8 years late, but <a href="/contest/58/problem/C" title="Codeforces Beta Round 54 (Div. 2)">58C - Trees</a> has weak testcases. some solutions pass although they allow some tree heights to become non positive. </p><p>Case:<br /><code>10</code><br /><code>1 1 1 2 3 3 2 1 1 1</code> </p><p>Answer should be 8, (correct sequence: <code>1 2 3 4 5 5 4 3 2 1</code>) </p><p>Wrong answer is 4, (Assumes the correct sequence is: <code>-1 0 1 2 3 3 2 1 0 -1</code>)</p><p>Wrong submission: <a href="/contest/58/submission/51244937" title="Submission 51244937 by Bekh">51244937</a><br />Correct submission: <a href="/contest/58/submission/51245002" title="Submission 51245002 by Bekh">51245002</a></p></div> </div> </div> <div class="reply info"> <a class="comment-498855 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-498855 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-498855"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="556210" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Kylin_" style="position: relative;"> <img src='https://userpic.codeforces.org/1193717/avatar/2296672a2c313067.jpg'/> </a> <div><a href="/profile/Kylin_" title="Expert Kylin_" class="rated-user user-blue">Kylin_</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Nov/05/2019 09:12">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-556210" href="?#comment-556210" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="556210" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1193717" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-556210"> <div class="moveup"> <div class="ttypography"><p>So when we can get the solution of E?</p></div> </div> </div> <div class="reply info"> <a class="comment-556210 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-556210 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-556210"> </ul> </div> <br/> <div id="editBox-1781" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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58E
58
E
en
E. Expression
<div class="problem-statement"><div class="header"><div class="title">E. Expression</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>One day Vasya was solving arithmetical problems. He wrote down an expression <span class="tex-span"><i>a</i> + <i>b</i> = <i>c</i></span> in his notebook. When the teacher checked Vasya's work it turned out that Vasya had solved the problem incorrectly. Now Vasya tries to find excuses. He says that he simply forgot to write down several digits in numbers <span class="tex-span"><i>a</i></span>, <span class="tex-span"><i>b</i></span> and <span class="tex-span"><i>c</i></span>, but he can't remember what numbers they actually were. Help Vasya, find such numbers <span class="tex-span"><i>x</i></span>, <span class="tex-span"><i>y</i></span> and <span class="tex-span"><i>z</i></span>, with which the following conditions are met: </p><ul> <li> <span class="tex-span"><i>x</i> + <i>y</i> = <i>z</i></span>, </li><li> from the expression <span class="tex-span"><i>x</i> + <i>y</i> = <i>z</i></span> several digits can be erased in such a way that the result will be <span class="tex-span"><i>a</i> + <i>b</i> = <i>c</i></span>, </li><li> the expression <span class="tex-span"><i>x</i> + <i>y</i> = <i>z</i></span> should have the minimal length. </li></ul></div><div class="input-specification"><div class="section-title">Input</div><p>The first and only input line contains the expression <span class="tex-span"><i>a</i> + <i>b</i> = <i>c</i></span> (<span class="tex-span">1 ≤ <i>a</i>, <i>b</i>, <i>c</i> ≤ 10<sup class="upper-index">6</sup></span>, <span class="tex-span"><i>a</i></span>, <span class="tex-span"><i>b</i></span> and <span class="tex-span"><i>c</i></span> don't contain leading zeroes) which is the expression Vasya wrote down.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print the correct expression <span class="tex-span"><i>x</i> + <i>y</i> = <i>z</i></span> (<span class="tex-span"><i>x</i></span>, <span class="tex-span"><i>y</i></span> and <span class="tex-span"><i>z</i></span> are non-negative numbers without leading zeroes). The expression <span class="tex-span"><i>a</i> + <i>b</i> = <i>c</i></span> must be met in <span class="tex-span"><i>x</i> + <i>y</i> = <i>z</i></span> as a subsequence. The printed solution should have the minimal possible number of characters. If there are several such solutions, you can print any of them.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2+4=5<br/></pre></div><div class="output"><div class="title">Output</div><pre>21+4=25<br/></pre></div><div class="input"><div class="title">Input</div><pre>1+1=3<br/></pre></div><div class="output"><div class="title">Output</div><pre>1+31=32<br/></pre></div><div class="input"><div class="title">Input</div><pre>1+1=2<br/></pre></div><div class="output"><div class="title">Output</div><pre>1+1=2<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="E" data-uuid="ps_54b7cf69a79fb0792663d105a87c484733974f30"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">E. Expression</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>One day Vasya was solving arithmetical problems. He wrote down an expression <span class="tex-span"><i>a</i> + <i>b</i> = <i>c</i></span> in his notebook. When the teacher checked Vasya's work it turned out that Vasya had solved the problem incorrectly. Now Vasya tries to find excuses. He says that he simply forgot to write down several digits in numbers <span class="tex-span"><i>a</i></span>, <span class="tex-span"><i>b</i></span> and <span class="tex-span"><i>c</i></span>, but he can't remember what numbers they actually were. Help Vasya, find such numbers <span class="tex-span"><i>x</i></span>, <span class="tex-span"><i>y</i></span> and <span class="tex-span"><i>z</i></span>, with which the following conditions are met: </p><ul> <li> <span class="tex-span"><i>x</i> + <i>y</i> = <i>z</i></span>, </li><li> from the expression <span class="tex-span"><i>x</i> + <i>y</i> = <i>z</i></span> several digits can be erased in such a way that the result will be <span class="tex-span"><i>a</i> + <i>b</i> = <i>c</i></span>, </li><li> the expression <span class="tex-span"><i>x</i> + <i>y</i> = <i>z</i></span> should have the minimal length. </li></ul></div><div class="input-specification"><div class="section-title">Input</div><p>The first and only input line contains the expression <span class="tex-span"><i>a</i> + <i>b</i> = <i>c</i></span> (<span class="tex-span">1 ≤ <i>a</i>, <i>b</i>, <i>c</i> ≤ 10<sup class="upper-index">6</sup></span>, <span class="tex-span"><i>a</i></span>, <span class="tex-span"><i>b</i></span> and <span class="tex-span"><i>c</i></span> don't contain leading zeroes) which is the expression Vasya wrote down.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print the correct expression <span class="tex-span"><i>x</i> + <i>y</i> = <i>z</i></span> (<span class="tex-span"><i>x</i></span>, <span class="tex-span"><i>y</i></span> and <span class="tex-span"><i>z</i></span> are non-negative numbers without leading zeroes). The expression <span class="tex-span"><i>a</i> + <i>b</i> = <i>c</i></span> must be met in <span class="tex-span"><i>x</i> + <i>y</i> = <i>z</i></span> as a subsequence. The printed solution should have the minimal possible number of characters. If there are several such solutions, you can print any of them.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2+4=5<br /></pre></div><div class="output"><div class="title">Output</div><pre>21+4=25<br /></pre></div><div class="input"><div class="title">Input</div><pre>1+1=3<br /></pre></div><div class="output"><div class="title">Output</div><pre>1+31=32<br /></pre></div><div class="input"><div class="title">Input</div><pre>1+1=2<br /></pre></div><div class="output"><div class="title">Output</div><pre>1+1=2<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=E]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); if (previousStatementText) { if (previousStatementText !== statementText) { $problem.find(".diff-notifier").show(); 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["Dynamic programming"]
["dp", "*2400"]
https://codeforces.com/blog/entry/1771
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Chat room<br /></b><div align="left">Solution is greedy algorithm. The first thing we do is find in our string the first letter 'h'. Then we find letter 'e' which is righter that found 'h'. If we find the whole word 'hello' in such way, obliviously, answer is YES.<br />Now let's prove that if answer exists, we find it. Let see on position of the 'h' in right answer. If we move it to the first 'h' in our string, nothing changes. But now we can say that our greedy algorithm correctly Now let's do such with the second letter, and so on.<br />We have greedy algorithm with work time O(n), where n - length of the input.<br /></div><br /><div align="left"><div align="center"><b>Problem B. Coins<br /></b><div align="left">This problem also have greedy solution: we run down all number from 2 and greater and while denomination of the last added to answer coin is divisible by current number, we divide and increase answer.<br />You can prove correctness, if you take a look at prime factorizations of coins' denominations. In each next denomination each prime have less or equal power than the current one (it's equivalent to '<span class="tex-span"><i>a</i></span> divide <span class="tex-span"><i>b</i></span>'). Obliviously, if summary degree of primes decreases at least two (for example, we had number<span class="tex-span"><i>a</i> = <i>x</i>· <i>y</i>· <i>z</i></span> (where <span class="tex-span"><i>y</i>, <i>z</i> &gt; 1</span>, and the current number is <span class="tex-span"><i>b</i> = <i>x</i></span>), then we can add one more coin with demonitaion <span class="tex-span"><i>a</i> &gt; <i>c</i> = <i>x</i>· <i>y</i> &gt; <i>b</i></span>. So, in the optimal answer sum of degrees decreasing at exactly one. Our greedy algorithm do exactly what it need.<br /><br /><div align="center"><b>Problem C. Trees.</b><br /><div align="left">The first thing we notice - beautiful sequence is can be determined with any member. The next thing - at least one tree will remain the same height. Prove: let's fix height of the first tree, and correct heights of all other ones. Obliviously, they all remain positive.<br />Solution with work time <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">2</sup>)</span>: we run down which tree we will fix, determine required height of the first tree and then relax answer.<br />This solution can be optimized to linear solution: if we don't touch some tree, we know the first element of sequence. Let's count for each possible element amount of trees, which have required height. It can be done with linear loop and the 'increment' operation on array. After that we just find value of the first element, for which amount of 'good' trees is maximal and output <span class="tex-span"><i>n</i> - <i>x</i></span>, where <span class="tex-span"><i>x</i></span> is this amount.<br /><div align="center"><b><br />Problem D. Calendar</b><br /><div align="left">We know, that all lines of calendar should have equal length, so we can find this length. It's just <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/8cef3c7e80f6e681d72233b1fd7d682f2480a9a7.png" style="max-width: 100.0%;max-height: 100.0%;" />, where <span class="tex-span"><i>suml</i></span> - summary length of all strings. Now let take a look at string, which will be the first one in our calendar. Obliviously, it's profitably to take string with maximal <span class="tex-span"><i>s</i> + <i>d</i></span> (where <span class="tex-span"><i>s</i></span> is our string and <span class="tex-span"><i>d</i></span> - is character from input). Such string is unique otherwise we have two equal strings in input (as <span class="tex-span"><i>d</i></span> is not contained in any string); Of cause, you should remember that if you fix the first string in a line, you fix length of the second one - it's required to have at least one such. Great, now we know the first string in our calendar. Now let's determine the second one. We know it's length, so we need just to take minimal string with such length.<br />We know one line, let's do similary with the second line and so on.<br /></div><div align="left"><br /><div align="center"><b>Problem E. Expression</b><br /><div align="left">Under construction. The main idea is 3D dynamic with O(<span class="tex-span">10<sup class="upper-index">2</sup></span>) transition.<br /></div></div></div></div></div></div></div></div></div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/58" class="notice" style="text-decoration: none;">Codeforces Beta Round 54 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-1484-1771").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "1484", blogEntryId: "1771", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=beta+round+%2354" class="tag notice" style="text-decoration: none;">beta round #54</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=tutorial" class="tag notice" style="text-decoration: none;">tutorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1771"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+25</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1771"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/yeputons"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/yeputons"> yeputons </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Apr/20/2011 14:44">12 years ago</span> </li> <li> <a href="/blog/entry/1771#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1771#comments"> 25 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1781"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (6)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="34253" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/iman_MC" style="position: relative;"> <img src='https://userpic.codeforces.org/2447/avatar/b2ab3e48d7eb8c6.jpg'/> </a> <div><a href="/profile/iman_MC" title="Pupil iman_MC" class="rated-user user-green">iman_MC</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/23/2011 19:32">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34253" href="?#comment-34253" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34253" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="2447" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34253"> <div class="moveup"> <div class="ttypography">Really thanks for your Problem analysis .<br />I hope you complete this with write part E , good luck man :D</div> </div> </div> <div class="reply info"> <a class="comment-34253 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34253 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34253"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="322835" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/1005032.maa2" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/1005032.maa2" title="Unrated, 1005032.maa2" class="rated-user user-black">1005032.maa2</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Oct/28/2016 08:13">7 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-322835" href="?#comment-322835" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="322835" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="483783" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-322835"> <div class="moveup"> <div class="ttypography"><p>Good Job Man</p></div> </div> </div> <div class="reply info"> <a class="comment-322835 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-322835 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-322835"> <li> <div class="comment"> <table class="comment-table" commentId="322890" commentParentId="322835"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Krktv" style="position: relative;"> <img src='https://userpic.codeforces.org/282980/avatar/a606aa5c5f801b89.jpg'/> </a> <div><a href="/profile/Krktv" title="Candidate Master Krktv" class="rated-user user-violet">Krktv</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Oct/29/2016 01:56">7 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-322890" href="?#comment-322890" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-322835" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="322890" class="CommentVoteFrame" data-commentRating="13" data-commentUserId="282980" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+13</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-322890"> <div class="moveup"> <div class="ttypography"><p>And necroposting is not a good job</p></div> </div> </div> <div class="reply info"> <a class="comment-322890 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-322890 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-322890"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="442334" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/berserker" style="position: relative;"> <img src='https://userpic.codeforces.org/492227/avatar/94b128dc6f18638b.jpg'/> </a> <div><a href="/profile/berserker" title="Expert berserker" class="rated-user user-blue">berserker</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jul/03/2018 20:57">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-442334" href="?#comment-442334" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="442334" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="492227" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-442334"> <div class="moveup"> <div class="ttypography"><p>Can anyone give ideas about the DP solution for E.</p></div> </div> </div> <div class="reply info"> <a class="comment-442334 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-442334 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-442334"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="498855" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Bekh" style="position: relative;"> <img src='https://userpic.codeforces.org/617670/avatar/3bb275557d131f6c.jpg'/> </a> <div><a href="/profile/Bekh" title="Master Bekh" class="rated-user user-orange">Bekh</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/13/2019 07:15">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-498855" href="?#comment-498855" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="498855" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="617670" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-498855"> <div class="moveup"> <div class="ttypography"><p>I'm 8 years late, but <a href="/contest/58/problem/C" title="Codeforces Beta Round 54 (Div. 2)">58C - Trees</a> has weak testcases. some solutions pass although they allow some tree heights to become non positive. </p><p>Case:<br /><code>10</code><br /><code>1 1 1 2 3 3 2 1 1 1</code> </p><p>Answer should be 8, (correct sequence: <code>1 2 3 4 5 5 4 3 2 1</code>) </p><p>Wrong answer is 4, (Assumes the correct sequence is: <code>-1 0 1 2 3 3 2 1 0 -1</code>)</p><p>Wrong submission: <a href="/contest/58/submission/51244937" title="Submission 51244937 by Bekh">51244937</a><br />Correct submission: <a href="/contest/58/submission/51245002" title="Submission 51245002 by Bekh">51245002</a></p></div> </div> </div> <div class="reply info"> <a class="comment-498855 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-498855 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-498855"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="556210" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Kylin_" style="position: relative;"> <img src='https://userpic.codeforces.org/1193717/avatar/2296672a2c313067.jpg'/> </a> <div><a href="/profile/Kylin_" title="Expert Kylin_" class="rated-user user-blue">Kylin_</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Nov/05/2019 09:12">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-556210" href="?#comment-556210" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="556210" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1193717" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-556210"> <div class="moveup"> <div class="ttypography"><p>So when we can get the solution of E?</p></div> </div> </div> <div class="reply info"> <a class="comment-556210 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-556210 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-556210"> </ul> </div> <br/> <div id="editBox-1781" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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59A
59
A
en
A. Word
<div class="problem-statement"><div class="header"><div class="title">A. Word</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Vasya is very upset that many people on the Net mix uppercase and lowercase letters in one word. That's why he decided to invent an extension for his favorite browser that would change the letters' register in every word so that it either only consisted of lowercase letters or, vice versa, only of uppercase ones. At that as little as possible letters should be changed in the word. For example, the word <span class="tex-font-style-tt">HoUse</span> must be replaced with <span class="tex-font-style-tt">house</span>, and the word <span class="tex-font-style-tt">ViP</span> — with <span class="tex-font-style-tt">VIP</span>. If a word contains an equal number of uppercase and lowercase letters, you should replace all the letters with lowercase ones. For example, <span class="tex-font-style-tt">maTRIx</span> should be replaced by <span class="tex-font-style-tt">matrix</span>. Your task is to use the given method on one given word.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains a word <span class="tex-span"><i>s</i></span> — it consists of uppercase and lowercase Latin letters and possesses the length from <span class="tex-span">1</span> to <span class="tex-span">100</span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print the corrected word <span class="tex-span"><i>s</i></span>. If the given word <span class="tex-span"><i>s</i></span> has strictly more uppercase letters, make the word written in the uppercase register, otherwise - in the lowercase one.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>HoUse<br/></pre></div><div class="output"><div class="title">Output</div><pre>house<br/></pre></div><div class="input"><div class="title">Input</div><pre>ViP<br/></pre></div><div class="output"><div class="title">Output</div><pre>VIP<br/></pre></div><div class="input"><div class="title">Input</div><pre>maTRIx<br/></pre></div><div class="output"><div class="title">Output</div><pre>matrix<br/></pre></div></div></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/59">Codeforces Beta Round 55 (Div. 2)</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? 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Word</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Vasya is very upset that many people on the Net mix uppercase and lowercase letters in one word. That's why he decided to invent an extension for his favorite browser that would change the letters' register in every word so that it either only consisted of lowercase letters or, vice versa, only of uppercase ones. At that as little as possible letters should be changed in the word. For example, the word <span class="tex-font-style-tt">HoUse</span> must be replaced with <span class="tex-font-style-tt">house</span>, and the word <span class="tex-font-style-tt">ViP</span> — with <span class="tex-font-style-tt">VIP</span>. If a word contains an equal number of uppercase and lowercase letters, you should replace all the letters with lowercase ones. For example, <span class="tex-font-style-tt">maTRIx</span> should be replaced by <span class="tex-font-style-tt">matrix</span>. Your task is to use the given method on one given word.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains a word <span class="tex-span"><i>s</i></span> — it consists of uppercase and lowercase Latin letters and possesses the length from <span class="tex-span">1</span> to <span class="tex-span">100</span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print the corrected word <span class="tex-span"><i>s</i></span>. If the given word <span class="tex-span"><i>s</i></span> has strictly more uppercase letters, make the word written in the uppercase register, otherwise - in the lowercase one.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>HoUse<br /></pre></div><div class="output"><div class="title">Output</div><pre>house<br /></pre></div><div class="input"><div class="title">Input</div><pre>ViP<br /></pre></div><div class="output"><div class="title">Output</div><pre>VIP<br /></pre></div><div class="input"><div class="title">Input</div><pre>maTRIx<br /></pre></div><div class="output"><div class="title">Output</div><pre>matrix<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=A]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); 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["Implementation problems, programming technics, simulation", "Prefix- and Z-functions, suffix structures, Knuth\u2013Morris\u2013Pratt algorithm, etc"]
["implementation", "strings", "*800"]
59B
59
B
en
B. Fortune Telling
<div class="problem-statement"><div class="header"><div class="title">B. Fortune Telling</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Marina loves Sasha. But she keeps wondering whether Sasha loves her. Of course, the best way to know it is fortune telling. There are many ways of telling fortune, but Marina has picked the easiest one. She takes in her hand one or several camomiles and tears off the petals one by one. After each petal she pronounces alternatively "Loves" and "Doesn't love", at that Marina always starts with "Loves". There are <span class="tex-span"><i>n</i></span> camomiles growing in the field, possessing the numbers of petals equal to <span class="tex-span"><i>a</i><sub class="lower-index">1</sub>, <i>a</i><sub class="lower-index">2</sub>, ... <i>a</i><sub class="lower-index"><i>n</i></sub></span>. Marina wants to pick a bouquet with the maximal possible total number of petals so that the result would still be "Loves". Help her do that; find the maximal number of petals possible in the bouquet.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains an integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 100</span>), which is the number of flowers growing in the field. The second line contains <span class="tex-span"><i>n</i></span> integers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 100</span>) which represent the number of petals on a given <span class="tex-span"><i>i</i></span>-th camomile.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single number which is the maximal number of petals in the bouquet, the fortune telling on which would result in "Loves". If there are no such bouquet, print <span class="tex-span">0</span> instead. The bouquet may consist of a single flower.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>1<br/>1<br/></pre></div><div class="output"><div class="title">Output</div><pre>1<br/></pre></div><div class="input"><div class="title">Input</div><pre>1<br/>2<br/></pre></div><div class="output"><div class="title">Output</div><pre>0<br/></pre></div><div class="input"><div class="title">Input</div><pre>3<br/>5 6 7<br/></pre></div><div class="output"><div class="title">Output</div><pre>13<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="B" data-uuid="ps_7b12bf9171131754c303070fd2335579caca1b1f"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">B. Fortune Telling</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Marina loves Sasha. But she keeps wondering whether Sasha loves her. Of course, the best way to know it is fortune telling. There are many ways of telling fortune, but Marina has picked the easiest one. She takes in her hand one or several camomiles and tears off the petals one by one. After each petal she pronounces alternatively &quot;Loves&quot; and &quot;Doesn't love&quot;, at that Marina always starts with &quot;Loves&quot;. There are <span class="tex-span"><i>n</i></span> camomiles growing in the field, possessing the numbers of petals equal to <span class="tex-span"><i>a</i><sub class="lower-index">1</sub>, <i>a</i><sub class="lower-index">2</sub>, ... <i>a</i><sub class="lower-index"><i>n</i></sub></span>. Marina wants to pick a bouquet with the maximal possible total number of petals so that the result would still be &quot;Loves&quot;. Help her do that; find the maximal number of petals possible in the bouquet.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains an integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 100</span>), which is the number of flowers growing in the field. The second line contains <span class="tex-span"><i>n</i></span> integers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 100</span>) which represent the number of petals on a given <span class="tex-span"><i>i</i></span>-th camomile.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single number which is the maximal number of petals in the bouquet, the fortune telling on which would result in &quot;Loves&quot;. If there are no such bouquet, print <span class="tex-span">0</span> instead. 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["Implementation problems, programming technics, simulation", "Number theory: Euler function, GCD, divisibility, etc"]
["implementation", "number theory", "*1200"]
59C
59
C
en
C. Title
<div class="problem-statement"><div class="header"><div class="title">C. Title</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Vasya has recently finished writing a book. Now he faces the problem of giving it the title. Vasya wants the title to be vague and mysterious for his book to be noticeable among others. That's why the title should be represented by a single word containing at least once each of the first <span class="tex-span"><i>k</i></span> Latin letters and not containing any other ones. Also, the title should be a palindrome, that is it should be read similarly from the left to the right and from the right to the left.</p><p>Vasya has already composed the approximate variant of the title. You are given the title template <span class="tex-span"><i>s</i></span> consisting of lowercase Latin letters and question marks. Your task is to replace all the question marks by lowercase Latin letters so that the resulting word satisfies the requirements, described above. Each question mark should be replaced by exactly one letter, it is not allowed to delete characters or add new ones to the template. If there are several suitable titles, choose the first in the alphabetical order, for Vasya's book to appear as early as possible in all the catalogues.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains an integer <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>k</i> ≤ 26</span>) which is the number of allowed alphabet letters. The second line contains <span class="tex-span"><i>s</i></span> which is the given template. In <span class="tex-span"><i>s</i></span> only the first <span class="tex-span"><i>k</i></span> lowercase letters of Latin alphabet and question marks can be present, the length of <span class="tex-span"><i>s</i></span> is from 1 to 100 characters inclusively.</p></div><div class="output-specification"><div class="section-title">Output</div><p>If there is no solution, print <span class="tex-font-style-tt">IMPOSSIBLE</span>. Otherwise, a single line should contain the required title, satisfying the given template. The title should be a palindrome and it can only contain the first <span class="tex-span"><i>k</i></span> letters of the Latin alphabet. At that, each of those <span class="tex-span"><i>k</i></span> letters must be present at least once. If there are several suitable titles, print the lexicographically minimal one. </p><p>The lexicographical comparison is performed by the standard &lt; operator in modern programming languages. The line <span class="tex-span"><i>a</i></span> is lexicographically smaller than the line <span class="tex-span"><i>b</i></span>, if exists such an <span class="tex-span"><i>i</i></span> (<span class="tex-span">1 ≤ <i>i</i> ≤ |<i>s</i>|</span>), that <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub> &lt; <i>b</i><sub class="lower-index"><i>i</i></sub></span>, and for any <span class="tex-span"><i>j</i></span> (<span class="tex-span">1 ≤ <i>j</i> &lt; <i>i</i></span>) <span class="tex-span"><i>a</i><sub class="lower-index"><i>j</i></sub> = <i>b</i><sub class="lower-index"><i>j</i></sub></span>. <span class="tex-span">|<i>s</i>|</span> stands for the length of the given template.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br/>a?c<br/></pre></div><div class="output"><div class="title">Output</div><pre>IMPOSSIBLE<br/></pre></div><div class="input"><div class="title">Input</div><pre>2<br/>a??a<br/></pre></div><div class="output"><div class="title">Output</div><pre>abba<br/></pre></div><div class="input"><div class="title">Input</div><pre>2<br/>?b?a<br/></pre></div><div class="output"><div class="title">Output</div><pre>abba<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="C" data-uuid="ps_201cdf5b2fdb114fc10922563c0f754a9c8aabc0"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. Title</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Vasya has recently finished writing a book. Now he faces the problem of giving it the title. Vasya wants the title to be vague and mysterious for his book to be noticeable among others. That's why the title should be represented by a single word containing at least once each of the first <span class="tex-span"><i>k</i></span> Latin letters and not containing any other ones. Also, the title should be a palindrome, that is it should be read similarly from the left to the right and from the right to the left.</p><p>Vasya has already composed the approximate variant of the title. You are given the title template <span class="tex-span"><i>s</i></span> consisting of lowercase Latin letters and question marks. Your task is to replace all the question marks by lowercase Latin letters so that the resulting word satisfies the requirements, described above. Each question mark should be replaced by exactly one letter, it is not allowed to delete characters or add new ones to the template. If there are several suitable titles, choose the first in the alphabetical order, for Vasya's book to appear as early as possible in all the catalogues.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains an integer <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>k</i> ≤ 26</span>) which is the number of allowed alphabet letters. The second line contains <span class="tex-span"><i>s</i></span> which is the given template. In <span class="tex-span"><i>s</i></span> only the first <span class="tex-span"><i>k</i></span> lowercase letters of Latin alphabet and question marks can be present, the length of <span class="tex-span"><i>s</i></span> is from 1 to 100 characters inclusively.</p></div><div class="output-specification"><div class="section-title">Output</div><p>If there is no solution, print <span class="tex-font-style-tt">IMPOSSIBLE</span>. Otherwise, a single line should contain the required title, satisfying the given template. The title should be a palindrome and it can only contain the first <span class="tex-span"><i>k</i></span> letters of the Latin alphabet. At that, each of those <span class="tex-span"><i>k</i></span> letters must be present at least once. If there are several suitable titles, print the lexicographically minimal one. </p><p>The lexicographical comparison is performed by the standard &lt; operator in modern programming languages. The line <span class="tex-span"><i>a</i></span> is lexicographically smaller than the line <span class="tex-span"><i>b</i></span>, if exists such an <span class="tex-span"><i>i</i></span> (<span class="tex-span">1 ≤ <i>i</i> ≤ |<i>s</i>|</span>), that <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub> &lt; <i>b</i><sub class="lower-index"><i>i</i></sub></span>, and for any <span class="tex-span"><i>j</i></span> (<span class="tex-span">1 ≤ <i>j</i> &lt; <i>i</i></span>) <span class="tex-span"><i>a</i><sub class="lower-index"><i>j</i></sub> = <i>b</i><sub class="lower-index"><i>j</i></sub></span>. <span class="tex-span">|<i>s</i>|</span> stands for the length of the given template.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br />a?c<br /></pre></div><div class="output"><div class="title">Output</div><pre>IMPOSSIBLE<br /></pre></div><div class="input"><div class="title">Input</div><pre>2<br />a??a<br /></pre></div><div class="output"><div class="title">Output</div><pre>abba<br /></pre></div><div class="input"><div class="title">Input</div><pre>2<br />?b?a<br /></pre></div><div class="output"><div class="title">Output</div><pre>abba<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=C]"); 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["Parsing expression grammar"]
["expression parsing", "*1600"]
59D
59
D
en
D. Team Arrangement
<div class="problem-statement"><div class="header"><div class="title">D. Team Arrangement</div><div class="time-limit"><div class="property-title">time limit per test</div>3 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Recently personal training sessions have finished in the Berland State University Olympiad Programmer Training Centre. By the results of these training sessions teams are composed for the oncoming team contest season. Each team consists of three people. All the students of the Centre possess numbers from <span class="tex-span">1</span> to <span class="tex-span">3<i>n</i></span>, and all the teams possess numbers from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span>. The splitting of students into teams is performed in the following manner: while there are people who are not part of a team, a person with the best total score is chosen among them (the captain of a new team), this person chooses for himself two teammates from those who is left according to his list of priorities. The list of every person's priorities is represented as a permutation from <span class="tex-font-style-bf">the rest of</span> <span class="tex-span">3<i>n</i> - 1</span> students who attend the centre, besides himself.</p><p>You are given the results of personal training sessions which are a permutation of numbers from <span class="tex-span">1</span> to <span class="tex-span">3<i>n</i></span>, where the <span class="tex-span"><i>i</i></span>-th number is the number of student who has won the <span class="tex-span"><i>i</i></span>-th place. No two students share a place. You are also given the arrangement of the already formed teams in the order in which they has been created. Your task is to determine the list of priorities for the student number <span class="tex-span"><i>k</i></span>. If there are several priority lists, choose the lexicographically minimal one.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains an integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup></span>) which is the number of resulting teams. The second line contains <span class="tex-span">3<i>n</i></span> space-separated integers from <span class="tex-span">1</span> to <span class="tex-span">3<i>n</i></span> which are the results of personal training sessions. It is guaranteed that every student appears in the results exactly once.</p><p>Then follow <span class="tex-span"><i>n</i></span> lines each containing three integers from <span class="tex-span">1</span> to <span class="tex-span">3<i>n</i></span> — each line describes the members of a given team. The members of one team can be listed in any order, but the teams themselves are listed in the order in which they were created. It is guaranteed that the arrangement is correct, that is that every student is a member of exactly one team and those teams could really be created from the given results using the method described above.</p><p>The last line contains number <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>k</i> ≤ 3<i>n</i></span>) which is the number of a student for who the list of priorities should be found.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span">3<i>n</i> - 1</span> numbers — the lexicographically smallest list of priorities for the student number <span class="tex-span"><i>k</i></span>. </p><p>The lexicographical comparison is performed by the standard &lt; operator in modern programming languages. The list <span class="tex-span"><i>a</i></span> is lexicographically less that the list <span class="tex-span"><i>b</i></span> if exists such an <span class="tex-span"><i>i</i></span> (<span class="tex-span">1 ≤ <i>i</i> ≤ 3<i>n</i></span>), that <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub> &lt; <i>b</i><sub class="lower-index"><i>i</i></sub></span>, and for any <span class="tex-span"><i>j</i></span> (<span class="tex-span">1 ≤ <i>j</i> &lt; <i>i</i></span>) <span class="tex-span"><i>a</i><sub class="lower-index"><i>j</i></sub> = <i>b</i><sub class="lower-index"><i>j</i></sub></span>. Note, that the list <span class="tex-font-style-tt">1 9 10</span> is lexicographically less than the list <span class="tex-font-style-tt">1 10 9</span>. That is, the comparison of lists is different from the comparison of lines.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br/>5 4 1 2 6 3 7 8 9<br/>5 6 2<br/>9 3 4<br/>1 7 8<br/>4<br/></pre></div><div class="output"><div class="title">Output</div><pre>2 3 5 6 9 1 7 8 </pre></div><div class="input"><div class="title">Input</div><pre>3<br/>5 4 1 2 6 3 7 8 9<br/>5 6 2<br/>9 3 4<br/>1 7 8<br/>8<br/></pre></div><div class="output"><div class="title">Output</div><pre>1 2 3 4 5 6 7 9 </pre></div><div class="input"><div class="title">Input</div><pre>2<br/>4 1 3 2 5 6<br/>4 6 5<br/>1 2 3<br/>4<br/></pre></div><div class="output"><div class="title">Output</div><pre>5 6 1 2 3 </pre></div></div></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/59">Codeforces Beta Round 55 (Div. 2)</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? 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If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="D" data-uuid="ps_a990877324169aadb29dbf1e9f74c9640a125f40"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">D. Team Arrangement</div><div class="time-limit"><div class="property-title">time limit per test</div>3 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Recently personal training sessions have finished in the Berland State University Olympiad Programmer Training Centre. By the results of these training sessions teams are composed for the oncoming team contest season. Each team consists of three people. All the students of the Centre possess numbers from <span class="tex-span">1</span> to <span class="tex-span">3<i>n</i></span>, and all the teams possess numbers from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span>. The splitting of students into teams is performed in the following manner: while there are people who are not part of a team, a person with the best total score is chosen among them (the captain of a new team), this person chooses for himself two teammates from those who is left according to his list of priorities. The list of every person's priorities is represented as a permutation from <span class="tex-font-style-bf">the rest of</span> <span class="tex-span">3<i>n</i> - 1</span> students who attend the centre, besides himself.</p><p>You are given the results of personal training sessions which are a permutation of numbers from <span class="tex-span">1</span> to <span class="tex-span">3<i>n</i></span>, where the <span class="tex-span"><i>i</i></span>-th number is the number of student who has won the <span class="tex-span"><i>i</i></span>-th place. No two students share a place. You are also given the arrangement of the already formed teams in the order in which they has been created. Your task is to determine the list of priorities for the student number <span class="tex-span"><i>k</i></span>. If there are several priority lists, choose the lexicographically minimal one.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains an integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup></span>) which is the number of resulting teams. The second line contains <span class="tex-span">3<i>n</i></span> space-separated integers from <span class="tex-span">1</span> to <span class="tex-span">3<i>n</i></span> which are the results of personal training sessions. It is guaranteed that every student appears in the results exactly once.</p><p>Then follow <span class="tex-span"><i>n</i></span> lines each containing three integers from <span class="tex-span">1</span> to <span class="tex-span">3<i>n</i></span> — each line describes the members of a given team. The members of one team can be listed in any order, but the teams themselves are listed in the order in which they were created. It is guaranteed that the arrangement is correct, that is that every student is a member of exactly one team and those teams could really be created from the given results using the method described above.</p><p>The last line contains number <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>k</i> ≤ 3<i>n</i></span>) which is the number of a student for who the list of priorities should be found.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span">3<i>n</i> - 1</span> numbers — the lexicographically smallest list of priorities for the student number <span class="tex-span"><i>k</i></span>. </p><p>The lexicographical comparison is performed by the standard &lt; operator in modern programming languages. The list <span class="tex-span"><i>a</i></span> is lexicographically less that the list <span class="tex-span"><i>b</i></span> if exists such an <span class="tex-span"><i>i</i></span> (<span class="tex-span">1 ≤ <i>i</i> ≤ 3<i>n</i></span>), that <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub> &lt; <i>b</i><sub class="lower-index"><i>i</i></sub></span>, and for any <span class="tex-span"><i>j</i></span> (<span class="tex-span">1 ≤ <i>j</i> &lt; <i>i</i></span>) <span class="tex-span"><i>a</i><sub class="lower-index"><i>j</i></sub> = <i>b</i><sub class="lower-index"><i>j</i></sub></span>. Note, that the list <span class="tex-font-style-tt">1 9 10</span> is lexicographically less than the list <span class="tex-font-style-tt">1 10 9</span>. That is, the comparison of lists is different from the comparison of lines.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br />5 4 1 2 6 3 7 8 9<br />5 6 2<br />9 3 4<br />1 7 8<br />4<br /></pre></div><div class="output"><div class="title">Output</div><pre>2 3 5 6 9 1 7 8 </pre></div><div class="input"><div class="title">Input</div><pre>3<br />5 4 1 2 6 3 7 8 9<br />5 6 2<br />9 3 4<br />1 7 8<br />8<br /></pre></div><div class="output"><div class="title">Output</div><pre>1 2 3 4 5 6 7 9 </pre></div><div class="input"><div class="title">Input</div><pre>2<br />4 1 3 2 5 6<br />4 6 5<br />1 2 3<br />4<br /></pre></div><div class="output"><div class="title">Output</div><pre>5 6 1 2 3 </pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=D]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); 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["Constructive algorithms", "Greedy algorithms", "Implementation problems, programming technics, simulation"]
["constructive algorithms", "greedy", "implementation", "*2000"]
59E
59
E
en
E. Shortest Path
<div class="problem-statement"><div class="header"><div class="title">E. Shortest Path</div><div class="time-limit"><div class="property-title">time limit per test</div>3 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>In Ancient Berland there were <span class="tex-span"><i>n</i></span> cities and <span class="tex-span"><i>m</i></span> two-way roads of equal length. The cities are numbered with integers from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span> inclusively. According to an ancient superstition, if a traveller visits three cities <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span> in row, without visiting other cities between them, a great disaster awaits him. Overall there are <span class="tex-span"><i>k</i></span> such city triplets. Each triplet is ordered, which means that, for example, you are allowed to visit the cities in the following order: <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span>. Vasya wants to get from the city <span class="tex-span">1</span> to the city <span class="tex-span"><i>n</i></span> and not fulfil the superstition. Find out which minimal number of roads he should take. Also you are required to find one of his possible path routes.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains three integers <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>m</i></span>, <span class="tex-span"><i>k</i></span> (<span class="tex-span">2 ≤ <i>n</i> ≤ 3000, 1 ≤ <i>m</i> ≤ 20000, 0 ≤ <i>k</i> ≤ 10<sup class="upper-index">5</sup></span>) which are the number of cities, the number of roads and the number of the forbidden triplets correspondingly. </p><p>Then follow <span class="tex-span"><i>m</i></span> lines each containing two integers <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>x</i><sub class="lower-index"><i>i</i></sub>, <i>y</i><sub class="lower-index"><i>i</i></sub> ≤ <i>n</i></span>) which are the road descriptions. The road is described by the numbers of the cities it joins. No road joins a city with itself, there cannot be more than one road between a pair of cities. </p><p>Then follow <span class="tex-span"><i>k</i></span> lines each containing three integers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub>, <i>b</i><sub class="lower-index"><i>i</i></sub>, <i>c</i><sub class="lower-index"><i>i</i></sub> ≤ <i>n</i></span>) which are the forbidden triplets. Each ordered triplet is listed mo more than one time. All three cities in each triplet are distinct.</p><p>City <span class="tex-span"><i>n</i></span> can be unreachable from city <span class="tex-span">1</span> by roads.</p></div><div class="output-specification"><div class="section-title">Output</div><p>If there are no path from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span> print <span class="tex-font-style-tt">-1</span>. Otherwise on the first line print the number of roads <span class="tex-span"><i>d</i></span> along the shortest path from the city <span class="tex-span">1</span> to the city <span class="tex-span"><i>n</i></span>. On the second line print <span class="tex-span"><i>d</i> + 1</span> numbers — any of the possible shortest paths for Vasya. The path should start in the city <span class="tex-span">1</span> and end in the city <span class="tex-span"><i>n</i></span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>4 4 1<br/>1 2<br/>2 3<br/>3 4<br/>1 3<br/>1 4 3<br/></pre></div><div class="output"><div class="title">Output</div><pre>2<br/>1 3 4<br/></pre></div><div class="input"><div class="title">Input</div><pre>3 1 0<br/>1 2<br/></pre></div><div class="output"><div class="title">Output</div><pre>-1<br/></pre></div><div class="input"><div class="title">Input</div><pre>4 4 2<br/>1 2<br/>2 3<br/>3 4<br/>1 3<br/>1 2 3<br/>1 3 4<br/></pre></div><div class="output"><div class="title">Output</div><pre>4<br/>1 3 2 3 4<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="E" data-uuid="ps_e16ba3b7181bf0a62f89a3dbb3984c0e23925cff"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">E. Shortest Path</div><div class="time-limit"><div class="property-title">time limit per test</div>3 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>In Ancient Berland there were <span class="tex-span"><i>n</i></span> cities and <span class="tex-span"><i>m</i></span> two-way roads of equal length. The cities are numbered with integers from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span> inclusively. According to an ancient superstition, if a traveller visits three cities <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span> in row, without visiting other cities between them, a great disaster awaits him. Overall there are <span class="tex-span"><i>k</i></span> such city triplets. Each triplet is ordered, which means that, for example, you are allowed to visit the cities in the following order: <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span>. Vasya wants to get from the city <span class="tex-span">1</span> to the city <span class="tex-span"><i>n</i></span> and not fulfil the superstition. Find out which minimal number of roads he should take. Also you are required to find one of his possible path routes.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains three integers <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>m</i></span>, <span class="tex-span"><i>k</i></span> (<span class="tex-span">2 ≤ <i>n</i> ≤ 3000, 1 ≤ <i>m</i> ≤ 20000, 0 ≤ <i>k</i> ≤ 10<sup class="upper-index">5</sup></span>) which are the number of cities, the number of roads and the number of the forbidden triplets correspondingly. </p><p>Then follow <span class="tex-span"><i>m</i></span> lines each containing two integers <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>x</i><sub class="lower-index"><i>i</i></sub>, <i>y</i><sub class="lower-index"><i>i</i></sub> ≤ <i>n</i></span>) which are the road descriptions. The road is described by the numbers of the cities it joins. No road joins a city with itself, there cannot be more than one road between a pair of cities. </p><p>Then follow <span class="tex-span"><i>k</i></span> lines each containing three integers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub>, <i>b</i><sub class="lower-index"><i>i</i></sub>, <i>c</i><sub class="lower-index"><i>i</i></sub> ≤ <i>n</i></span>) which are the forbidden triplets. Each ordered triplet is listed mo more than one time. All three cities in each triplet are distinct.</p><p>City <span class="tex-span"><i>n</i></span> can be unreachable from city <span class="tex-span">1</span> by roads.</p></div><div class="output-specification"><div class="section-title">Output</div><p>If there are no path from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span> print <span class="tex-font-style-tt">-1</span>. Otherwise on the first line print the number of roads <span class="tex-span"><i>d</i></span> along the shortest path from the city <span class="tex-span">1</span> to the city <span class="tex-span"><i>n</i></span>. On the second line print <span class="tex-span"><i>d</i> + 1</span> numbers — any of the possible shortest paths for Vasya. The path should start in the city <span class="tex-span">1</span> and end in the city <span class="tex-span"><i>n</i></span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>4 4 1<br />1 2<br />2 3<br />3 4<br />1 3<br />1 4 3<br /></pre></div><div class="output"><div class="title">Output</div><pre>2<br />1 3 4<br /></pre></div><div class="input"><div class="title">Input</div><pre>3 1 0<br />1 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>-1<br /></pre></div><div class="input"><div class="title">Input</div><pre>4 4 2<br />1 2<br />2 3<br />3 4<br />1 3<br />1 2 3<br />1 3 4<br /></pre></div><div class="output"><div class="title">Output</div><pre>4<br />1 3 2 3 4<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=E]"); let uuid = $problem.attr("data-uuid"); 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["Graphs", "Shortest paths on weighted and unweighted graphs"]
["graphs", "shortest paths", "*2000"]
60A
60
A
en
A. Where Are My Flakes?
<div class="problem-statement"><div class="header"><div class="title">A. Where Are My Flakes?</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><center> <img class="tex-graphics" src="https://espresso.codeforces.com/d1498b1262e9be4d39048f1d8d3113d0d81e77f4.png" style="max-width: 100.0%;max-height: 100.0%;"/> </center><p>One morning the Cereal Guy found out that all his cereal flakes were gone. He found a note instead of them. It turned out that his smart roommate hid the flakes in one of <span class="tex-span"><i>n</i></span> boxes. The boxes stand in one row, they are numbered from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span> from the left to the right. The roommate left hints like "Hidden to the left of the <span class="tex-span"><i>i</i></span>-th box" ("<span class="tex-font-style-tt">To the left of <span class="tex-span"><i>i</i></span></span>"), "Hidden to the right of the <span class="tex-span"><i>i</i></span>-th box" ("<span class="tex-font-style-tt">To the right of <span class="tex-span"><i>i</i></span></span>"). Such hints mean that there are no flakes in the <span class="tex-span"><i>i</i></span>-th box as well. The Cereal Guy wants to know the minimal number of boxes he necessarily needs to check to find the flakes considering all the hints. Or he wants to find out that the hints are contradictory and the roommate lied to him, that is, no box has the flakes.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>m</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 1000, 0 ≤ <i>m</i> ≤ 1000</span>) which represent the number of boxes and the number of hints correspondingly. Next <span class="tex-span"><i>m</i></span> lines contain hints like "<span class="tex-font-style-tt">To the left of <span class="tex-span"><i>i</i></span></span>" and "<span class="tex-font-style-tt">To the right of <span class="tex-span"><i>i</i></span></span>", where <span class="tex-span"><i>i</i></span> is integer (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>n</i></span>). The hints may coincide.</p></div><div class="output-specification"><div class="section-title">Output</div><p>The answer should contain exactly one integer — the number of boxes that should necessarily be checked or "<span class="tex-font-style-tt">-1</span>" if the hints are contradictory.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2 1<br/>To the left of 2<br/></pre></div><div class="output"><div class="title">Output</div><pre>1<br/></pre></div><div class="input"><div class="title">Input</div><pre>3 2<br/>To the right of 1<br/>To the right of 2<br/></pre></div><div class="output"><div class="title">Output</div><pre>1<br/></pre></div><div class="input"><div class="title">Input</div><pre>3 1<br/>To the left of 3<br/></pre></div><div class="output"><div class="title">Output</div><pre>2<br/></pre></div><div class="input"><div class="title">Input</div><pre>3 2<br/>To the left of 2<br/>To the right of 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>-1<br/></pre></div></div></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/60">Codeforces Beta Round 56</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? 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} </style> <div class="roundbox sidebox sidebar-menu borderTopRound " style=""> <div class="caption titled">&rarr; Contest materials <div class="top-links"> </div> </div> <ul> <li> <span> <a href="/blog/entry/1309" title="Codeforces Beta Round #56" target="_blank">Announcement</a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="216:217" resourceName="Announcement" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1317" title="Solutions for Codeforces Beta Round #56" target="_blank">Tutorial</a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="218:219" resourceName="Tutorial" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> </ul> </div></div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li class="current selectedLava"><a href="/contest/60">Problems</a></li> <li><a href="/contest/60/submit">Submit Code</a></li> <li><a href="/contest/60/my">My Submissions</a></li> <li><a href="/contest/60/status">Status</a></li> <li><a href="/contest/60/hacks">Hacks</a></li> <li><a href="/contest/60/room/1">Room</a></li> <li><a href="/contest/60/standings">Standings</a></li> <li><a href="/contest/60/customtest">Custom Invocation</a></li> </ul> </div> <style> #facebox .content:has(.diff-popup) { width: 90vw; 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="A" data-uuid="ps_9907a8f0e0852b9f1b5a6f88e8ce6034a48408a7"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">A. Where Are My Flakes?</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><center> <img class="tex-graphics" src="https://espresso.codeforces.com/d1498b1262e9be4d39048f1d8d3113d0d81e77f4.png" style="max-width: 100.0%;max-height: 100.0%;" /> </center><p>One morning the Cereal Guy found out that all his cereal flakes were gone. He found a note instead of them. It turned out that his smart roommate hid the flakes in one of <span class="tex-span"><i>n</i></span> boxes. The boxes stand in one row, they are numbered from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span> from the left to the right. The roommate left hints like &quot;Hidden to the left of the <span class="tex-span"><i>i</i></span>-th box&quot; (&quot;<span class="tex-font-style-tt">To the left of <span class="tex-span"><i>i</i></span></span>&quot;), &quot;Hidden to the right of the <span class="tex-span"><i>i</i></span>-th box&quot; (&quot;<span class="tex-font-style-tt">To the right of <span class="tex-span"><i>i</i></span></span>&quot;). Such hints mean that there are no flakes in the <span class="tex-span"><i>i</i></span>-th box as well. The Cereal Guy wants to know the minimal number of boxes he necessarily needs to check to find the flakes considering all the hints. Or he wants to find out that the hints are contradictory and the roommate lied to him, that is, no box has the flakes.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>m</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 1000, 0 ≤ <i>m</i> ≤ 1000</span>) which represent the number of boxes and the number of hints correspondingly. Next <span class="tex-span"><i>m</i></span> lines contain hints like &quot;<span class="tex-font-style-tt">To the left of <span class="tex-span"><i>i</i></span></span>&quot; and &quot;<span class="tex-font-style-tt">To the right of <span class="tex-span"><i>i</i></span></span>&quot;, where <span class="tex-span"><i>i</i></span> is integer (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>n</i></span>). The hints may coincide.</p></div><div class="output-specification"><div class="section-title">Output</div><p>The answer should contain exactly one integer — the number of boxes that should necessarily be checked or &quot;<span class="tex-font-style-tt">-1</span>&quot; if the hints are contradictory.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2 1<br />To the left of 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>1<br /></pre></div><div class="input"><div class="title">Input</div><pre>3 2<br />To the right of 1<br />To the right of 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>1<br /></pre></div><div class="input"><div class="title">Input</div><pre>3 1<br />To the left of 3<br /></pre></div><div class="output"><div class="title">Output</div><pre>2<br /></pre></div><div class="input"><div class="title">Input</div><pre>3 2<br />To the left of 2<br />To the right of 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>-1<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=A]"); 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["Implementation problems, programming technics, simulation", "Two pointers"]
["implementation", "two pointers", "*1300"]
https://codeforces.com/blog/entry/1317
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<a href="/blog/entry/120644">Codeforces Round 899 (Div. 2)</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/Misa-Misa" title="Expert Misa-Misa" class="rated-user user-blue">Misa-Misa</a> &rarr; <a href="/blog/entry/121157">Someone please help me understand this.</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/shivam565" title="Specialist shivam565" class="rated-user user-cyan">shivam565</a> &rarr; <a href="/blog/entry/108348">Total number of subarrays with sum atmost k</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> </ul> </div> <div class="bottom-links"> <table style="width:100%;"> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:right;"> <a href="/recent-actions">Detailed &rarr;</a> </td> </tr> </tbody> </table> </div> </div> </div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li><a href="/profile/Aksenov239">Aksenov239</a></li> <li class="current selectedLava"><a href="/blog/Aksenov239">Blog</a></li> <li><a href="/teams/with/Aksenov239">Teams</a></li> <li><a href="/submissions/Aksenov239">Submissions</a></li> <li><a href="/groups/with/Aksenov239">Groups</a></li> <li><a href="/contests/with/Aksenov239">Contests</a></li> <li><a href="/contests/writer/Aksenov239">Problemsetting</a></li> </ul> </div> <div style="margin-top:0;"> <div> <h3><a href="/blog/Aksenov239" style="text-decoration:none;color:black !important;">Aksenov239's blog</a></h3> </div> <div style="margin-top:2em;"> <div class="has-topic-id topic" topicId="1317"> <div class="title"> <a href="/blog/entry/1317"> Solutions for Codeforces Beta Round #56 </a> </div> <div class="info" style="position:relative;"> By&nbsp;<a href="/profile/Aksenov239" title="Candidate Master Aksenov239" class="rated-user user-violet">Aksenov239</a>, <span class="format-humantime" title="Feb/19/2011 23:22">13 years ago</span>, translation, <img style="position: relative;top: 5px;" src="//codeforces.org/s/81027/images/flags/24/gb.png" alt="In English" title="In English"/> <span style="position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;"> <div style="margin-top:0.25em;"> </div> </span> </div> <div class="content"> <div class="ttypography"><div><div><div><b>Problem A.</b> Solution - <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">2</sup>)</span>. </div><div>We take phrase and parse it. Mark all cells, that obviously didn't match - <span class="tex-span"><i>O</i>(<i>n</i>)</span>. In the end we go through the array and count all unmarked cells.</div><div>If 0 - we print &quot;-1&quot;, else - amount of unmarked cells.</div><div><br /></div><div><b>Problem B.</b> Solution - <span class="tex-span"><i>O</i>(<i>k</i> × <i>n</i> × <i>m</i>)</span>. </div><div>We start BFS from given point. Go from cell to all 6 directions. The answer - number of visited cells.</div><div><br /></div><div><b>Problem C</b>. Solution - <span class="tex-span"><i>O</i>(2<sup class="upper-index">7</sup> × <i>n</i><sup class="upper-index">2</sup>)</span>. </div><div>We can see, that in connected component - if we know 1 number - then we know all others in component, because in each pare we know minimal and maximal</div><div>power of each primes. Because number of different primes in one number &quot;<span class="tex-span"> &lt;  = 1000000</span>&quot; is less, than 7, we can look over all possibilities of 1 number in connected compoment - and for each number, that we get, we check, that it suits.</div><div><br /></div><div>How to check? We can notice, that if we know <span class="tex-span"><i>a</i></span>, <span class="tex-span">(<i>a</i>, <i>b</i>)</span>, <span class="tex-span">[<i>a</i>, <i>b</i>]</span>, then <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/ec0a60c5e7d57fce4b1519a30d222c3563f64d0d.png" style="max-width: 100.0%;max-height: 100.0%;" />, start DFS and check.</div><div><br /></div><div><b>Problem D.</b> Solution - <span class="tex-span"><i>O</i>(</span>max numebr<span class="tex-span">)</span>.</div><div>We can notice, that each beautiful triplet has form - <span class="tex-span">(<i>x</i><sup class="upper-index">2</sup> - <i>y</i><sup class="upper-index">2</sup>, 2<i>xy</i>, <i>x</i><sup class="upper-index">2</sup> + <i>y</i><sup class="upper-index">2</sup>)</span>. Now we can gen all such triples. For each triple, we watch - if we have more than 1 number in given set - we union them.</div><div><br /></div><div>How to gen all the triples?</div><div><br /></div><div><span class="tex-span"><i>x</i> &gt; <i>y</i></span>.</div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/49af3a586cdbbcb471801cc55ed10df7fdd2474b.png" style="max-width: 100.0%;max-height: 100.0%;" />. This means, that <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/338034360a12a7a2ca8523c67346f08047fcd975.png" style="max-width: 100.0%;max-height: 100.0%;" />.</div><div>Now for gen all this triples we an take - <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/bed025bc1334b2defa84303530e904c69f148f81.png" style="max-width: 100.0%;max-height: 100.0%;" /> и <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/3af1f7f66b4dcfc2e7a2a39e3509a177f2f614c3.png" style="max-width: 100.0%;max-height: 100.0%;" />. The number of iterations - <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/e1a0bc527cbbd27a97b9e94fc55c42c5174c46af.png" style="max-width: 100.0%;max-height: 100.0%;" />.</div><div><br /></div><div>what means - &quot;union&quot;?</div><div>We take a data structure named DSU. If two number belong to one beautiful triple - they are connected with edge, in our situation - we can union corresponding to them unions.</div><div><br /></div><div><b>Problem E</b>. Solution - <span class="tex-span"><i>O</i>(<i>n</i> + <i>log</i>(<i>xy</i>))</span>.</div><div>We can see, that after one minute the sum changes - it multiply on 3, and substract first and last elements of sequence. Because of that we can count of sum with help of power of matrix.</div><div><br /></div><div>What happens after sorting.</div><div><br /></div><div>First number stay on his place. On the last place - <span class="tex-span"><i>F</i><sub class="lower-index"><i>x</i></sub><i>a</i><sub class="lower-index"><i>n</i></sub> + <i>F</i><sub class="lower-index"><i>x</i> - 1</sub><i>a</i><sub class="lower-index"><i>n</i> - 1</sub></span>. Where <span class="tex-span"><i>n</i></span> - number of elements, ans <span class="tex-span"><i>F</i><sub class="lower-index"><i>x</i></sub></span> - <span class="tex-span"><i>x</i></span> Fibonacci number - with <span class="tex-span"><i>F</i><sub class="lower-index"> - 1</sub> = 0</span> and <span class="tex-span"><i>F</i><sub class="lower-index">0</sub> = 1</span>.</div><div><br /></div><div>This means - that we can count the last number with matrix too.</div><div><br /></div><div>After that we use the first idea.</div><div><br /></div><div>If you have questions - ask them.</div><div style="font-weight: bold;"><br /></div></div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/60" class="notice" style="text-decoration: none;">Codeforces Beta Round 56</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-3573-1317").click(function() { var that = this; 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line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/Aksenov239"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/Aksenov239"> Aksenov239 </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Feb/19/2011 23:22">13 years ago</span> </li> <li> <a href="/blog/entry/1317#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1317#comments"> 5 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1327"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (4)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="23572" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/21/2011 15:14">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-23572" href="?#comment-23572" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="23572" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-23572"> <div class="moveup"> <div class="ttypography">Hi,<br /><br />To get the sum quickly, what I did was this:<br /><br /><span>Let the array be S with elements from 1 to N. Let f(x) be the sum of all elements after k moves. <br /><br />Then f(x) = 3*f(x) - (S[1] + S[N]); f(0) = sum, where sum == summation of all elements in S.<br /><br />The solution to this recursion is sum * 3^X - (S[1] + S[N]) * (3^X - 1) / 2<br /><br />However, I have division by 2, and division with modulo seems very tricky to handle. May I know how you solve this issue?<br /><br />Thanks!<br /></span></div> </div> </div> <div class="reply info"> <a class="comment-23572 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-23572 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-23572"> <li> <div class="comment"> <table class="comment-table" commentId="24441" commentParentId="23572"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/madkite" style="position: relative;"> <img src='https://userpic.codeforces.org/7462/avatar/69de282c387fb448.jpg'/> </a> <div><a href="/profile/madkite" title="Expert madkite" class="rated-user user-blue">madkite</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/26/2011 02:12">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-24441" href="?#comment-24441" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-23572" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="24441" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="7462" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-24441"> <div class="moveup"> <div class="ttypography">I'm doing something like this: ... * (3^X - 1 + 2 * p) % (2 * p) / 2</div> </div> </div> <div class="reply info"> <a class="comment-24441 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-24441 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-24441"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="388053" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/hpkt.pkt" style="position: relative;"> <img src='https://userpic.codeforces.org/573762/avatar/822d5bb5d0cbe6cb.jpg'/> </a> <div><a href="/profile/hpkt.pkt" title="Specialist hpkt.pkt" class="rated-user user-cyan">hpkt.pkt</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Sep/28/2017 09:10">6 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-388053" href="?#comment-388053" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="388053" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="573762" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-388053"> <div class="moveup"> <div class="ttypography"><p>How can problem B be solved using DSU. I see DSU tag over there.</p></div> </div> </div> <div class="reply info"> <a class="comment-388053 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-388053 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-388053"> <li> <div class="comment"> <table class="comment-table" commentId="388091" commentParentId="388053"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/SummerSky" style="position: relative;"> <img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a> <div><a href="/profile/SummerSky" title="Expert SummerSky" class="rated-user user-blue">SummerSky</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Sep/28/2017 18:02">6 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-388091" href="?#comment-388091" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-388053" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="388091" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="419016" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-388091"> <div class="moveup"> <div class="ttypography"><p>Hmm, I think perhaps you mean DSU=Disjoint Set, while I usually call it Union-Find...</p><p>I solved this problem by using BFS, but I think as union-find can be used to find out the connected components, I guess that it is used there to find out all the '.' positions that can be reached from the initial position. Nevertheless, I think it is a little weird to use union-find there, since as far as I consider, union-find usually appears with a sparse graph that is described with connected edges, while it seems straightforward to use BFS in this problem...</p></div> </div> </div> <div class="reply info"> <a class="comment-388091 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-388091 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-388091"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1327" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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60B
60
B
en
B. Serial Time!
<div class="problem-statement"><div class="header"><div class="title">B. Serial Time!</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>The Cereal Guy's friend Serial Guy likes to watch soap operas. An episode is about to start, and he hasn't washed his plate yet. But he decided to at least put in under the tap to be filled with water. The plate can be represented by a parallelepiped <span class="tex-span"><i>k</i> × <i>n</i> × <i>m</i></span>, that is, it has <span class="tex-span"><i>k</i></span> layers (the first layer is the upper one), each of which is a rectangle <span class="tex-span"><i>n</i> × <i>m</i></span> with empty squares ('.') and obstacles ('#'). The water can only be present in the empty squares. The tap is positioned above the square <span class="tex-span">(<i>x</i>, <i>y</i>)</span> of the first layer, it is guaranteed that this square is empty. Every minute a cubical unit of water falls into the plate. Find out in how many minutes the Serial Guy should unglue himself from the soap opera and turn the water off for it not to overfill the plate. That is, you should find the moment of time when the plate is absolutely full and is going to be overfilled in the next moment.</p><p>Note: the water fills all the area within reach (see sample 4). Water flows in <span class="tex-font-style-bf">each</span> of the 6 directions, through faces of <span class="tex-span">1 × 1 × 1</span> cubes.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains three numbers <span class="tex-span"><i>k</i></span>, <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>m</i></span> (<span class="tex-span">1 ≤ <i>k</i>, <i>n</i>, <i>m</i> ≤ 10</span>) which are the sizes of the plate. Then follow <span class="tex-span"><i>k</i></span> rectangles consisting of <span class="tex-span"><i>n</i></span> lines each containing <span class="tex-span"><i>m</i></span> characters '.' or '#', which represents the "layers" of the plate in the order from the top to the bottom. The rectangles are separated by empty lines (see the samples). The last line contains <span class="tex-span"><i>x</i></span> and <span class="tex-span"><i>y</i></span> (<span class="tex-span">1 ≤ <i>x</i> ≤ <i>n</i>, 1 ≤ <i>y</i> ≤ <i>m</i></span>) which are the tap's coordinates. <span class="tex-span"><i>x</i></span> is the number of the line and <span class="tex-span"><i>y</i></span> is the number of the column. Lines of each layer are numbered from left to right by the integers from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span>, columns of each layer are numbered from top to bottom by the integers from <span class="tex-span">1</span> to <span class="tex-span"><i>m</i></span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>The answer should contain a single number, showing in how many minutes the plate will be filled.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>1 1 1<br/><br/>.<br/><br/>1 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>1<br/></pre></div><div class="input"><div class="title">Input</div><pre>2 1 1<br/><br/>.<br/><br/>#<br/><br/>1 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>1<br/></pre></div><div class="input"><div class="title">Input</div><pre>2 2 2<br/><br/>.#<br/>##<br/><br/>..<br/>..<br/><br/>1 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>5<br/></pre></div><div class="input"><div class="title">Input</div><pre>3 2 2<br/><br/>#.<br/>##<br/><br/>#.<br/>.#<br/><br/>..<br/>..<br/><br/>1 2<br/></pre></div><div class="output"><div class="title">Output</div><pre>7<br/></pre></div><div class="input"><div class="title">Input</div><pre>3 3 3<br/><br/>.#.<br/>###<br/>##.<br/><br/>.##<br/>###<br/>##.<br/><br/>...<br/>...<br/>...<br/><br/>1 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>13<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="B" data-uuid="ps_09a944e80ae656d7ff0ecc7e734861e076ee6ce6"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">B. Serial Time!</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>The Cereal Guy's friend Serial Guy likes to watch soap operas. An episode is about to start, and he hasn't washed his plate yet. But he decided to at least put in under the tap to be filled with water. The plate can be represented by a parallelepiped <span class="tex-span"><i>k</i> × <i>n</i> × <i>m</i></span>, that is, it has <span class="tex-span"><i>k</i></span> layers (the first layer is the upper one), each of which is a rectangle <span class="tex-span"><i>n</i> × <i>m</i></span> with empty squares ('.') and obstacles ('#'). The water can only be present in the empty squares. The tap is positioned above the square <span class="tex-span">(<i>x</i>, <i>y</i>)</span> of the first layer, it is guaranteed that this square is empty. Every minute a cubical unit of water falls into the plate. Find out in how many minutes the Serial Guy should unglue himself from the soap opera and turn the water off for it not to overfill the plate. That is, you should find the moment of time when the plate is absolutely full and is going to be overfilled in the next moment.</p><p>Note: the water fills all the area within reach (see sample 4). Water flows in <span class="tex-font-style-bf">each</span> of the 6 directions, through faces of <span class="tex-span">1 × 1 × 1</span> cubes.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains three numbers <span class="tex-span"><i>k</i></span>, <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>m</i></span> (<span class="tex-span">1 ≤ <i>k</i>, <i>n</i>, <i>m</i> ≤ 10</span>) which are the sizes of the plate. Then follow <span class="tex-span"><i>k</i></span> rectangles consisting of <span class="tex-span"><i>n</i></span> lines each containing <span class="tex-span"><i>m</i></span> characters '.' or '#', which represents the &quot;layers&quot; of the plate in the order from the top to the bottom. The rectangles are separated by empty lines (see the samples). The last line contains <span class="tex-span"><i>x</i></span> and <span class="tex-span"><i>y</i></span> (<span class="tex-span">1 ≤ <i>x</i> ≤ <i>n</i>, 1 ≤ <i>y</i> ≤ <i>m</i></span>) which are the tap's coordinates. <span class="tex-span"><i>x</i></span> is the number of the line and <span class="tex-span"><i>y</i></span> is the number of the column. Lines of each layer are numbered from left to right by the integers from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span>, columns of each layer are numbered from top to bottom by the integers from <span class="tex-span">1</span> to <span class="tex-span"><i>m</i></span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>The answer should contain a single number, showing in how many minutes the plate will be filled.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>1 1 1<br /><br />.<br /><br />1 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>1<br /></pre></div><div class="input"><div class="title">Input</div><pre>2 1 1<br /><br />.<br /><br />#<br /><br />1 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>1<br /></pre></div><div class="input"><div class="title">Input</div><pre>2 2 2<br /><br />.#<br />##<br /><br />..<br />..<br /><br />1 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>5<br /></pre></div><div class="input"><div class="title">Input</div><pre>3 2 2<br /><br />#.<br />##<br /><br />#.<br />.#<br /><br />..<br />..<br /><br />1 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>7<br /></pre></div><div class="input"><div class="title">Input</div><pre>3 3 3<br /><br />.#.<br />###<br />##.<br /><br />.##<br />###<br />##.<br /><br />...<br />...<br />...<br /><br />1 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>13<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=B]"); 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["Dfs and similar", "Disjoint set union"]
["dfs and similar", "dsu", "*1400"]
https://codeforces.com/blog/entry/1317
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Mark all cells, that obviously didn't match - <span class="tex-span"><i>O</i>(<i>n</i>)</span>. In the end we go through the array and count all unmarked cells.</div><div>If 0 - we print &quot;-1&quot;, else - amount of unmarked cells.</div><div><br /></div><div><b>Problem B.</b> Solution - <span class="tex-span"><i>O</i>(<i>k</i> × <i>n</i> × <i>m</i>)</span>. </div><div>We start BFS from given point. Go from cell to all 6 directions. The answer - number of visited cells.</div><div><br /></div><div><b>Problem C</b>. Solution - <span class="tex-span"><i>O</i>(2<sup class="upper-index">7</sup> × <i>n</i><sup class="upper-index">2</sup>)</span>. </div><div>We can see, that in connected component - if we know 1 number - then we know all others in component, because in each pare we know minimal and maximal</div><div>power of each primes. Because number of different primes in one number &quot;<span class="tex-span"> &lt;  = 1000000</span>&quot; is less, than 7, we can look over all possibilities of 1 number in connected compoment - and for each number, that we get, we check, that it suits.</div><div><br /></div><div>How to check? We can notice, that if we know <span class="tex-span"><i>a</i></span>, <span class="tex-span">(<i>a</i>, <i>b</i>)</span>, <span class="tex-span">[<i>a</i>, <i>b</i>]</span>, then <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/ec0a60c5e7d57fce4b1519a30d222c3563f64d0d.png" style="max-width: 100.0%;max-height: 100.0%;" />, start DFS and check.</div><div><br /></div><div><b>Problem D.</b> Solution - <span class="tex-span"><i>O</i>(</span>max numebr<span class="tex-span">)</span>.</div><div>We can notice, that each beautiful triplet has form - <span class="tex-span">(<i>x</i><sup class="upper-index">2</sup> - <i>y</i><sup class="upper-index">2</sup>, 2<i>xy</i>, <i>x</i><sup class="upper-index">2</sup> + <i>y</i><sup class="upper-index">2</sup>)</span>. Now we can gen all such triples. For each triple, we watch - if we have more than 1 number in given set - we union them.</div><div><br /></div><div>How to gen all the triples?</div><div><br /></div><div><span class="tex-span"><i>x</i> &gt; <i>y</i></span>.</div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/49af3a586cdbbcb471801cc55ed10df7fdd2474b.png" style="max-width: 100.0%;max-height: 100.0%;" />. This means, that <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/338034360a12a7a2ca8523c67346f08047fcd975.png" style="max-width: 100.0%;max-height: 100.0%;" />.</div><div>Now for gen all this triples we an take - <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/bed025bc1334b2defa84303530e904c69f148f81.png" style="max-width: 100.0%;max-height: 100.0%;" /> и <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/3af1f7f66b4dcfc2e7a2a39e3509a177f2f614c3.png" style="max-width: 100.0%;max-height: 100.0%;" />. The number of iterations - <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/e1a0bc527cbbd27a97b9e94fc55c42c5174c46af.png" style="max-width: 100.0%;max-height: 100.0%;" />.</div><div><br /></div><div>what means - &quot;union&quot;?</div><div>We take a data structure named DSU. If two number belong to one beautiful triple - they are connected with edge, in our situation - we can union corresponding to them unions.</div><div><br /></div><div><b>Problem E</b>. Solution - <span class="tex-span"><i>O</i>(<i>n</i> + <i>log</i>(<i>xy</i>))</span>.</div><div>We can see, that after one minute the sum changes - it multiply on 3, and substract first and last elements of sequence. Because of that we can count of sum with help of power of matrix.</div><div><br /></div><div>What happens after sorting.</div><div><br /></div><div>First number stay on his place. On the last place - <span class="tex-span"><i>F</i><sub class="lower-index"><i>x</i></sub><i>a</i><sub class="lower-index"><i>n</i></sub> + <i>F</i><sub class="lower-index"><i>x</i> - 1</sub><i>a</i><sub class="lower-index"><i>n</i> - 1</sub></span>. Where <span class="tex-span"><i>n</i></span> - number of elements, ans <span class="tex-span"><i>F</i><sub class="lower-index"><i>x</i></sub></span> - <span class="tex-span"><i>x</i></span> Fibonacci number - with <span class="tex-span"><i>F</i><sub class="lower-index"> - 1</sub> = 0</span> and <span class="tex-span"><i>F</i><sub class="lower-index">0</sub> = 1</span>.</div><div><br /></div><div>This means - that we can count the last number with matrix too.</div><div><br /></div><div>After that we use the first idea.</div><div><br /></div><div>If you have questions - ask them.</div><div style="font-weight: bold;"><br /></div></div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/60" class="notice" style="text-decoration: none;">Codeforces Beta Round 56</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-3573-1317").click(function() { var that = this; 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top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="23572" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-23572"> <div class="moveup"> <div class="ttypography">Hi,<br /><br />To get the sum quickly, what I did was this:<br /><br /><span>Let the array be S with elements from 1 to N. Let f(x) be the sum of all elements after k moves. <br /><br />Then f(x) = 3*f(x) - (S[1] + S[N]); f(0) = sum, where sum == summation of all elements in S.<br /><br />The solution to this recursion is sum * 3^X - (S[1] + S[N]) * (3^X - 1) / 2<br /><br />However, I have division by 2, and division with modulo seems very tricky to handle. May I know how you solve this issue?<br /><br />Thanks!<br /></span></div> </div> </div> <div class="reply info"> <a class="comment-23572 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-23572 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-23572"> <li> <div class="comment"> <table class="comment-table" commentId="24441" commentParentId="23572"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/madkite" style="position: relative;"> <img src='https://userpic.codeforces.org/7462/avatar/69de282c387fb448.jpg'/> </a> <div><a href="/profile/madkite" title="Expert madkite" class="rated-user user-blue">madkite</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/26/2011 02:12">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-24441" href="?#comment-24441" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-23572" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="24441" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="7462" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-24441"> <div class="moveup"> <div class="ttypography">I'm doing something like this: ... * (3^X - 1 + 2 * p) % (2 * p) / 2</div> </div> </div> <div class="reply info"> <a class="comment-24441 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-24441 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-24441"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="388053" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/hpkt.pkt" style="position: relative;"> <img src='https://userpic.codeforces.org/573762/avatar/822d5bb5d0cbe6cb.jpg'/> </a> <div><a href="/profile/hpkt.pkt" title="Specialist hpkt.pkt" class="rated-user user-cyan">hpkt.pkt</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Sep/28/2017 09:10">6 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-388053" href="?#comment-388053" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="388053" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="573762" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-388053"> <div class="moveup"> <div class="ttypography"><p>How can problem B be solved using DSU. I see DSU tag over there.</p></div> </div> </div> <div class="reply info"> <a class="comment-388053 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-388053 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-388053"> <li> <div class="comment"> <table class="comment-table" commentId="388091" commentParentId="388053"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/SummerSky" style="position: relative;"> <img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a> <div><a href="/profile/SummerSky" title="Expert SummerSky" class="rated-user user-blue">SummerSky</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Sep/28/2017 18:02">6 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-388091" href="?#comment-388091" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-388053" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="388091" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="419016" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-388091"> <div class="moveup"> <div class="ttypography"><p>Hmm, I think perhaps you mean DSU=Disjoint Set, while I usually call it Union-Find...</p><p>I solved this problem by using BFS, but I think as union-find can be used to find out the connected components, I guess that it is used there to find out all the '.' positions that can be reached from the initial position. Nevertheless, I think it is a little weird to use union-find there, since as far as I consider, union-find usually appears with a sparse graph that is described with connected edges, while it seems straightforward to use BFS in this problem...</p></div> </div> </div> <div class="reply info"> <a class="comment-388091 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-388091 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-388091"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1327" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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60C
60
C
en
C. Mushroom Strife
<div class="problem-statement"><div class="header"><div class="title">C. Mushroom Strife</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Pasha and Akim were making a forest map — the lawns were the graph's vertexes and the roads joining the lawns were its edges. They decided to encode the number of laughy mushrooms on every lawn in the following way: on every edge between two lawns they wrote two numbers, the greatest common divisor (GCD) and the least common multiple (LCM) of the number of mushrooms on these lawns. But one day Pasha and Akim had an argument about the laughy mushrooms and tore the map. Pasha was left with just some part of it, containing only <span class="tex-span"><i>m</i></span> roads. Your task is to help Pasha — use the map he has to restore the number of mushrooms on every lawn. As the result is not necessarily unique, help Pasha to restore any one or report that such arrangement of mushrooms does not exist. It is guaranteed that the numbers on the roads on the initial map were no less that <span class="tex-span">1</span> and did not exceed <span class="tex-span">10<sup class="upper-index">6</sup></span>.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two numbers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>m</i></span> (<img align="middle" class="tex-formula" src="https://espresso.codeforces.com/a187a1d9b67001db2abcc54c470f3f166a0fd081.png" style="max-width: 100.0%;max-height: 100.0%;"/>) which are the numbers of lawns and roads we know about. Each of the following <span class="tex-span"><i>m</i></span> lines contains four numbers which are the numbers of lawns the road connects, the GCD and the LCM of the numbers of mushrooms on these lawns (<span class="tex-span">1 ≤ <i>GCD</i>, <i>LCM</i> ≤ 10<sup class="upper-index">6</sup></span>).</p><p>It is guaranteed, that no road connects lawn to itself, and no two lawns are connected by more than one road.</p></div><div class="output-specification"><div class="section-title">Output</div><p>The answer should contain "<span class="tex-font-style-tt">YES</span>" or "<span class="tex-font-style-tt">NO</span>" on the first line, saying whether it is possible or not to perform the arrangement. If the answer is "<span class="tex-font-style-tt">YES</span>", print on the following line <span class="tex-span"><i>n</i></span> numbers which are the numbers of mushrooms on the corresponding lawns.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>1 0<br/></pre></div><div class="output"><div class="title">Output</div><pre>YES<br/>1 </pre></div><div class="input"><div class="title">Input</div><pre>2 1<br/>1 2 1 3<br/></pre></div><div class="output"><div class="title">Output</div><pre>YES<br/>1 3 </pre></div><div class="input"><div class="title">Input</div><pre>3 2<br/>3 2 1 2<br/>3 1 1 10<br/></pre></div><div class="output"><div class="title">Output</div><pre>YES<br/>5 1 2 </pre></div><div class="input"><div class="title">Input</div><pre>2 1<br/>1 2 3 7<br/></pre></div><div class="output"><div class="title">Output</div><pre>NO<br/></pre></div></div></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/60">Codeforces Beta Round 56</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? 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If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="C" data-uuid="ps_f35f338679a99ae4f54591c3ca270c429e9a0919"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. Mushroom Strife</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Pasha and Akim were making a forest map — the lawns were the graph's vertexes and the roads joining the lawns were its edges. They decided to encode the number of laughy mushrooms on every lawn in the following way: on every edge between two lawns they wrote two numbers, the greatest common divisor (GCD) and the least common multiple (LCM) of the number of mushrooms on these lawns. But one day Pasha and Akim had an argument about the laughy mushrooms and tore the map. Pasha was left with just some part of it, containing only <span class="tex-span"><i>m</i></span> roads. Your task is to help Pasha — use the map he has to restore the number of mushrooms on every lawn. As the result is not necessarily unique, help Pasha to restore any one or report that such arrangement of mushrooms does not exist. It is guaranteed that the numbers on the roads on the initial map were no less that <span class="tex-span">1</span> and did not exceed <span class="tex-span">10<sup class="upper-index">6</sup></span>.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two numbers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>m</i></span> (<img align="middle" class="tex-formula" src="https://espresso.codeforces.com/a187a1d9b67001db2abcc54c470f3f166a0fd081.png" style="max-width: 100.0%;max-height: 100.0%;" />) which are the numbers of lawns and roads we know about. Each of the following <span class="tex-span"><i>m</i></span> lines contains four numbers which are the numbers of lawns the road connects, the GCD and the LCM of the numbers of mushrooms on these lawns (<span class="tex-span">1 ≤ <i>GCD</i>, <i>LCM</i> ≤ 10<sup class="upper-index">6</sup></span>).</p><p>It is guaranteed, that no road connects lawn to itself, and no two lawns are connected by more than one road.</p></div><div class="output-specification"><div class="section-title">Output</div><p>The answer should contain &quot;<span class="tex-font-style-tt">YES</span>&quot; or &quot;<span class="tex-font-style-tt">NO</span>&quot; on the first line, saying whether it is possible or not to perform the arrangement. If the answer is &quot;<span class="tex-font-style-tt">YES</span>&quot;, print on the following line <span class="tex-span"><i>n</i></span> numbers which are the numbers of mushrooms on the corresponding lawns.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>1 0<br /></pre></div><div class="output"><div class="title">Output</div><pre>YES<br />1 </pre></div><div class="input"><div class="title">Input</div><pre>2 1<br />1 2 1 3<br /></pre></div><div class="output"><div class="title">Output</div><pre>YES<br />1 3 </pre></div><div class="input"><div class="title">Input</div><pre>3 2<br />3 2 1 2<br />3 1 1 10<br /></pre></div><div class="output"><div class="title">Output</div><pre>YES<br />5 1 2 </pre></div><div class="input"><div class="title">Input</div><pre>2 1<br />1 2 3 7<br /></pre></div><div class="output"><div class="title">Output</div><pre>NO<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=C]"); 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["Brute force", "Dfs and similar"]
["brute force", "dfs and similar", "*2100"]
https://codeforces.com/blog/entry/1317
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Mark all cells, that obviously didn't match - <span class="tex-span"><i>O</i>(<i>n</i>)</span>. In the end we go through the array and count all unmarked cells.</div><div>If 0 - we print &quot;-1&quot;, else - amount of unmarked cells.</div><div><br /></div><div><b>Problem B.</b> Solution - <span class="tex-span"><i>O</i>(<i>k</i> × <i>n</i> × <i>m</i>)</span>. </div><div>We start BFS from given point. Go from cell to all 6 directions. The answer - number of visited cells.</div><div><br /></div><div><b>Problem C</b>. Solution - <span class="tex-span"><i>O</i>(2<sup class="upper-index">7</sup> × <i>n</i><sup class="upper-index">2</sup>)</span>. </div><div>We can see, that in connected component - if we know 1 number - then we know all others in component, because in each pare we know minimal and maximal</div><div>power of each primes. Because number of different primes in one number &quot;<span class="tex-span"> &lt;  = 1000000</span>&quot; is less, than 7, we can look over all possibilities of 1 number in connected compoment - and for each number, that we get, we check, that it suits.</div><div><br /></div><div>How to check? We can notice, that if we know <span class="tex-span"><i>a</i></span>, <span class="tex-span">(<i>a</i>, <i>b</i>)</span>, <span class="tex-span">[<i>a</i>, <i>b</i>]</span>, then <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/ec0a60c5e7d57fce4b1519a30d222c3563f64d0d.png" style="max-width: 100.0%;max-height: 100.0%;" />, start DFS and check.</div><div><br /></div><div><b>Problem D.</b> Solution - <span class="tex-span"><i>O</i>(</span>max numebr<span class="tex-span">)</span>.</div><div>We can notice, that each beautiful triplet has form - <span class="tex-span">(<i>x</i><sup class="upper-index">2</sup> - <i>y</i><sup class="upper-index">2</sup>, 2<i>xy</i>, <i>x</i><sup class="upper-index">2</sup> + <i>y</i><sup class="upper-index">2</sup>)</span>. Now we can gen all such triples. For each triple, we watch - if we have more than 1 number in given set - we union them.</div><div><br /></div><div>How to gen all the triples?</div><div><br /></div><div><span class="tex-span"><i>x</i> &gt; <i>y</i></span>.</div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/49af3a586cdbbcb471801cc55ed10df7fdd2474b.png" style="max-width: 100.0%;max-height: 100.0%;" />. This means, that <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/338034360a12a7a2ca8523c67346f08047fcd975.png" style="max-width: 100.0%;max-height: 100.0%;" />.</div><div>Now for gen all this triples we an take - <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/bed025bc1334b2defa84303530e904c69f148f81.png" style="max-width: 100.0%;max-height: 100.0%;" /> и <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/3af1f7f66b4dcfc2e7a2a39e3509a177f2f614c3.png" style="max-width: 100.0%;max-height: 100.0%;" />. The number of iterations - <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/e1a0bc527cbbd27a97b9e94fc55c42c5174c46af.png" style="max-width: 100.0%;max-height: 100.0%;" />.</div><div><br /></div><div>what means - &quot;union&quot;?</div><div>We take a data structure named DSU. If two number belong to one beautiful triple - they are connected with edge, in our situation - we can union corresponding to them unions.</div><div><br /></div><div><b>Problem E</b>. Solution - <span class="tex-span"><i>O</i>(<i>n</i> + <i>log</i>(<i>xy</i>))</span>.</div><div>We can see, that after one minute the sum changes - it multiply on 3, and substract first and last elements of sequence. Because of that we can count of sum with help of power of matrix.</div><div><br /></div><div>What happens after sorting.</div><div><br /></div><div>First number stay on his place. On the last place - <span class="tex-span"><i>F</i><sub class="lower-index"><i>x</i></sub><i>a</i><sub class="lower-index"><i>n</i></sub> + <i>F</i><sub class="lower-index"><i>x</i> - 1</sub><i>a</i><sub class="lower-index"><i>n</i> - 1</sub></span>. Where <span class="tex-span"><i>n</i></span> - number of elements, ans <span class="tex-span"><i>F</i><sub class="lower-index"><i>x</i></sub></span> - <span class="tex-span"><i>x</i></span> Fibonacci number - with <span class="tex-span"><i>F</i><sub class="lower-index"> - 1</sub> = 0</span> and <span class="tex-span"><i>F</i><sub class="lower-index">0</sub> = 1</span>.</div><div><br /></div><div>This means - that we can count the last number with matrix too.</div><div><br /></div><div>After that we use the first idea.</div><div><br /></div><div>If you have questions - ask them.</div><div style="font-weight: bold;"><br /></div></div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/60" class="notice" style="text-decoration: none;">Codeforces Beta Round 56</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-3573-1317").click(function() { var that = this; 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line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/Aksenov239"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/Aksenov239"> Aksenov239 </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Feb/19/2011 23:22">13 years ago</span> </li> <li> <a href="/blog/entry/1317#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1317#comments"> 5 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1327"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (4)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="23572" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/21/2011 15:14">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-23572" href="?#comment-23572" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="23572" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-23572"> <div class="moveup"> <div class="ttypography">Hi,<br /><br />To get the sum quickly, what I did was this:<br /><br /><span>Let the array be S with elements from 1 to N. Let f(x) be the sum of all elements after k moves. <br /><br />Then f(x) = 3*f(x) - (S[1] + S[N]); f(0) = sum, where sum == summation of all elements in S.<br /><br />The solution to this recursion is sum * 3^X - (S[1] + S[N]) * (3^X - 1) / 2<br /><br />However, I have division by 2, and division with modulo seems very tricky to handle. May I know how you solve this issue?<br /><br />Thanks!<br /></span></div> </div> </div> <div class="reply info"> <a class="comment-23572 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-23572 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-23572"> <li> <div class="comment"> <table class="comment-table" commentId="24441" commentParentId="23572"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/madkite" style="position: relative;"> <img src='https://userpic.codeforces.org/7462/avatar/69de282c387fb448.jpg'/> </a> <div><a href="/profile/madkite" title="Expert madkite" class="rated-user user-blue">madkite</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/26/2011 02:12">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-24441" href="?#comment-24441" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-23572" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="24441" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="7462" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-24441"> <div class="moveup"> <div class="ttypography">I'm doing something like this: ... * (3^X - 1 + 2 * p) % (2 * p) / 2</div> </div> </div> <div class="reply info"> <a class="comment-24441 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-24441 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-24441"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="388053" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/hpkt.pkt" style="position: relative;"> <img src='https://userpic.codeforces.org/573762/avatar/822d5bb5d0cbe6cb.jpg'/> </a> <div><a href="/profile/hpkt.pkt" title="Specialist hpkt.pkt" class="rated-user user-cyan">hpkt.pkt</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Sep/28/2017 09:10">6 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-388053" href="?#comment-388053" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="388053" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="573762" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-388053"> <div class="moveup"> <div class="ttypography"><p>How can problem B be solved using DSU. I see DSU tag over there.</p></div> </div> </div> <div class="reply info"> <a class="comment-388053 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-388053 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-388053"> <li> <div class="comment"> <table class="comment-table" commentId="388091" commentParentId="388053"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/SummerSky" style="position: relative;"> <img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a> <div><a href="/profile/SummerSky" title="Expert SummerSky" class="rated-user user-blue">SummerSky</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Sep/28/2017 18:02">6 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-388091" href="?#comment-388091" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-388053" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="388091" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="419016" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-388091"> <div class="moveup"> <div class="ttypography"><p>Hmm, I think perhaps you mean DSU=Disjoint Set, while I usually call it Union-Find...</p><p>I solved this problem by using BFS, but I think as union-find can be used to find out the connected components, I guess that it is used there to find out all the '.' positions that can be reached from the initial position. Nevertheless, I think it is a little weird to use union-find there, since as far as I consider, union-find usually appears with a sparse graph that is described with connected edges, while it seems straightforward to use BFS in this problem...</p></div> </div> </div> <div class="reply info"> <a class="comment-388091 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-388091 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-388091"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1327" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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60D
60
D
en
D. Savior
<div class="problem-statement"><div class="header"><div class="title">D. Savior</div><div class="time-limit"><div class="property-title">time limit per test</div>4 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Misha decided to help Pasha and Akim be friends again. He had a cunning plan — to destroy all the laughy mushrooms. He knows that the laughy mushrooms can easily burst when they laugh. Mushrooms grow on the lawns. There are <span class="tex-span"><i>a</i>[<i>t</i>]</span> mushrooms on the <span class="tex-span"><i>t</i></span>-th lawn.</p><p>Misha knows that the lawns where the mushrooms grow have a unique ability. A lawn (say, <span class="tex-span"><i>i</i></span>) can transfer laugh to other lawn (say, <span class="tex-span"><i>j</i></span>) if there exists an integer (say, <span class="tex-span"><i>b</i></span>) such, that some permutation of numbers <span class="tex-span"><i>a</i>[<i>i</i>], <i>a</i>[<i>j</i>]</span> and <span class="tex-span"><i>b</i></span> is a <span class="tex-font-style-it">beautiful triple</span> (<span class="tex-span"><i>i</i> ≠ <i>j</i></span>). A beautiful triple is such three pairwise coprime numbers <span class="tex-span"><i>x</i>, <i>y</i>, <i>z</i></span>, which satisfy the following condition: <span class="tex-span"><i>x</i><sup class="upper-index">2</sup> + <i>y</i><sup class="upper-index">2</sup> = <i>z</i><sup class="upper-index">2</sup></span>.</p><p>Misha wants to know on which minimal number of lawns he should laugh for all the laughy mushrooms to burst.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains one integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">6</sup></span>) which is the number of lawns. The next line contains <span class="tex-span"><i>n</i></span> integers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> which are the number of mushrooms on the <span class="tex-span"><i>i</i></span>-lawn (<span class="tex-span">1 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">7</sup></span>). All the numbers are different.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single number — the minimal number of lawns on which Misha should laugh for all the mushrooms to burst.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>1<br/>2<br/></pre></div><div class="output"><div class="title">Output</div><pre>1<br/></pre></div><div class="input"><div class="title">Input</div><pre>2<br/>1 2<br/></pre></div><div class="output"><div class="title">Output</div><pre>2<br/></pre></div><div class="input"><div class="title">Input</div><pre>2<br/>3 5<br/></pre></div><div class="output"><div class="title">Output</div><pre>1<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="D" data-uuid="ps_677fbb976f2618aafbb0f684fda7569acd4a3282"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">D. Savior</div><div class="time-limit"><div class="property-title">time limit per test</div>4 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Misha decided to help Pasha and Akim be friends again. He had a cunning plan — to destroy all the laughy mushrooms. He knows that the laughy mushrooms can easily burst when they laugh. Mushrooms grow on the lawns. There are <span class="tex-span"><i>a</i>[<i>t</i>]</span> mushrooms on the <span class="tex-span"><i>t</i></span>-th lawn.</p><p>Misha knows that the lawns where the mushrooms grow have a unique ability. A lawn (say, <span class="tex-span"><i>i</i></span>) can transfer laugh to other lawn (say, <span class="tex-span"><i>j</i></span>) if there exists an integer (say, <span class="tex-span"><i>b</i></span>) such, that some permutation of numbers <span class="tex-span"><i>a</i>[<i>i</i>], <i>a</i>[<i>j</i>]</span> and <span class="tex-span"><i>b</i></span> is a <span class="tex-font-style-it">beautiful triple</span> (<span class="tex-span"><i>i</i> ≠ <i>j</i></span>). A beautiful triple is such three pairwise coprime numbers <span class="tex-span"><i>x</i>, <i>y</i>, <i>z</i></span>, which satisfy the following condition: <span class="tex-span"><i>x</i><sup class="upper-index">2</sup> + <i>y</i><sup class="upper-index">2</sup> = <i>z</i><sup class="upper-index">2</sup></span>.</p><p>Misha wants to know on which minimal number of lawns he should laugh for all the laughy mushrooms to burst.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains one integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">6</sup></span>) which is the number of lawns. The next line contains <span class="tex-span"><i>n</i></span> integers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> which are the number of mushrooms on the <span class="tex-span"><i>i</i></span>-lawn (<span class="tex-span">1 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">7</sup></span>). All the numbers are different.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single number — the minimal number of lawns on which Misha should laugh for all the mushrooms to burst.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>1<br />2<br /></pre></div><div class="output"><div class="title">Output</div><pre>1<br /></pre></div><div class="input"><div class="title">Input</div><pre>2<br />1 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>2<br /></pre></div><div class="input"><div class="title">Input</div><pre>2<br />3 5<br /></pre></div><div class="output"><div class="title">Output</div><pre>1<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=D]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); 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["Brute force", "Disjoint set union", "Mathematics including integration, differential equations, etc"]
["brute force", "dsu", "math", "*2500"]
https://codeforces.com/blog/entry/1317
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Mark all cells, that obviously didn't match - <span class="tex-span"><i>O</i>(<i>n</i>)</span>. In the end we go through the array and count all unmarked cells.</div><div>If 0 - we print &quot;-1&quot;, else - amount of unmarked cells.</div><div><br /></div><div><b>Problem B.</b> Solution - <span class="tex-span"><i>O</i>(<i>k</i> × <i>n</i> × <i>m</i>)</span>. </div><div>We start BFS from given point. Go from cell to all 6 directions. The answer - number of visited cells.</div><div><br /></div><div><b>Problem C</b>. Solution - <span class="tex-span"><i>O</i>(2<sup class="upper-index">7</sup> × <i>n</i><sup class="upper-index">2</sup>)</span>. </div><div>We can see, that in connected component - if we know 1 number - then we know all others in component, because in each pare we know minimal and maximal</div><div>power of each primes. Because number of different primes in one number &quot;<span class="tex-span"> &lt;  = 1000000</span>&quot; is less, than 7, we can look over all possibilities of 1 number in connected compoment - and for each number, that we get, we check, that it suits.</div><div><br /></div><div>How to check? We can notice, that if we know <span class="tex-span"><i>a</i></span>, <span class="tex-span">(<i>a</i>, <i>b</i>)</span>, <span class="tex-span">[<i>a</i>, <i>b</i>]</span>, then <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/ec0a60c5e7d57fce4b1519a30d222c3563f64d0d.png" style="max-width: 100.0%;max-height: 100.0%;" />, start DFS and check.</div><div><br /></div><div><b>Problem D.</b> Solution - <span class="tex-span"><i>O</i>(</span>max numebr<span class="tex-span">)</span>.</div><div>We can notice, that each beautiful triplet has form - <span class="tex-span">(<i>x</i><sup class="upper-index">2</sup> - <i>y</i><sup class="upper-index">2</sup>, 2<i>xy</i>, <i>x</i><sup class="upper-index">2</sup> + <i>y</i><sup class="upper-index">2</sup>)</span>. Now we can gen all such triples. For each triple, we watch - if we have more than 1 number in given set - we union them.</div><div><br /></div><div>How to gen all the triples?</div><div><br /></div><div><span class="tex-span"><i>x</i> &gt; <i>y</i></span>.</div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/49af3a586cdbbcb471801cc55ed10df7fdd2474b.png" style="max-width: 100.0%;max-height: 100.0%;" />. This means, that <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/338034360a12a7a2ca8523c67346f08047fcd975.png" style="max-width: 100.0%;max-height: 100.0%;" />.</div><div>Now for gen all this triples we an take - <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/bed025bc1334b2defa84303530e904c69f148f81.png" style="max-width: 100.0%;max-height: 100.0%;" /> и <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/3af1f7f66b4dcfc2e7a2a39e3509a177f2f614c3.png" style="max-width: 100.0%;max-height: 100.0%;" />. The number of iterations - <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/e1a0bc527cbbd27a97b9e94fc55c42c5174c46af.png" style="max-width: 100.0%;max-height: 100.0%;" />.</div><div><br /></div><div>what means - &quot;union&quot;?</div><div>We take a data structure named DSU. If two number belong to one beautiful triple - they are connected with edge, in our situation - we can union corresponding to them unions.</div><div><br /></div><div><b>Problem E</b>. Solution - <span class="tex-span"><i>O</i>(<i>n</i> + <i>log</i>(<i>xy</i>))</span>.</div><div>We can see, that after one minute the sum changes - it multiply on 3, and substract first and last elements of sequence. Because of that we can count of sum with help of power of matrix.</div><div><br /></div><div>What happens after sorting.</div><div><br /></div><div>First number stay on his place. On the last place - <span class="tex-span"><i>F</i><sub class="lower-index"><i>x</i></sub><i>a</i><sub class="lower-index"><i>n</i></sub> + <i>F</i><sub class="lower-index"><i>x</i> - 1</sub><i>a</i><sub class="lower-index"><i>n</i> - 1</sub></span>. Where <span class="tex-span"><i>n</i></span> - number of elements, ans <span class="tex-span"><i>F</i><sub class="lower-index"><i>x</i></sub></span> - <span class="tex-span"><i>x</i></span> Fibonacci number - with <span class="tex-span"><i>F</i><sub class="lower-index"> - 1</sub> = 0</span> and <span class="tex-span"><i>F</i><sub class="lower-index">0</sub> = 1</span>.</div><div><br /></div><div>This means - that we can count the last number with matrix too.</div><div><br /></div><div>After that we use the first idea.</div><div><br /></div><div>If you have questions - ask them.</div><div style="font-weight: bold;"><br /></div></div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/60" class="notice" style="text-decoration: none;">Codeforces Beta Round 56</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-3573-1317").click(function() { var that = this; 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line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/Aksenov239"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/Aksenov239"> Aksenov239 </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Feb/19/2011 23:22">13 years ago</span> </li> <li> <a href="/blog/entry/1317#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1317#comments"> 5 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1327"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (4)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="23572" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/21/2011 15:14">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-23572" href="?#comment-23572" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="23572" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-23572"> <div class="moveup"> <div class="ttypography">Hi,<br /><br />To get the sum quickly, what I did was this:<br /><br /><span>Let the array be S with elements from 1 to N. Let f(x) be the sum of all elements after k moves. <br /><br />Then f(x) = 3*f(x) - (S[1] + S[N]); f(0) = sum, where sum == summation of all elements in S.<br /><br />The solution to this recursion is sum * 3^X - (S[1] + S[N]) * (3^X - 1) / 2<br /><br />However, I have division by 2, and division with modulo seems very tricky to handle. May I know how you solve this issue?<br /><br />Thanks!<br /></span></div> </div> </div> <div class="reply info"> <a class="comment-23572 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-23572 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-23572"> <li> <div class="comment"> <table class="comment-table" commentId="24441" commentParentId="23572"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/madkite" style="position: relative;"> <img src='https://userpic.codeforces.org/7462/avatar/69de282c387fb448.jpg'/> </a> <div><a href="/profile/madkite" title="Expert madkite" class="rated-user user-blue">madkite</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/26/2011 02:12">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-24441" href="?#comment-24441" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-23572" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="24441" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="7462" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-24441"> <div class="moveup"> <div class="ttypography">I'm doing something like this: ... * (3^X - 1 + 2 * p) % (2 * p) / 2</div> </div> </div> <div class="reply info"> <a class="comment-24441 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-24441 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-24441"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="388053" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/hpkt.pkt" style="position: relative;"> <img src='https://userpic.codeforces.org/573762/avatar/822d5bb5d0cbe6cb.jpg'/> </a> <div><a href="/profile/hpkt.pkt" title="Specialist hpkt.pkt" class="rated-user user-cyan">hpkt.pkt</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Sep/28/2017 09:10">6 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-388053" href="?#comment-388053" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="388053" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="573762" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-388053"> <div class="moveup"> <div class="ttypography"><p>How can problem B be solved using DSU. I see DSU tag over there.</p></div> </div> </div> <div class="reply info"> <a class="comment-388053 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-388053 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-388053"> <li> <div class="comment"> <table class="comment-table" commentId="388091" commentParentId="388053"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/SummerSky" style="position: relative;"> <img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a> <div><a href="/profile/SummerSky" title="Expert SummerSky" class="rated-user user-blue">SummerSky</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Sep/28/2017 18:02">6 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-388091" href="?#comment-388091" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-388053" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="388091" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="419016" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-388091"> <div class="moveup"> <div class="ttypography"><p>Hmm, I think perhaps you mean DSU=Disjoint Set, while I usually call it Union-Find...</p><p>I solved this problem by using BFS, but I think as union-find can be used to find out the connected components, I guess that it is used there to find out all the '.' positions that can be reached from the initial position. Nevertheless, I think it is a little weird to use union-find there, since as far as I consider, union-find usually appears with a sparse graph that is described with connected edges, while it seems straightforward to use BFS in this problem...</p></div> </div> </div> <div class="reply info"> <a class="comment-388091 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-388091 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-388091"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1327" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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60E
60
E
en
E. Mushroom Gnomes
<div class="problem-statement"><div class="header"><div class="title">E. Mushroom Gnomes</div><div class="time-limit"><div class="property-title">time limit per test</div>3 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Once upon a time in the thicket of the mushroom forest lived mushroom gnomes. They were famous among their neighbors for their magic mushrooms. Their magic nature made it possible that between every two neighboring mushrooms every minute grew another mushroom with the weight equal to the sum of weights of two neighboring ones. </p><p>The mushroom gnomes loved it when everything was in order, that's why they always planted the mushrooms in one line in the order of their weights' increasing. Well... The gnomes planted the mushrooms and went to eat. After <span class="tex-span"><i>x</i></span> minutes they returned and saw that new mushrooms had grown up, so that the increasing order had been violated. The gnomes replanted all the mushrooms in the correct order, that is, they sorted the mushrooms in the order of the weights' increasing. And went to eat again (those gnomes were quite big eaters). What total weights modulo <span class="tex-span"><i>p</i></span> will the mushrooms have in another <span class="tex-span"><i>y</i></span> minutes?</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains four integers <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>x</i></span>, <span class="tex-span"><i>y</i></span>, <span class="tex-span"><i>p</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">6</sup>, 0 ≤ <i>x</i>, <i>y</i> ≤ 10<sup class="upper-index">18</sup>, <i>x</i> + <i>y</i> &gt; 0, 2 ≤ <i>p</i> ≤ 10<sup class="upper-index">9</sup></span>) which represent the number of mushrooms, the number of minutes after the first replanting, the number of minutes after the second replanting and the module. The next line contains <span class="tex-span"><i>n</i></span> integers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> which represent the mushrooms' weight in the non-decreasing order (<span class="tex-span">0 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">9</sup></span>).</p><p>Please, do not use <span class="tex-font-style-tt">%lld</span> specificator to read or write 64-bit integers in C++. It is preffered to use <span class="tex-font-style-tt">cin</span> (also you may use <span class="tex-font-style-tt">%I64d</span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>The answer should contain a single number which is the total weights of the mushrooms modulo <span class="tex-span"><i>p</i></span> in the end after <span class="tex-span"><i>x</i> + <i>y</i></span> minutes.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2 1 0 657276545<br/>1 2<br/></pre></div><div class="output"><div class="title">Output</div><pre>6<br/></pre></div><div class="input"><div class="title">Input</div><pre>2 1 1 888450282<br/>1 2<br/></pre></div><div class="output"><div class="title">Output</div><pre>14<br/></pre></div><div class="input"><div class="title">Input</div><pre>4 5 0 10000<br/>1 2 3 4<br/></pre></div><div class="output"><div class="title">Output</div><pre>1825<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="E" data-uuid="ps_a928bd86bfde0ee517ffe0cd739e4ba331862af2"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">E. Mushroom Gnomes</div><div class="time-limit"><div class="property-title">time limit per test</div>3 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Once upon a time in the thicket of the mushroom forest lived mushroom gnomes. They were famous among their neighbors for their magic mushrooms. Their magic nature made it possible that between every two neighboring mushrooms every minute grew another mushroom with the weight equal to the sum of weights of two neighboring ones. </p><p>The mushroom gnomes loved it when everything was in order, that's why they always planted the mushrooms in one line in the order of their weights' increasing. Well... The gnomes planted the mushrooms and went to eat. After <span class="tex-span"><i>x</i></span> minutes they returned and saw that new mushrooms had grown up, so that the increasing order had been violated. The gnomes replanted all the mushrooms in the correct order, that is, they sorted the mushrooms in the order of the weights' increasing. And went to eat again (those gnomes were quite big eaters). What total weights modulo <span class="tex-span"><i>p</i></span> will the mushrooms have in another <span class="tex-span"><i>y</i></span> minutes?</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains four integers <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>x</i></span>, <span class="tex-span"><i>y</i></span>, <span class="tex-span"><i>p</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">6</sup>, 0 ≤ <i>x</i>, <i>y</i> ≤ 10<sup class="upper-index">18</sup>, <i>x</i> + <i>y</i> &gt; 0, 2 ≤ <i>p</i> ≤ 10<sup class="upper-index">9</sup></span>) which represent the number of mushrooms, the number of minutes after the first replanting, the number of minutes after the second replanting and the module. The next line contains <span class="tex-span"><i>n</i></span> integers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> which represent the mushrooms' weight in the non-decreasing order (<span class="tex-span">0 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">9</sup></span>).</p><p>Please, do not use <span class="tex-font-style-tt">%lld</span> specificator to read or write 64-bit integers in C++. It is preffered to use <span class="tex-font-style-tt">cin</span> (also you may use <span class="tex-font-style-tt">%I64d</span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>The answer should contain a single number which is the total weights of the mushrooms modulo <span class="tex-span"><i>p</i></span> in the end after <span class="tex-span"><i>x</i> + <i>y</i></span> minutes.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2 1 0 657276545<br />1 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>6<br /></pre></div><div class="input"><div class="title">Input</div><pre>2 1 1 888450282<br />1 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>14<br /></pre></div><div class="input"><div class="title">Input</div><pre>4 5 0 10000<br />1 2 3 4<br /></pre></div><div class="output"><div class="title">Output</div><pre>1825<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=E]"); 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["Mathematics including integration, differential equations, etc", "Matrix multiplication, determinant, Cramer's rule, systems of linear equations"]
["math", "matrices", "*2600"]
https://codeforces.com/blog/entry/1317
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Mark all cells, that obviously didn't match - <span class="tex-span"><i>O</i>(<i>n</i>)</span>. In the end we go through the array and count all unmarked cells.</div><div>If 0 - we print &quot;-1&quot;, else - amount of unmarked cells.</div><div><br /></div><div><b>Problem B.</b> Solution - <span class="tex-span"><i>O</i>(<i>k</i> × <i>n</i> × <i>m</i>)</span>. </div><div>We start BFS from given point. Go from cell to all 6 directions. The answer - number of visited cells.</div><div><br /></div><div><b>Problem C</b>. Solution - <span class="tex-span"><i>O</i>(2<sup class="upper-index">7</sup> × <i>n</i><sup class="upper-index">2</sup>)</span>. </div><div>We can see, that in connected component - if we know 1 number - then we know all others in component, because in each pare we know minimal and maximal</div><div>power of each primes. Because number of different primes in one number &quot;<span class="tex-span"> &lt;  = 1000000</span>&quot; is less, than 7, we can look over all possibilities of 1 number in connected compoment - and for each number, that we get, we check, that it suits.</div><div><br /></div><div>How to check? We can notice, that if we know <span class="tex-span"><i>a</i></span>, <span class="tex-span">(<i>a</i>, <i>b</i>)</span>, <span class="tex-span">[<i>a</i>, <i>b</i>]</span>, then <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/ec0a60c5e7d57fce4b1519a30d222c3563f64d0d.png" style="max-width: 100.0%;max-height: 100.0%;" />, start DFS and check.</div><div><br /></div><div><b>Problem D.</b> Solution - <span class="tex-span"><i>O</i>(</span>max numebr<span class="tex-span">)</span>.</div><div>We can notice, that each beautiful triplet has form - <span class="tex-span">(<i>x</i><sup class="upper-index">2</sup> - <i>y</i><sup class="upper-index">2</sup>, 2<i>xy</i>, <i>x</i><sup class="upper-index">2</sup> + <i>y</i><sup class="upper-index">2</sup>)</span>. Now we can gen all such triples. For each triple, we watch - if we have more than 1 number in given set - we union them.</div><div><br /></div><div>How to gen all the triples?</div><div><br /></div><div><span class="tex-span"><i>x</i> &gt; <i>y</i></span>.</div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/49af3a586cdbbcb471801cc55ed10df7fdd2474b.png" style="max-width: 100.0%;max-height: 100.0%;" />. This means, that <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/338034360a12a7a2ca8523c67346f08047fcd975.png" style="max-width: 100.0%;max-height: 100.0%;" />.</div><div>Now for gen all this triples we an take - <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/bed025bc1334b2defa84303530e904c69f148f81.png" style="max-width: 100.0%;max-height: 100.0%;" /> и <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/3af1f7f66b4dcfc2e7a2a39e3509a177f2f614c3.png" style="max-width: 100.0%;max-height: 100.0%;" />. The number of iterations - <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/e1a0bc527cbbd27a97b9e94fc55c42c5174c46af.png" style="max-width: 100.0%;max-height: 100.0%;" />.</div><div><br /></div><div>what means - &quot;union&quot;?</div><div>We take a data structure named DSU. If two number belong to one beautiful triple - they are connected with edge, in our situation - we can union corresponding to them unions.</div><div><br /></div><div><b>Problem E</b>. Solution - <span class="tex-span"><i>O</i>(<i>n</i> + <i>log</i>(<i>xy</i>))</span>.</div><div>We can see, that after one minute the sum changes - it multiply on 3, and substract first and last elements of sequence. Because of that we can count of sum with help of power of matrix.</div><div><br /></div><div>What happens after sorting.</div><div><br /></div><div>First number stay on his place. On the last place - <span class="tex-span"><i>F</i><sub class="lower-index"><i>x</i></sub><i>a</i><sub class="lower-index"><i>n</i></sub> + <i>F</i><sub class="lower-index"><i>x</i> - 1</sub><i>a</i><sub class="lower-index"><i>n</i> - 1</sub></span>. Where <span class="tex-span"><i>n</i></span> - number of elements, ans <span class="tex-span"><i>F</i><sub class="lower-index"><i>x</i></sub></span> - <span class="tex-span"><i>x</i></span> Fibonacci number - with <span class="tex-span"><i>F</i><sub class="lower-index"> - 1</sub> = 0</span> and <span class="tex-span"><i>F</i><sub class="lower-index">0</sub> = 1</span>.</div><div><br /></div><div>This means - that we can count the last number with matrix too.</div><div><br /></div><div>After that we use the first idea.</div><div><br /></div><div>If you have questions - ask them.</div><div style="font-weight: bold;"><br /></div></div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/60" class="notice" style="text-decoration: none;">Codeforces Beta Round 56</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-3573-1317").click(function() { var that = this; 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line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/Aksenov239"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/Aksenov239"> Aksenov239 </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Feb/19/2011 23:22">13 years ago</span> </li> <li> <a href="/blog/entry/1317#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1317#comments"> 5 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1327"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (4)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="23572" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/21/2011 15:14">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-23572" href="?#comment-23572" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="23572" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-23572"> <div class="moveup"> <div class="ttypography">Hi,<br /><br />To get the sum quickly, what I did was this:<br /><br /><span>Let the array be S with elements from 1 to N. Let f(x) be the sum of all elements after k moves. <br /><br />Then f(x) = 3*f(x) - (S[1] + S[N]); f(0) = sum, where sum == summation of all elements in S.<br /><br />The solution to this recursion is sum * 3^X - (S[1] + S[N]) * (3^X - 1) / 2<br /><br />However, I have division by 2, and division with modulo seems very tricky to handle. May I know how you solve this issue?<br /><br />Thanks!<br /></span></div> </div> </div> <div class="reply info"> <a class="comment-23572 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-23572 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-23572"> <li> <div class="comment"> <table class="comment-table" commentId="24441" commentParentId="23572"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/madkite" style="position: relative;"> <img src='https://userpic.codeforces.org/7462/avatar/69de282c387fb448.jpg'/> </a> <div><a href="/profile/madkite" title="Expert madkite" class="rated-user user-blue">madkite</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/26/2011 02:12">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-24441" href="?#comment-24441" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-23572" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="24441" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="7462" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-24441"> <div class="moveup"> <div class="ttypography">I'm doing something like this: ... * (3^X - 1 + 2 * p) % (2 * p) / 2</div> </div> </div> <div class="reply info"> <a class="comment-24441 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-24441 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-24441"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="388053" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/hpkt.pkt" style="position: relative;"> <img src='https://userpic.codeforces.org/573762/avatar/822d5bb5d0cbe6cb.jpg'/> </a> <div><a href="/profile/hpkt.pkt" title="Specialist hpkt.pkt" class="rated-user user-cyan">hpkt.pkt</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Sep/28/2017 09:10">6 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-388053" href="?#comment-388053" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="388053" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="573762" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-388053"> <div class="moveup"> <div class="ttypography"><p>How can problem B be solved using DSU. I see DSU tag over there.</p></div> </div> </div> <div class="reply info"> <a class="comment-388053 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-388053 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-388053"> <li> <div class="comment"> <table class="comment-table" commentId="388091" commentParentId="388053"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/SummerSky" style="position: relative;"> <img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a> <div><a href="/profile/SummerSky" title="Expert SummerSky" class="rated-user user-blue">SummerSky</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Sep/28/2017 18:02">6 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-388091" href="?#comment-388091" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-388053" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="388091" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="419016" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-388091"> <div class="moveup"> <div class="ttypography"><p>Hmm, I think perhaps you mean DSU=Disjoint Set, while I usually call it Union-Find...</p><p>I solved this problem by using BFS, but I think as union-find can be used to find out the connected components, I guess that it is used there to find out all the '.' positions that can be reached from the initial position. Nevertheless, I think it is a little weird to use union-find there, since as far as I consider, union-find usually appears with a sparse graph that is described with connected edges, while it seems straightforward to use BFS in this problem...</p></div> </div> </div> <div class="reply info"> <a class="comment-388091 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-388091 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-388091"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1327" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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61A
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A
en
A. Ultra-Fast Mathematician
<div class="problem-statement"><div class="header"><div class="title">A. Ultra-Fast Mathematician</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Shapur was an extremely gifted student. He was great at everything including Combinatorics, Algebra, Number Theory, Geometry, Calculus, etc. He was not only smart but extraordinarily fast! He could manage to sum <span class="tex-span">10<sup class="upper-index">18</sup></span> numbers in a single second.</p><p>One day in 230 AD Shapur was trying to find out if any one can possibly do calculations faster than him. As a result he made a very great contest and asked every one to come and take part.</p><p>In his contest he gave the contestants many different pairs of numbers. Each number is made from digits <span class="tex-span">0</span> or <span class="tex-span">1</span>. The contestants should write a new number corresponding to the given pair of numbers. The rule is simple: The <span class="tex-span"><i>i</i></span>-th digit of the answer is <span class="tex-span">1</span> if and only if the <span class="tex-span"><i>i</i></span>-th digit of the two given numbers differ. In the other case the <span class="tex-span"><i>i</i></span>-th digit of the answer is <span class="tex-span">0</span>.</p><p>Shapur made many numbers and first tried his own speed. He saw that he can perform these operations on numbers of length <span class="tex-span">∞</span> (length of a number is number of digits in it) in a glance! He always gives correct answers so he expects the contestants to give correct answers, too. He is a good fellow so he won't give anyone very big numbers and he always gives one person numbers of same length.</p><p>Now you are going to take part in Shapur's contest. See if you are faster and more accurate.</p></div><div class="input-specification"><div class="section-title">Input</div><p>There are two lines in each input. Each of them contains a single number. It is guaranteed that the numbers are made from <span class="tex-span">0</span> and <span class="tex-span">1</span> only and that their length is same. The numbers may start with <span class="tex-span">0</span>. The length of each number doesn't exceed 100.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Write one line — the corresponding answer. Do not omit the leading <span class="tex-span">0</span>s.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>1010100<br/>0100101<br/></pre></div><div class="output"><div class="title">Output</div><pre>1110001<br/></pre></div><div class="input"><div class="title">Input</div><pre>000<br/>111<br/></pre></div><div class="output"><div class="title">Output</div><pre>111<br/></pre></div><div class="input"><div class="title">Input</div><pre>1110<br/>1010<br/></pre></div><div class="output"><div class="title">Output</div><pre>0100<br/></pre></div><div class="input"><div class="title">Input</div><pre>01110<br/>01100<br/></pre></div><div class="output"><div class="title">Output</div><pre>00010<br/></pre></div></div></div></div>
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} </style> <div class="roundbox sidebox sidebar-menu borderTopRound " style=""> <div class="caption titled">&rarr; Contest materials <div class="top-links"> </div> </div> <ul> <li> <span> <a href="/blog/entry/1338" title="Codeforces Beta round #57 (Div 2)" target="_blank">Announcement <span class="resource-locale">(oth)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="224" resourceName="Codeforces Beta round #57 (Div 2)" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1347" title="Round 57-E" target="_blank">Round 57-E <span class="resource-locale">(en)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="229" resourceName="Round 57-E" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1343" title="Round 57-B" target="_blank">Round 57-B <span class="resource-locale">(en)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="226" resourceName="Round 57-B" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1346" title="Round 57-D" target="_blank">Round 57-D <span class="resource-locale">(en)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="228" resourceName="Round 57-D" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1345" title="Round 57-C" target="_blank">Round 57-C <span class="resource-locale">(en)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="227" resourceName="Round 57-C" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1342" title="Round 57-A" target="_blank">Round 57-A <span class="resource-locale">(en)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="225" resourceName="Round 57-A" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> </ul> </div></div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li class="current selectedLava"><a href="/contest/61">Problems</a></li> <li><a href="/contest/61/submit">Submit Code</a></li> <li><a href="/contest/61/my">My Submissions</a></li> <li><a href="/contest/61/status">Status</a></li> <li><a href="/contest/61/hacks">Hacks</a></li> <li><a href="/contest/61/room/1">Room</a></li> <li><a href="/contest/61/standings">Standings</a></li> <li><a href="/contest/61/customtest">Custom Invocation</a></li> </ul> </div> <style> #facebox .content:has(.diff-popup) { width: 90vw; max-width: 120rem !important; } .testCaseMarker { position: absolute; font-weight: bold; font-size: 1rem; } .diff-popup { width: 90vw; max-width: 120rem !important; display: none; overflow: auto; } .input-output-copier { font-size: 1.2rem; float: right; color: #888 !important; cursor: pointer; border: 1px solid rgb(185, 185, 185); padding: 3px; margin: 1px; line-height: 1.1rem; text-transform: none; } .input-output-copier:hover { background-color: #def; } .test-explanation textarea { width: 100%; height: 1.5em; } .pending-submission-message { color: darkorange !important; } </style> <script> const OPENING_SPACE = String.fromCharCode(1001); const CLOSING_SPACE = String.fromCharCode(1002); const nodeToText = function (node, pre) { let result = []; if (node.tagName === "SCRIPT" || node.tagName === "math" || (node.classList && node.classList.contains("input-output-copier"))) return []; if (node.tagName === "NOBR") { result.push(OPENING_SPACE); } if (node.nodeType === Node.TEXT_NODE) { let s = node.textContent; 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="A" data-uuid="ps_e184103cf6edcb4bc3f958b761f574384c74dd40"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">A. Ultra-Fast Mathematician</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Shapur was an extremely gifted student. He was great at everything including Combinatorics, Algebra, Number Theory, Geometry, Calculus, etc. He was not only smart but extraordinarily fast! He could manage to sum <span class="tex-span">10<sup class="upper-index">18</sup></span> numbers in a single second.</p><p>One day in 230 AD Shapur was trying to find out if any one can possibly do calculations faster than him. As a result he made a very great contest and asked every one to come and take part.</p><p>In his contest he gave the contestants many different pairs of numbers. Each number is made from digits <span class="tex-span">0</span> or <span class="tex-span">1</span>. The contestants should write a new number corresponding to the given pair of numbers. The rule is simple: The <span class="tex-span"><i>i</i></span>-th digit of the answer is <span class="tex-span">1</span> if and only if the <span class="tex-span"><i>i</i></span>-th digit of the two given numbers differ. In the other case the <span class="tex-span"><i>i</i></span>-th digit of the answer is <span class="tex-span">0</span>.</p><p>Shapur made many numbers and first tried his own speed. He saw that he can perform these operations on numbers of length <span class="tex-span">∞</span> (length of a number is number of digits in it) in a glance! He always gives correct answers so he expects the contestants to give correct answers, too. He is a good fellow so he won't give anyone very big numbers and he always gives one person numbers of same length.</p><p>Now you are going to take part in Shapur's contest. See if you are faster and more accurate.</p></div><div class="input-specification"><div class="section-title">Input</div><p>There are two lines in each input. Each of them contains a single number. It is guaranteed that the numbers are made from <span class="tex-span">0</span> and <span class="tex-span">1</span> only and that their length is same. The numbers may start with <span class="tex-span">0</span>. The length of each number doesn't exceed 100.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Write one line — the corresponding answer. Do not omit the leading <span class="tex-span">0</span>s.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>1010100<br />0100101<br /></pre></div><div class="output"><div class="title">Output</div><pre>1110001<br /></pre></div><div class="input"><div class="title">Input</div><pre>000<br />111<br /></pre></div><div class="output"><div class="title">Output</div><pre>111<br /></pre></div><div class="input"><div class="title">Input</div><pre>1110<br />1010<br /></pre></div><div class="output"><div class="title">Output</div><pre>0100<br /></pre></div><div class="input"><div class="title">Input</div><pre>01110<br />01100<br /></pre></div><div class="output"><div class="title">Output</div><pre>00010<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=A]"); let uuid = $problem.attr("data-uuid"); 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["Implementation problems, programming technics, simulation"]
["implementation", "*800"]
61B
61
B
en
B. Hard Work
<div class="problem-statement"><div class="header"><div class="title">B. Hard Work</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>After the contest in comparing numbers, Shapur's teacher found out that he is a real genius and that no one could possibly do the calculations faster than him even using a super computer!</p><p>Some days before the contest, the teacher took a very simple-looking exam and all his <span class="tex-span"><i>n</i></span> students took part in the exam. The teacher gave them <span class="tex-span">3</span> strings and asked them to <span class="tex-font-style-underline">concatenate</span> them. Concatenating strings means to put them in some arbitrary order one after the other. For example from concatenating <span class="tex-font-style-tt">Alireza</span> and <span class="tex-font-style-tt">Amir</span> we can get to <span class="tex-font-style-tt">AlirezaAmir</span> or <span class="tex-font-style-tt">AmirAlireza</span> depending on the order of concatenation.</p><p>Unfortunately enough, the teacher forgot to ask students to concatenate their strings in a pre-defined order so each student did it the way he/she liked.</p><p>Now the teacher knows that Shapur is such a fast-calculating genius boy and asks him to correct the students' papers.</p><p>Shapur is not good at doing such a time-taking task. He rather likes to finish up with it as soon as possible and take his time to solve 3-SAT in polynomial time. Moreover, the teacher has given some advice that Shapur has to follow. Here's what the teacher said: </p><ul> <li> As I expect you know, the strings I gave to my students (including you) contained only lowercase and uppercase Persian Mikhi-Script letters. These letters are too much like Latin letters, so to make your task much harder I converted all the initial strings and all of the students' answers to Latin. </li><li> As latin alphabet has much less characters than Mikhi-Script, I added three odd-looking characters to the answers, these include "<span class="tex-font-style-tt">-</span>", "<span class="tex-font-style-tt">;</span>" and "<span class="tex-font-style-tt">_</span>". These characters are my own invention of course! And I call them <span class="tex-font-style-underline">Signs</span>. </li><li> The length of all initial strings was less than or equal to <span class="tex-span">100</span> and the lengths of my students' answers are less than or equal to <span class="tex-span">600</span> </li><li> My son, not all students are genius as you are. It is quite possible that they make minor mistakes changing case of some characters. For example they may write <span class="tex-font-style-tt">ALiReZaAmIR</span> instead of <span class="tex-font-style-tt">AlirezaAmir</span>. Don't be picky and ignore these mistakes. </li><li> Those signs which I previously talked to you about are not important. You can ignore them, since many students are in the mood for adding extra signs or forgetting about a sign. So something like <span class="tex-font-style-tt">Iran;;--</span> is the same as <span class="tex-font-style-tt">--;IRAN</span> </li><li> You should indicate for any of my students if his answer was right or wrong. Do this by writing "<span class="tex-font-style-tt">WA</span>" for Wrong answer or "<span class="tex-font-style-tt">ACC</span>" for a correct answer. </li><li> I should remind you that none of the strings (initial strings or answers) are empty. </li><li> Finally, do these as soon as possible. You have less than <span class="tex-span">2</span> hours to complete this. </li></ul> </div><div class="input-specification"><div class="section-title">Input</div><p>The first three lines contain a string each. These are the initial strings. They consists only of lowercase and uppercase Latin letters and signs ("<span class="tex-font-style-tt">-</span>", "<span class="tex-font-style-tt">;</span>" and "<span class="tex-font-style-tt">_</span>"). All the initial strings have length from 1 to 100, inclusively.</p><p>In the fourth line there is a single integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">0 ≤ <i>n</i> ≤ 1000</span>), the number of students.</p><p>Next <span class="tex-span"><i>n</i></span> lines contain a student's answer each. It is guaranteed that the answer meets what the teacher said. Each answer iconsists only of lowercase and uppercase Latin letters and signs ("<span class="tex-font-style-tt">-</span>", "<span class="tex-font-style-tt">;</span>" and "<span class="tex-font-style-tt">_</span>"). Length is from 1 to 600, inclusively.</p></div><div class="output-specification"><div class="section-title">Output</div><p>For each student write in a different line. Print "<span class="tex-font-style-tt">WA</span>" if his answer is wrong or "<span class="tex-font-style-tt">ACC</span>" if his answer is OK.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>Iran_<br/>Persian;<br/>W_o;n;d;e;r;f;u;l;<br/>7<br/>WonderfulPersianIran<br/>wonderful_PersIAN_IRAN;;_<br/>WONDERFUL___IRAN__PERSIAN__;;<br/>Ira__Persiann__Wonderful<br/>Wonder;;fulPersian___;I;r;a;n;<br/>__________IranPersianWonderful__________<br/>PersianIran_is_Wonderful<br/></pre></div><div class="output"><div class="title">Output</div><pre>ACC<br/>ACC<br/>ACC<br/>WA<br/>ACC<br/>ACC<br/>WA<br/></pre></div><div class="input"><div class="title">Input</div><pre>Shapur;;<br/>is___<br/>a_genius<br/>3<br/>Shapur__a_is___geniUs<br/>is___shapur___a__Genius;<br/>Shapur;;is;;a;;geni;;us;;<br/></pre></div><div class="output"><div class="title">Output</div><pre>WA<br/>ACC<br/>ACC<br/></pre></div></div></div></div>
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} </style> <div class="roundbox sidebox sidebar-menu borderTopRound " style=""> <div class="caption titled">&rarr; Contest materials <div class="top-links"> </div> </div> <ul> <li> <span> <a href="/blog/entry/1338" title="Codeforces Beta round #57 (Div 2)" target="_blank">Announcement <span class="resource-locale">(oth)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="224" resourceName="Codeforces Beta round #57 (Div 2)" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1347" title="Round 57-E" target="_blank">Round 57-E <span class="resource-locale">(en)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="229" resourceName="Round 57-E" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1343" title="Round 57-B" target="_blank">Round 57-B <span class="resource-locale">(en)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="226" resourceName="Round 57-B" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1346" title="Round 57-D" target="_blank">Round 57-D <span class="resource-locale">(en)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="228" resourceName="Round 57-D" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1345" title="Round 57-C" target="_blank">Round 57-C <span class="resource-locale">(en)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="227" resourceName="Round 57-C" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1342" title="Round 57-A" target="_blank">Round 57-A <span class="resource-locale">(en)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="225" resourceName="Round 57-A" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> </ul> </div></div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li class="current selectedLava"><a href="/contest/61">Problems</a></li> <li><a href="/contest/61/submit">Submit Code</a></li> <li><a href="/contest/61/my">My Submissions</a></li> <li><a href="/contest/61/status">Status</a></li> <li><a href="/contest/61/hacks">Hacks</a></li> <li><a href="/contest/61/room/1">Room</a></li> <li><a href="/contest/61/standings">Standings</a></li> <li><a href="/contest/61/customtest">Custom Invocation</a></li> </ul> </div> <style> #facebox .content:has(.diff-popup) { width: 90vw; 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="B" data-uuid="ps_88d3ad6e8ecadd8aca954a25621ed67ad22beefa"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">B. Hard Work</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>After the contest in comparing numbers, Shapur's teacher found out that he is a real genius and that no one could possibly do the calculations faster than him even using a super computer!</p><p>Some days before the contest, the teacher took a very simple-looking exam and all his <span class="tex-span"><i>n</i></span> students took part in the exam. The teacher gave them <span class="tex-span">3</span> strings and asked them to <span class="tex-font-style-underline">concatenate</span> them. Concatenating strings means to put them in some arbitrary order one after the other. For example from concatenating <span class="tex-font-style-tt">Alireza</span> and <span class="tex-font-style-tt">Amir</span> we can get to <span class="tex-font-style-tt">AlirezaAmir</span> or <span class="tex-font-style-tt">AmirAlireza</span> depending on the order of concatenation.</p><p>Unfortunately enough, the teacher forgot to ask students to concatenate their strings in a pre-defined order so each student did it the way he/she liked.</p><p>Now the teacher knows that Shapur is such a fast-calculating genius boy and asks him to correct the students' papers.</p><p>Shapur is not good at doing such a time-taking task. He rather likes to finish up with it as soon as possible and take his time to solve 3-SAT in polynomial time. Moreover, the teacher has given some advice that Shapur has to follow. Here's what the teacher said: </p><ul> <li> As I expect you know, the strings I gave to my students (including you) contained only lowercase and uppercase Persian Mikhi-Script letters. These letters are too much like Latin letters, so to make your task much harder I converted all the initial strings and all of the students' answers to Latin. </li><li> As latin alphabet has much less characters than Mikhi-Script, I added three odd-looking characters to the answers, these include &quot;<span class="tex-font-style-tt">-</span>&quot;, &quot;<span class="tex-font-style-tt">;</span>&quot; and &quot;<span class="tex-font-style-tt">_</span>&quot;. These characters are my own invention of course! And I call them <span class="tex-font-style-underline">Signs</span>. </li><li> The length of all initial strings was less than or equal to <span class="tex-span">100</span> and the lengths of my students' answers are less than or equal to <span class="tex-span">600</span> </li><li> My son, not all students are genius as you are. It is quite possible that they make minor mistakes changing case of some characters. For example they may write <span class="tex-font-style-tt">ALiReZaAmIR</span> instead of <span class="tex-font-style-tt">AlirezaAmir</span>. Don't be picky and ignore these mistakes. </li><li> Those signs which I previously talked to you about are not important. You can ignore them, since many students are in the mood for adding extra signs or forgetting about a sign. So something like <span class="tex-font-style-tt">Iran;;--</span> is the same as <span class="tex-font-style-tt">--;IRAN</span> </li><li> You should indicate for any of my students if his answer was right or wrong. Do this by writing &quot;<span class="tex-font-style-tt">WA</span>&quot; for Wrong answer or &quot;<span class="tex-font-style-tt">ACC</span>&quot; for a correct answer. </li><li> I should remind you that none of the strings (initial strings or answers) are empty. </li><li> Finally, do these as soon as possible. You have less than <span class="tex-span">2</span> hours to complete this. </li></ul> </div><div class="input-specification"><div class="section-title">Input</div><p>The first three lines contain a string each. These are the initial strings. They consists only of lowercase and uppercase Latin letters and signs (&quot;<span class="tex-font-style-tt">-</span>&quot;, &quot;<span class="tex-font-style-tt">;</span>&quot; and &quot;<span class="tex-font-style-tt">_</span>&quot;). All the initial strings have length from 1 to 100, inclusively.</p><p>In the fourth line there is a single integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">0 ≤ <i>n</i> ≤ 1000</span>), the number of students.</p><p>Next <span class="tex-span"><i>n</i></span> lines contain a student's answer each. It is guaranteed that the answer meets what the teacher said. Each answer iconsists only of lowercase and uppercase Latin letters and signs (&quot;<span class="tex-font-style-tt">-</span>&quot;, &quot;<span class="tex-font-style-tt">;</span>&quot; and &quot;<span class="tex-font-style-tt">_</span>&quot;). Length is from 1 to 600, inclusively.</p></div><div class="output-specification"><div class="section-title">Output</div><p>For each student write in a different line. Print &quot;<span class="tex-font-style-tt">WA</span>&quot; if his answer is wrong or &quot;<span class="tex-font-style-tt">ACC</span>&quot; if his answer is OK.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>Iran_<br />Persian;<br />W_o;n;d;e;r;f;u;l;<br />7<br />WonderfulPersianIran<br />wonderful_PersIAN_IRAN;;_<br />WONDERFUL___IRAN__PERSIAN__;;<br />Ira__Persiann__Wonderful<br />Wonder;;fulPersian___;I;r;a;n;<br />__________IranPersianWonderful__________<br />PersianIran_is_Wonderful<br /></pre></div><div class="output"><div class="title">Output</div><pre>ACC<br />ACC<br />ACC<br />WA<br />ACC<br />ACC<br />WA<br /></pre></div><div class="input"><div class="title">Input</div><pre>Shapur;;<br />is___<br />a_genius<br />3<br />Shapur__a_is___geniUs<br />is___shapur___a__Genius;<br />Shapur;;is;;a;;geni;;us;;<br /></pre></div><div class="output"><div class="title">Output</div><pre>WA<br />ACC<br />ACC<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=B]"); 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["Prefix- and Z-functions, suffix structures, Knuth\u2013Morris\u2013Pratt algorithm, etc"]
["strings", "*1300"]
61C
61
C
en
C. Capture Valerian
<div class="problem-statement"><div class="header"><div class="title">C. Capture Valerian</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>It's now <span class="tex-span">260</span> AD. Shapur, being extremely smart, became the King of Persia. He is now called Shapur, His majesty King of kings of Iran and Aniran.</p><p>Recently the Romans declared war on Persia. They dreamed to occupy Armenia. In the recent war, the Romans were badly defeated. Now their senior army general, Philip is captured by Shapur and Shapur is now going to capture Valerian, the Roman emperor.</p><p>Being defeated, the cowardly Valerian hid in a room at the top of one of his castles. To capture him, Shapur has to open many doors. Fortunately Valerian was too scared to make impenetrable locks for the doors.</p><p>Each door has <span class="tex-span">4</span> parts. The first part is an integer number <span class="tex-span"><i>a</i></span>. The second part is either an integer number <span class="tex-span"><i>b</i></span> or some really odd sign which looks like <span class="tex-font-style-tt">R</span>. The third one is an integer <span class="tex-span"><i>c</i></span> and the fourth part is empty! As if it was laid for writing something. Being extremely gifted, after opening the first few doors, Shapur found out the secret behind the locks.</p><p><span class="tex-span"><i>c</i></span> is an integer written in base <span class="tex-span"><i>a</i></span>, to open the door we should write it in base <span class="tex-span"><i>b</i></span>. The only bad news is that this <span class="tex-font-style-tt">R</span> is some sort of special numbering system that is used only in Roman empire, so opening the doors is not just a piece of cake!</p><p>Here's an explanation of this really weird number system that even doesn't have zero:</p><p>Roman numerals are based on seven symbols: a stroke (identified with the letter <span class="tex-font-style-tt">I</span>) for a unit, a chevron (identified with the letter <span class="tex-font-style-tt">V</span>) for a five, a cross-stroke (identified with the letter <span class="tex-font-style-tt">X</span>) for a ten, a <span class="tex-font-style-tt">C</span> (identified as an abbreviation of Centum) for a hundred, etc.:</p><ul><li> <span class="tex-font-style-tt">I</span>=<span class="tex-span">1</span></li><li> <span class="tex-font-style-tt">V</span>=<span class="tex-span">5</span></li><li> <span class="tex-font-style-tt">X</span>=<span class="tex-span">10</span></li><li> <span class="tex-font-style-tt">L</span>=<span class="tex-span">50</span></li><li> <span class="tex-font-style-tt">C</span>=<span class="tex-span">100</span></li><li> <span class="tex-font-style-tt">D</span>=<span class="tex-span">500</span></li><li> <span class="tex-font-style-tt">M</span>=<span class="tex-span">1000</span></li></ul><p>Symbols are iterated to produce multiples of the decimal (<span class="tex-span">1</span>, <span class="tex-span">10</span>, <span class="tex-span">100</span>, <span class="tex-span">1, 000</span>) values, with <span class="tex-font-style-tt">V</span>, <span class="tex-font-style-tt">L</span>, <span class="tex-font-style-tt">D</span> substituted for a multiple of five, and the iteration continuing: <span class="tex-font-style-tt">I</span> <span class="tex-span">1</span>, <span class="tex-font-style-tt">II</span> <span class="tex-span">2</span>, <span class="tex-font-style-tt">III</span> <span class="tex-span">3</span>, <span class="tex-font-style-tt">V</span> <span class="tex-span">5</span>, <span class="tex-font-style-tt">VI</span> <span class="tex-span">6</span>, <span class="tex-font-style-tt">VII</span> <span class="tex-span">7</span>, etc., and the same for other bases: <span class="tex-font-style-tt">X</span> <span class="tex-span">10</span>, <span class="tex-font-style-tt">XX</span> <span class="tex-span">20</span>, <span class="tex-font-style-tt">XXX</span> <span class="tex-span">30</span>, <span class="tex-font-style-tt">L</span> <span class="tex-span">50</span>, <span class="tex-font-style-tt">LXXX</span> <span class="tex-span">80</span>; <span class="tex-font-style-tt">CC</span> <span class="tex-span">200</span>, <span class="tex-font-style-tt">DCC</span> <span class="tex-span">700</span>, etc. At the fourth and ninth iteration, a subtractive principle must be employed, with the base placed before the higher base: <span class="tex-font-style-tt">IV</span> <span class="tex-span">4</span>, <span class="tex-font-style-tt">IX</span> <span class="tex-span">9</span>, <span class="tex-font-style-tt">XL</span> <span class="tex-span">40</span>, <span class="tex-font-style-tt">XC</span> <span class="tex-span">90</span>, <span class="tex-font-style-tt">CD</span> <span class="tex-span">400</span>, <span class="tex-font-style-tt">CM</span> <span class="tex-span">900</span>.</p><p>Also in bases greater than <span class="tex-span">10</span> we use <span class="tex-font-style-tt">A</span> for <span class="tex-span">10</span>, <span class="tex-font-style-tt">B</span> for <span class="tex-span">11</span>, etc.</p><p>Help Shapur capture Valerian and bring peace back to Persia, especially Armenia.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>a</i></span> and <span class="tex-span"><i>b</i></span> (<span class="tex-span">2 ≤ <i>a</i>, <i>b</i> ≤ 25</span>). Only <span class="tex-span"><i>b</i></span> may be replaced by an <span class="tex-font-style-tt">R</span> which indicates Roman numbering system.</p><p>The next line contains a single non-negative integer <span class="tex-span"><i>c</i></span> in base <span class="tex-span"><i>a</i></span> which may contain leading zeros but its length doesn't exceed <span class="tex-span">10<sup class="upper-index">3</sup></span>. </p><p>It is guaranteed that if we have Roman numerals included the number would be less than or equal to <span class="tex-span">3000<sub class="lower-index">10</sub></span> and it won't be <span class="tex-span">0</span>. In any other case the number won't be greater than <span class="tex-span">10<sup class="upper-index">15</sup><sub class="lower-index">10</sub></span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Write a single line that contains integer <span class="tex-span"><i>c</i></span> in base <span class="tex-span"><i>b</i></span>. You must omit leading zeros.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>10 2<br/>1<br/></pre></div><div class="output"><div class="title">Output</div><pre>1<br/></pre></div><div class="input"><div class="title">Input</div><pre>16 R<br/>5<br/></pre></div><div class="output"><div class="title">Output</div><pre>V<br/></pre></div><div class="input"><div class="title">Input</div><pre>5 R<br/>4<br/></pre></div><div class="output"><div class="title">Output</div><pre>IV<br/></pre></div><div class="input"><div class="title">Input</div><pre>2 2<br/>1111001<br/></pre></div><div class="output"><div class="title">Output</div><pre>1111001<br/></pre></div><div class="input"><div class="title">Input</div><pre>12 13<br/>A<br/></pre></div><div class="output"><div class="title">Output</div><pre>A<br/></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>You can find more information about roman numerals here: http://en.wikipedia.org/wiki/Roman_numerals</p></div></div>
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Just register for practice and you will be able to submit solutions. </div> <div style="text-align:center;margin:1em;"> <form action="" method="post"><input type='hidden' name='csrf_token' value='d821ddd2f647fdbefc7ecacf28701dd3'/> <input type="hidden" name="action" value="registerForPractice"/> <input type="submit" name="submit" value="Register for practice" style="padding:0 0.5em;"> </form> </div> </div> </div> <div class="roundbox sidebox ContestVirtualFrame borderTopRound " style=""> <div class="caption titled">&rarr; Virtual participation <i class="sidebar-caption-icon las la-angle-down"></i> <div class="top-links"> </div> </div> <div style=" " data-page-url="/data/sidebarFrames" > <div style="margin:1em;font-size:0.8em;"> Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests. If you've seen these problems, a virtual contest is not for you - solve these problems in the archive. If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="C" data-uuid="ps_a8ab1a92180a05418518698782eb658eec0065ad"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. Capture Valerian</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>It's now <span class="tex-span">260</span> AD. Shapur, being extremely smart, became the King of Persia. He is now called Shapur, His majesty King of kings of Iran and Aniran.</p><p>Recently the Romans declared war on Persia. They dreamed to occupy Armenia. In the recent war, the Romans were badly defeated. Now their senior army general, Philip is captured by Shapur and Shapur is now going to capture Valerian, the Roman emperor.</p><p>Being defeated, the cowardly Valerian hid in a room at the top of one of his castles. To capture him, Shapur has to open many doors. Fortunately Valerian was too scared to make impenetrable locks for the doors.</p><p>Each door has <span class="tex-span">4</span> parts. The first part is an integer number <span class="tex-span"><i>a</i></span>. The second part is either an integer number <span class="tex-span"><i>b</i></span> or some really odd sign which looks like <span class="tex-font-style-tt">R</span>. The third one is an integer <span class="tex-span"><i>c</i></span> and the fourth part is empty! As if it was laid for writing something. Being extremely gifted, after opening the first few doors, Shapur found out the secret behind the locks.</p><p><span class="tex-span"><i>c</i></span> is an integer written in base <span class="tex-span"><i>a</i></span>, to open the door we should write it in base <span class="tex-span"><i>b</i></span>. The only bad news is that this <span class="tex-font-style-tt">R</span> is some sort of special numbering system that is used only in Roman empire, so opening the doors is not just a piece of cake!</p><p>Here's an explanation of this really weird number system that even doesn't have zero:</p><p>Roman numerals are based on seven symbols: a stroke (identified with the letter <span class="tex-font-style-tt">I</span>) for a unit, a chevron (identified with the letter <span class="tex-font-style-tt">V</span>) for a five, a cross-stroke (identified with the letter <span class="tex-font-style-tt">X</span>) for a ten, a <span class="tex-font-style-tt">C</span> (identified as an abbreviation of Centum) for a hundred, etc.:</p><ul><li> <span class="tex-font-style-tt">I</span>=<span class="tex-span">1</span></li><li> <span class="tex-font-style-tt">V</span>=<span class="tex-span">5</span></li><li> <span class="tex-font-style-tt">X</span>=<span class="tex-span">10</span></li><li> <span class="tex-font-style-tt">L</span>=<span class="tex-span">50</span></li><li> <span class="tex-font-style-tt">C</span>=<span class="tex-span">100</span></li><li> <span class="tex-font-style-tt">D</span>=<span class="tex-span">500</span></li><li> <span class="tex-font-style-tt">M</span>=<span class="tex-span">1000</span></li></ul><p>Symbols are iterated to produce multiples of the decimal (<span class="tex-span">1</span>, <span class="tex-span">10</span>, <span class="tex-span">100</span>, <span class="tex-span">1, 000</span>) values, with <span class="tex-font-style-tt">V</span>, <span class="tex-font-style-tt">L</span>, <span class="tex-font-style-tt">D</span> substituted for a multiple of five, and the iteration continuing: <span class="tex-font-style-tt">I</span> <span class="tex-span">1</span>, <span class="tex-font-style-tt">II</span> <span class="tex-span">2</span>, <span class="tex-font-style-tt">III</span> <span class="tex-span">3</span>, <span class="tex-font-style-tt">V</span> <span class="tex-span">5</span>, <span class="tex-font-style-tt">VI</span> <span class="tex-span">6</span>, <span class="tex-font-style-tt">VII</span> <span class="tex-span">7</span>, etc., and the same for other bases: <span class="tex-font-style-tt">X</span> <span class="tex-span">10</span>, <span class="tex-font-style-tt">XX</span> <span class="tex-span">20</span>, <span class="tex-font-style-tt">XXX</span> <span class="tex-span">30</span>, <span class="tex-font-style-tt">L</span> <span class="tex-span">50</span>, <span class="tex-font-style-tt">LXXX</span> <span class="tex-span">80</span>; <span class="tex-font-style-tt">CC</span> <span class="tex-span">200</span>, <span class="tex-font-style-tt">DCC</span> <span class="tex-span">700</span>, etc. At the fourth and ninth iteration, a subtractive principle must be employed, with the base placed before the higher base: <span class="tex-font-style-tt">IV</span> <span class="tex-span">4</span>, <span class="tex-font-style-tt">IX</span> <span class="tex-span">9</span>, <span class="tex-font-style-tt">XL</span> <span class="tex-span">40</span>, <span class="tex-font-style-tt">XC</span> <span class="tex-span">90</span>, <span class="tex-font-style-tt">CD</span> <span class="tex-span">400</span>, <span class="tex-font-style-tt">CM</span> <span class="tex-span">900</span>.</p><p>Also in bases greater than <span class="tex-span">10</span> we use <span class="tex-font-style-tt">A</span> for <span class="tex-span">10</span>, <span class="tex-font-style-tt">B</span> for <span class="tex-span">11</span>, etc.</p><p>Help Shapur capture Valerian and bring peace back to Persia, especially Armenia.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>a</i></span> and <span class="tex-span"><i>b</i></span> (<span class="tex-span">2 ≤ <i>a</i>, <i>b</i> ≤ 25</span>). Only <span class="tex-span"><i>b</i></span> may be replaced by an <span class="tex-font-style-tt">R</span> which indicates Roman numbering system.</p><p>The next line contains a single non-negative integer <span class="tex-span"><i>c</i></span> in base <span class="tex-span"><i>a</i></span> which may contain leading zeros but its length doesn't exceed <span class="tex-span">10<sup class="upper-index">3</sup></span>. </p><p>It is guaranteed that if we have Roman numerals included the number would be less than or equal to <span class="tex-span">3000<sub class="lower-index">10</sub></span> and it won't be <span class="tex-span">0</span>. In any other case the number won't be greater than <span class="tex-span">10<sup class="upper-index">15</sup><sub class="lower-index">10</sub></span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Write a single line that contains integer <span class="tex-span"><i>c</i></span> in base <span class="tex-span"><i>b</i></span>. You must omit leading zeros.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>10 2<br />1<br /></pre></div><div class="output"><div class="title">Output</div><pre>1<br /></pre></div><div class="input"><div class="title">Input</div><pre>16 R<br />5<br /></pre></div><div class="output"><div class="title">Output</div><pre>V<br /></pre></div><div class="input"><div class="title">Input</div><pre>5 R<br />4<br /></pre></div><div class="output"><div class="title">Output</div><pre>IV<br /></pre></div><div class="input"><div class="title">Input</div><pre>2 2<br />1111001<br /></pre></div><div class="output"><div class="title">Output</div><pre>1111001<br /></pre></div><div class="input"><div class="title">Input</div><pre>12 13<br />A<br /></pre></div><div class="output"><div class="title">Output</div><pre>A<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>You can find more information about roman numerals here: http://en.wikipedia.org/wiki/Roman_numerals</p></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=C]"); 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["Mathematics including integration, differential equations, etc"]
["math", "*2000"]
61D
61
D
en
D. Eternal Victory
<div class="problem-statement"><div class="header"><div class="title">D. Eternal Victory</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Valerian was captured by Shapur. The victory was such a great one that Shapur decided to carve a scene of Valerian's defeat on a mountain. So he had to find the best place to make his victory eternal!</p><p>He decided to visit all <span class="tex-span"><i>n</i></span> cities of Persia to find the best available mountain, but after the recent war he was too tired and didn't want to traverse a lot. So he wanted to visit each of these <span class="tex-span"><i>n</i></span> cities at least once with smallest possible traverse. Persian cities are connected with bidirectional roads. You can go from any city to any other one using these roads and there is a unique path between each two cities.</p><p>All cities are numbered <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span>. Shapur is currently in the city <span class="tex-span">1</span> and he wants to visit all other cities with minimum possible traverse. He can finish his travels in any city.</p><p>Help Shapur find how much He should travel.</p></div><div class="input-specification"><div class="section-title">Input</div><p>First line contains a single natural number <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup></span>) — the amount of cities.</p><p>Next <span class="tex-span"><i>n</i> - 1</span> lines contain <span class="tex-span">3</span> integer numbers each <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>w</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>x</i><sub class="lower-index"><i>i</i></sub>, <i>y</i><sub class="lower-index"><i>i</i></sub> ≤ <i>n</i>, 0 ≤ <i>w</i><sub class="lower-index"><i>i</i></sub> ≤ 2 × 10<sup class="upper-index">4</sup></span>). <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span> are two ends of a road and <span class="tex-span"><i>w</i><sub class="lower-index"><i>i</i></sub></span> is the length of that road.</p></div><div class="output-specification"><div class="section-title">Output</div><p>A single integer number, the minimal length of Shapur's travel.</p><p>Please, do not use <span class="tex-font-style-tt">%lld</span> specificator to read or write 64-bit integers in C++. It is preffered to use <span class="tex-font-style-tt">cout</span> (also you may use <span class="tex-font-style-tt">%I64d</span>).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br/>1 2 3<br/>2 3 4<br/></pre></div><div class="output"><div class="title">Output</div><pre>7<br/></pre></div><div class="input"><div class="title">Input</div><pre>3<br/>1 2 3<br/>1 3 3<br/></pre></div><div class="output"><div class="title">Output</div><pre>9<br/></pre></div></div></div></div>
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If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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} }); $.post(dataPageUrl, params, function (result) { if (result["success"] !== "true") { Codeforces.showMessage("Failed to save collapsed state."); } }, "json"); return false; }); }) </script> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Problem tags <div class="top-links"> </div> </div> <div style="padding: 0.5em;"> <div class="roundbox borderTopRound borderBottomRound" style="margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;"> <span class="tag-box" style="font-size:1.2rem;" title="Dfs and similar"> dfs and similar </span> </div> <div class="roundbox borderTopRound borderBottomRound" style="margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;"> <span class="tag-box" style="font-size:1.2rem;" title="Graphs"> graphs </span> </div> <div class="roundbox borderTopRound borderBottomRound" style="margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;"> <span class="tag-box" style="font-size:1.2rem;" title="Greedy algorithms"> greedy </span> </div> <div class="roundbox borderTopRound borderBottomRound" style="margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;"> <span class="tag-box" style="font-size:1.2rem;" title="Shortest paths on weighted and unweighted graphs"> shortest paths </span> </div> <div class="roundbox borderTopRound borderBottomRound" style="margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;"> <span class="tag-box" style="font-size:1.2rem;" title="Trees"> trees </span> </div> <div class="roundbox borderTopRound borderBottomRound" style="margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;"> <span class="tag-box" style="font-size:1.2rem;" title="Difficulty"> *1800 </span> </div> <div style="clear:both;text-align:right;font-size:1.1rem;"> <span title="Please login into the Codeforces" class="notice">No tag edit access</span> </div> </div> </div> <form id="addTagForm" action="/data/problemTags" method="post" style="display:none;"><input type='hidden' name='csrf_token' value='2c1db63c58bf2bdaa406ecfeaa47669a'/> <input name="action" type="hidden" value="addTag"/> <input name="problemId" type="hidden" value="329"/> <input name="tagName" type="hidden" value=""/> </form> <form id="removeTagForm" action="/data/problemTags" method="post" style="display:none;"><input type='hidden' name='csrf_token' value='2c1db63c58bf2bdaa406ecfeaa47669a'/> <input name="action" type="hidden" value="removeTag"/> <input name="problemId" type="hidden" value="329"/> <input name="tagName" type="hidden" value=""/> </form> <script type="text/javascript"> $(".tag-box img").click(function () { var tagName = $(this).attr("value"); 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} </style> <div class="roundbox sidebox sidebar-menu borderTopRound " style=""> <div class="caption titled">&rarr; Contest materials <div class="top-links"> </div> </div> <ul> <li> <span> <a href="/blog/entry/1338" title="Codeforces Beta round #57 (Div 2)" target="_blank">Announcement <span class="resource-locale">(oth)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="224" resourceName="Codeforces Beta round #57 (Div 2)" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1347" title="Round 57-E" target="_blank">Round 57-E <span class="resource-locale">(en)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="229" resourceName="Round 57-E" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1343" title="Round 57-B" target="_blank">Round 57-B <span class="resource-locale">(en)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="226" resourceName="Round 57-B" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1346" title="Round 57-D" target="_blank">Round 57-D <span class="resource-locale">(en)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="228" resourceName="Round 57-D" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1345" title="Round 57-C" target="_blank">Round 57-C <span class="resource-locale">(en)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="227" resourceName="Round 57-C" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1342" title="Round 57-A" target="_blank">Round 57-A <span class="resource-locale">(en)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="225" resourceName="Round 57-A" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> </ul> </div></div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li class="current selectedLava"><a href="/contest/61">Problems</a></li> <li><a href="/contest/61/submit">Submit Code</a></li> <li><a href="/contest/61/my">My Submissions</a></li> <li><a href="/contest/61/status">Status</a></li> <li><a href="/contest/61/hacks">Hacks</a></li> <li><a href="/contest/61/room/1">Room</a></li> <li><a href="/contest/61/standings">Standings</a></li> <li><a href="/contest/61/customtest">Custom Invocation</a></li> </ul> </div> <style> #facebox .content:has(.diff-popup) { width: 90vw; 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Eternal Victory</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Valerian was captured by Shapur. The victory was such a great one that Shapur decided to carve a scene of Valerian's defeat on a mountain. So he had to find the best place to make his victory eternal!</p><p>He decided to visit all <span class="tex-span"><i>n</i></span> cities of Persia to find the best available mountain, but after the recent war he was too tired and didn't want to traverse a lot. So he wanted to visit each of these <span class="tex-span"><i>n</i></span> cities at least once with smallest possible traverse. Persian cities are connected with bidirectional roads. You can go from any city to any other one using these roads and there is a unique path between each two cities.</p><p>All cities are numbered <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span>. Shapur is currently in the city <span class="tex-span">1</span> and he wants to visit all other cities with minimum possible traverse. He can finish his travels in any city.</p><p>Help Shapur find how much He should travel.</p></div><div class="input-specification"><div class="section-title">Input</div><p>First line contains a single natural number <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup></span>) — the amount of cities.</p><p>Next <span class="tex-span"><i>n</i> - 1</span> lines contain <span class="tex-span">3</span> integer numbers each <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>w</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>x</i><sub class="lower-index"><i>i</i></sub>, <i>y</i><sub class="lower-index"><i>i</i></sub> ≤ <i>n</i>, 0 ≤ <i>w</i><sub class="lower-index"><i>i</i></sub> ≤ 2 × 10<sup class="upper-index">4</sup></span>). <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span> are two ends of a road and <span class="tex-span"><i>w</i><sub class="lower-index"><i>i</i></sub></span> is the length of that road.</p></div><div class="output-specification"><div class="section-title">Output</div><p>A single integer number, the minimal length of Shapur's travel.</p><p>Please, do not use <span class="tex-font-style-tt">%lld</span> specificator to read or write 64-bit integers in C++. It is preffered to use <span class="tex-font-style-tt">cout</span> (also you may use <span class="tex-font-style-tt">%I64d</span>).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br />1 2 3<br />2 3 4<br /></pre></div><div class="output"><div class="title">Output</div><pre>7<br /></pre></div><div class="input"><div class="title">Input</div><pre>3<br />1 2 3<br />1 3 3<br /></pre></div><div class="output"><div class="title">Output</div><pre>9<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=D]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); if (previousStatementText) { if (previousStatementText !== statementText) { $problem.find(".diff-notifier").show(); 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["Dfs and similar", "Graphs", "Greedy algorithms", "Shortest paths on weighted and unweighted graphs", "Trees"]
["dfs and similar", "graphs", "greedy", "shortest paths", "trees", "*1800"]
61E
61
E
en
E. Enemy is weak
<div class="problem-statement"><div class="header"><div class="title">E. Enemy is weak</div><div class="time-limit"><div class="property-title">time limit per test</div>5 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>The Romans have attacked again. This time they are much more than the Persians but Shapur is ready to defeat them. He says: "A lion is never afraid of a hundred sheep". </p><p>Nevertheless Shapur has to find weaknesses in the Roman army to defeat them. So he gives the army a weakness number.</p><p>In Shapur's opinion the weakness of an army is equal to the number of triplets <span class="tex-span"><i>i</i>, <i>j</i>, <i>k</i></span> such that <span class="tex-span"><i>i</i> &lt; <i>j</i> &lt; <i>k</i></span> and <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub> &gt; <i>a</i><sub class="lower-index"><i>j</i></sub> &gt; <i>a</i><sub class="lower-index"><i>k</i></sub></span> where <span class="tex-span"><i>a</i><sub class="lower-index"><i>x</i></sub></span> is the power of man standing at position <span class="tex-span"><i>x</i></span>. The Roman army has one special trait — powers of all the people in it are distinct.</p><p>Help Shapur find out how weak the Romans are.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of input contains a single number <span class="tex-span"><i>n</i></span> (<span class="tex-span">3 ≤ <i>n</i> ≤ 10<sup class="upper-index">6</sup></span>) — the number of men in Roman army. Next line contains <span class="tex-span"><i>n</i></span> different positive integers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>n</i>, 1 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">9</sup></span>) — powers of men in the Roman army. </p></div><div class="output-specification"><div class="section-title">Output</div><p>A single integer number, the weakness of the Roman army. </p><p>Please, do not use <span class="tex-font-style-tt">%lld</span> specificator to read or write 64-bit integers in C++. It is preffered to use <span class="tex-font-style-tt">cout</span> (also you may use <span class="tex-font-style-tt">%I64d</span>).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br/>3 2 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>1<br/></pre></div><div class="input"><div class="title">Input</div><pre>3<br/>2 3 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>0<br/></pre></div><div class="input"><div class="title">Input</div><pre>4<br/>10 8 3 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>4<br/></pre></div><div class="input"><div class="title">Input</div><pre>4<br/>1 5 4 3<br/></pre></div><div class="output"><div class="title">Output</div><pre>1<br/></pre></div></div></div></div>
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max-width: 120rem !important; } .testCaseMarker { position: absolute; font-weight: bold; font-size: 1rem; } .diff-popup { width: 90vw; max-width: 120rem !important; display: none; overflow: auto; } .input-output-copier { font-size: 1.2rem; float: right; color: #888 !important; cursor: pointer; border: 1px solid rgb(185, 185, 185); padding: 3px; margin: 1px; line-height: 1.1rem; text-transform: none; } .input-output-copier:hover { background-color: #def; } .test-explanation textarea { width: 100%; height: 1.5em; } .pending-submission-message { color: darkorange !important; } </style> <script> const OPENING_SPACE = String.fromCharCode(1001); const CLOSING_SPACE = String.fromCharCode(1002); const nodeToText = function (node, pre) { let result = []; if (node.tagName === "SCRIPT" || node.tagName === "math" || (node.classList && node.classList.contains("input-output-copier"))) return []; if (node.tagName === "NOBR") { result.push(OPENING_SPACE); } if (node.nodeType === Node.TEXT_NODE) { let s = node.textContent; 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="E" data-uuid="ps_c7e1bef1085a5190e19d24b0ede330c7bc248579"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">E. Enemy is weak</div><div class="time-limit"><div class="property-title">time limit per test</div>5 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>The Romans have attacked again. This time they are much more than the Persians but Shapur is ready to defeat them. He says: &quot;A lion is never afraid of a hundred sheep&quot;. </p><p>Nevertheless Shapur has to find weaknesses in the Roman army to defeat them. So he gives the army a weakness number.</p><p>In Shapur's opinion the weakness of an army is equal to the number of triplets <span class="tex-span"><i>i</i>, <i>j</i>, <i>k</i></span> such that <span class="tex-span"><i>i</i> &lt; <i>j</i> &lt; <i>k</i></span> and <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub> &gt; <i>a</i><sub class="lower-index"><i>j</i></sub> &gt; <i>a</i><sub class="lower-index"><i>k</i></sub></span> where <span class="tex-span"><i>a</i><sub class="lower-index"><i>x</i></sub></span> is the power of man standing at position <span class="tex-span"><i>x</i></span>. The Roman army has one special trait — powers of all the people in it are distinct.</p><p>Help Shapur find out how weak the Romans are.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of input contains a single number <span class="tex-span"><i>n</i></span> (<span class="tex-span">3 ≤ <i>n</i> ≤ 10<sup class="upper-index">6</sup></span>) — the number of men in Roman army. Next line contains <span class="tex-span"><i>n</i></span> different positive integers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>n</i>, 1 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">9</sup></span>) — powers of men in the Roman army. </p></div><div class="output-specification"><div class="section-title">Output</div><p>A single integer number, the weakness of the Roman army. </p><p>Please, do not use <span class="tex-font-style-tt">%lld</span> specificator to read or write 64-bit integers in C++. It is preffered to use <span class="tex-font-style-tt">cout</span> (also you may use <span class="tex-font-style-tt">%I64d</span>).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br />3 2 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>1<br /></pre></div><div class="input"><div class="title">Input</div><pre>3<br />2 3 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>0<br /></pre></div><div class="input"><div class="title">Input</div><pre>4<br />10 8 3 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>4<br /></pre></div><div class="input"><div class="title">Input</div><pre>4<br />1 5 4 3<br /></pre></div><div class="output"><div class="title">Output</div><pre>1<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=E]"); 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["Heaps, binary search trees, segment trees, hash tables, etc", "Trees"]
["data structures", "trees", "*1900"]
62A
62
A
en
A. A Student's Dream
<div class="problem-statement"><div class="header"><div class="title">A. A Student's Dream</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Statistics claims that students sleep no more than three hours a day. But even in the world of their dreams, while they are snoring peacefully, the sense of impending doom is still upon them.</p><p>A poor student is dreaming that he is sitting the mathematical analysis exam. And he is examined by the most formidable professor of all times, a three times Soviet Union Hero, a Noble Prize laureate in student expulsion, venerable Petr Palych.</p><p>The poor student couldn't answer a single question. Thus, instead of a large spacious office he is going to apply for a job to thorium mines. But wait a minute! Petr Palych decided to give the student the last chance! Yes, that is possible only in dreams. </p><p>So the professor began: "Once a Venusian girl and a Marsian boy met on the Earth and decided to take a walk holding hands. But the problem is the girl has <span class="tex-span"><i>a</i><sub class="lower-index"><i>l</i></sub></span> fingers on her left hand and <span class="tex-span"><i>a</i><sub class="lower-index"><i>r</i></sub></span> fingers on the right one. The boy correspondingly has <span class="tex-span"><i>b</i><sub class="lower-index"><i>l</i></sub></span> and <span class="tex-span"><i>b</i><sub class="lower-index"><i>r</i></sub></span> fingers. They can only feel comfortable when holding hands, when no pair of the girl's fingers will touch each other. That is, they are comfortable when between any two girl's fingers there is a boy's finger. <span class="tex-font-style-bf">And in addition, no three fingers of the boy should touch each other.</span> Determine if they can hold hands so that the both were comfortable."</p><p>The boy any the girl don't care who goes to the left and who goes to the right. The difference is only that if the boy goes to the left of the girl, he will take her left hand with his right one, and if he goes to the right of the girl, then it is vice versa.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two positive integers not exceeding <span class="tex-span">100</span>. They are the number of fingers on the Venusian girl's left and right hand correspondingly. The second line contains two integers not exceeding <span class="tex-span">100</span>. They are the number of fingers on the Marsian boy's left and right hands correspondingly.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-font-style-tt">YES</span> or <span class="tex-font-style-tt">NO</span>, that is, the answer to Petr Palych's question.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>5 1<br/>10 5<br/></pre></div><div class="output"><div class="title">Output</div><pre>YES</pre></div><div class="input"><div class="title">Input</div><pre>4 5<br/>3 3<br/></pre></div><div class="output"><div class="title">Output</div><pre>YES</pre></div><div class="input"><div class="title">Input</div><pre>1 2<br/>11 6<br/></pre></div><div class="output"><div class="title">Output</div><pre>NO</pre></div></div></div><div class="note"><div class="section-title">Note</div><p>The boy and the girl don't really care who goes to the left.</p></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/62">Codeforces Beta Round 58</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? 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A Student's Dream</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Statistics claims that students sleep no more than three hours a day. But even in the world of their dreams, while they are snoring peacefully, the sense of impending doom is still upon them.</p><p>A poor student is dreaming that he is sitting the mathematical analysis exam. And he is examined by the most formidable professor of all times, a three times Soviet Union Hero, a Noble Prize laureate in student expulsion, venerable Petr Palych.</p><p>The poor student couldn't answer a single question. Thus, instead of a large spacious office he is going to apply for a job to thorium mines. But wait a minute! Petr Palych decided to give the student the last chance! Yes, that is possible only in dreams. </p><p>So the professor began: &quot;Once a Venusian girl and a Marsian boy met on the Earth and decided to take a walk holding hands. But the problem is the girl has <span class="tex-span"><i>a</i><sub class="lower-index"><i>l</i></sub></span> fingers on her left hand and <span class="tex-span"><i>a</i><sub class="lower-index"><i>r</i></sub></span> fingers on the right one. The boy correspondingly has <span class="tex-span"><i>b</i><sub class="lower-index"><i>l</i></sub></span> and <span class="tex-span"><i>b</i><sub class="lower-index"><i>r</i></sub></span> fingers. They can only feel comfortable when holding hands, when no pair of the girl's fingers will touch each other. That is, they are comfortable when between any two girl's fingers there is a boy's finger. <span class="tex-font-style-bf">And in addition, no three fingers of the boy should touch each other.</span> Determine if they can hold hands so that the both were comfortable.&quot;</p><p>The boy any the girl don't care who goes to the left and who goes to the right. The difference is only that if the boy goes to the left of the girl, he will take her left hand with his right one, and if he goes to the right of the girl, then it is vice versa.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two positive integers not exceeding <span class="tex-span">100</span>. They are the number of fingers on the Venusian girl's left and right hand correspondingly. The second line contains two integers not exceeding <span class="tex-span">100</span>. They are the number of fingers on the Marsian boy's left and right hands correspondingly.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-font-style-tt">YES</span> or <span class="tex-font-style-tt">NO</span>, that is, the answer to Petr Palych's question.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>5 1<br />10 5<br /></pre></div><div class="output"><div class="title">Output</div><pre>YES</pre></div><div class="input"><div class="title">Input</div><pre>4 5<br />3 3<br /></pre></div><div class="output"><div class="title">Output</div><pre>YES</pre></div><div class="input"><div class="title">Input</div><pre>1 2<br />11 6<br /></pre></div><div class="output"><div class="title">Output</div><pre>NO</pre></div></div></div><div class="note"><div class="section-title">Note</div><p>The boy and the girl don't really care who goes to the left.</p></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=A]"); 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["Greedy algorithms", "Mathematics including integration, differential equations, etc"]
["greedy", "math", "*1300"]
https://codeforces.com/blog/entry/1363
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A Student's Dream.<br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">There was a lot of troubles because of incorrect statement. Now I hope statement is ok. Let's solve it. =)</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">If boy will goes to the left he will take her left hand with his right one and boy's left hand and girl's right hand will be unused. Situation is looks like the same if we swap them vice versa. So, we need to check two situations and choose the best one.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">There is a simple way to check comfortableness, let's assume that boy has <span class="tex-span"><i>B</i></span> fingers on active hand and girl has <span class="tex-span"><i>G</i></span> fingers on active hand, so:</div><div style="text-align: justify;"> <br /></div><div style="text-align: justify;"><ul><li>If <span class="tex-span"><i>B</i> &lt; <i>G</i></span> they will be happy only when <span class="tex-span"><i>B</i> = <i>G</i> - 1</span>, you may see a pattern <span class="tex-span"><i>GBGBGBG</i>...<i>GBGBG</i></span>. In this pattern you can add no girl's finger for save the condition in statement<br /></li><li>If <span class="tex-span"><i>B</i> &gt; <i>G</i></span> the worst but correct situation for them is a pattern <span class="tex-span"><i>BBGBBGBB</i>...<i>BBGBB</i></span>. As you may see this way must be satisfy <span class="tex-span">2<i>G</i> + 2 &gt;  = <i>B</i></span> condition<br /></li><li>Simple situation is <span class="tex-span"><i>B</i> = <i>G</i></span>, obviously answer is &quot;yes&quot;<br /></li></ul></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Problem B. Tyndex.Brome.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Let's define <span class="tex-span"><i>p</i></span> as total length of all potential addresses <span class="tex-span"><i>c</i></span>. In this problem obvious solution has O(<span class="tex-span"><i>p</i>· <i>k</i></span>) difficulty and it is getting a TLE verdict. Let's speed up it by next way: we will save all position of letters 'a', 'b', ..., 'z' in address entered by user <span class="tex-span"><i>s</i></span> separately in increasing order. After this step we can find closest position of letter <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span> in <span class="tex-span"><i>s</i></span> for logarithmic time by binary search. This solution has O(<span class="tex-span"><i>p</i> · <i>logk</i></span>) difficulty that gives &quot;accepted&quot;.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Look carefully for length of potential address (it can be more than <span class="tex-span">10<sup class="upper-index">5</sup></span>). Answer can be too big and asks you for using integer 64-bit type.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Problem C. Inquisition.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">All triangles are located strickly inside of square. It makes problem more simplify, because you don't need to check situations of touching sides.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Let's save all segments of every triangle and cross them in pairs. There are many points at every segment - the results of crossing. Look at the every subsegment which do not contain any points of crossing inside. There are two situations: this subsegment completely lie on the side of some triangle or this subsegment completely lie inside of some triangle.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">We may check what is situation by this way: let's take a point at the middle of subsegment. If this point is strickly inside of some triangle then all subsegment is located inside and vice versa. We should calculate only subsegments located on the side of triangles and print their total length.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">If you are using integer numbers you should be careful for some operations like vector multiplication because it may leave 32-bit type.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">If you are using real numbers you should change you types for as large as possible for good precision (long long in c++, extended in pascal).</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Problem D. Wormhouse.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">In this problem you asks to find lexicographically next euler cycle or say that there is no way. Let's solve this problem backwards.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">We should repeat way of Arnie. Now it needs to rollback every his step and add edges for empty graph (graph without edges). Let's assume we had rollback edge from some vertix <span class="tex-span"><i>x</i></span> to vertix <span class="tex-span"><i>y</i></span>. We need to check is there some vertix <span class="tex-span"><i>z</i></span> that is connected to <span class="tex-span"><i>x</i></span> by an edge and value of <span class="tex-span"><i>z</i></span> is more than <span class="tex-span"><i>y</i></span>? Besides edge (<span class="tex-span"><i>x</i></span>; <span class="tex-span"><i>z</i></span>) shouldn't be a bridge because our component needs to be connected. </div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">No solution answer if it's impossible to find such <span class="tex-span"><i>z</i></span> at any step.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">But if edge (<span class="tex-span"><i>x</i></span>; <span class="tex-span"><i>z</i></span>) satisfied to conditions upper is exists let's change it to move and after this step our problem is to find lexicographically smallest euler way. It is possible to find only in unbreaked component of graph so every next step must going along non-brigde edges in vertix with as low number as possible. Of course, we must destroy unachievable vertices and do not destroy initial vertix.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">We can check is edge a bridge for O(<span class="tex-span"><i>E</i></span>) time by depth first search. Total difficulty of algorithm represented above is O(<span class="tex-span"><i>N</i>· <i>E</i><sup class="upper-index">2</sup></span>).</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Problem E. World Evil.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><i>Author of this problem is Vasily Vadimov, NNSU. He wrote her own tutorial for you.</i></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">In this problem you were to find the maximal flow in network with a cyllinder structure. The dynamic solution with complexity <span class="tex-span"><i>O</i>(<i>mn</i>2<sup class="upper-index"><i>n</i></sup>)</span> was considered.It's well known that the maximal flow is equal to value of the minimal cut. Also all the sources must belong to one part of the cut and all the drains --- to the other part. Then we look over all the vertices from the left to the right, from the top to the bottom and append to the one or the other part of the cut, recalculating the answer during the process. The trivial solution has complexity <span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>mn</i></sup>)</span> and doesn't fit the time limit.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">But we can notice the number add to the answer after appending a new vertice to some part of the cut depends only on what parts of the cut the vertices in the current and the previous columns belong to. So we can calculate such a value using dynamic programming: what is the minimal cut can be obtained by adding <span class="tex-span"><i>i</i></span> columns and the mask of belongings of vertices of the <span class="tex-span"><i>i</i></span>th column to the parts of the cut is <span class="tex-span"><i>mask</i></span>. Then we have <span class="tex-span">2<sup class="upper-index"><i>n</i></sup></span> conversions because there are <span class="tex-span">2<sup class="upper-index"><i>n</i></sup></span> different states of the <span class="tex-span"><i>i</i> - 1</span>th column. So we have the <span class="tex-span"><i>O</i>(<i>mn</i>2<sup class="upper-index">2<i>n</i></sup>)</span> solution.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">But this solution also can be improved. We calculate the minimal cut, if <span class="tex-span"><i>i</i> - 1</span> columns are added completely and <span class="tex-span"><i>j</i></span> vertices from the <span class="tex-span"><i>i</i></span>th column are added, and mask of belongings of vertices that have no neighbours on the right is <span class="tex-span"><i>mask</i></span>. Then we append <span class="tex-span"><i>j</i></span>-th vertice to one of the parts, recalculate the value of the cut and do the conversion. So we have <span class="tex-span"><i>mn</i>2<sup class="upper-index"><i>n</i></sup></span> conditions and <span class="tex-span"><i>O</i>(1)</span> conversions from the every condition and the solution's complexity is <span class="tex-span"><i>O</i>(<i>mn</i>2<sup class="upper-index"><i>n</i></sup>)</span>.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Also congratulations to the participants rng_58 and Ra16bit who solved this problem during the contest!<br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><i>Thanks to boys from NNSU (Vladislav Epifanov, Alexey Shmelev) who helps us with alternating solutions and etc.</i></div><div style="text-align: justify;"><i><br /></i></div><div style="text-align: justify;"><i>Sorry for poor english</i></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/62" class="notice" style="text-decoration: none;">Codeforces Beta Round 58</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-86-1363").click(function() { var that = this; 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line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/Alex_KPR"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/Alex_KPR"> Alex_KPR </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Feb/26/2011 14:56">13 years ago</span> </li> <li> <a href="/blog/entry/1363#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1363#comments"> 2 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1373"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (2)</a> </div> <div class="comments-actions-div"> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="24708" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/coders1122" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/coders1122" title="Expert coders1122" class="rated-user user-blue">coders1122</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/27/2011 10:35">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-24708" href="?#comment-24708" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="24708" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4531" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-24708"> <div class="moveup"> <div class="ttypography">I saw a lot of O(p.k) solutions pass in time after the contest end.I assume that they are tested against the same system tests used during the contest.<br /><br />Maybe few cases like<br />1 1<br />a<br />aa......a<br />where there are around 2*MAXN a's in the second line.(Actually this was a case that i were hacked with during the contest,but it failed due to a runtime error and not TLE).<br /><br />Another tricky case where people tricked their greedy to work incase we already dont have minimum |j-i| = 0, could be<br />1 1<br />a....ab.....b<br />b....ba.....a<br />where the a's and b's = MAXN/2<br /><br />MAXN = 99999 everywhere.<br /><br />O(p*k) solutions could use the above tests to understand why according to the problem setter were expected to TLE and might have got lucky on the judge.<br />Hope this helps.Appreciate any comments.</div> </div> </div> <div class="reply info"> <a class="comment-24708 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-24708 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-24708"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="24769" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kang205" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/kang205" title="Expert kang205" class="rated-user user-blue">kang205</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/27/2011 17:23">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-24769" href="?#comment-24769" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="24769" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="13097" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-24769"> <div class="moveup"> <div class="ttypography">Problem B<br />If you make a queue to find When you find closest position,it will be O(P) :D<br /><br />My Solution cost least time.</div> </div> </div> <div class="reply info"> <a class="comment-24769 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-24769 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-24769"> </ul> </div> <br/> <div id="editBox-1373" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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62B
62
B
en
B. Tyndex.Brome
<div class="problem-statement"><div class="header"><div class="title">B. Tyndex.Brome</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Tyndex is again well ahead of the rivals! The reaction to the release of Zoozle Chrome browser was the release of a new browser Tyndex.Brome!</p><p>The popularity of the new browser is growing daily. And the secret is not even the Tyndex.Bar installed (the Tyndex.Bar automatically fills the glass with the finest 1664 cognac after you buy Tyndex.Bottles and insert in into a USB port). It is highly popular due to the well-thought interaction with the user.</p><p>Let us take, for example, the system of automatic address correction. Have you entered <span class="tex-font-style-tt">codehorses</span> instead of <span class="tex-font-style-tt">codeforces</span>? The gloomy Zoozle Chrome will sadly say that the address does not exist. Tyndex.Brome at the same time will automatically find the closest address and sent you there. That's brilliant!</p><p>How does this splendid function work? That's simple! For each potential address a function of the <span class="tex-span"><i>F</i></span> error is calculated by the following rules:</p><ul> <li> for every letter <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span> from the potential address <span class="tex-span"><i>c</i></span> the closest position <span class="tex-span"><i>j</i></span> of the letter <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span> in the address (<span class="tex-span"><i>s</i></span>) entered by the user is found. The absolute difference <span class="tex-span">|<i>i</i> - <i>j</i>|</span> of these positions is added to <span class="tex-span"><i>F</i></span>. So for every <span class="tex-span"><i>i</i></span> (<span class="tex-span">1 ≤ <i>i</i> ≤ |<i>c</i>|</span>) the position <span class="tex-span"><i>j</i></span> is chosen such, that <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub> = <i>s</i><sub class="lower-index"><i>j</i></sub></span>, and <span class="tex-span">|<i>i</i> - <i>j</i>|</span> is minimal possible. </li><li> if no such letter <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span> exists in the address entered by the user, then the length of the potential address <span class="tex-span">|<i>c</i>|</span> is added to <span class="tex-span"><i>F</i></span>. </li></ul><p>After the values of the error function have been calculated for all the potential addresses the most suitable one is found. </p><p>To understand the special features of the above described method better, it is recommended to realize the algorithm of calculating the <span class="tex-span"><i>F</i></span> function for an address given by the user and some set of potential addresses. Good luck!</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup>, 1 ≤ <i>k</i> ≤ 10<sup class="upper-index">5</sup></span>). They are the number of potential addresses and the length of the address entered by the user. The next line contains <span class="tex-span"><i>k</i></span> lowercase Latin letters. They are the address entered by the user (<span class="tex-span"><i>s</i></span>). Each next <span class="tex-span"><i>i</i></span>-th (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>n</i></span>) line contains a non-empty sequence of lowercase Latin letters. They are the potential address. It is guaranteed that the total length of all the lines does not exceed <span class="tex-span">2·10<sup class="upper-index">5</sup></span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>On each <span class="tex-span"><i>n</i></span> line of the output file print a single number: the value of the error function when the current potential address is chosen.</p><p>Please, do not use <span class="tex-font-style-tt">%lld</span> specificator to read or write 64-bit integers in C++. It is preffered to use <span class="tex-font-style-tt">cout</span> (also you may use <span class="tex-font-style-tt">%I64d</span>).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2 10<br/>codeforces<br/>codeforces<br/>codehorses<br/></pre></div><div class="output"><div class="title">Output</div><pre>0<br/>12<br/></pre></div><div class="input"><div class="title">Input</div><pre>9 9<br/>vkontakte<br/>vcontacte<br/>vkontrakte<br/>vkollapse<br/>vkrokodile<br/>vtopke<br/>vkapuste<br/>vpechke<br/>vk<br/>vcodeforcese<br/></pre></div><div class="output"><div class="title">Output</div><pre>18<br/>14<br/>36<br/>47<br/>14<br/>29<br/>30<br/>0<br/>84<br/></pre></div></div></div></div>
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} </style> <div class="roundbox sidebox sidebar-menu borderTopRound " style=""> <div class="caption titled">&rarr; Contest materials <div class="top-links"> </div> </div> <ul> <li> <span> <a href="/blog/entry/1356" title="Codeforces Beta Round #58" target="_blank">Announcement</a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="230:231" resourceName="Announcement" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1363" title="Codeforces Beta Round #58 tutorial" target="_blank">Tutorial</a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="816:817" resourceName="Tutorial" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> </ul> </div></div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li class="current selectedLava"><a href="/contest/62">Problems</a></li> <li><a href="/contest/62/submit">Submit Code</a></li> <li><a href="/contest/62/my">My Submissions</a></li> <li><a href="/contest/62/status">Status</a></li> <li><a href="/contest/62/hacks">Hacks</a></li> <li><a href="/contest/62/room/1">Room</a></li> <li><a href="/contest/62/standings">Standings</a></li> <li><a href="/contest/62/customtest">Custom Invocation</a></li> </ul> </div> <style> #facebox .content:has(.diff-popup) { width: 90vw; 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="B" data-uuid="ps_d0a002cbb136f7c1aeda46b69cdb321ee75a25b0"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">B. Tyndex.Brome</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Tyndex is again well ahead of the rivals! The reaction to the release of Zoozle Chrome browser was the release of a new browser Tyndex.Brome!</p><p>The popularity of the new browser is growing daily. And the secret is not even the Tyndex.Bar installed (the Tyndex.Bar automatically fills the glass with the finest 1664 cognac after you buy Tyndex.Bottles and insert in into a USB port). It is highly popular due to the well-thought interaction with the user.</p><p>Let us take, for example, the system of automatic address correction. Have you entered <span class="tex-font-style-tt">codehorses</span> instead of <span class="tex-font-style-tt">codeforces</span>? The gloomy Zoozle Chrome will sadly say that the address does not exist. Tyndex.Brome at the same time will automatically find the closest address and sent you there. That's brilliant!</p><p>How does this splendid function work? That's simple! For each potential address a function of the <span class="tex-span"><i>F</i></span> error is calculated by the following rules:</p><ul> <li> for every letter <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span> from the potential address <span class="tex-span"><i>c</i></span> the closest position <span class="tex-span"><i>j</i></span> of the letter <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span> in the address (<span class="tex-span"><i>s</i></span>) entered by the user is found. The absolute difference <span class="tex-span">|<i>i</i> - <i>j</i>|</span> of these positions is added to <span class="tex-span"><i>F</i></span>. So for every <span class="tex-span"><i>i</i></span> (<span class="tex-span">1 ≤ <i>i</i> ≤ |<i>c</i>|</span>) the position <span class="tex-span"><i>j</i></span> is chosen such, that <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub> = <i>s</i><sub class="lower-index"><i>j</i></sub></span>, and <span class="tex-span">|<i>i</i> - <i>j</i>|</span> is minimal possible. </li><li> if no such letter <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span> exists in the address entered by the user, then the length of the potential address <span class="tex-span">|<i>c</i>|</span> is added to <span class="tex-span"><i>F</i></span>. </li></ul><p>After the values of the error function have been calculated for all the potential addresses the most suitable one is found. </p><p>To understand the special features of the above described method better, it is recommended to realize the algorithm of calculating the <span class="tex-span"><i>F</i></span> function for an address given by the user and some set of potential addresses. Good luck!</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup>, 1 ≤ <i>k</i> ≤ 10<sup class="upper-index">5</sup></span>). They are the number of potential addresses and the length of the address entered by the user. The next line contains <span class="tex-span"><i>k</i></span> lowercase Latin letters. They are the address entered by the user (<span class="tex-span"><i>s</i></span>). Each next <span class="tex-span"><i>i</i></span>-th (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>n</i></span>) line contains a non-empty sequence of lowercase Latin letters. They are the potential address. It is guaranteed that the total length of all the lines does not exceed <span class="tex-span">2·10<sup class="upper-index">5</sup></span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>On each <span class="tex-span"><i>n</i></span> line of the output file print a single number: the value of the error function when the current potential address is chosen.</p><p>Please, do not use <span class="tex-font-style-tt">%lld</span> specificator to read or write 64-bit integers in C++. It is preffered to use <span class="tex-font-style-tt">cout</span> (also you may use <span class="tex-font-style-tt">%I64d</span>).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2 10<br />codeforces<br />codeforces<br />codehorses<br /></pre></div><div class="output"><div class="title">Output</div><pre>0<br />12<br /></pre></div><div class="input"><div class="title">Input</div><pre>9 9<br />vkontakte<br />vcontacte<br />vkontrakte<br />vkollapse<br />vkrokodile<br />vtopke<br />vkapuste<br />vpechke<br />vk<br />vcodeforcese<br /></pre></div><div class="output"><div class="title">Output</div><pre>18<br />14<br />36<br />47<br />14<br />29<br />30<br />0<br />84<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=B]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); 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["Binary search", "Implementation problems, programming technics, simulation"]
["binary search", "implementation", "*1800"]
https://codeforces.com/blog/entry/1363
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<a href="/blog/entry/120644">Codeforces Round 899 (Div. 2)</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/Misa-Misa" title="Expert Misa-Misa" class="rated-user user-blue">Misa-Misa</a> &rarr; <a href="/blog/entry/121157">Someone please help me understand this.</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/shivam565" title="Specialist shivam565" class="rated-user user-cyan">shivam565</a> &rarr; <a href="/blog/entry/108348">Total number of subarrays with sum atmost k</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> </ul> </div> <div class="bottom-links"> <table style="width:100%;"> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:right;"> <a href="/recent-actions">Detailed &rarr;</a> </td> </tr> </tbody> </table> </div> </div> </div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li><a href="/profile/Alex_KPR">Alex_KPR</a></li> <li class="current selectedLava"><a href="/blog/Alex_KPR">Blog</a></li> <li><a href="/teams/with/Alex_KPR">Teams</a></li> <li><a href="/submissions/Alex_KPR">Submissions</a></li> <li><a href="/contests/with/Alex_KPR">Contests</a></li> <li><a href="/contests/writer/Alex_KPR">Problemsetting</a></li> </ul> </div> <div style="margin-top:0;"> <div> <h3><a href="/blog/Alex_KPR" style="text-decoration:none;color:black !important;">Alex_KPR's blog</a></h3> </div> <div style="margin-top:2em;"> <div class="has-topic-id topic" topicId="1363"> <div class="title"> <a href="/blog/entry/1363"> Codeforces Beta Round #58 tutorial </a> </div> <div class="info" style="position:relative;"> By&nbsp;<a href="/profile/Alex_KPR" title="Master Alex_KPR" class="rated-user user-orange">Alex_KPR</a>, <span class="format-humantime" title="Feb/26/2011 14:56">13 years ago</span>, translation, <img style="position: relative;top: 5px;" src="//codeforces.org/s/81027/images/flags/24/gb.png" alt="In English" title="In English"/> <span style="position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;"> <div style="margin-top:0.25em;"> </div> </span> </div> <div class="content"> <div class="ttypography"><div style="text-align: justify;">Problem A. A Student's Dream.<br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">There was a lot of troubles because of incorrect statement. Now I hope statement is ok. Let's solve it. =)</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">If boy will goes to the left he will take her left hand with his right one and boy's left hand and girl's right hand will be unused. Situation is looks like the same if we swap them vice versa. So, we need to check two situations and choose the best one.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">There is a simple way to check comfortableness, let's assume that boy has <span class="tex-span"><i>B</i></span> fingers on active hand and girl has <span class="tex-span"><i>G</i></span> fingers on active hand, so:</div><div style="text-align: justify;"> <br /></div><div style="text-align: justify;"><ul><li>If <span class="tex-span"><i>B</i> &lt; <i>G</i></span> they will be happy only when <span class="tex-span"><i>B</i> = <i>G</i> - 1</span>, you may see a pattern <span class="tex-span"><i>GBGBGBG</i>...<i>GBGBG</i></span>. In this pattern you can add no girl's finger for save the condition in statement<br /></li><li>If <span class="tex-span"><i>B</i> &gt; <i>G</i></span> the worst but correct situation for them is a pattern <span class="tex-span"><i>BBGBBGBB</i>...<i>BBGBB</i></span>. As you may see this way must be satisfy <span class="tex-span">2<i>G</i> + 2 &gt;  = <i>B</i></span> condition<br /></li><li>Simple situation is <span class="tex-span"><i>B</i> = <i>G</i></span>, obviously answer is &quot;yes&quot;<br /></li></ul></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Problem B. Tyndex.Brome.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Let's define <span class="tex-span"><i>p</i></span> as total length of all potential addresses <span class="tex-span"><i>c</i></span>. In this problem obvious solution has O(<span class="tex-span"><i>p</i>· <i>k</i></span>) difficulty and it is getting a TLE verdict. Let's speed up it by next way: we will save all position of letters 'a', 'b', ..., 'z' in address entered by user <span class="tex-span"><i>s</i></span> separately in increasing order. After this step we can find closest position of letter <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span> in <span class="tex-span"><i>s</i></span> for logarithmic time by binary search. This solution has O(<span class="tex-span"><i>p</i> · <i>logk</i></span>) difficulty that gives &quot;accepted&quot;.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Look carefully for length of potential address (it can be more than <span class="tex-span">10<sup class="upper-index">5</sup></span>). Answer can be too big and asks you for using integer 64-bit type.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Problem C. Inquisition.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">All triangles are located strickly inside of square. It makes problem more simplify, because you don't need to check situations of touching sides.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Let's save all segments of every triangle and cross them in pairs. There are many points at every segment - the results of crossing. Look at the every subsegment which do not contain any points of crossing inside. There are two situations: this subsegment completely lie on the side of some triangle or this subsegment completely lie inside of some triangle.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">We may check what is situation by this way: let's take a point at the middle of subsegment. If this point is strickly inside of some triangle then all subsegment is located inside and vice versa. We should calculate only subsegments located on the side of triangles and print their total length.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">If you are using integer numbers you should be careful for some operations like vector multiplication because it may leave 32-bit type.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">If you are using real numbers you should change you types for as large as possible for good precision (long long in c++, extended in pascal).</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Problem D. Wormhouse.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">In this problem you asks to find lexicographically next euler cycle or say that there is no way. Let's solve this problem backwards.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">We should repeat way of Arnie. Now it needs to rollback every his step and add edges for empty graph (graph without edges). Let's assume we had rollback edge from some vertix <span class="tex-span"><i>x</i></span> to vertix <span class="tex-span"><i>y</i></span>. We need to check is there some vertix <span class="tex-span"><i>z</i></span> that is connected to <span class="tex-span"><i>x</i></span> by an edge and value of <span class="tex-span"><i>z</i></span> is more than <span class="tex-span"><i>y</i></span>? Besides edge (<span class="tex-span"><i>x</i></span>; <span class="tex-span"><i>z</i></span>) shouldn't be a bridge because our component needs to be connected. </div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">No solution answer if it's impossible to find such <span class="tex-span"><i>z</i></span> at any step.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">But if edge (<span class="tex-span"><i>x</i></span>; <span class="tex-span"><i>z</i></span>) satisfied to conditions upper is exists let's change it to move and after this step our problem is to find lexicographically smallest euler way. It is possible to find only in unbreaked component of graph so every next step must going along non-brigde edges in vertix with as low number as possible. Of course, we must destroy unachievable vertices and do not destroy initial vertix.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">We can check is edge a bridge for O(<span class="tex-span"><i>E</i></span>) time by depth first search. Total difficulty of algorithm represented above is O(<span class="tex-span"><i>N</i>· <i>E</i><sup class="upper-index">2</sup></span>).</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Problem E. World Evil.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><i>Author of this problem is Vasily Vadimov, NNSU. He wrote her own tutorial for you.</i></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">In this problem you were to find the maximal flow in network with a cyllinder structure. The dynamic solution with complexity <span class="tex-span"><i>O</i>(<i>mn</i>2<sup class="upper-index"><i>n</i></sup>)</span> was considered.It's well known that the maximal flow is equal to value of the minimal cut. Also all the sources must belong to one part of the cut and all the drains --- to the other part. Then we look over all the vertices from the left to the right, from the top to the bottom and append to the one or the other part of the cut, recalculating the answer during the process. The trivial solution has complexity <span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>mn</i></sup>)</span> and doesn't fit the time limit.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">But we can notice the number add to the answer after appending a new vertice to some part of the cut depends only on what parts of the cut the vertices in the current and the previous columns belong to. So we can calculate such a value using dynamic programming: what is the minimal cut can be obtained by adding <span class="tex-span"><i>i</i></span> columns and the mask of belongings of vertices of the <span class="tex-span"><i>i</i></span>th column to the parts of the cut is <span class="tex-span"><i>mask</i></span>. Then we have <span class="tex-span">2<sup class="upper-index"><i>n</i></sup></span> conversions because there are <span class="tex-span">2<sup class="upper-index"><i>n</i></sup></span> different states of the <span class="tex-span"><i>i</i> - 1</span>th column. So we have the <span class="tex-span"><i>O</i>(<i>mn</i>2<sup class="upper-index">2<i>n</i></sup>)</span> solution.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">But this solution also can be improved. We calculate the minimal cut, if <span class="tex-span"><i>i</i> - 1</span> columns are added completely and <span class="tex-span"><i>j</i></span> vertices from the <span class="tex-span"><i>i</i></span>th column are added, and mask of belongings of vertices that have no neighbours on the right is <span class="tex-span"><i>mask</i></span>. Then we append <span class="tex-span"><i>j</i></span>-th vertice to one of the parts, recalculate the value of the cut and do the conversion. So we have <span class="tex-span"><i>mn</i>2<sup class="upper-index"><i>n</i></sup></span> conditions and <span class="tex-span"><i>O</i>(1)</span> conversions from the every condition and the solution's complexity is <span class="tex-span"><i>O</i>(<i>mn</i>2<sup class="upper-index"><i>n</i></sup>)</span>.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Also congratulations to the participants rng_58 and Ra16bit who solved this problem during the contest!<br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><i>Thanks to boys from NNSU (Vladislav Epifanov, Alexey Shmelev) who helps us with alternating solutions and etc.</i></div><div style="text-align: justify;"><i><br /></i></div><div style="text-align: justify;"><i>Sorry for poor english</i></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/62" class="notice" style="text-decoration: none;">Codeforces Beta Round 58</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-86-1363").click(function() { var that = this; 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line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/Alex_KPR"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/Alex_KPR"> Alex_KPR </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Feb/26/2011 14:56">13 years ago</span> </li> <li> <a href="/blog/entry/1363#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1363#comments"> 2 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; 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top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="24708" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4531" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-24708"> <div class="moveup"> <div class="ttypography">I saw a lot of O(p.k) solutions pass in time after the contest end.I assume that they are tested against the same system tests used during the contest.<br /><br />Maybe few cases like<br />1 1<br />a<br />aa......a<br />where there are around 2*MAXN a's in the second line.(Actually this was a case that i were hacked with during the contest,but it failed due to a runtime error and not TLE).<br /><br />Another tricky case where people tricked their greedy to work incase we already dont have minimum |j-i| = 0, could be<br />1 1<br />a....ab.....b<br />b....ba.....a<br />where the a's and b's = MAXN/2<br /><br />MAXN = 99999 everywhere.<br /><br />O(p*k) solutions could use the above tests to understand why according to the problem setter were expected to TLE and might have got lucky on the judge.<br />Hope this helps.Appreciate any comments.</div> </div> </div> <div class="reply info"> <a class="comment-24708 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-24708 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-24708"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="24769" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kang205" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/kang205" title="Expert kang205" class="rated-user user-blue">kang205</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/27/2011 17:23">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-24769" href="?#comment-24769" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="24769" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="13097" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-24769"> <div class="moveup"> <div class="ttypography">Problem B<br />If you make a queue to find When you find closest position,it will be O(P) :D<br /><br />My Solution cost least time.</div> </div> </div> <div class="reply info"> <a class="comment-24769 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-24769 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-24769"> </ul> </div> <br/> <div id="editBox-1373" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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62C
62
C
en
C. Inquisition
<div class="problem-statement"><div class="header"><div class="title">C. Inquisition</div><div class="time-limit"><div class="property-title">time limit per test</div>3 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>In Medieval times existed the tradition of burning witches at steaks together with their pets, black cats. By the end of the 15-th century the population of black cats ceased to exist. The difficulty of the situation led to creating the EIC - the Emergency Inquisitory Commission.</p><p>The resolution #666 says that a white cat is considered black when and only when the perimeter of its black spots exceeds the acceptable norm. But what does the acceptable norm equal to? Every inquisitor will choose it himself depending on the situation. And your task is to find the perimeter of black spots on the cat's fur.</p><p>The very same resolution says that the cat's fur is a white square with the length of <span class="tex-span">10<sup class="upper-index">5</sup></span>. During the measurement of spots it is customary to put the lower left corner of the fur into the origin of axes <span class="tex-span">(0;0)</span> and the upper right one — to the point with coordinates <span class="tex-span">(10<sup class="upper-index">5</sup>;10<sup class="upper-index">5</sup>)</span>. The cats' spots are nondegenerate triangles. The spots can intersect and overlap with each other, but it is guaranteed that each pair of the triangular spots' sides have no more than one common point.</p><p>We'll regard the perimeter in this problem as the total length of the boarders where a cat's fur changes color.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first input line contains a single integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">0 ≤ <i>n</i> ≤ 100</span>). It is the number of spots on the cat's fur. The <span class="tex-span"><i>i</i></span>-th of the last <span class="tex-span"><i>n</i></span> lines contains <span class="tex-span">6</span> integers: <span class="tex-span"><i>x</i><sub class="lower-index">1<i>i</i></sub></span>, <span class="tex-span"><i>y</i><sub class="lower-index">1<i>i</i></sub></span>, <span class="tex-span"><i>x</i><sub class="lower-index">2<i>i</i></sub></span>, <span class="tex-span"><i>y</i><sub class="lower-index">2<i>i</i></sub></span>, <span class="tex-span"><i>x</i><sub class="lower-index">3<i>i</i></sub></span>, <span class="tex-span"><i>y</i><sub class="lower-index">3<i>i</i></sub></span>. They are the coordinates of the <span class="tex-span"><i>i</i></span>-th triangular spot <span class="tex-span">(0 &lt; <i>x</i><sub class="lower-index"><i>ji</i></sub>, <i>y</i><sub class="lower-index"><i>ji</i></sub> &lt; 10<sup class="upper-index">5</sup>)</span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single number, the answer to the problem, perimeter of the union of triangles. Your answer should differ from the correct one in no more than <span class="tex-span">10<sup class="upper-index"> - 6</sup></span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>1<br/>1 1 2 1 1 2<br/></pre></div><div class="output"><div class="title">Output</div><pre>3.4142135624<br/></pre></div><div class="input"><div class="title">Input</div><pre>3<br/>3 3 10 3 3 10<br/>1 1 9 4 5 6<br/>2 2 11 7 6 11<br/></pre></div><div class="output"><div class="title">Output</div><pre>37.7044021497<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="C" data-uuid="ps_dcdb1ceb9ac0ebc147b0ae622a16cb92d4924919"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. Inquisition</div><div class="time-limit"><div class="property-title">time limit per test</div>3 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>In Medieval times existed the tradition of burning witches at steaks together with their pets, black cats. By the end of the 15-th century the population of black cats ceased to exist. The difficulty of the situation led to creating the EIC - the Emergency Inquisitory Commission.</p><p>The resolution #666 says that a white cat is considered black when and only when the perimeter of its black spots exceeds the acceptable norm. But what does the acceptable norm equal to? Every inquisitor will choose it himself depending on the situation. And your task is to find the perimeter of black spots on the cat's fur.</p><p>The very same resolution says that the cat's fur is a white square with the length of <span class="tex-span">10<sup class="upper-index">5</sup></span>. During the measurement of spots it is customary to put the lower left corner of the fur into the origin of axes <span class="tex-span">(0;0)</span> and the upper right one — to the point with coordinates <span class="tex-span">(10<sup class="upper-index">5</sup>;10<sup class="upper-index">5</sup>)</span>. The cats' spots are nondegenerate triangles. The spots can intersect and overlap with each other, but it is guaranteed that each pair of the triangular spots' sides have no more than one common point.</p><p>We'll regard the perimeter in this problem as the total length of the boarders where a cat's fur changes color.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first input line contains a single integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">0 ≤ <i>n</i> ≤ 100</span>). It is the number of spots on the cat's fur. The <span class="tex-span"><i>i</i></span>-th of the last <span class="tex-span"><i>n</i></span> lines contains <span class="tex-span">6</span> integers: <span class="tex-span"><i>x</i><sub class="lower-index">1<i>i</i></sub></span>, <span class="tex-span"><i>y</i><sub class="lower-index">1<i>i</i></sub></span>, <span class="tex-span"><i>x</i><sub class="lower-index">2<i>i</i></sub></span>, <span class="tex-span"><i>y</i><sub class="lower-index">2<i>i</i></sub></span>, <span class="tex-span"><i>x</i><sub class="lower-index">3<i>i</i></sub></span>, <span class="tex-span"><i>y</i><sub class="lower-index">3<i>i</i></sub></span>. They are the coordinates of the <span class="tex-span"><i>i</i></span>-th triangular spot <span class="tex-span">(0 &lt; <i>x</i><sub class="lower-index"><i>ji</i></sub>, <i>y</i><sub class="lower-index"><i>ji</i></sub> &lt; 10<sup class="upper-index">5</sup>)</span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single number, the answer to the problem, perimeter of the union of triangles. Your answer should differ from the correct one in no more than <span class="tex-span">10<sup class="upper-index"> - 6</sup></span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>1<br />1 1 2 1 1 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>3.4142135624<br /></pre></div><div class="input"><div class="title">Input</div><pre>3<br />3 3 10 3 3 10<br />1 1 9 4 5 6<br />2 2 11 7 6 11<br /></pre></div><div class="output"><div class="title">Output</div><pre>37.7044021497<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=C]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); if (previousStatementText) { if (previousStatementText !== statementText) { $problem.find(".diff-notifier").show(); 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["Geometry, computational geometry", "Implementation problems, programming technics, simulation", "Sortings, orderings"]
["geometry", "implementation", "sortings", "*2300"]
https://codeforces.com/blog/entry/1363
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<a href="/blog/entry/120644">Codeforces Round 899 (Div. 2)</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/Misa-Misa" title="Expert Misa-Misa" class="rated-user user-blue">Misa-Misa</a> &rarr; <a href="/blog/entry/121157">Someone please help me understand this.</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/shivam565" title="Specialist shivam565" class="rated-user user-cyan">shivam565</a> &rarr; <a href="/blog/entry/108348">Total number of subarrays with sum atmost k</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> </ul> </div> <div class="bottom-links"> <table style="width:100%;"> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:right;"> <a href="/recent-actions">Detailed &rarr;</a> </td> </tr> </tbody> </table> </div> </div> </div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li><a href="/profile/Alex_KPR">Alex_KPR</a></li> <li class="current selectedLava"><a href="/blog/Alex_KPR">Blog</a></li> <li><a href="/teams/with/Alex_KPR">Teams</a></li> <li><a href="/submissions/Alex_KPR">Submissions</a></li> <li><a href="/contests/with/Alex_KPR">Contests</a></li> <li><a href="/contests/writer/Alex_KPR">Problemsetting</a></li> </ul> </div> <div style="margin-top:0;"> <div> <h3><a href="/blog/Alex_KPR" style="text-decoration:none;color:black !important;">Alex_KPR's blog</a></h3> </div> <div style="margin-top:2em;"> <div class="has-topic-id topic" topicId="1363"> <div class="title"> <a href="/blog/entry/1363"> Codeforces Beta Round #58 tutorial </a> </div> <div class="info" style="position:relative;"> By&nbsp;<a href="/profile/Alex_KPR" title="Master Alex_KPR" class="rated-user user-orange">Alex_KPR</a>, <span class="format-humantime" title="Feb/26/2011 14:56">13 years ago</span>, translation, <img style="position: relative;top: 5px;" src="//codeforces.org/s/81027/images/flags/24/gb.png" alt="In English" title="In English"/> <span style="position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;"> <div style="margin-top:0.25em;"> </div> </span> </div> <div class="content"> <div class="ttypography"><div style="text-align: justify;">Problem A. A Student's Dream.<br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">There was a lot of troubles because of incorrect statement. Now I hope statement is ok. Let's solve it. =)</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">If boy will goes to the left he will take her left hand with his right one and boy's left hand and girl's right hand will be unused. Situation is looks like the same if we swap them vice versa. So, we need to check two situations and choose the best one.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">There is a simple way to check comfortableness, let's assume that boy has <span class="tex-span"><i>B</i></span> fingers on active hand and girl has <span class="tex-span"><i>G</i></span> fingers on active hand, so:</div><div style="text-align: justify;"> <br /></div><div style="text-align: justify;"><ul><li>If <span class="tex-span"><i>B</i> &lt; <i>G</i></span> they will be happy only when <span class="tex-span"><i>B</i> = <i>G</i> - 1</span>, you may see a pattern <span class="tex-span"><i>GBGBGBG</i>...<i>GBGBG</i></span>. In this pattern you can add no girl's finger for save the condition in statement<br /></li><li>If <span class="tex-span"><i>B</i> &gt; <i>G</i></span> the worst but correct situation for them is a pattern <span class="tex-span"><i>BBGBBGBB</i>...<i>BBGBB</i></span>. As you may see this way must be satisfy <span class="tex-span">2<i>G</i> + 2 &gt;  = <i>B</i></span> condition<br /></li><li>Simple situation is <span class="tex-span"><i>B</i> = <i>G</i></span>, obviously answer is &quot;yes&quot;<br /></li></ul></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Problem B. Tyndex.Brome.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Let's define <span class="tex-span"><i>p</i></span> as total length of all potential addresses <span class="tex-span"><i>c</i></span>. In this problem obvious solution has O(<span class="tex-span"><i>p</i>· <i>k</i></span>) difficulty and it is getting a TLE verdict. Let's speed up it by next way: we will save all position of letters 'a', 'b', ..., 'z' in address entered by user <span class="tex-span"><i>s</i></span> separately in increasing order. After this step we can find closest position of letter <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span> in <span class="tex-span"><i>s</i></span> for logarithmic time by binary search. This solution has O(<span class="tex-span"><i>p</i> · <i>logk</i></span>) difficulty that gives &quot;accepted&quot;.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Look carefully for length of potential address (it can be more than <span class="tex-span">10<sup class="upper-index">5</sup></span>). Answer can be too big and asks you for using integer 64-bit type.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Problem C. Inquisition.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">All triangles are located strickly inside of square. It makes problem more simplify, because you don't need to check situations of touching sides.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Let's save all segments of every triangle and cross them in pairs. There are many points at every segment - the results of crossing. Look at the every subsegment which do not contain any points of crossing inside. There are two situations: this subsegment completely lie on the side of some triangle or this subsegment completely lie inside of some triangle.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">We may check what is situation by this way: let's take a point at the middle of subsegment. If this point is strickly inside of some triangle then all subsegment is located inside and vice versa. We should calculate only subsegments located on the side of triangles and print their total length.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">If you are using integer numbers you should be careful for some operations like vector multiplication because it may leave 32-bit type.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">If you are using real numbers you should change you types for as large as possible for good precision (long long in c++, extended in pascal).</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Problem D. Wormhouse.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">In this problem you asks to find lexicographically next euler cycle or say that there is no way. Let's solve this problem backwards.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">We should repeat way of Arnie. Now it needs to rollback every his step and add edges for empty graph (graph without edges). Let's assume we had rollback edge from some vertix <span class="tex-span"><i>x</i></span> to vertix <span class="tex-span"><i>y</i></span>. We need to check is there some vertix <span class="tex-span"><i>z</i></span> that is connected to <span class="tex-span"><i>x</i></span> by an edge and value of <span class="tex-span"><i>z</i></span> is more than <span class="tex-span"><i>y</i></span>? Besides edge (<span class="tex-span"><i>x</i></span>; <span class="tex-span"><i>z</i></span>) shouldn't be a bridge because our component needs to be connected. </div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">No solution answer if it's impossible to find such <span class="tex-span"><i>z</i></span> at any step.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">But if edge (<span class="tex-span"><i>x</i></span>; <span class="tex-span"><i>z</i></span>) satisfied to conditions upper is exists let's change it to move and after this step our problem is to find lexicographically smallest euler way. It is possible to find only in unbreaked component of graph so every next step must going along non-brigde edges in vertix with as low number as possible. Of course, we must destroy unachievable vertices and do not destroy initial vertix.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">We can check is edge a bridge for O(<span class="tex-span"><i>E</i></span>) time by depth first search. Total difficulty of algorithm represented above is O(<span class="tex-span"><i>N</i>· <i>E</i><sup class="upper-index">2</sup></span>).</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Problem E. World Evil.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><i>Author of this problem is Vasily Vadimov, NNSU. He wrote her own tutorial for you.</i></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">In this problem you were to find the maximal flow in network with a cyllinder structure. The dynamic solution with complexity <span class="tex-span"><i>O</i>(<i>mn</i>2<sup class="upper-index"><i>n</i></sup>)</span> was considered.It's well known that the maximal flow is equal to value of the minimal cut. Also all the sources must belong to one part of the cut and all the drains --- to the other part. Then we look over all the vertices from the left to the right, from the top to the bottom and append to the one or the other part of the cut, recalculating the answer during the process. The trivial solution has complexity <span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>mn</i></sup>)</span> and doesn't fit the time limit.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">But we can notice the number add to the answer after appending a new vertice to some part of the cut depends only on what parts of the cut the vertices in the current and the previous columns belong to. So we can calculate such a value using dynamic programming: what is the minimal cut can be obtained by adding <span class="tex-span"><i>i</i></span> columns and the mask of belongings of vertices of the <span class="tex-span"><i>i</i></span>th column to the parts of the cut is <span class="tex-span"><i>mask</i></span>. Then we have <span class="tex-span">2<sup class="upper-index"><i>n</i></sup></span> conversions because there are <span class="tex-span">2<sup class="upper-index"><i>n</i></sup></span> different states of the <span class="tex-span"><i>i</i> - 1</span>th column. So we have the <span class="tex-span"><i>O</i>(<i>mn</i>2<sup class="upper-index">2<i>n</i></sup>)</span> solution.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">But this solution also can be improved. We calculate the minimal cut, if <span class="tex-span"><i>i</i> - 1</span> columns are added completely and <span class="tex-span"><i>j</i></span> vertices from the <span class="tex-span"><i>i</i></span>th column are added, and mask of belongings of vertices that have no neighbours on the right is <span class="tex-span"><i>mask</i></span>. Then we append <span class="tex-span"><i>j</i></span>-th vertice to one of the parts, recalculate the value of the cut and do the conversion. So we have <span class="tex-span"><i>mn</i>2<sup class="upper-index"><i>n</i></sup></span> conditions and <span class="tex-span"><i>O</i>(1)</span> conversions from the every condition and the solution's complexity is <span class="tex-span"><i>O</i>(<i>mn</i>2<sup class="upper-index"><i>n</i></sup>)</span>.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Also congratulations to the participants rng_58 and Ra16bit who solved this problem during the contest!<br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><i>Thanks to boys from NNSU (Vladislav Epifanov, Alexey Shmelev) who helps us with alternating solutions and etc.</i></div><div style="text-align: justify;"><i><br /></i></div><div style="text-align: justify;"><i>Sorry for poor english</i></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/62" class="notice" style="text-decoration: none;">Codeforces Beta Round 58</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-86-1363").click(function() { var that = this; 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top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="24708" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4531" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-24708"> <div class="moveup"> <div class="ttypography">I saw a lot of O(p.k) solutions pass in time after the contest end.I assume that they are tested against the same system tests used during the contest.<br /><br />Maybe few cases like<br />1 1<br />a<br />aa......a<br />where there are around 2*MAXN a's in the second line.(Actually this was a case that i were hacked with during the contest,but it failed due to a runtime error and not TLE).<br /><br />Another tricky case where people tricked their greedy to work incase we already dont have minimum |j-i| = 0, could be<br />1 1<br />a....ab.....b<br />b....ba.....a<br />where the a's and b's = MAXN/2<br /><br />MAXN = 99999 everywhere.<br /><br />O(p*k) solutions could use the above tests to understand why according to the problem setter were expected to TLE and might have got lucky on the judge.<br />Hope this helps.Appreciate any comments.</div> </div> </div> <div class="reply info"> <a class="comment-24708 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-24708 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-24708"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="24769" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kang205" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/kang205" title="Expert kang205" class="rated-user user-blue">kang205</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/27/2011 17:23">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-24769" href="?#comment-24769" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="24769" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="13097" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-24769"> <div class="moveup"> <div class="ttypography">Problem B<br />If you make a queue to find When you find closest position,it will be O(P) :D<br /><br />My Solution cost least time.</div> </div> </div> <div class="reply info"> <a class="comment-24769 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-24769 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-24769"> </ul> </div> <br/> <div id="editBox-1373" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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62D
62
D
en
D. Wormhouse
<div class="problem-statement"><div class="header"><div class="title">D. Wormhouse</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Arnie the Worm has finished eating an apple house yet again and decided to move. He made up his mind on the plan, the way the rooms are located and how they are joined by corridors. He numbered all the rooms from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span>. All the corridors are bidirectional.</p><p>Arnie wants the new house to look just like the previous one. That is, it should have exactly <span class="tex-span"><i>n</i></span> rooms and, if a corridor from room <span class="tex-span"><i>i</i></span> to room <span class="tex-span"><i>j</i></span> existed in the old house, it should be built in the new one. </p><p>We know that during the house constructing process Arnie starts to eat an apple starting from some room and only stops when he eats his way through all the corridors and returns to the starting room. It is also known that Arnie eats without stopping. That is, until Arnie finishes constructing the house, he is busy every moment of his time gnawing a new corridor. Arnie doesn't move along the already built corridors.</p><p>However, gnawing out corridors in one and the same order any time you change a house is a very difficult activity. That's why Arnie, knowing the order in which the corridors were located in the previous house, wants to gnaw corridors in another order. It is represented as a list of rooms in the order in which they should be visited. The new list should be lexicographically smallest, but it also should be strictly lexicographically greater than the previous one. Help the worm. </p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>m</i></span> (<span class="tex-span">3 ≤ <i>n</i> ≤ 100, 3 ≤ <i>m</i> ≤ 2000</span>). It is the number of rooms and corridors in Arnie's house correspondingly. The next line contains <span class="tex-span"><i>m</i> + 1</span> positive integers that do not exceed <span class="tex-span"><i>n</i></span>. They are the description of Arnie's old path represented as a list of rooms he visited during the gnawing. It is guaranteed that the last number in the list coincides with the first one.</p><p>The first room described in the list is the main entrance, that's why Arnie should begin gnawing from it.</p><p>You may assume that there is no room which is connected to itself and there is at most one corridor between any pair of rooms. However, it is possible to find some isolated rooms which are disconnected from others.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span"><i>m</i> + 1</span> positive integers that do not exceed <span class="tex-span"><i>n</i></span>. Those numbers are the description of the new path, according to which Arnie should gnaw out his new house. If it is impossible to find new path you should print out <span class="tex-font-style-tt">No solution</span>. The first number in your answer should be equal to the last one. Also it should be equal to the main entrance.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3 3<br/>1 2 3 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>1 3 2 1 </pre></div><div class="input"><div class="title">Input</div><pre>3 3<br/>1 3 2 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>No solution</pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="D" data-uuid="ps_0c946f1fe8acbb6c85f3c84d22d998e38fd5c455"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">D. Wormhouse</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Arnie the Worm has finished eating an apple house yet again and decided to move. He made up his mind on the plan, the way the rooms are located and how they are joined by corridors. He numbered all the rooms from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span>. All the corridors are bidirectional.</p><p>Arnie wants the new house to look just like the previous one. That is, it should have exactly <span class="tex-span"><i>n</i></span> rooms and, if a corridor from room <span class="tex-span"><i>i</i></span> to room <span class="tex-span"><i>j</i></span> existed in the old house, it should be built in the new one. </p><p>We know that during the house constructing process Arnie starts to eat an apple starting from some room and only stops when he eats his way through all the corridors and returns to the starting room. It is also known that Arnie eats without stopping. That is, until Arnie finishes constructing the house, he is busy every moment of his time gnawing a new corridor. Arnie doesn't move along the already built corridors.</p><p>However, gnawing out corridors in one and the same order any time you change a house is a very difficult activity. That's why Arnie, knowing the order in which the corridors were located in the previous house, wants to gnaw corridors in another order. It is represented as a list of rooms in the order in which they should be visited. The new list should be lexicographically smallest, but it also should be strictly lexicographically greater than the previous one. Help the worm. </p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>m</i></span> (<span class="tex-span">3 ≤ <i>n</i> ≤ 100, 3 ≤ <i>m</i> ≤ 2000</span>). It is the number of rooms and corridors in Arnie's house correspondingly. The next line contains <span class="tex-span"><i>m</i> + 1</span> positive integers that do not exceed <span class="tex-span"><i>n</i></span>. They are the description of Arnie's old path represented as a list of rooms he visited during the gnawing. It is guaranteed that the last number in the list coincides with the first one.</p><p>The first room described in the list is the main entrance, that's why Arnie should begin gnawing from it.</p><p>You may assume that there is no room which is connected to itself and there is at most one corridor between any pair of rooms. However, it is possible to find some isolated rooms which are disconnected from others.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span"><i>m</i> + 1</span> positive integers that do not exceed <span class="tex-span"><i>n</i></span>. Those numbers are the description of the new path, according to which Arnie should gnaw out his new house. If it is impossible to find new path you should print out <span class="tex-font-style-tt">No solution</span>. The first number in your answer should be equal to the last one. 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["Dfs and similar", "Graphs"]
["dfs and similar", "graphs", "*2300"]
https://codeforces.com/blog/entry/1363
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<a href="/blog/entry/120644">Codeforces Round 899 (Div. 2)</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/Misa-Misa" title="Expert Misa-Misa" class="rated-user user-blue">Misa-Misa</a> &rarr; <a href="/blog/entry/121157">Someone please help me understand this.</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/shivam565" title="Specialist shivam565" class="rated-user user-cyan">shivam565</a> &rarr; <a href="/blog/entry/108348">Total number of subarrays with sum atmost k</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> </ul> </div> <div class="bottom-links"> <table style="width:100%;"> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:right;"> <a href="/recent-actions">Detailed &rarr;</a> </td> </tr> </tbody> </table> </div> </div> </div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li><a href="/profile/Alex_KPR">Alex_KPR</a></li> <li class="current selectedLava"><a href="/blog/Alex_KPR">Blog</a></li> <li><a href="/teams/with/Alex_KPR">Teams</a></li> <li><a href="/submissions/Alex_KPR">Submissions</a></li> <li><a href="/contests/with/Alex_KPR">Contests</a></li> <li><a href="/contests/writer/Alex_KPR">Problemsetting</a></li> </ul> </div> <div style="margin-top:0;"> <div> <h3><a href="/blog/Alex_KPR" style="text-decoration:none;color:black !important;">Alex_KPR's blog</a></h3> </div> <div style="margin-top:2em;"> <div class="has-topic-id topic" topicId="1363"> <div class="title"> <a href="/blog/entry/1363"> Codeforces Beta Round #58 tutorial </a> </div> <div class="info" style="position:relative;"> By&nbsp;<a href="/profile/Alex_KPR" title="Master Alex_KPR" class="rated-user user-orange">Alex_KPR</a>, <span class="format-humantime" title="Feb/26/2011 14:56">13 years ago</span>, translation, <img style="position: relative;top: 5px;" src="//codeforces.org/s/81027/images/flags/24/gb.png" alt="In English" title="In English"/> <span style="position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;"> <div style="margin-top:0.25em;"> </div> </span> </div> <div class="content"> <div class="ttypography"><div style="text-align: justify;">Problem A. A Student's Dream.<br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">There was a lot of troubles because of incorrect statement. Now I hope statement is ok. Let's solve it. =)</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">If boy will goes to the left he will take her left hand with his right one and boy's left hand and girl's right hand will be unused. Situation is looks like the same if we swap them vice versa. So, we need to check two situations and choose the best one.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">There is a simple way to check comfortableness, let's assume that boy has <span class="tex-span"><i>B</i></span> fingers on active hand and girl has <span class="tex-span"><i>G</i></span> fingers on active hand, so:</div><div style="text-align: justify;"> <br /></div><div style="text-align: justify;"><ul><li>If <span class="tex-span"><i>B</i> &lt; <i>G</i></span> they will be happy only when <span class="tex-span"><i>B</i> = <i>G</i> - 1</span>, you may see a pattern <span class="tex-span"><i>GBGBGBG</i>...<i>GBGBG</i></span>. In this pattern you can add no girl's finger for save the condition in statement<br /></li><li>If <span class="tex-span"><i>B</i> &gt; <i>G</i></span> the worst but correct situation for them is a pattern <span class="tex-span"><i>BBGBBGBB</i>...<i>BBGBB</i></span>. As you may see this way must be satisfy <span class="tex-span">2<i>G</i> + 2 &gt;  = <i>B</i></span> condition<br /></li><li>Simple situation is <span class="tex-span"><i>B</i> = <i>G</i></span>, obviously answer is &quot;yes&quot;<br /></li></ul></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Problem B. Tyndex.Brome.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Let's define <span class="tex-span"><i>p</i></span> as total length of all potential addresses <span class="tex-span"><i>c</i></span>. In this problem obvious solution has O(<span class="tex-span"><i>p</i>· <i>k</i></span>) difficulty and it is getting a TLE verdict. Let's speed up it by next way: we will save all position of letters 'a', 'b', ..., 'z' in address entered by user <span class="tex-span"><i>s</i></span> separately in increasing order. After this step we can find closest position of letter <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span> in <span class="tex-span"><i>s</i></span> for logarithmic time by binary search. This solution has O(<span class="tex-span"><i>p</i> · <i>logk</i></span>) difficulty that gives &quot;accepted&quot;.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Look carefully for length of potential address (it can be more than <span class="tex-span">10<sup class="upper-index">5</sup></span>). Answer can be too big and asks you for using integer 64-bit type.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Problem C. Inquisition.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">All triangles are located strickly inside of square. It makes problem more simplify, because you don't need to check situations of touching sides.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Let's save all segments of every triangle and cross them in pairs. There are many points at every segment - the results of crossing. Look at the every subsegment which do not contain any points of crossing inside. There are two situations: this subsegment completely lie on the side of some triangle or this subsegment completely lie inside of some triangle.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">We may check what is situation by this way: let's take a point at the middle of subsegment. If this point is strickly inside of some triangle then all subsegment is located inside and vice versa. We should calculate only subsegments located on the side of triangles and print their total length.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">If you are using integer numbers you should be careful for some operations like vector multiplication because it may leave 32-bit type.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">If you are using real numbers you should change you types for as large as possible for good precision (long long in c++, extended in pascal).</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Problem D. Wormhouse.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">In this problem you asks to find lexicographically next euler cycle or say that there is no way. Let's solve this problem backwards.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">We should repeat way of Arnie. Now it needs to rollback every his step and add edges for empty graph (graph without edges). Let's assume we had rollback edge from some vertix <span class="tex-span"><i>x</i></span> to vertix <span class="tex-span"><i>y</i></span>. We need to check is there some vertix <span class="tex-span"><i>z</i></span> that is connected to <span class="tex-span"><i>x</i></span> by an edge and value of <span class="tex-span"><i>z</i></span> is more than <span class="tex-span"><i>y</i></span>? Besides edge (<span class="tex-span"><i>x</i></span>; <span class="tex-span"><i>z</i></span>) shouldn't be a bridge because our component needs to be connected. </div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">No solution answer if it's impossible to find such <span class="tex-span"><i>z</i></span> at any step.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">But if edge (<span class="tex-span"><i>x</i></span>; <span class="tex-span"><i>z</i></span>) satisfied to conditions upper is exists let's change it to move and after this step our problem is to find lexicographically smallest euler way. It is possible to find only in unbreaked component of graph so every next step must going along non-brigde edges in vertix with as low number as possible. Of course, we must destroy unachievable vertices and do not destroy initial vertix.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">We can check is edge a bridge for O(<span class="tex-span"><i>E</i></span>) time by depth first search. Total difficulty of algorithm represented above is O(<span class="tex-span"><i>N</i>· <i>E</i><sup class="upper-index">2</sup></span>).</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Problem E. World Evil.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><i>Author of this problem is Vasily Vadimov, NNSU. He wrote her own tutorial for you.</i></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">In this problem you were to find the maximal flow in network with a cyllinder structure. The dynamic solution with complexity <span class="tex-span"><i>O</i>(<i>mn</i>2<sup class="upper-index"><i>n</i></sup>)</span> was considered.It's well known that the maximal flow is equal to value of the minimal cut. Also all the sources must belong to one part of the cut and all the drains --- to the other part. Then we look over all the vertices from the left to the right, from the top to the bottom and append to the one or the other part of the cut, recalculating the answer during the process. The trivial solution has complexity <span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>mn</i></sup>)</span> and doesn't fit the time limit.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">But we can notice the number add to the answer after appending a new vertice to some part of the cut depends only on what parts of the cut the vertices in the current and the previous columns belong to. So we can calculate such a value using dynamic programming: what is the minimal cut can be obtained by adding <span class="tex-span"><i>i</i></span> columns and the mask of belongings of vertices of the <span class="tex-span"><i>i</i></span>th column to the parts of the cut is <span class="tex-span"><i>mask</i></span>. Then we have <span class="tex-span">2<sup class="upper-index"><i>n</i></sup></span> conversions because there are <span class="tex-span">2<sup class="upper-index"><i>n</i></sup></span> different states of the <span class="tex-span"><i>i</i> - 1</span>th column. So we have the <span class="tex-span"><i>O</i>(<i>mn</i>2<sup class="upper-index">2<i>n</i></sup>)</span> solution.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">But this solution also can be improved. We calculate the minimal cut, if <span class="tex-span"><i>i</i> - 1</span> columns are added completely and <span class="tex-span"><i>j</i></span> vertices from the <span class="tex-span"><i>i</i></span>th column are added, and mask of belongings of vertices that have no neighbours on the right is <span class="tex-span"><i>mask</i></span>. Then we append <span class="tex-span"><i>j</i></span>-th vertice to one of the parts, recalculate the value of the cut and do the conversion. So we have <span class="tex-span"><i>mn</i>2<sup class="upper-index"><i>n</i></sup></span> conditions and <span class="tex-span"><i>O</i>(1)</span> conversions from the every condition and the solution's complexity is <span class="tex-span"><i>O</i>(<i>mn</i>2<sup class="upper-index"><i>n</i></sup>)</span>.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Also congratulations to the participants rng_58 and Ra16bit who solved this problem during the contest!<br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><i>Thanks to boys from NNSU (Vladislav Epifanov, Alexey Shmelev) who helps us with alternating solutions and etc.</i></div><div style="text-align: justify;"><i><br /></i></div><div style="text-align: justify;"><i>Sorry for poor english</i></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/62" class="notice" style="text-decoration: none;">Codeforces Beta Round 58</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-86-1363").click(function() { var that = this; 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top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="24708" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4531" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-24708"> <div class="moveup"> <div class="ttypography">I saw a lot of O(p.k) solutions pass in time after the contest end.I assume that they are tested against the same system tests used during the contest.<br /><br />Maybe few cases like<br />1 1<br />a<br />aa......a<br />where there are around 2*MAXN a's in the second line.(Actually this was a case that i were hacked with during the contest,but it failed due to a runtime error and not TLE).<br /><br />Another tricky case where people tricked their greedy to work incase we already dont have minimum |j-i| = 0, could be<br />1 1<br />a....ab.....b<br />b....ba.....a<br />where the a's and b's = MAXN/2<br /><br />MAXN = 99999 everywhere.<br /><br />O(p*k) solutions could use the above tests to understand why according to the problem setter were expected to TLE and might have got lucky on the judge.<br />Hope this helps.Appreciate any comments.</div> </div> </div> <div class="reply info"> <a class="comment-24708 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-24708 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-24708"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="24769" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kang205" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/kang205" title="Expert kang205" class="rated-user user-blue">kang205</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/27/2011 17:23">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-24769" href="?#comment-24769" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="24769" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="13097" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-24769"> <div class="moveup"> <div class="ttypography">Problem B<br />If you make a queue to find When you find closest position,it will be O(P) :D<br /><br />My Solution cost least time.</div> </div> </div> <div class="reply info"> <a class="comment-24769 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-24769 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-24769"> </ul> </div> <br/> <div id="editBox-1373" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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62E
62
E
en
E. World Evil
<div class="problem-statement"><div class="header"><div class="title">E. World Evil</div><div class="time-limit"><div class="property-title">time limit per test</div>5 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>As a result of Pinky and Brain's mysterious experiments in the Large Hadron Collider some portals or black holes opened to the parallel dimension. And the World Evil has crept to the veil between their world and ours. Brain quickly evaluated the situation and he understood that the more evil tentacles creep out and become free, the higher is the possibility that Brain will rule the world.</p><p>The collider's constriction is a rectangular grid rolled into a cylinder and consisting of <span class="tex-span"><i>n</i></span> rows and <span class="tex-span"><i>m</i></span> columns such as is shown in the picture below:</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/4e10a3e9266cb910e1524bed0390c5c8980df589.png" style="max-width: 100.0%;max-height: 100.0%;"/> </center><p>In this example <span class="tex-span"><i>n</i> = 4</span>, <span class="tex-span"><i>m</i> = 5</span>. Dotted lines are corridores that close each column to a ring, i. e. connect the <span class="tex-span"><i>n</i></span>-th and the <span class="tex-span">1</span>-th rows of the grid.</p><p>In the leftmost column of the grid the portals are situated and the tentacles of the World Evil are ready to creep out from there. In the rightmost column the exit doors are located. The tentacles can only get out through those doors. The segments joining the nodes of the grid are corridors.</p><p>Brain would be glad to let all the tentacles out but he faces a problem: the infinite number of tentacles can creep out of the portals, every tentacle possesses infinite length and some width and the volume of the corridors are, unfortunately, quite limited. Brain could approximately evaluate the maximal number of tentacles that will be able to crawl through every corridor.</p><p>Now help the mice to determine the maximal number of tentacles of the World Evil that will crawl out of the Large Hadron Collider.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of the input file contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>m</i></span> (<span class="tex-span">2 ≤ <i>n</i> ≤ 5</span>, <span class="tex-span">2 ≤ <i>m</i> ≤ 10<sup class="upper-index">5</sup></span>). They are the sizes of the Large Hadron Collider grid. The next <span class="tex-span"><i>m</i> - 1</span> lines contain <span class="tex-span"><i>n</i></span> numbers each. They are the horizontal corridors' capacities. The next <span class="tex-span"><i>m</i></span> lines contain <span class="tex-span"><i>n</i></span> numbers each. They are the vertical corridors' capacities. Corridors are described from left to right and from top to bottom. Every <span class="tex-span"><i>n</i></span>-th vertical corridor connects nodes of the <span class="tex-span"><i>n</i></span>-th and <span class="tex-span">1</span>-th rows. A corridor's capacity is a non-negative integer that does not exceed <span class="tex-span">10<sup class="upper-index">9</sup></span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single number, the number of the World Evil tentacles Pinky and Brain will command.</p><p>Please, do not use <span class="tex-font-style-tt">%lld</span> specificator to read or write 64-bit integers in C++. It is preffered to use <span class="tex-font-style-tt">cout</span> (also you may use <span class="tex-font-style-tt">%I64d</span>).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3 4<br/>4 4 4<br/>1 1 5<br/>5 5 3<br/>4 1 2<br/>1 3 1<br/>3 5 4<br/>1 4 3<br/></pre></div><div class="output"><div class="title">Output</div><pre>7<br/></pre></div><div class="input"><div class="title">Input</div><pre>2 2<br/>9 2<br/>2 3<br/>6 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>11<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="E" data-uuid="ps_c4d6362cd5418df1f6150f3e07c6837a4557fe02"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">E. World Evil</div><div class="time-limit"><div class="property-title">time limit per test</div>5 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>As a result of Pinky and Brain's mysterious experiments in the Large Hadron Collider some portals or black holes opened to the parallel dimension. And the World Evil has crept to the veil between their world and ours. Brain quickly evaluated the situation and he understood that the more evil tentacles creep out and become free, the higher is the possibility that Brain will rule the world.</p><p>The collider's constriction is a rectangular grid rolled into a cylinder and consisting of <span class="tex-span"><i>n</i></span> rows and <span class="tex-span"><i>m</i></span> columns such as is shown in the picture below:</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/4e10a3e9266cb910e1524bed0390c5c8980df589.png" style="max-width: 100.0%;max-height: 100.0%;" /> </center><p>In this example <span class="tex-span"><i>n</i> = 4</span>, <span class="tex-span"><i>m</i> = 5</span>. Dotted lines are corridores that close each column to a ring, i. e. connect the <span class="tex-span"><i>n</i></span>-th and the <span class="tex-span">1</span>-th rows of the grid.</p><p>In the leftmost column of the grid the portals are situated and the tentacles of the World Evil are ready to creep out from there. In the rightmost column the exit doors are located. The tentacles can only get out through those doors. The segments joining the nodes of the grid are corridors.</p><p>Brain would be glad to let all the tentacles out but he faces a problem: the infinite number of tentacles can creep out of the portals, every tentacle possesses infinite length and some width and the volume of the corridors are, unfortunately, quite limited. Brain could approximately evaluate the maximal number of tentacles that will be able to crawl through every corridor.</p><p>Now help the mice to determine the maximal number of tentacles of the World Evil that will crawl out of the Large Hadron Collider.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of the input file contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>m</i></span> (<span class="tex-span">2 ≤ <i>n</i> ≤ 5</span>, <span class="tex-span">2 ≤ <i>m</i> ≤ 10<sup class="upper-index">5</sup></span>). They are the sizes of the Large Hadron Collider grid. The next <span class="tex-span"><i>m</i> - 1</span> lines contain <span class="tex-span"><i>n</i></span> numbers each. They are the horizontal corridors' capacities. The next <span class="tex-span"><i>m</i></span> lines contain <span class="tex-span"><i>n</i></span> numbers each. They are the vertical corridors' capacities. Corridors are described from left to right and from top to bottom. Every <span class="tex-span"><i>n</i></span>-th vertical corridor connects nodes of the <span class="tex-span"><i>n</i></span>-th and <span class="tex-span">1</span>-th rows. A corridor's capacity is a non-negative integer that does not exceed <span class="tex-span">10<sup class="upper-index">9</sup></span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single number, the number of the World Evil tentacles Pinky and Brain will command.</p><p>Please, do not use <span class="tex-font-style-tt">%lld</span> specificator to read or write 64-bit integers in C++. It is preffered to use <span class="tex-font-style-tt">cout</span> (also you may use <span class="tex-font-style-tt">%I64d</span>).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3 4<br />4 4 4<br />1 1 5<br />5 5 3<br />4 1 2<br />1 3 1<br />3 5 4<br />1 4 3<br /></pre></div><div class="output"><div class="title">Output</div><pre>7<br /></pre></div><div class="input"><div class="title">Input</div><pre>2 2<br />9 2<br />2 3<br />6 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>11<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=E]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); if (previousStatementText) { if (previousStatementText !== statementText) { $problem.find(".diff-notifier").show(); 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["Dynamic programming", "Graph network flows"]
["dp", "flows", "*2700"]
https://codeforces.com/blog/entry/1363
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<a href="/blog/entry/120644">Codeforces Round 899 (Div. 2)</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/Misa-Misa" title="Expert Misa-Misa" class="rated-user user-blue">Misa-Misa</a> &rarr; <a href="/blog/entry/121157">Someone please help me understand this.</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/shivam565" title="Specialist shivam565" class="rated-user user-cyan">shivam565</a> &rarr; <a href="/blog/entry/108348">Total number of subarrays with sum atmost k</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> </ul> </div> <div class="bottom-links"> <table style="width:100%;"> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:right;"> <a href="/recent-actions">Detailed &rarr;</a> </td> </tr> </tbody> </table> </div> </div> </div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li><a href="/profile/Alex_KPR">Alex_KPR</a></li> <li class="current selectedLava"><a href="/blog/Alex_KPR">Blog</a></li> <li><a href="/teams/with/Alex_KPR">Teams</a></li> <li><a href="/submissions/Alex_KPR">Submissions</a></li> <li><a href="/contests/with/Alex_KPR">Contests</a></li> <li><a href="/contests/writer/Alex_KPR">Problemsetting</a></li> </ul> </div> <div style="margin-top:0;"> <div> <h3><a href="/blog/Alex_KPR" style="text-decoration:none;color:black !important;">Alex_KPR's blog</a></h3> </div> <div style="margin-top:2em;"> <div class="has-topic-id topic" topicId="1363"> <div class="title"> <a href="/blog/entry/1363"> Codeforces Beta Round #58 tutorial </a> </div> <div class="info" style="position:relative;"> By&nbsp;<a href="/profile/Alex_KPR" title="Master Alex_KPR" class="rated-user user-orange">Alex_KPR</a>, <span class="format-humantime" title="Feb/26/2011 14:56">13 years ago</span>, translation, <img style="position: relative;top: 5px;" src="//codeforces.org/s/81027/images/flags/24/gb.png" alt="In English" title="In English"/> <span style="position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;"> <div style="margin-top:0.25em;"> </div> </span> </div> <div class="content"> <div class="ttypography"><div style="text-align: justify;">Problem A. A Student's Dream.<br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">There was a lot of troubles because of incorrect statement. Now I hope statement is ok. Let's solve it. =)</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">If boy will goes to the left he will take her left hand with his right one and boy's left hand and girl's right hand will be unused. Situation is looks like the same if we swap them vice versa. So, we need to check two situations and choose the best one.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">There is a simple way to check comfortableness, let's assume that boy has <span class="tex-span"><i>B</i></span> fingers on active hand and girl has <span class="tex-span"><i>G</i></span> fingers on active hand, so:</div><div style="text-align: justify;"> <br /></div><div style="text-align: justify;"><ul><li>If <span class="tex-span"><i>B</i> &lt; <i>G</i></span> they will be happy only when <span class="tex-span"><i>B</i> = <i>G</i> - 1</span>, you may see a pattern <span class="tex-span"><i>GBGBGBG</i>...<i>GBGBG</i></span>. In this pattern you can add no girl's finger for save the condition in statement<br /></li><li>If <span class="tex-span"><i>B</i> &gt; <i>G</i></span> the worst but correct situation for them is a pattern <span class="tex-span"><i>BBGBBGBB</i>...<i>BBGBB</i></span>. As you may see this way must be satisfy <span class="tex-span">2<i>G</i> + 2 &gt;  = <i>B</i></span> condition<br /></li><li>Simple situation is <span class="tex-span"><i>B</i> = <i>G</i></span>, obviously answer is &quot;yes&quot;<br /></li></ul></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Problem B. Tyndex.Brome.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Let's define <span class="tex-span"><i>p</i></span> as total length of all potential addresses <span class="tex-span"><i>c</i></span>. In this problem obvious solution has O(<span class="tex-span"><i>p</i>· <i>k</i></span>) difficulty and it is getting a TLE verdict. Let's speed up it by next way: we will save all position of letters 'a', 'b', ..., 'z' in address entered by user <span class="tex-span"><i>s</i></span> separately in increasing order. After this step we can find closest position of letter <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span> in <span class="tex-span"><i>s</i></span> for logarithmic time by binary search. This solution has O(<span class="tex-span"><i>p</i> · <i>logk</i></span>) difficulty that gives &quot;accepted&quot;.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Look carefully for length of potential address (it can be more than <span class="tex-span">10<sup class="upper-index">5</sup></span>). Answer can be too big and asks you for using integer 64-bit type.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Problem C. Inquisition.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">All triangles are located strickly inside of square. It makes problem more simplify, because you don't need to check situations of touching sides.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Let's save all segments of every triangle and cross them in pairs. There are many points at every segment - the results of crossing. Look at the every subsegment which do not contain any points of crossing inside. There are two situations: this subsegment completely lie on the side of some triangle or this subsegment completely lie inside of some triangle.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">We may check what is situation by this way: let's take a point at the middle of subsegment. If this point is strickly inside of some triangle then all subsegment is located inside and vice versa. We should calculate only subsegments located on the side of triangles and print their total length.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">If you are using integer numbers you should be careful for some operations like vector multiplication because it may leave 32-bit type.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">If you are using real numbers you should change you types for as large as possible for good precision (long long in c++, extended in pascal).</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Problem D. Wormhouse.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">In this problem you asks to find lexicographically next euler cycle or say that there is no way. Let's solve this problem backwards.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">We should repeat way of Arnie. Now it needs to rollback every his step and add edges for empty graph (graph without edges). Let's assume we had rollback edge from some vertix <span class="tex-span"><i>x</i></span> to vertix <span class="tex-span"><i>y</i></span>. We need to check is there some vertix <span class="tex-span"><i>z</i></span> that is connected to <span class="tex-span"><i>x</i></span> by an edge and value of <span class="tex-span"><i>z</i></span> is more than <span class="tex-span"><i>y</i></span>? Besides edge (<span class="tex-span"><i>x</i></span>; <span class="tex-span"><i>z</i></span>) shouldn't be a bridge because our component needs to be connected. </div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">No solution answer if it's impossible to find such <span class="tex-span"><i>z</i></span> at any step.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">But if edge (<span class="tex-span"><i>x</i></span>; <span class="tex-span"><i>z</i></span>) satisfied to conditions upper is exists let's change it to move and after this step our problem is to find lexicographically smallest euler way. It is possible to find only in unbreaked component of graph so every next step must going along non-brigde edges in vertix with as low number as possible. Of course, we must destroy unachievable vertices and do not destroy initial vertix.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">We can check is edge a bridge for O(<span class="tex-span"><i>E</i></span>) time by depth first search. Total difficulty of algorithm represented above is O(<span class="tex-span"><i>N</i>· <i>E</i><sup class="upper-index">2</sup></span>).</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Problem E. World Evil.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><i>Author of this problem is Vasily Vadimov, NNSU. He wrote her own tutorial for you.</i></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">In this problem you were to find the maximal flow in network with a cyllinder structure. The dynamic solution with complexity <span class="tex-span"><i>O</i>(<i>mn</i>2<sup class="upper-index"><i>n</i></sup>)</span> was considered.It's well known that the maximal flow is equal to value of the minimal cut. Also all the sources must belong to one part of the cut and all the drains --- to the other part. Then we look over all the vertices from the left to the right, from the top to the bottom and append to the one or the other part of the cut, recalculating the answer during the process. The trivial solution has complexity <span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>mn</i></sup>)</span> and doesn't fit the time limit.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">But we can notice the number add to the answer after appending a new vertice to some part of the cut depends only on what parts of the cut the vertices in the current and the previous columns belong to. So we can calculate such a value using dynamic programming: what is the minimal cut can be obtained by adding <span class="tex-span"><i>i</i></span> columns and the mask of belongings of vertices of the <span class="tex-span"><i>i</i></span>th column to the parts of the cut is <span class="tex-span"><i>mask</i></span>. Then we have <span class="tex-span">2<sup class="upper-index"><i>n</i></sup></span> conversions because there are <span class="tex-span">2<sup class="upper-index"><i>n</i></sup></span> different states of the <span class="tex-span"><i>i</i> - 1</span>th column. So we have the <span class="tex-span"><i>O</i>(<i>mn</i>2<sup class="upper-index">2<i>n</i></sup>)</span> solution.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">But this solution also can be improved. We calculate the minimal cut, if <span class="tex-span"><i>i</i> - 1</span> columns are added completely and <span class="tex-span"><i>j</i></span> vertices from the <span class="tex-span"><i>i</i></span>th column are added, and mask of belongings of vertices that have no neighbours on the right is <span class="tex-span"><i>mask</i></span>. Then we append <span class="tex-span"><i>j</i></span>-th vertice to one of the parts, recalculate the value of the cut and do the conversion. So we have <span class="tex-span"><i>mn</i>2<sup class="upper-index"><i>n</i></sup></span> conditions and <span class="tex-span"><i>O</i>(1)</span> conversions from the every condition and the solution's complexity is <span class="tex-span"><i>O</i>(<i>mn</i>2<sup class="upper-index"><i>n</i></sup>)</span>.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Also congratulations to the participants rng_58 and Ra16bit who solved this problem during the contest!<br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><i>Thanks to boys from NNSU (Vladislav Epifanov, Alexey Shmelev) who helps us with alternating solutions and etc.</i></div><div style="text-align: justify;"><i><br /></i></div><div style="text-align: justify;"><i>Sorry for poor english</i></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/62" class="notice" style="text-decoration: none;">Codeforces Beta Round 58</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-86-1363").click(function() { var that = this; 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top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="24708" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4531" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-24708"> <div class="moveup"> <div class="ttypography">I saw a lot of O(p.k) solutions pass in time after the contest end.I assume that they are tested against the same system tests used during the contest.<br /><br />Maybe few cases like<br />1 1<br />a<br />aa......a<br />where there are around 2*MAXN a's in the second line.(Actually this was a case that i were hacked with during the contest,but it failed due to a runtime error and not TLE).<br /><br />Another tricky case where people tricked their greedy to work incase we already dont have minimum |j-i| = 0, could be<br />1 1<br />a....ab.....b<br />b....ba.....a<br />where the a's and b's = MAXN/2<br /><br />MAXN = 99999 everywhere.<br /><br />O(p*k) solutions could use the above tests to understand why according to the problem setter were expected to TLE and might have got lucky on the judge.<br />Hope this helps.Appreciate any comments.</div> </div> </div> <div class="reply info"> <a class="comment-24708 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-24708 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-24708"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="24769" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kang205" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/kang205" title="Expert kang205" class="rated-user user-blue">kang205</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/27/2011 17:23">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-24769" href="?#comment-24769" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="24769" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="13097" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-24769"> <div class="moveup"> <div class="ttypography">Problem B<br />If you make a queue to find When you find closest position,it will be O(P) :D<br /><br />My Solution cost least time.</div> </div> </div> <div class="reply info"> <a class="comment-24769 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-24769 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-24769"> </ul> </div> <br/> <div id="editBox-1373" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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63A
63
A
en
A. Sinking Ship
<div class="problem-statement"><div class="header"><div class="title">A. Sinking Ship</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>The ship crashed into a reef and is sinking. Now the entire crew must be evacuated. All <span class="tex-span"><i>n</i></span> crew members have already lined up in a row (for convenience let's label them all from left to right with positive integers from 1 to <span class="tex-span"><i>n</i></span>) and await further instructions. However, one should evacuate the crew properly, in a strict order. Specifically:</p><p>The first crew members to leave the ship are rats. Then women and children (both groups have the same priority) leave the ship. After that all men are evacuated from the ship. The captain leaves the sinking ship last.</p><p>If we cannot determine exactly who should leave the ship first for any two members of the crew by the rules from the previous paragraph, then the one who stands to the left in the line leaves the ship first (or in other words, the one whose number in the line is less).</p><p>For each crew member we know his status as a crew member, and also his name. All crew members have different names. Determine the order in which to evacuate the crew.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains an integer <span class="tex-span"><i>n</i></span>, which is the number of people in the crew (<span class="tex-span">1 ≤ <i>n</i> ≤ 100</span>). Then follow <span class="tex-span"><i>n</i></span> lines. The <span class="tex-span"><i>i</i></span>-th of those lines contains two words — the name of the crew member who is <span class="tex-span"><i>i</i></span>-th in line, and his status on the ship. The words are separated by exactly one space. There are no other spaces in the line. The names consist of Latin letters, the first letter is uppercase, the rest are lowercase. The length of any name is from 1 to 10 characters. The status can have the following values: <span class="tex-font-style-tt">rat</span> for a rat, <span class="tex-font-style-tt">woman</span> for a woman, <span class="tex-font-style-tt">child</span> for a child, <span class="tex-font-style-tt">man</span> for a man, <span class="tex-font-style-tt">captain</span> for the captain. The crew contains exactly one captain.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span"><i>n</i></span> lines. The <span class="tex-span"><i>i</i></span>-th of them should contain the name of the crew member who must be the <span class="tex-span"><i>i</i></span>-th one to leave the ship.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>6<br/>Jack captain<br/>Alice woman<br/>Charlie man<br/>Teddy rat<br/>Bob child<br/>Julia woman<br/></pre></div><div class="output"><div class="title">Output</div><pre>Teddy<br/>Alice<br/>Bob<br/>Julia<br/>Charlie<br/>Jack<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="A" data-uuid="ps_6c8dcf082c25e88aeb61248a176f907b141d2268"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">A. Sinking Ship</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>The ship crashed into a reef and is sinking. Now the entire crew must be evacuated. All <span class="tex-span"><i>n</i></span> crew members have already lined up in a row (for convenience let's label them all from left to right with positive integers from 1 to <span class="tex-span"><i>n</i></span>) and await further instructions. However, one should evacuate the crew properly, in a strict order. Specifically:</p><p>The first crew members to leave the ship are rats. Then women and children (both groups have the same priority) leave the ship. After that all men are evacuated from the ship. The captain leaves the sinking ship last.</p><p>If we cannot determine exactly who should leave the ship first for any two members of the crew by the rules from the previous paragraph, then the one who stands to the left in the line leaves the ship first (or in other words, the one whose number in the line is less).</p><p>For each crew member we know his status as a crew member, and also his name. All crew members have different names. Determine the order in which to evacuate the crew.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains an integer <span class="tex-span"><i>n</i></span>, which is the number of people in the crew (<span class="tex-span">1 ≤ <i>n</i> ≤ 100</span>). Then follow <span class="tex-span"><i>n</i></span> lines. The <span class="tex-span"><i>i</i></span>-th of those lines contains two words — the name of the crew member who is <span class="tex-span"><i>i</i></span>-th in line, and his status on the ship. The words are separated by exactly one space. There are no other spaces in the line. The names consist of Latin letters, the first letter is uppercase, the rest are lowercase. The length of any name is from 1 to 10 characters. The status can have the following values: <span class="tex-font-style-tt">rat</span> for a rat, <span class="tex-font-style-tt">woman</span> for a woman, <span class="tex-font-style-tt">child</span> for a child, <span class="tex-font-style-tt">man</span> for a man, <span class="tex-font-style-tt">captain</span> for the captain. The crew contains exactly one captain.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span"><i>n</i></span> lines. The <span class="tex-span"><i>i</i></span>-th of them should contain the name of the crew member who must be the <span class="tex-span"><i>i</i></span>-th one to leave the ship.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>6<br />Jack captain<br />Alice woman<br />Charlie man<br />Teddy rat<br />Bob child<br />Julia woman<br /></pre></div><div class="output"><div class="title">Output</div><pre>Teddy<br />Alice<br />Bob<br />Julia<br />Charlie<br />Jack<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=A]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); if (previousStatementText) { if (previousStatementText !== statementText) { $problem.find(".diff-notifier").show(); 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["Implementation problems, programming technics, simulation", "Sortings, orderings", "Prefix- and Z-functions, suffix structures, Knuth\u2013Morris\u2013Pratt algorithm, etc"]
["implementation", "sortings", "strings", "*900"]
https://codeforces.com/blog/entry/1391
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63B
63
B
en
B. Settlers' Training
<div class="problem-statement"><div class="header"><div class="title">B. Settlers' Training</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>In a strategic computer game "Settlers II" one has to build defense structures to expand and protect the territory. Let's take one of these buildings. At the moment the defense structure accommodates exactly <span class="tex-span"><i>n</i></span> soldiers. Within this task we can assume that the number of soldiers in the defense structure won't either increase or decrease.</p><p>Every soldier has a rank — some natural number from <span class="tex-span">1</span> to <span class="tex-span"><i>k</i></span>. <span class="tex-span">1</span> stands for a private and <span class="tex-span"><i>k</i></span> stands for a general. The higher the rank of the soldier is, the better he fights. Therefore, the player profits from having the soldiers of the highest possible rank.</p><p>To increase the ranks of soldiers they need to train. But the soldiers won't train for free, and each training session requires one golden coin. On each training session all the <span class="tex-span"><i>n</i></span> soldiers are present.</p><p>At the end of each training session the soldiers' ranks increase as follows. First all the soldiers are divided into groups with the same rank, so that the least possible number of groups is formed. Then, within each of the groups where the soldiers below the rank <span class="tex-span"><i>k</i></span> are present, exactly one soldier increases his rank by one.</p><p>You know the ranks of all <span class="tex-span"><i>n</i></span> soldiers at the moment. Determine the number of golden coins that are needed to increase the ranks of all the soldiers to the rank <span class="tex-span"><i>k</i></span>.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>n</i>, <i>k</i> ≤ 100</span>). They represent the number of soldiers and the number of different ranks correspondingly. The second line contains <span class="tex-span"><i>n</i></span> numbers <span class="tex-font-style-bf">in the non-decreasing order</span>. The <span class="tex-span"><i>i</i></span>-th of them, <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span>, represents the rank of the <span class="tex-span"><i>i</i></span>-th soldier in the defense building (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>n</i></span>, <span class="tex-span">1 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ <i>k</i></span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single integer — the number of golden coins needed to raise all the soldiers to the maximal rank.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>4 4<br/>1 2 2 3<br/></pre></div><div class="output"><div class="title">Output</div><pre>4</pre></div><div class="input"><div class="title">Input</div><pre>4 3<br/>1 1 1 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>5</pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first example the ranks will be raised in the following manner:</p><p><span class="tex-font-style-tt">1 2 2 3</span> <span class="tex-span"> → </span> <span class="tex-font-style-tt">2 2 3 4</span> <span class="tex-span"> → </span> <span class="tex-font-style-tt">2 3 4 4</span> <span class="tex-span"> → </span> <span class="tex-font-style-tt">3 4 4 4</span> <span class="tex-span"> → </span> <span class="tex-font-style-tt">4 4 4 4</span></p><p>Thus totals to 4 training sessions that require 4 golden coins.</p></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/63">Codeforces Beta Round 59 (Div. 2)</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? Just register for practice and you will be able to submit solutions. </div> <div style="text-align:center;margin:1em;"> <form action="" method="post"><input type='hidden' name='csrf_token' value='5f5491514a3dd96c9f10fbee7d7bdb89'/> <input type="hidden" name="action" value="registerForPractice"/> <input type="submit" name="submit" value="Register for practice" style="padding:0 0.5em;"> </form> </div> </div> </div> <div class="roundbox sidebox ContestVirtualFrame borderTopRound " style=""> <div class="caption titled">&rarr; Virtual participation <i class="sidebar-caption-icon las la-angle-down"></i> <div class="top-links"> </div> </div> <div style=" " data-page-url="/data/sidebarFrames" > <div style="margin:1em;font-size:0.8em;"> Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests. If you've seen these problems, a virtual contest is not for you - solve these problems in the archive. If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="B" data-uuid="ps_cfdb8d99c21764e652ea9ce0dd91fe66daf1f1f2"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">B. Settlers' Training</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>In a strategic computer game &quot;Settlers II&quot; one has to build defense structures to expand and protect the territory. Let's take one of these buildings. At the moment the defense structure accommodates exactly <span class="tex-span"><i>n</i></span> soldiers. Within this task we can assume that the number of soldiers in the defense structure won't either increase or decrease.</p><p>Every soldier has a rank — some natural number from <span class="tex-span">1</span> to <span class="tex-span"><i>k</i></span>. <span class="tex-span">1</span> stands for a private and <span class="tex-span"><i>k</i></span> stands for a general. The higher the rank of the soldier is, the better he fights. Therefore, the player profits from having the soldiers of the highest possible rank.</p><p>To increase the ranks of soldiers they need to train. But the soldiers won't train for free, and each training session requires one golden coin. On each training session all the <span class="tex-span"><i>n</i></span> soldiers are present.</p><p>At the end of each training session the soldiers' ranks increase as follows. First all the soldiers are divided into groups with the same rank, so that the least possible number of groups is formed. Then, within each of the groups where the soldiers below the rank <span class="tex-span"><i>k</i></span> are present, exactly one soldier increases his rank by one.</p><p>You know the ranks of all <span class="tex-span"><i>n</i></span> soldiers at the moment. Determine the number of golden coins that are needed to increase the ranks of all the soldiers to the rank <span class="tex-span"><i>k</i></span>.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>n</i>, <i>k</i> ≤ 100</span>). They represent the number of soldiers and the number of different ranks correspondingly. The second line contains <span class="tex-span"><i>n</i></span> numbers <span class="tex-font-style-bf">in the non-decreasing order</span>. The <span class="tex-span"><i>i</i></span>-th of them, <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span>, represents the rank of the <span class="tex-span"><i>i</i></span>-th soldier in the defense building (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>n</i></span>, <span class="tex-span">1 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ <i>k</i></span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single integer — the number of golden coins needed to raise all the soldiers to the maximal rank.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>4 4<br />1 2 2 3<br /></pre></div><div class="output"><div class="title">Output</div><pre>4</pre></div><div class="input"><div class="title">Input</div><pre>4 3<br />1 1 1 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>5</pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first example the ranks will be raised in the following manner:</p><p><span class="tex-font-style-tt">1 2 2 3</span> <span class="tex-span"> → </span> <span class="tex-font-style-tt">2 2 3 4</span> <span class="tex-span"> → </span> <span class="tex-font-style-tt">2 3 4 4</span> <span class="tex-span"> → </span> <span class="tex-font-style-tt">3 4 4 4</span> <span class="tex-span"> → </span> <span class="tex-font-style-tt">4 4 4 4</span></p><p>Thus totals to 4 training sessions that require 4 golden coins.</p></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=B]"); 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["Implementation problems, programming technics, simulation"]
["implementation", "*1200"]
https://codeforces.com/blog/entry/1391
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63C
63
C
en
C. Bulls and Cows
<div class="problem-statement"><div class="header"><div class="title">C. Bulls and Cows</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>The "Bulls and Cows" game needs two people to play. The thinker thinks of a number and the guesser tries to guess it.</p><p>The thinker thinks of a four-digit number in the decimal system. All the digits in the number are different and the number may have a leading zero. It can't have more than one leading zero, because all it's digits should be different. The guesser tries to guess the number. He makes a series of guesses, trying experimental numbers and receives answers from the first person in the format "<span class="tex-span"><i>x</i></span> bulls <span class="tex-span"><i>y</i></span> cows". <span class="tex-span"><i>x</i></span> represents the number of digits in the experimental number that occupy the same positions as in the sought number. <span class="tex-span"><i>y</i></span> represents the number of digits of the experimental number that present in the sought number, but occupy different positions. Naturally, the experimental numbers, as well as the sought number, are represented by four-digit numbers where all digits are different and a leading zero can be present.</p><p>For example, let's suppose that the thinker thought of the number <span class="tex-font-style-tt">0123</span>. Then the guessers' experimental number <span class="tex-font-style-tt">1263</span> will receive a reply "1 bull 2 cows" (3 occupies the same positions in both numbers and 1 and 2 are present in both numbers but they occupy different positions). Also, the answer to number <span class="tex-font-style-tt">8103</span> will be "2 bulls 1 cow" (analogically, 1 and 3 occupy the same positions and 0 occupies a different one). </p><p>When the guesser is answered "4 bulls 0 cows", the game is over.</p><p>Now the guesser has already made several guesses and wants to know whether his next guess can possibly be the last one.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first input line contains an integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10</span>) which represents the number of already made guesses. Then follow <span class="tex-span"><i>n</i></span> lines in the form of "<span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span>", where <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> is the <span class="tex-span"><i>i</i></span>-th experimental number, <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> is the number of bulls, <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span> is the number of cows (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>n</i></span>, <span class="tex-span">0 ≤ <i>b</i><sub class="lower-index"><i>i</i></sub>, <i>c</i><sub class="lower-index"><i>i</i></sub>, <i>b</i><sub class="lower-index"><i>i</i></sub> + <i>c</i><sub class="lower-index"><i>i</i></sub> ≤ 4</span>). The experimental numbers are correct, i.e., each of them contains exactly four digits, in each of them all the four digits are different, and there can be a leading zero. All the experimental numbers are different. As the guesser hasn't guessed the number yet, the answer "4 bulls 0 cows" is not present.</p></div><div class="output-specification"><div class="section-title">Output</div><p>If the input data is enough to determine the sought number, print the number with four digits on a single line. If it has less than four digits, add leading zero. If the data is not enough, print "<span class="tex-font-style-tt">Need more data</span>" without the quotes. If the thinker happens to have made a mistake in his replies, print "<span class="tex-font-style-tt">Incorrect data</span>" without the quotes.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2<br/>1263 1 2<br/>8103 2 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>Need more data</pre></div><div class="input"><div class="title">Input</div><pre>2<br/>1234 2 2<br/>1256 0 2<br/></pre></div><div class="output"><div class="title">Output</div><pre>2134</pre></div><div class="input"><div class="title">Input</div><pre>2<br/>0123 1 1<br/>4567 1 2<br/></pre></div><div class="output"><div class="title">Output</div><pre>Incorrect data</pre></div></div></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/63">Codeforces Beta Round 59 (Div. 2)</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? 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If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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} </style> <div class="roundbox sidebox sidebar-menu borderTopRound " style=""> <div class="caption titled">&rarr; Contest materials <div class="top-links"> </div> </div> <ul> <li> <span> <a href="/blog/entry/1380" title="Codeforces Beta Round #59 (Div. 2)" target="_blank">Announcement</a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="232:233" resourceName="Announcement" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1391" title="Solutions Codeforces Round #59" target="_blank">Tutorial #1 <span class="resource-locale">(en)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="822" resourceName="Solutions Codeforces Round #59" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1384" title="CFBR #59 - Solutions to problems A, B, C, D" target="_blank">Tutorial #2</a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="818:819" resourceName="Tutorial #2" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1385" title="Разбор задач Codeforces Round #59 (Div. 2)" target="_blank">Tutorial #3</a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="234:235" resourceName="Tutorial #3" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> </ul> </div></div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li class="current selectedLava"><a href="/contest/63">Problems</a></li> <li><a href="/contest/63/submit">Submit Code</a></li> <li><a href="/contest/63/my">My Submissions</a></li> <li><a href="/contest/63/status">Status</a></li> <li><a href="/contest/63/hacks">Hacks</a></li> <li><a href="/contest/63/room/1">Room</a></li> <li><a href="/contest/63/standings">Standings</a></li> <li><a href="/contest/63/customtest">Custom Invocation</a></li> </ul> </div> <style> #facebox .content:has(.diff-popup) { width: 90vw; 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="C" data-uuid="ps_38ea31c5b92194920c318535fb6be7136c6073d7"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. Bulls and Cows</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>The &quot;Bulls and Cows&quot; game needs two people to play. The thinker thinks of a number and the guesser tries to guess it.</p><p>The thinker thinks of a four-digit number in the decimal system. All the digits in the number are different and the number may have a leading zero. It can't have more than one leading zero, because all it's digits should be different. The guesser tries to guess the number. He makes a series of guesses, trying experimental numbers and receives answers from the first person in the format &quot;<span class="tex-span"><i>x</i></span> bulls <span class="tex-span"><i>y</i></span> cows&quot;. <span class="tex-span"><i>x</i></span> represents the number of digits in the experimental number that occupy the same positions as in the sought number. <span class="tex-span"><i>y</i></span> represents the number of digits of the experimental number that present in the sought number, but occupy different positions. Naturally, the experimental numbers, as well as the sought number, are represented by four-digit numbers where all digits are different and a leading zero can be present.</p><p>For example, let's suppose that the thinker thought of the number <span class="tex-font-style-tt">0123</span>. Then the guessers' experimental number <span class="tex-font-style-tt">1263</span> will receive a reply &quot;1 bull 2 cows&quot; (3 occupies the same positions in both numbers and 1 and 2 are present in both numbers but they occupy different positions). Also, the answer to number <span class="tex-font-style-tt">8103</span> will be &quot;2 bulls 1 cow&quot; (analogically, 1 and 3 occupy the same positions and 0 occupies a different one). </p><p>When the guesser is answered &quot;4 bulls 0 cows&quot;, the game is over.</p><p>Now the guesser has already made several guesses and wants to know whether his next guess can possibly be the last one.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first input line contains an integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10</span>) which represents the number of already made guesses. Then follow <span class="tex-span"><i>n</i></span> lines in the form of &quot;<span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span>&quot;, where <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> is the <span class="tex-span"><i>i</i></span>-th experimental number, <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> is the number of bulls, <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span> is the number of cows (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>n</i></span>, <span class="tex-span">0 ≤ <i>b</i><sub class="lower-index"><i>i</i></sub>, <i>c</i><sub class="lower-index"><i>i</i></sub>, <i>b</i><sub class="lower-index"><i>i</i></sub> + <i>c</i><sub class="lower-index"><i>i</i></sub> ≤ 4</span>). The experimental numbers are correct, i.e., each of them contains exactly four digits, in each of them all the four digits are different, and there can be a leading zero. All the experimental numbers are different. As the guesser hasn't guessed the number yet, the answer &quot;4 bulls 0 cows&quot; is not present.</p></div><div class="output-specification"><div class="section-title">Output</div><p>If the input data is enough to determine the sought number, print the number with four digits on a single line. If it has less than four digits, add leading zero. If the data is not enough, print &quot;<span class="tex-font-style-tt">Need more data</span>&quot; without the quotes. If the thinker happens to have made a mistake in his replies, print &quot;<span class="tex-font-style-tt">Incorrect data</span>&quot; without the quotes.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2<br />1263 1 2<br />8103 2 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>Need more data</pre></div><div class="input"><div class="title">Input</div><pre>2<br />1234 2 2<br />1256 0 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>2134</pre></div><div class="input"><div class="title">Input</div><pre>2<br />0123 1 1<br />4567 1 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>Incorrect data</pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=C]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); 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["Brute force", "Implementation problems, programming technics, simulation"]
["brute force", "implementation", "*1700"]
https://codeforces.com/blog/entry/1391
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63D
63
D
en
D. Dividing Island
<div class="problem-statement"><div class="header"><div class="title">D. Dividing Island</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>A revolution took place on the Buka Island. New government replaced the old one. The new government includes <span class="tex-span"><i>n</i></span> parties and each of them is entitled to some part of the island according to their contribution to the revolution. However, they can't divide the island.</p><p>The island can be conventionally represented as two rectangles <span class="tex-span"><i>a</i> × <i>b</i></span> and <span class="tex-span"><i>c</i> × <i>d</i></span> unit squares in size correspondingly. The rectangles are located close to each other. At that, one of the sides with the length of <span class="tex-span"><i>a</i></span> and one of the sides with the length of <span class="tex-span"><i>c</i></span> lie on one line. You can see this in more details on the picture.</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/c919851573257c51c49fd0bc2857509b3d8bc159.png" style="max-width: 100.0%;max-height: 100.0%;"/> </center><p>The <span class="tex-span"><i>i</i></span>-th party is entitled to a part of the island equal to <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> unit squares. Every such part should fully cover several squares of the island (it is not allowed to cover the squares partially) and be a connected figure. A "connected figure" presupposes that from any square of this party one can move to any other square of the same party moving through edge-adjacent squares also belonging to that party.</p><p>Your task is to divide the island between parties.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains 5 space-separated integers — <span class="tex-span"><i>a</i></span>, <span class="tex-span"><i>b</i></span>, <span class="tex-span"><i>c</i></span>, <span class="tex-span"><i>d</i></span> and <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>a</i>, <i>b</i>, <i>c</i>, <i>d</i> ≤ 50</span>, <span class="tex-span"><i>b</i> ≠ <i>d</i></span>, <span class="tex-span">1 ≤ <i>n</i> ≤ 26</span>). The second line contains <span class="tex-span"><i>n</i></span> space-separated numbers. The <span class="tex-span"><i>i</i></span>-th of them is equal to number <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>x</i><sub class="lower-index"><i>i</i></sub> ≤ <i>a</i> × <i>b</i> + <i>c</i> × <i>d</i></span>). It is guaranteed that <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/35d7a672005b7ad5e3d4935e2cb8334465a0bee4.png" style="max-width: 100.0%;max-height: 100.0%;"/>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>If dividing the island between parties in the required manner is impossible, print "<span class="tex-font-style-tt">NO</span>" (without the quotes). Otherwise, print "<span class="tex-font-style-tt">YES</span>" (also without the quotes) and, starting from the next line, print <span class="tex-span"><i>max</i>(<i>b</i>, <i>d</i>)</span> lines each containing <span class="tex-span"><i>a</i> + <i>c</i></span> characters. To mark what square should belong to what party, use lowercase Latin letters. For the party that is first in order in the input data, use "<span class="tex-font-style-tt">a</span>", for the second one use "<span class="tex-font-style-tt">b</span>" and so on. Use "<span class="tex-font-style-tt">.</span>" for the squares that belong to the sea. The first symbol of the second line of the output data should correspond to the square that belongs to the rectangle <span class="tex-span"><i>a</i> × <i>b</i></span>. The last symbol of the second line should correspond to the square that belongs to the rectangle <span class="tex-span"><i>c</i> × <i>d</i></span>.</p><p>If there are several solutions output any.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3 4 2 2 3<br/>5 8 3<br/></pre></div><div class="output"><div class="title">Output</div><pre>YES<br/>aaabb<br/>aabbb<br/>cbb..<br/>ccb..<br/></pre></div><div class="input"><div class="title">Input</div><pre>3 2 1 4 4<br/>1 2 3 4<br/></pre></div><div class="output"><div class="title">Output</div><pre>YES<br/>abbd<br/>cccd<br/>...d<br/>...d<br/></pre></div></div></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/63">Codeforces Beta Round 59 (Div. 2)</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="D" data-uuid="ps_6fca8b94c030fba3baa0e7a94c7ba5c6095a07b7"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">D. Dividing Island</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>A revolution took place on the Buka Island. New government replaced the old one. The new government includes <span class="tex-span"><i>n</i></span> parties and each of them is entitled to some part of the island according to their contribution to the revolution. However, they can't divide the island.</p><p>The island can be conventionally represented as two rectangles <span class="tex-span"><i>a</i> × <i>b</i></span> and <span class="tex-span"><i>c</i> × <i>d</i></span> unit squares in size correspondingly. The rectangles are located close to each other. At that, one of the sides with the length of <span class="tex-span"><i>a</i></span> and one of the sides with the length of <span class="tex-span"><i>c</i></span> lie on one line. You can see this in more details on the picture.</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/c919851573257c51c49fd0bc2857509b3d8bc159.png" style="max-width: 100.0%;max-height: 100.0%;" /> </center><p>The <span class="tex-span"><i>i</i></span>-th party is entitled to a part of the island equal to <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> unit squares. Every such part should fully cover several squares of the island (it is not allowed to cover the squares partially) and be a connected figure. A &quot;connected figure&quot; presupposes that from any square of this party one can move to any other square of the same party moving through edge-adjacent squares also belonging to that party.</p><p>Your task is to divide the island between parties.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains 5 space-separated integers — <span class="tex-span"><i>a</i></span>, <span class="tex-span"><i>b</i></span>, <span class="tex-span"><i>c</i></span>, <span class="tex-span"><i>d</i></span> and <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>a</i>, <i>b</i>, <i>c</i>, <i>d</i> ≤ 50</span>, <span class="tex-span"><i>b</i> ≠ <i>d</i></span>, <span class="tex-span">1 ≤ <i>n</i> ≤ 26</span>). The second line contains <span class="tex-span"><i>n</i></span> space-separated numbers. The <span class="tex-span"><i>i</i></span>-th of them is equal to number <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>x</i><sub class="lower-index"><i>i</i></sub> ≤ <i>a</i> × <i>b</i> + <i>c</i> × <i>d</i></span>). It is guaranteed that <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/35d7a672005b7ad5e3d4935e2cb8334465a0bee4.png" style="max-width: 100.0%;max-height: 100.0%;" />.</p></div><div class="output-specification"><div class="section-title">Output</div><p>If dividing the island between parties in the required manner is impossible, print &quot;<span class="tex-font-style-tt">NO</span>&quot; (without the quotes). Otherwise, print &quot;<span class="tex-font-style-tt">YES</span>&quot; (also without the quotes) and, starting from the next line, print <span class="tex-span"><i>max</i>(<i>b</i>, <i>d</i>)</span> lines each containing <span class="tex-span"><i>a</i> + <i>c</i></span> characters. To mark what square should belong to what party, use lowercase Latin letters. For the party that is first in order in the input data, use &quot;<span class="tex-font-style-tt">a</span>&quot;, for the second one use &quot;<span class="tex-font-style-tt">b</span>&quot; and so on. Use &quot;<span class="tex-font-style-tt">.</span>&quot; for the squares that belong to the sea. The first symbol of the second line of the output data should correspond to the square that belongs to the rectangle <span class="tex-span"><i>a</i> × <i>b</i></span>. The last symbol of the second line should correspond to the square that belongs to the rectangle <span class="tex-span"><i>c</i> × <i>d</i></span>.</p><p>If there are several solutions output any.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3 4 2 2 3<br />5 8 3<br /></pre></div><div class="output"><div class="title">Output</div><pre>YES<br />aaabb<br />aabbb<br />cbb..<br />ccb..<br /></pre></div><div class="input"><div class="title">Input</div><pre>3 2 1 4 4<br />1 2 3 4<br /></pre></div><div class="output"><div class="title">Output</div><pre>YES<br />abbd<br />cccd<br />...d<br />...d<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=D]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); 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["Constructive algorithms"]
["constructive algorithms", "*1900"]
https://codeforces.com/blog/entry/1391
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63E
63
E
en
E. Sweets Game
<div class="problem-statement"><div class="header"><div class="title">E. Sweets Game</div><div class="time-limit"><div class="property-title">time limit per test</div>3 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Karlsson has visited Lillebror again. They found a box of chocolates and a big whipped cream cake at Lillebror's place. Karlsson immediately suggested to divide the sweets fairly between Lillebror and himself. Specifically, to play together a game he has just invented with the chocolates. The winner will get the cake as a reward.</p><p>The box of chocolates has the form of a hexagon. It contains 19 cells for the chocolates, some of which contain a chocolate. The players move in turns. During one move it is allowed to eat one or several chocolates that lay in the neighboring cells on one line, parallel to one of the box's sides. The picture below shows the examples of allowed moves and of an unacceptable one. The player who cannot make a move loses.</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/865a3fc458e9c1e00d1738029da9808f92e0fe0b.png" style="max-width: 100.0%;max-height: 100.0%;"/> </center><p>Karlsson makes the first move as he is Lillebror's guest and not vice versa. The players play optimally. Determine who will get the cake.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The input data contains 5 lines, containing 19 words consisting of one symbol. The word "<span class="tex-font-style-tt">O</span>" means that the cell contains a chocolate and a "<span class="tex-font-style-tt">.</span>" stands for an empty cell. It is guaranteed that the box contains at least one chocolate. See the examples for better understanding.</p></div><div class="output-specification"><div class="section-title">Output</div><p>If Karlsson gets the cake, print "<span class="tex-font-style-tt">Karlsson</span>" (without the quotes), otherwise print "<span class="tex-font-style-tt">Lillebror</span>" (yet again without the quotes).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre> . . .<br/> . . O .<br/>. . O O .<br/> . . . .<br/> . . .<br/></pre></div><div class="output"><div class="title">Output</div><pre>Lillebror</pre></div><div class="input"><div class="title">Input</div><pre> . . .<br/> . . . O<br/>. . . O .<br/> O . O .<br/> . O .<br/></pre></div><div class="output"><div class="title">Output</div><pre>Karlsson</pre></div></div></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/63">Codeforces Beta Round 59 (Div. 2)</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? 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If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="E" data-uuid="ps_31c2df8d09acbb07fb68898b2e5a7ed8b2fd9b97"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">E. Sweets Game</div><div class="time-limit"><div class="property-title">time limit per test</div>3 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Karlsson has visited Lillebror again. They found a box of chocolates and a big whipped cream cake at Lillebror's place. Karlsson immediately suggested to divide the sweets fairly between Lillebror and himself. Specifically, to play together a game he has just invented with the chocolates. The winner will get the cake as a reward.</p><p>The box of chocolates has the form of a hexagon. It contains 19 cells for the chocolates, some of which contain a chocolate. The players move in turns. During one move it is allowed to eat one or several chocolates that lay in the neighboring cells on one line, parallel to one of the box's sides. The picture below shows the examples of allowed moves and of an unacceptable one. The player who cannot make a move loses.</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/865a3fc458e9c1e00d1738029da9808f92e0fe0b.png" style="max-width: 100.0%;max-height: 100.0%;" /> </center><p>Karlsson makes the first move as he is Lillebror's guest and not vice versa. The players play optimally. Determine who will get the cake.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The input data contains 5 lines, containing 19 words consisting of one symbol. The word &quot;<span class="tex-font-style-tt">O</span>&quot; means that the cell contains a chocolate and a &quot;<span class="tex-font-style-tt">.</span>&quot; stands for an empty cell. It is guaranteed that the box contains at least one chocolate. See the examples for better understanding.</p></div><div class="output-specification"><div class="section-title">Output</div><p>If Karlsson gets the cake, print &quot;<span class="tex-font-style-tt">Karlsson</span>&quot; (without the quotes), otherwise print &quot;<span class="tex-font-style-tt">Lillebror</span>&quot; (yet again without the quotes).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre> . . .<br /> . . O .<br />. . O O .<br /> . . . .<br /> . . .<br /></pre></div><div class="output"><div class="title">Output</div><pre>Lillebror</pre></div><div class="input"><div class="title">Input</div><pre> . . .<br /> . . . O<br />. . . O .<br /> O . O .<br /> . O .<br /></pre></div><div class="output"><div class="title">Output</div><pre>Karlsson</pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=E]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); if (previousStatementText) { if (previousStatementText !== statementText) { $problem.find(".diff-notifier").show(); $problem.find(".diff-notifier-close").click(function() { Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60); $problem.find(".diff-notifier").hide(); }); $problem.find("a.view-changes").click(function() { $.post("/data/diff", {action: "getDiff", a: previousStatementText, b: statementText}, function (result) { if (result["success"] === "true") { Codeforces.facebox(".diff-popup", "//codeforces.org/s/73366"); $("#facebox .diff-popup").html(result["diff"]); 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["Bitmasks", "Dfs and similar", "Dynamic programming", "Games, Sprague\u2013Grundy theorem", "Implementation problems, programming technics, simulation"]
["bitmasks", "dfs and similar", "dp", "games", "implementation", "*2000"]
https://codeforces.com/blog/entry/1391
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A. Harry Potter and Three Spells
<div class="problem-statement"><div class="header"><div class="title">A. Harry Potter and Three Spells</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>A long time ago (probably even in the first book), Nicholas Flamel, a great alchemist and the creator of the Philosopher's Stone, taught Harry Potter three useful spells. The first one allows you to convert <span class="tex-span"><i>a</i></span> grams of sand into <span class="tex-span"><i>b</i></span> grams of lead, the second one allows you to convert <span class="tex-span"><i>c</i></span> grams of lead into <span class="tex-span"><i>d</i></span> grams of gold and third one allows you to convert <span class="tex-span"><i>e</i></span> grams of gold into <span class="tex-span"><i>f</i></span> grams of sand. When Harry told his friends about these spells, Ron Weasley was amazed. After all, if they succeed in turning sand into lead, lead into gold, and then turning part of the gold into sand again and so on, then it will be possible to start with a small amount of sand and get huge amounts of gold! Even an infinite amount of gold! Hermione Granger, by contrast, was skeptical about that idea. She argues that according to the law of conservation of matter getting an infinite amount of matter, even using magic, is impossible. On the contrary, the amount of matter may even decrease during transformation, being converted to magical energy. Though Hermione's theory seems convincing, Ron won't believe her. As far as Ron is concerned, Hermione made up her law of conservation of matter to stop Harry and Ron wasting their time with this nonsense, and to make them go and do homework instead. That's why Ron has already collected a certain amount of sand for the experiments. A quarrel between the friends seems unavoidable...</p><p>Help Harry to determine which one of his friends is right, and avoid the quarrel after all. To do this you have to figure out whether it is possible to get the amount of gold greater than any preassigned number from some finite amount of sand.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains <span class="tex-span">6</span> integers <span class="tex-span"><i>a</i></span>, <span class="tex-span"><i>b</i></span>, <span class="tex-span"><i>c</i></span>, <span class="tex-span"><i>d</i></span>, <span class="tex-span"><i>e</i></span>, <span class="tex-span"><i>f</i></span> (<span class="tex-span">0 ≤ <i>a</i>, <i>b</i>, <i>c</i>, <i>d</i>, <i>e</i>, <i>f</i> ≤ 1000</span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print "Ron", if it is possible to get an infinitely large amount of gold having a certain finite amount of sand (and not having any gold and lead at all), i.e., Ron is right. Otherwise, print "Hermione".</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>100 200 250 150 200 250<br/></pre></div><div class="output"><div class="title">Output</div><pre>Ron<br/></pre></div><div class="input"><div class="title">Input</div><pre>100 50 50 200 200 100<br/></pre></div><div class="output"><div class="title">Output</div><pre>Hermione<br/></pre></div><div class="input"><div class="title">Input</div><pre>100 10 200 20 300 30<br/></pre></div><div class="output"><div class="title">Output</div><pre>Hermione<br/></pre></div><div class="input"><div class="title">Input</div><pre>0 0 0 0 0 0<br/></pre></div><div class="output"><div class="title">Output</div><pre>Hermione<br/></pre></div><div class="input"><div class="title">Input</div><pre>1 1 0 1 1 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>Ron<br/></pre></div><div class="input"><div class="title">Input</div><pre>1 0 1 2 1 2<br/></pre></div><div class="output"><div class="title">Output</div><pre>Hermione<br/></pre></div><div class="input"><div class="title">Input</div><pre>100 1 100 1 0 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>Ron<br/></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>Consider the first sample. Let's start with the <span class="tex-span">500</span> grams of sand. Apply the first spell <span class="tex-span">5</span> times and turn the sand into <span class="tex-span">1000</span> grams of lead. Then apply the second spell <span class="tex-span">4</span> times to get <span class="tex-span">600</span> grams of gold. Let’s take <span class="tex-span">400</span> grams from the resulting amount of gold turn them back into sand. We get <span class="tex-span">500</span> grams of sand and <span class="tex-span">200</span> grams of gold. If we apply the same operations to <span class="tex-span">500</span> grams of sand again, we can get extra <span class="tex-span">200</span> grams of gold every time. Thus, you can get <span class="tex-span">200</span>, <span class="tex-span">400</span>, <span class="tex-span">600</span> etc. grams of gold, i.e., starting with a finite amount of sand (<span class="tex-span">500</span> grams), you can get the amount of gold which is greater than any preassigned number.</p><p>In the forth sample it is impossible to get sand, or lead, or gold, applying the spells.</p><p>In the fifth sample an infinitely large amount of gold can be obtained by using only the second spell, which allows you to receive <span class="tex-span">1</span> gram of gold out of nothing. Note that if such a second spell is available, then the first and the third one do not affect the answer at all.</p><p>The seventh sample is more interesting. We can also start with a zero amount of sand there. With the aid of the third spell you can get sand out of nothing. We get <span class="tex-span">10000</span> grams of sand in this manner. Let's get <span class="tex-span">100</span> grams of lead using the first spell <span class="tex-span">100</span> times. Then make <span class="tex-span">1</span> gram of gold from them. We managed to receive <span class="tex-span">1</span> gram of gold, starting with a zero amount of sand! Clearly, in this manner you can get an infinitely large amount of gold.</p></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/65">Codeforces Beta Round 60</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? 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If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="A" data-uuid="ps_81c0e1743ab2858ec6f5c75ce6c708dd20ff0a81"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">A. Harry Potter and Three Spells</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>A long time ago (probably even in the first book), Nicholas Flamel, a great alchemist and the creator of the Philosopher's Stone, taught Harry Potter three useful spells. The first one allows you to convert <span class="tex-span"><i>a</i></span> grams of sand into <span class="tex-span"><i>b</i></span> grams of lead, the second one allows you to convert <span class="tex-span"><i>c</i></span> grams of lead into <span class="tex-span"><i>d</i></span> grams of gold and third one allows you to convert <span class="tex-span"><i>e</i></span> grams of gold into <span class="tex-span"><i>f</i></span> grams of sand. When Harry told his friends about these spells, Ron Weasley was amazed. After all, if they succeed in turning sand into lead, lead into gold, and then turning part of the gold into sand again and so on, then it will be possible to start with a small amount of sand and get huge amounts of gold! Even an infinite amount of gold! Hermione Granger, by contrast, was skeptical about that idea. She argues that according to the law of conservation of matter getting an infinite amount of matter, even using magic, is impossible. On the contrary, the amount of matter may even decrease during transformation, being converted to magical energy. Though Hermione's theory seems convincing, Ron won't believe her. As far as Ron is concerned, Hermione made up her law of conservation of matter to stop Harry and Ron wasting their time with this nonsense, and to make them go and do homework instead. That's why Ron has already collected a certain amount of sand for the experiments. A quarrel between the friends seems unavoidable...</p><p>Help Harry to determine which one of his friends is right, and avoid the quarrel after all. To do this you have to figure out whether it is possible to get the amount of gold greater than any preassigned number from some finite amount of sand.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains <span class="tex-span">6</span> integers <span class="tex-span"><i>a</i></span>, <span class="tex-span"><i>b</i></span>, <span class="tex-span"><i>c</i></span>, <span class="tex-span"><i>d</i></span>, <span class="tex-span"><i>e</i></span>, <span class="tex-span"><i>f</i></span> (<span class="tex-span">0 ≤ <i>a</i>, <i>b</i>, <i>c</i>, <i>d</i>, <i>e</i>, <i>f</i> ≤ 1000</span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print &quot;Ron&quot;, if it is possible to get an infinitely large amount of gold having a certain finite amount of sand (and not having any gold and lead at all), i.e., Ron is right. Otherwise, print &quot;Hermione&quot;.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>100 200 250 150 200 250<br /></pre></div><div class="output"><div class="title">Output</div><pre>Ron<br /></pre></div><div class="input"><div class="title">Input</div><pre>100 50 50 200 200 100<br /></pre></div><div class="output"><div class="title">Output</div><pre>Hermione<br /></pre></div><div class="input"><div class="title">Input</div><pre>100 10 200 20 300 30<br /></pre></div><div class="output"><div class="title">Output</div><pre>Hermione<br /></pre></div><div class="input"><div class="title">Input</div><pre>0 0 0 0 0 0<br /></pre></div><div class="output"><div class="title">Output</div><pre>Hermione<br /></pre></div><div class="input"><div class="title">Input</div><pre>1 1 0 1 1 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>Ron<br /></pre></div><div class="input"><div class="title">Input</div><pre>1 0 1 2 1 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>Hermione<br /></pre></div><div class="input"><div class="title">Input</div><pre>100 1 100 1 0 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>Ron<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>Consider the first sample. Let's start with the <span class="tex-span">500</span> grams of sand. Apply the first spell <span class="tex-span">5</span> times and turn the sand into <span class="tex-span">1000</span> grams of lead. Then apply the second spell <span class="tex-span">4</span> times to get <span class="tex-span">600</span> grams of gold. Let’s take <span class="tex-span">400</span> grams from the resulting amount of gold turn them back into sand. We get <span class="tex-span">500</span> grams of sand and <span class="tex-span">200</span> grams of gold. If we apply the same operations to <span class="tex-span">500</span> grams of sand again, we can get extra <span class="tex-span">200</span> grams of gold every time. Thus, you can get <span class="tex-span">200</span>, <span class="tex-span">400</span>, <span class="tex-span">600</span> etc. grams of gold, i.e., starting with a finite amount of sand (<span class="tex-span">500</span> grams), you can get the amount of gold which is greater than any preassigned number.</p><p>In the forth sample it is impossible to get sand, or lead, or gold, applying the spells.</p><p>In the fifth sample an infinitely large amount of gold can be obtained by using only the second spell, which allows you to receive <span class="tex-span">1</span> gram of gold out of nothing. Note that if such a second spell is available, then the first and the third one do not affect the answer at all.</p><p>The seventh sample is more interesting. We can also start with a zero amount of sand there. With the aid of the third spell you can get sand out of nothing. We get <span class="tex-span">10000</span> grams of sand in this manner. Let's get <span class="tex-span">100</span> grams of lead using the first spell <span class="tex-span">100</span> times. Then make <span class="tex-span">1</span> gram of gold from them. We managed to receive <span class="tex-span">1</span> gram of gold, starting with a zero amount of sand! 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["Implementation problems, programming technics, simulation", "Mathematics including integration, differential equations, etc"]
["implementation", "math", "*1800"]
https://codeforces.com/blog/entry/1431
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<a href="/blog/entry/120644">Codeforces Round 899 (Div. 2)</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/Misa-Misa" title="Expert Misa-Misa" class="rated-user user-blue">Misa-Misa</a> &rarr; <a href="/blog/entry/121157">Someone please help me understand this.</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/shivam565" title="Specialist shivam565" class="rated-user user-cyan">shivam565</a> &rarr; <a href="/blog/entry/108348">Total number of subarrays with sum atmost k</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> </ul> </div> <div class="bottom-links"> <table style="width:100%;"> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:right;"> <a href="/recent-actions">Detailed &rarr;</a> </td> </tr> </tbody> </table> </div> </div> </div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li><a href="/profile/natalia">natalia</a></li> <li class="current selectedLava"><a href="/blog/natalia">Blog</a></li> <li><a href="/teams/with/natalia">Teams</a></li> <li><a href="/submissions/natalia">Submissions</a></li> <li><a href="/groups/with/natalia">Groups</a></li> <li><a href="/contests/with/natalia">Contests</a></li> <li><a href="/contests/writer/natalia">Problemsetting</a></li> </ul> </div> <div style="margin-top:0;"> <div> <h3><a href="/blog/natalia" style="text-decoration:none;color:black !important;">natalia's blog</a></h3> </div> <div style="margin-top:2em;"> <div class="has-topic-id topic" topicId="1431"> <div class="title"> <a href="/blog/entry/1431"> Codeforces Beta Round #60: tutorial </a> </div> <div class="info" style="position:relative;"> By&nbsp;<a href="/profile/natalia" title="Master natalia" class="rated-user user-orange">natalia</a>, <span class="format-humantime" title="Mar/06/2011 08:27">13 years ago</span>, translation, <img style="position: relative;top: 5px;" src="//codeforces.org/s/81027/images/flags/24/gb.png" alt="In English" title="In English"/> <span style="position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;"> <div style="margin-top:0.25em;"> </div> </span> </div> <div class="content"> <div class="ttypography"><b>Problem A</b><div><br /></div><div><div>Fist, consider the case when all the numbers are non-zero. You can take a*c*e grams of sand, turn them into b*c*e grams of lead, and them turn into b*d*e grams of gold, and them turn into b*d*f grams of sand. If b*d*f &gt; a*c*e, you can infinitely increase the amount of sand and consequently the amount of gold. Otherwise, if b*d*f &lt;= a*c*e, it is impossible to get infinitely large amount of gold. The same is true when the fraction  (a*c*e)/(b*d*f) has zero numerator only or zero denuminator only. Otherwise there is 0/0, and  you have to check cases specially.</div><div><br /></div><div>I explain, why I make this problem to be problem A.</div><div><br /></div><div>1. Solution of the problem requires very little knowledge of programming (only &quot;if&quot;), so it was feasible for all participants.</div><div>2. Tricky cases really exist, but I hoped that &quot;<span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">stronger competitors will ... help newcomers to catch all bugs by their hacks&quot;. </span>And so it happened.</div><div><br /></div><div>Maybe I was wrong: this problem is too complex for A.</div><div><br /></div><div>A large number of hacks for this problem is a quite foreseen circumstance. I haven't include the special class of tests into the pretests intendently, to make hacking more interesting. In fairness I should note that Artem Rakhov was against this idea. Beause of this task the problem surfaced that Gassa writes about <a href="https://codeforces.com/comments/1432#comment-26176">here</a> in Russian: pretests cover some incomplete set of cases and it is not clear in advance what the event &quot;solution passed pretests&quot; means. I think it should be discussed, and strong principles of pretests development should be stated.</div></div><div><br /></div><div><b>Problem B</b></div><div> </div><div><br /></div><div>The problem has greedy solution. Change a digit in the first date to make it as small as possible. At each of the next steps try all one-digit exchanges in the current date and choose one that makes the date not less than the previous one and as small as possible at the same time. If the last year won't exceed 2011 - the answer is found. Otherwise there is no solution.</div><div><br /></div><div>How to prove that? Consider any correct answer. Clearly, if the first date in it is different from the smallest possible number that can be obtained from the first of given years, your can put the smallest number instead of it. The second date can be exchanged by the smallest possible number not exceeding the first number, etc.Ar a result you obtain a greedy solution that is built by the algorithm described above. If the greedy solution doesn't exist, solution doesn't esist too.</div><div><div><div><br /></div><div>The problem also has a dynamic solution.</div></div><div><br /></div><div><div><div><b>Problem C</b></div><div><div><br /></div><div>Check for each segment in the polyline if Harry can catch the snitch in it. Note that since <span class="tex-span"><i>v</i><sub class="lower-index"><i>p</i></sub> ≥ <i>v</i><sub class="lower-index"><i>s</i></sub></span>, if Harry can catch the snitch at some moment of time, he can catch it at any later moment. He can just follow snitch along its trajectory. So use binary search in each segment.</div><div><br /></div><div>About problems with EPS that participants got. The problems may be caused by</div><div>1) some EPS in the condition: while (leftTime + EPS &lt; rightTime) &lt;do binary search&gt;. The task was to output with a fixed accurancy not only the time, but also the point coordinates. If the difference between the time and the right one is less than EPS, the difference between coordinates may be significantly larger. In such cases you should compare not arguments of a function, but values of the function with EPS. Or the way that I usually follow and that once was not liked by the teacher of numerical methods - to implement some fixed number of iterations of the binary search (say, 60).  </div><div>2) EPS in comparison of time moments inside the binary search like this:</div><div>if (currentTime + addTime &gt; distance / potterSpeed - EPS)</div><div>                                                rightTime = currentTime;</div><div>                                        else</div><div>                                                leftTime = currentTime;</div><div>Here it is better to remove EPS at all. Or to put EPS significantly smaller than the required accurancy for printing the point.</div><div><br /></div><div>(Code fragments are from Egor's solution.)</div></div><div><br /></div><div>Thus, there was no crime with severe limitations. Probably for such problems extreme accurancy tests should be in pretests? It is about principles of pretests making again. </div><div><br /></div><div><b>UPD.</b> The problem has an analytical solution too. Consider the i-th segment. Let <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i></sub>, <i>y</i><sub class="lower-index"><i>i</i></sub>, <i>z</i><sub class="lower-index"><i>i</i></sub>)</span> and <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i> + 1</sub>, <i>y</i><sub class="lower-index"><i>i</i> + 1</sub>, <i>z</i><sub class="lower-index"><i>i</i> + 1</sub>)</span> be its ends, and let <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub></span> be the time required for the snitch to reach the beginning of the segment. Then at the moment t the snitch will be at the point (x, y, z), <span class="tex-span"><i>x</i> = <i>x</i><sub class="lower-index"><i>i</i></sub> + (<i>x</i><sub class="lower-index"><i>i</i> + 1</sub> - <i>x</i><sub class="lower-index"><i>i</i></sub>)(<i>t</i> - <i>t</i><sub class="lower-index"><i>i</i></sub>) / <i>T</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>y</i> = <i>y</i><sub class="lower-index"><i>i</i></sub> + (<i>y</i><sub class="lower-index"><i>i</i> + 1</sub> - <i>y</i><sub class="lower-index"><i>i</i></sub>)(<i>t</i> - <i>t</i><sub class="lower-index"><i>i</i></sub>) / <i>T</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>z</i> = <i>z</i><sub class="lower-index"><i>i</i></sub> + (<i>z</i><sub class="lower-index"><i>i</i> + 1</sub> - <i>z</i><sub class="lower-index"><i>i</i></sub>)(<i>t</i> - <i>t</i><sub class="lower-index"><i>i</i></sub>) / <i>T</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>T</i><sub class="lower-index"><i>i</i></sub></span> is a time necessary for snitch to overcome the segment. To catch the snitch at the point (x, y, z), Harry have to overcome the distance that squared is equal to <span class="tex-span">(<i>x</i> - <i>P</i><sub class="lower-index"><i>x</i></sub>)<sup class="upper-index">2</sup> + (<i>y</i> - <i>P</i><sub class="lower-index"><i>y</i></sub>)<sup class="upper-index">2</sup> + (<i>z</i> - <i>P</i><sub class="lower-index"><i>z</i></sub>)<sup class="upper-index">2</sup></span> for the time t. It is possible if <span class="tex-span">(<i>x</i> - <i>P</i><sub class="lower-index"><i>x</i></sub>)<sup class="upper-index">2</sup> + (<i>y</i> - <i>P</i><sub class="lower-index"><i>y</i></sub>)<sup class="upper-index">2</sup> + (<i>z</i> - <i>P</i><sub class="lower-index"><i>z</i></sub>)<sup class="upper-index">2</sup> ≤ (<i>tv</i><sub class="lower-index"><i>p</i></sub>)<sup class="upper-index">2</sup></span>. To find the minimal proper moment t, solve the corresponding quadratic equation.<br /></div><div><br /></div><div><div style="font-weight: normal;"><b>Problem D</b></div><div style="font-weight: normal;"><br /></div><div><div style="font-weight: normal;">Let <span class="tex-span"><i>S</i><sub class="lower-index"><i>i</i></sub></span> be a set of all possible assignments of the first <span class="tex-span"><i>i</i></span> students to the houses, that is a set of tuples <span class="tex-span">(<i>a</i><sub class="lower-index">1</sub>, <i>a</i><sub class="lower-index">2</sub>, <i>a</i><sub class="lower-index">3</sub>, <i>a</i><sub class="lower-index">4</sub>)</span>, where <span class="tex-span"><i>a</i><sub class="lower-index">1</sub></span> is a number of students sent to Gryffindor, <span class="tex-span"><i>a</i><sub class="lower-index">2</sub></span> - to Ravenclaw, etc. It's intuitively clear that these sets will not be large. So you can get <span class="tex-span"><i>S</i><sub class="lower-index"><i>i</i> - 1</sub></span> from <span class="tex-span"><i>S</i><sub class="lower-index"><i>i</i></sub></span> in a trivial way, and get finally <span class="tex-span"><i>S</i><sub class="lower-index"><i>n</i></sub></span>, and determine the answer from it. </div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"><br /></div></div></b></div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;">What is a rigorous proof of the algorithm? Let us have a set<b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"> <span class="tex-span"><i>S</i> = {(<i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">1</sub>, <i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">2</sub>, <i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">3</sub>, <i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">4</sub>)}<sub class="lower-index"><i>i</i> = 1, 2, ..., <i>k</i></sub></span>. Represent its elements as <span class="tex-span"><i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub> = <i>b</i><sub class="lower-index"><i>j</i></sub> + <i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub></span>, <span class="tex-span"><i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub> ≥ 0</span>, where <span class="tex-span"><i>b</i><sub class="lower-index"><i>j</i></sub></span> are maximal possible, i.e. there is i for each j such that <span class="tex-span"><i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub> = 0</span>. Let the tuple <span class="tex-span">(<i>b</i><sub class="lower-index">1</sub>, <i>b</i><sub class="lower-index">2</sub>, <i>b</i><sub class="lower-index">3</sub>, <i>b</i><sub class="lower-index">4</sub>)</span> be called the base part of S, and the set <span class="tex-span">{(<i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">1</sub>, <i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">2</sub>, <i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">3</sub>, <i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">4</sub>)}<sub class="lower-index"><i>i</i> = 1, 2, ..., <i>k</i></sub></span> be called the variant part of S. </div></div></b></div></div></b><br /></div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Initially for <span class="tex-span"><i>S</i><sub class="lower-index">0</sub></span> both base and variant parts are zeroes. Let us see how base and variant parts change when a current student is added. If a house is fixed for the student, only the base part changes. It increases by 1 at the position corresponding to the house. In particular, it follows that a set with every base part can be obtained (since the string given in the input can contain every combination of symbols G, H, R, S). If the current symbol in the string is '?', it can influence both base and variant parts.</div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">For example, for the string '????' we have:</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">0</sub> = {(0 + 0, 0 + 0, 0 + 0, 0 + 0)}</span>,</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">1</sub> = {(0 + 1, 0 + 0, 0 + 0, 0 + 0), (0 + 0, 0 + 1, 0 + 0, 0 + 0), (0 + 0, 0 + 0, 0 + 1, 0 + 0), (0 + 0, 0 + 0, 0 + 0, 0 + 1)}</span>,</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">2</sub> = {(0 + 1, 0 + 1, 0 + 0, 0 + 0), (0 + 1, 0 + 0, 0 + 1, 0 + 0), (0 + 1, 0 + 0, 0 + 0, 0 + 1), (0 + 0, 0 + 1, 0 + 1, 0 + 0), (0 + 0, 0 + 1, 0 + 0, 0 + 1), (0 + 0, 0 + 0, 0 + 1, 0 + 1)}</span>,</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">3</sub> = {(0 + 1, 0 + 1, 0 + 1, 0 + 0), (0 + 1, 0 + 1, 0 + 0, 0 + 1), (0 + 1, 0 + 0, 0 + 1, 0 + 1), (0 + 0, 0 + 1, 0 + 1, 0 + 1)}</span>,</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">4</sub> = {(1 + 0, 1 + 0, 1 + 0, 1 + 0)}</span>.</div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Let us investigate the question of what species a variant part may have. It can be analyzed independently from a base one, taking into account that a base part can be any. Consider a directed graph with vertices corresponding to variant parts and with edges determined by the existence of<b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"> at least one base part that let go from one variant part to another. We are interested only in vertices reachable from <span class="tex-span">{(0, 0, 0, 0)}</span>.</div></div></b></div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Proposition. For all the vertices reachable from zero the following properties hold</div><div style="font-weight: normal;">(1) <span class="tex-span"><i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub> ≤ 2</span>,</div><div style="font-weight: normal;">(2) <span class="tex-span"><i>k</i> ≤ 13</span>.</div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Let us prove that all the vertices not having the properties (1) and (2) are unreachable from zero. Consider a variant part with the property (1). To get all edges going from it you have to try all possible base parts. Note that base parts, that consist of the numbers 0, 1, 2, 3 and contain at lest one 0, are enough. Indeed, base part influence which elements are minimal, and 1 will be added to them. A base part can be always normed to contain at least one 0. If a base part contains numbers greater than 3, then the corresponding positions will never be minimal (since 4+0 &gt; 0+2) and they can be changed equivalently by 3 (3+0 &gt; 0+2).</div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Unfortunately, my attempts to deal with cases by hand were unsuccessful, so I wrote <a href="http://pastebin.com/p3sFKKya">the program</a> that traverse the described graph. Starting from 0, it builds edges trying only &quot;small&quot; base parts described in the previous paragraph. As a result, the program obtains all the reachable variant parts (there is a little more than 1000 of them) and check (1) and (2) for them. In addition, the program helps to construct a test with<b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"> <span class="tex-span"><i>k</i> = 13</span>.</div></div></b></div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"><br /></div></div></b></div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;">The problem was supposed to be a problem on intuition. Participants have another solution passed. Their solution generate all permutations and distribute students greedily with respect to each permutation.</div></div></b><b><div style="font-weight: normal;display: inline !important;"><b><div style="font-weight: normal;display: inline !important;">This solution was a complete surprise for me. Unfortunately, it is wrong. Test 66 against it was added. Of course, submissions accepted during the round won't be rejudged. If such a solution be expected, most likely I wouldn't give such a task. In terms of intuition this solution is not better and not worse than mine. I hope you will not judge me strictly: it is a beautiful problem, and it was interesting to see how it would be solved. </div></b></div></b></div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><b><div style="font-weight: normal;display: inline !important;"><br /></div></b></div></b></div><div><div style="display: inline !important;"><div style="display: inline !important;"><div style="font-weight: normal;"><b>Problem E</b></div><div style="font-weight: normal;"><b><br /></b></div><div><div><div><div style="display: inline !important;"><div style="display: inline !important;">Consider a graph with floors as vertices and staircases as edges. It is clear that Harry can visit the whole connected component in which he is currently located.<br /></div></div></div><div style="font-weight: normal;"><br /></div></div></div><div>Every edge can be used to reach a new vertex for not more than two times. If a connected component contains n vertices and m edges, only n - 1 edges are used to reach a new vertex during its traversal. The remaining m - n + 1 edges are not used to reach a new vertex in their initial placement. So they will be used to reach a new vertex not more than once.</div><div><div><br /></div><div>So using edges of only one connected component you can reach no more than n - m + 1 new vertices. Totally there are not more than  <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7fae5c87930e2f915b8c632872cc1662dd30fa09.png" style="max-width: 100.0%;max-height: 100.0%;" /> reachable vertices. If m &lt; k - 1, it is impossible to visit all the vertices.  </div><div><br /></div><div>We show that otherwise (m &gt;= k - 1), if the degree of the vertex 0 is different from zero, it is possible to visit all the vertices. In other words, there is such a traversal that every edge can be moved.  Use depth-first search for the current component. If a current edge goes to an already visited vertex, move it to a new component and traverse it recursively. If a current edge goes to a new vertex, after you visit this vertex and go back, you also can move this edge to a new component. As a result each edge can be moved and used again, if you reach all the components. If a component contains at least one edge, you can go from it to the next one. First visit components with edges, and you will visit them all and by the inequality (m &gt;= k - 1) there are enough edges to visit all the isolated vertices.  </div><div><br /></div><div>If the degree of the vertex 1 is zero, you can not start a traversal before you move some edge to it. After that you can go by this edge and remove it with the vertex 1 from the graph, becase you can not use this edge once more. If the chose edge is a bridge, you get k connected components and m - 1 egdes. If it is not a bridge, you get k - 1 components and m - 1 edges. In the first case the inequality m &gt;= k - 1 turns m &gt;= k. In the second case -  m &gt;= k - 1. So if not all the edges are bridges, you should not take a bridge. If they all are bridges, you should disconnect an edge from a vertex of degree &gt;= 2 not to came back to the initial situation with the zero degree of the first vertex. If there is no such vertex, it is easy to check that there is no solution.</div></div></div></div></div></div></div></div></div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/65" class="notice" style="text-decoration: none;">Codeforces Beta Round 60</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-2326-1431").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "2326", blogEntryId: "1431", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=beta+round+%2360" class="tag notice" style="text-decoration: none;">beta round #60</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces" class="tag notice" style="text-decoration: none;">codeforces</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=tutorial" class="tag notice" style="text-decoration: none;">tutorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1431"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+33</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1431"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/natalia"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/natalia"> natalia </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Mar/06/2011 08:27">13 years ago</span> </li> <li> <a href="/blog/entry/1431#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1431#comments"> 10 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1441"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (10)</a> </div> <div class="comments-actions-div"> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="26324" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/lyrics" style="position: relative;"> <img src='https://userpic.codeforces.org/3858/avatar/29787cdba9b12888.jpg'/> </a> <div><a href="/profile/lyrics" title="Expert lyrics" class="rated-user user-blue">lyrics</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/06/2011 12:30">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26324" href="?#comment-26324" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26324" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="3858" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26324"> <div class="moveup"> <div class="ttypography">good analysis...</div> </div> </div> <div class="reply info"> <a class="comment-26324 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26324 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26324"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="26331" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/A.K.Goharshady" style="position: relative;"> <img src='https://userpic.codeforces.org/9153/avatar/358f1b75189ae870.jpg'/> </a> <div><a href="/profile/A.K.Goharshady" title="Candidate Master A.K.Goharshady" class="rated-user user-violet">A.K.Goharshady</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/06/2011 12:52">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26331" href="?#comment-26331" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26331" class="CommentVoteFrame" data-commentRating="2" data-commentUserId="9153" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+2</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26331"> <div class="moveup"> <div class="ttypography">Problem A was harder than D :D</div> </div> </div> <div class="reply info"> <a class="comment-26331 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26331 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26331"> <li> <div class="comment"> <table class="comment-table" commentId="26336" commentParentId="26331"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Alex_KPR" style="position: relative;"> <img src='https://userpic.codeforces.org/209/avatar/b403606b22dc5082.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/Alex_KPR" title="Master Alex_KPR" class="rated-user user-orange">Alex_KPR</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/06/2011 13:03">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26336" href="?#comment-26336" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-26331" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26336" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="209" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26336"> <div class="moveup"> <div class="ttypography">agree with you =)</div> </div> </div> <div class="reply info"> <a class="comment-26336 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26336 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26336"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="26374" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mR.ilchi" style="position: relative;"> <img src='https://userpic.codeforces.org/11753/avatar/b0675918b77546aa.jpg'/> </a> <div><a href="/profile/mR.ilchi" title="International Grandmaster mR.ilchi" class="rated-user user-red">mR.ilchi</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/06/2011 15:58">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26374" href="?#comment-26374" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="26374" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="26374" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="11753" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26374"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">please translate problem D and E too.</div><div class="from-renderer"><div>thank's for your nice contest!!!</div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-26374 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26374 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26374"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="26587" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/sunhaowen567" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/sunhaowen567" title="Expert sunhaowen567" class="rated-user user-blue">sunhaowen567</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/07/2011 07:43">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26587" href="?#comment-26587" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26587" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3232" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26587"> <div class="moveup"> <div class="ttypography">waiting for problem E......</div> </div> </div> <div class="reply info"> <a class="comment-26587 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26587 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26587"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="26588" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kang205" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/kang205" title="Expert kang205" class="rated-user user-blue">kang205</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/07/2011 08:13">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26588" href="?#comment-26588" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26588" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13097" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26588"> <div class="moveup"> <div class="ttypography">Problem D's proof is very NICE.<br /><br /><br /><br /></div> </div> </div> <div class="reply info"> <a class="comment-26588 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26588 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26588"> <li> <div class="comment"> <table class="comment-table" commentId="26589" commentParentId="26588"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kang205" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/kang205" title="Expert kang205" class="rated-user user-blue">kang205</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/07/2011 08:16">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26589" href="?#comment-26589" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-26588" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26589" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13097" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26589"> <div class="moveup"> <div class="ttypography">I use <b>random <b><b><b> generate permutations</b></b></b></b>,but the random times be set 10000,so I got TLE.<br /><br />If set 2000,I got AC....</div> </div> </div> <div class="reply info"> <a class="comment-26589 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26589 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26589"> <li> <div class="comment"> <table class="comment-table" commentId="194733" commentParentId="26589"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/wjh720" style="position: relative;"> <img src='https://userpic.codeforces.org/210352/avatar/d212772572283d08.jpg'/> </a> <div><a href="/profile/wjh720" title="International Grandmaster wjh720" class="rated-user user-red">wjh720</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Oct/30/2014 09:43">9 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-194733" href="?#comment-194733" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-26589" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="194733" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="210352" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-194733"> <div class="moveup"> <div class="ttypography"><p>You can have a try with {&quot;?HRS&quot;*2500} :)</p></div> </div> </div> <div class="reply info"> <a class="comment-194733 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-194733 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-194733"> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="310517" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/throwaways" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/throwaways" title="Unrated, throwaways" class="rated-user user-black">throwaways</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Aug/17/2016 00:08">7 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-310517" href="?#comment-310517" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="310517" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="310517" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="401734" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-310517"> <div class="moveup"> <div class="ttypography"><p>what might the time complexity of D be?</p></div> </div> </div> <div class="reply info"> <a class="comment-310517 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-310517 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-310517"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="555734" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/roll_no_1" style="position: relative;"> <img src='https://userpic.codeforces.org/631859/avatar/36d157f91f64fe7f.jpg'/> </a> <div><a href="/profile/roll_no_1" title="Master roll_no_1" class="rated-user user-orange">roll_no_1</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Nov/03/2019 08:56">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-555734" href="?#comment-555734" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="555734" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="631859" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-555734"> <div class="moveup"> <div class="ttypography"><p>Here are the 2 interpretations of problem A's solution as I understood them:</p><p><a href="/contest/65/submission/64128016" title="Submission 64128016 by roll_no_1">64128016</a></p><p><a href="/contest/65/submission/64128379" title="Submission 64128379 by roll_no_1">64128379</a></p></div> </div> </div> <div class="reply info"> <a class="comment-555734 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-555734 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-555734"> </ul> </div> <br/> <div id="editBox-1441" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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65B
65
B
en
B. Harry Potter and the History of Magic
<div class="problem-statement"><div class="header"><div class="title">B. Harry Potter and the History of Magic</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>The History of Magic is perhaps the most boring subject in the Hogwarts school of Witchcraft and Wizardry. Harry Potter is usually asleep during history lessons, and his magical quill writes the lectures for him. Professor Binns, the history of magic teacher, lectures in such a boring and monotonous voice, that he has a soporific effect even on the quill. That's why the quill often makes mistakes, especially in dates.</p><p>So, at the end of the semester Professor Binns decided to collect the students' parchments with notes and check them. Ron Weasley is in a panic: Harry's notes may contain errors, but at least he has some notes, whereas Ron does not have any. Ronald also has been sleeping during the lectures and his quill had been eaten by his rat Scabbers. Hermione Granger refused to give Ron her notes, because, in her opinion, everyone should learn on their own. Therefore, Ron has no choice but to copy Harry's notes.</p><p>Due to the quill's errors Harry's dates are absolutely confused: the years of goblin rebellions and other important events for the wizarding world do not follow in order, and sometimes even dates from the future occur. Now Ron wants to change some of the digits while he copies the notes so that the dates were in the chronological (i.e. non-decreasing) order and so that the notes did not have any dates strictly later than <span class="tex-span">2011</span>, or strictly before than <span class="tex-span">1000</span>. To make the resulting sequence as close as possible to the one dictated by Professor Binns, Ron will change no more than one digit in each date into other digit. Help him do it.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first input line contains an integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 1000</span>). It represents the number of dates in Harry's notes. Next <span class="tex-span"><i>n</i></span> lines contain the actual dates <span class="tex-span"><i>y</i><sub class="lower-index">1</sub></span>, <span class="tex-span"><i>y</i><sub class="lower-index">2</sub></span>, ..., <span class="tex-span"><i>y</i><sub class="lower-index"><i>n</i></sub></span>, each line contains a date. Each date is a four-digit integer (<span class="tex-span">1000 ≤ <i>y</i><sub class="lower-index"><i>i</i></sub> ≤ 9999</span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span"><i>n</i></span> numbers <span class="tex-span"><i>z</i><sub class="lower-index">1</sub></span>, <span class="tex-span"><i>z</i><sub class="lower-index">2</sub></span>, ..., <span class="tex-span"><i>z</i><sub class="lower-index"><i>n</i></sub></span> (<span class="tex-span">1000 ≤ <i>z</i><sub class="lower-index"><i>i</i></sub> ≤ 2011</span>). They are Ron's resulting dates. Print each number on a single line. Numbers <span class="tex-span"><i>z</i><sub class="lower-index"><i>i</i></sub></span> must form the non-decreasing sequence. Each number <span class="tex-span"><i>z</i><sub class="lower-index"><i>i</i></sub></span> should differ from the corresponding date <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span> in no more than one digit. It is not allowed to change the first digit of a number into <span class="tex-span">0</span>. If there are several possible solutions, print any of them. If there's no solution, print "No solution" (without the quotes).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br/>1875<br/>1936<br/>1721<br/></pre></div><div class="output"><div class="title">Output</div><pre>1835<br/>1836<br/>1921<br/></pre></div><div class="input"><div class="title">Input</div><pre>4<br/>9999<br/>2000<br/>3000<br/>3011<br/></pre></div><div class="output"><div class="title">Output</div><pre>1999<br/>2000<br/>2000<br/>2011<br/></pre></div><div class="input"><div class="title">Input</div><pre>3<br/>1999<br/>5055<br/>2000<br/></pre></div><div class="output"><div class="title">Output</div><pre>No solution<br/></pre></div></div></div></div>
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Just register for practice and you will be able to submit solutions. </div> <div style="text-align:center;margin:1em;"> <form action="" method="post"><input type='hidden' name='csrf_token' value='075399f541228178fec927286621fbef'/> <input type="hidden" name="action" value="registerForPractice"/> <input type="submit" name="submit" value="Register for practice" style="padding:0 0.5em;"> </form> </div> </div> </div> <div class="roundbox sidebox ContestVirtualFrame borderTopRound " style=""> <div class="caption titled">&rarr; Virtual participation <i class="sidebar-caption-icon las la-angle-down"></i> <div class="top-links"> </div> </div> <div style=" " data-page-url="/data/sidebarFrames" > <div style="margin:1em;font-size:0.8em;"> Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests. If you've seen these problems, a virtual contest is not for you - solve these problems in the archive. If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. Never use someone else's code, read the tutorials or communicate with other person during a virtual contest. </div> <div style="text-align:center;margin:1em;"> <form action="/contest/65/virtual" method="get"> <input type="submit" name="submit" value="Start virtual contest" style="padding:0 0.5em;"> </form> </div> </div> <script> $(function () { $(".ContestVirtualFrame .sidebar-caption-icon").click(function() { $(this).toggleClass("la-angle-down la-angle-right"); const $target = $(this).parent().next(); $target.toggle(); const dataPageUrl = $target.attr("data-page-url"); const collapsed = $(this).hasClass("la-angle-right"); const params = { action: "setCollapsed", sidebarFrameSimpleClassName: "ContestVirtualFrame", collapsed }; $.each($target[0].attributes, function(i, a) { const name = a.name; if (name.startsWith("data-extra-key-")) { const key = a.value; const keyIndex = parseInt(name.substring("data-extra-key-".length)); const value = $target.attr("data-extra-value-" + keyIndex); params[key] = value; 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="B" data-uuid="ps_a5e611f79a810233a2f4602eec7cc745176ad018"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">B. Harry Potter and the History of Magic</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>The History of Magic is perhaps the most boring subject in the Hogwarts school of Witchcraft and Wizardry. Harry Potter is usually asleep during history lessons, and his magical quill writes the lectures for him. Professor Binns, the history of magic teacher, lectures in such a boring and monotonous voice, that he has a soporific effect even on the quill. That's why the quill often makes mistakes, especially in dates.</p><p>So, at the end of the semester Professor Binns decided to collect the students' parchments with notes and check them. Ron Weasley is in a panic: Harry's notes may contain errors, but at least he has some notes, whereas Ron does not have any. Ronald also has been sleeping during the lectures and his quill had been eaten by his rat Scabbers. Hermione Granger refused to give Ron her notes, because, in her opinion, everyone should learn on their own. Therefore, Ron has no choice but to copy Harry's notes.</p><p>Due to the quill's errors Harry's dates are absolutely confused: the years of goblin rebellions and other important events for the wizarding world do not follow in order, and sometimes even dates from the future occur. Now Ron wants to change some of the digits while he copies the notes so that the dates were in the chronological (i.e. non-decreasing) order and so that the notes did not have any dates strictly later than <span class="tex-span">2011</span>, or strictly before than <span class="tex-span">1000</span>. To make the resulting sequence as close as possible to the one dictated by Professor Binns, Ron will change no more than one digit in each date into other digit. Help him do it.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first input line contains an integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 1000</span>). It represents the number of dates in Harry's notes. Next <span class="tex-span"><i>n</i></span> lines contain the actual dates <span class="tex-span"><i>y</i><sub class="lower-index">1</sub></span>, <span class="tex-span"><i>y</i><sub class="lower-index">2</sub></span>, ..., <span class="tex-span"><i>y</i><sub class="lower-index"><i>n</i></sub></span>, each line contains a date. Each date is a four-digit integer (<span class="tex-span">1000 ≤ <i>y</i><sub class="lower-index"><i>i</i></sub> ≤ 9999</span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span"><i>n</i></span> numbers <span class="tex-span"><i>z</i><sub class="lower-index">1</sub></span>, <span class="tex-span"><i>z</i><sub class="lower-index">2</sub></span>, ..., <span class="tex-span"><i>z</i><sub class="lower-index"><i>n</i></sub></span> (<span class="tex-span">1000 ≤ <i>z</i><sub class="lower-index"><i>i</i></sub> ≤ 2011</span>). They are Ron's resulting dates. Print each number on a single line. Numbers <span class="tex-span"><i>z</i><sub class="lower-index"><i>i</i></sub></span> must form the non-decreasing sequence. Each number <span class="tex-span"><i>z</i><sub class="lower-index"><i>i</i></sub></span> should differ from the corresponding date <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span> in no more than one digit. It is not allowed to change the first digit of a number into <span class="tex-span">0</span>. If there are several possible solutions, print any of them. If there's no solution, print &quot;No solution&quot; (without the quotes).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br />1875<br />1936<br />1721<br /></pre></div><div class="output"><div class="title">Output</div><pre>1835<br />1836<br />1921<br /></pre></div><div class="input"><div class="title">Input</div><pre>4<br />9999<br />2000<br />3000<br />3011<br /></pre></div><div class="output"><div class="title">Output</div><pre>1999<br />2000<br />2000<br />2011<br /></pre></div><div class="input"><div class="title">Input</div><pre>3<br />1999<br />5055<br />2000<br /></pre></div><div class="output"><div class="title">Output</div><pre>No solution<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=B]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); 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["Brute force", "Greedy algorithms", "Implementation problems, programming technics, simulation"]
["brute force", "greedy", "implementation", "*1700"]
https://codeforces.com/blog/entry/1431
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You can take a*c*e grams of sand, turn them into b*c*e grams of lead, and them turn into b*d*e grams of gold, and them turn into b*d*f grams of sand. If b*d*f &gt; a*c*e, you can infinitely increase the amount of sand and consequently the amount of gold. Otherwise, if b*d*f &lt;= a*c*e, it is impossible to get infinitely large amount of gold. The same is true when the fraction  (a*c*e)/(b*d*f) has zero numerator only or zero denuminator only. Otherwise there is 0/0, and  you have to check cases specially.</div><div><br /></div><div>I explain, why I make this problem to be problem A.</div><div><br /></div><div>1. Solution of the problem requires very little knowledge of programming (only &quot;if&quot;), so it was feasible for all participants.</div><div>2. Tricky cases really exist, but I hoped that &quot;<span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">stronger competitors will ... help newcomers to catch all bugs by their hacks&quot;. </span>And so it happened.</div><div><br /></div><div>Maybe I was wrong: this problem is too complex for A.</div><div><br /></div><div>A large number of hacks for this problem is a quite foreseen circumstance. I haven't include the special class of tests into the pretests intendently, to make hacking more interesting. In fairness I should note that Artem Rakhov was against this idea. Beause of this task the problem surfaced that Gassa writes about <a href="https://codeforces.com/comments/1432#comment-26176">here</a> in Russian: pretests cover some incomplete set of cases and it is not clear in advance what the event &quot;solution passed pretests&quot; means. I think it should be discussed, and strong principles of pretests development should be stated.</div></div><div><br /></div><div><b>Problem B</b></div><div> </div><div><br /></div><div>The problem has greedy solution. Change a digit in the first date to make it as small as possible. At each of the next steps try all one-digit exchanges in the current date and choose one that makes the date not less than the previous one and as small as possible at the same time. If the last year won't exceed 2011 - the answer is found. Otherwise there is no solution.</div><div><br /></div><div>How to prove that? Consider any correct answer. Clearly, if the first date in it is different from the smallest possible number that can be obtained from the first of given years, your can put the smallest number instead of it. The second date can be exchanged by the smallest possible number not exceeding the first number, etc.Ar a result you obtain a greedy solution that is built by the algorithm described above. If the greedy solution doesn't exist, solution doesn't esist too.</div><div><div><div><br /></div><div>The problem also has a dynamic solution.</div></div><div><br /></div><div><div><div><b>Problem C</b></div><div><div><br /></div><div>Check for each segment in the polyline if Harry can catch the snitch in it. Note that since <span class="tex-span"><i>v</i><sub class="lower-index"><i>p</i></sub> ≥ <i>v</i><sub class="lower-index"><i>s</i></sub></span>, if Harry can catch the snitch at some moment of time, he can catch it at any later moment. He can just follow snitch along its trajectory. So use binary search in each segment.</div><div><br /></div><div>About problems with EPS that participants got. The problems may be caused by</div><div>1) some EPS in the condition: while (leftTime + EPS &lt; rightTime) &lt;do binary search&gt;. The task was to output with a fixed accurancy not only the time, but also the point coordinates. If the difference between the time and the right one is less than EPS, the difference between coordinates may be significantly larger. In such cases you should compare not arguments of a function, but values of the function with EPS. Or the way that I usually follow and that once was not liked by the teacher of numerical methods - to implement some fixed number of iterations of the binary search (say, 60).  </div><div>2) EPS in comparison of time moments inside the binary search like this:</div><div>if (currentTime + addTime &gt; distance / potterSpeed - EPS)</div><div>                                                rightTime = currentTime;</div><div>                                        else</div><div>                                                leftTime = currentTime;</div><div>Here it is better to remove EPS at all. Or to put EPS significantly smaller than the required accurancy for printing the point.</div><div><br /></div><div>(Code fragments are from Egor's solution.)</div></div><div><br /></div><div>Thus, there was no crime with severe limitations. Probably for such problems extreme accurancy tests should be in pretests? It is about principles of pretests making again. </div><div><br /></div><div><b>UPD.</b> The problem has an analytical solution too. Consider the i-th segment. Let <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i></sub>, <i>y</i><sub class="lower-index"><i>i</i></sub>, <i>z</i><sub class="lower-index"><i>i</i></sub>)</span> and <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i> + 1</sub>, <i>y</i><sub class="lower-index"><i>i</i> + 1</sub>, <i>z</i><sub class="lower-index"><i>i</i> + 1</sub>)</span> be its ends, and let <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub></span> be the time required for the snitch to reach the beginning of the segment. Then at the moment t the snitch will be at the point (x, y, z), <span class="tex-span"><i>x</i> = <i>x</i><sub class="lower-index"><i>i</i></sub> + (<i>x</i><sub class="lower-index"><i>i</i> + 1</sub> - <i>x</i><sub class="lower-index"><i>i</i></sub>)(<i>t</i> - <i>t</i><sub class="lower-index"><i>i</i></sub>) / <i>T</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>y</i> = <i>y</i><sub class="lower-index"><i>i</i></sub> + (<i>y</i><sub class="lower-index"><i>i</i> + 1</sub> - <i>y</i><sub class="lower-index"><i>i</i></sub>)(<i>t</i> - <i>t</i><sub class="lower-index"><i>i</i></sub>) / <i>T</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>z</i> = <i>z</i><sub class="lower-index"><i>i</i></sub> + (<i>z</i><sub class="lower-index"><i>i</i> + 1</sub> - <i>z</i><sub class="lower-index"><i>i</i></sub>)(<i>t</i> - <i>t</i><sub class="lower-index"><i>i</i></sub>) / <i>T</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>T</i><sub class="lower-index"><i>i</i></sub></span> is a time necessary for snitch to overcome the segment. To catch the snitch at the point (x, y, z), Harry have to overcome the distance that squared is equal to <span class="tex-span">(<i>x</i> - <i>P</i><sub class="lower-index"><i>x</i></sub>)<sup class="upper-index">2</sup> + (<i>y</i> - <i>P</i><sub class="lower-index"><i>y</i></sub>)<sup class="upper-index">2</sup> + (<i>z</i> - <i>P</i><sub class="lower-index"><i>z</i></sub>)<sup class="upper-index">2</sup></span> for the time t. It is possible if <span class="tex-span">(<i>x</i> - <i>P</i><sub class="lower-index"><i>x</i></sub>)<sup class="upper-index">2</sup> + (<i>y</i> - <i>P</i><sub class="lower-index"><i>y</i></sub>)<sup class="upper-index">2</sup> + (<i>z</i> - <i>P</i><sub class="lower-index"><i>z</i></sub>)<sup class="upper-index">2</sup> ≤ (<i>tv</i><sub class="lower-index"><i>p</i></sub>)<sup class="upper-index">2</sup></span>. To find the minimal proper moment t, solve the corresponding quadratic equation.<br /></div><div><br /></div><div><div style="font-weight: normal;"><b>Problem D</b></div><div style="font-weight: normal;"><br /></div><div><div style="font-weight: normal;">Let <span class="tex-span"><i>S</i><sub class="lower-index"><i>i</i></sub></span> be a set of all possible assignments of the first <span class="tex-span"><i>i</i></span> students to the houses, that is a set of tuples <span class="tex-span">(<i>a</i><sub class="lower-index">1</sub>, <i>a</i><sub class="lower-index">2</sub>, <i>a</i><sub class="lower-index">3</sub>, <i>a</i><sub class="lower-index">4</sub>)</span>, where <span class="tex-span"><i>a</i><sub class="lower-index">1</sub></span> is a number of students sent to Gryffindor, <span class="tex-span"><i>a</i><sub class="lower-index">2</sub></span> - to Ravenclaw, etc. It's intuitively clear that these sets will not be large. So you can get <span class="tex-span"><i>S</i><sub class="lower-index"><i>i</i> - 1</sub></span> from <span class="tex-span"><i>S</i><sub class="lower-index"><i>i</i></sub></span> in a trivial way, and get finally <span class="tex-span"><i>S</i><sub class="lower-index"><i>n</i></sub></span>, and determine the answer from it. </div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"><br /></div></div></b></div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;">What is a rigorous proof of the algorithm? Let us have a set<b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"> <span class="tex-span"><i>S</i> = {(<i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">1</sub>, <i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">2</sub>, <i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">3</sub>, <i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">4</sub>)}<sub class="lower-index"><i>i</i> = 1, 2, ..., <i>k</i></sub></span>. Represent its elements as <span class="tex-span"><i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub> = <i>b</i><sub class="lower-index"><i>j</i></sub> + <i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub></span>, <span class="tex-span"><i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub> ≥ 0</span>, where <span class="tex-span"><i>b</i><sub class="lower-index"><i>j</i></sub></span> are maximal possible, i.e. there is i for each j such that <span class="tex-span"><i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub> = 0</span>. Let the tuple <span class="tex-span">(<i>b</i><sub class="lower-index">1</sub>, <i>b</i><sub class="lower-index">2</sub>, <i>b</i><sub class="lower-index">3</sub>, <i>b</i><sub class="lower-index">4</sub>)</span> be called the base part of S, and the set <span class="tex-span">{(<i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">1</sub>, <i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">2</sub>, <i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">3</sub>, <i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">4</sub>)}<sub class="lower-index"><i>i</i> = 1, 2, ..., <i>k</i></sub></span> be called the variant part of S. </div></div></b></div></div></b><br /></div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Initially for <span class="tex-span"><i>S</i><sub class="lower-index">0</sub></span> both base and variant parts are zeroes. Let us see how base and variant parts change when a current student is added. If a house is fixed for the student, only the base part changes. It increases by 1 at the position corresponding to the house. In particular, it follows that a set with every base part can be obtained (since the string given in the input can contain every combination of symbols G, H, R, S). If the current symbol in the string is '?', it can influence both base and variant parts.</div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">For example, for the string '????' we have:</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">0</sub> = {(0 + 0, 0 + 0, 0 + 0, 0 + 0)}</span>,</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">1</sub> = {(0 + 1, 0 + 0, 0 + 0, 0 + 0), (0 + 0, 0 + 1, 0 + 0, 0 + 0), (0 + 0, 0 + 0, 0 + 1, 0 + 0), (0 + 0, 0 + 0, 0 + 0, 0 + 1)}</span>,</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">2</sub> = {(0 + 1, 0 + 1, 0 + 0, 0 + 0), (0 + 1, 0 + 0, 0 + 1, 0 + 0), (0 + 1, 0 + 0, 0 + 0, 0 + 1), (0 + 0, 0 + 1, 0 + 1, 0 + 0), (0 + 0, 0 + 1, 0 + 0, 0 + 1), (0 + 0, 0 + 0, 0 + 1, 0 + 1)}</span>,</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">3</sub> = {(0 + 1, 0 + 1, 0 + 1, 0 + 0), (0 + 1, 0 + 1, 0 + 0, 0 + 1), (0 + 1, 0 + 0, 0 + 1, 0 + 1), (0 + 0, 0 + 1, 0 + 1, 0 + 1)}</span>,</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">4</sub> = {(1 + 0, 1 + 0, 1 + 0, 1 + 0)}</span>.</div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Let us investigate the question of what species a variant part may have. It can be analyzed independently from a base one, taking into account that a base part can be any. Consider a directed graph with vertices corresponding to variant parts and with edges determined by the existence of<b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"> at least one base part that let go from one variant part to another. We are interested only in vertices reachable from <span class="tex-span">{(0, 0, 0, 0)}</span>.</div></div></b></div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Proposition. For all the vertices reachable from zero the following properties hold</div><div style="font-weight: normal;">(1) <span class="tex-span"><i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub> ≤ 2</span>,</div><div style="font-weight: normal;">(2) <span class="tex-span"><i>k</i> ≤ 13</span>.</div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Let us prove that all the vertices not having the properties (1) and (2) are unreachable from zero. Consider a variant part with the property (1). To get all edges going from it you have to try all possible base parts. Note that base parts, that consist of the numbers 0, 1, 2, 3 and contain at lest one 0, are enough. Indeed, base part influence which elements are minimal, and 1 will be added to them. A base part can be always normed to contain at least one 0. If a base part contains numbers greater than 3, then the corresponding positions will never be minimal (since 4+0 &gt; 0+2) and they can be changed equivalently by 3 (3+0 &gt; 0+2).</div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Unfortunately, my attempts to deal with cases by hand were unsuccessful, so I wrote <a href="http://pastebin.com/p3sFKKya">the program</a> that traverse the described graph. Starting from 0, it builds edges trying only &quot;small&quot; base parts described in the previous paragraph. As a result, the program obtains all the reachable variant parts (there is a little more than 1000 of them) and check (1) and (2) for them. In addition, the program helps to construct a test with<b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"> <span class="tex-span"><i>k</i> = 13</span>.</div></div></b></div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"><br /></div></div></b></div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;">The problem was supposed to be a problem on intuition. Participants have another solution passed. Their solution generate all permutations and distribute students greedily with respect to each permutation.</div></div></b><b><div style="font-weight: normal;display: inline !important;"><b><div style="font-weight: normal;display: inline !important;">This solution was a complete surprise for me. Unfortunately, it is wrong. Test 66 against it was added. Of course, submissions accepted during the round won't be rejudged. If such a solution be expected, most likely I wouldn't give such a task. In terms of intuition this solution is not better and not worse than mine. I hope you will not judge me strictly: it is a beautiful problem, and it was interesting to see how it would be solved. </div></b></div></b></div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><b><div style="font-weight: normal;display: inline !important;"><br /></div></b></div></b></div><div><div style="display: inline !important;"><div style="display: inline !important;"><div style="font-weight: normal;"><b>Problem E</b></div><div style="font-weight: normal;"><b><br /></b></div><div><div><div><div style="display: inline !important;"><div style="display: inline !important;">Consider a graph with floors as vertices and staircases as edges. It is clear that Harry can visit the whole connected component in which he is currently located.<br /></div></div></div><div style="font-weight: normal;"><br /></div></div></div><div>Every edge can be used to reach a new vertex for not more than two times. If a connected component contains n vertices and m edges, only n - 1 edges are used to reach a new vertex during its traversal. The remaining m - n + 1 edges are not used to reach a new vertex in their initial placement. So they will be used to reach a new vertex not more than once.</div><div><div><br /></div><div>So using edges of only one connected component you can reach no more than n - m + 1 new vertices. Totally there are not more than  <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7fae5c87930e2f915b8c632872cc1662dd30fa09.png" style="max-width: 100.0%;max-height: 100.0%;" /> reachable vertices. If m &lt; k - 1, it is impossible to visit all the vertices.  </div><div><br /></div><div>We show that otherwise (m &gt;= k - 1), if the degree of the vertex 0 is different from zero, it is possible to visit all the vertices. In other words, there is such a traversal that every edge can be moved.  Use depth-first search for the current component. If a current edge goes to an already visited vertex, move it to a new component and traverse it recursively. If a current edge goes to a new vertex, after you visit this vertex and go back, you also can move this edge to a new component. As a result each edge can be moved and used again, if you reach all the components. If a component contains at least one edge, you can go from it to the next one. First visit components with edges, and you will visit them all and by the inequality (m &gt;= k - 1) there are enough edges to visit all the isolated vertices.  </div><div><br /></div><div>If the degree of the vertex 1 is zero, you can not start a traversal before you move some edge to it. After that you can go by this edge and remove it with the vertex 1 from the graph, becase you can not use this edge once more. If the chose edge is a bridge, you get k connected components and m - 1 egdes. If it is not a bridge, you get k - 1 components and m - 1 edges. In the first case the inequality m &gt;= k - 1 turns m &gt;= k. In the second case -  m &gt;= k - 1. So if not all the edges are bridges, you should not take a bridge. If they all are bridges, you should disconnect an edge from a vertex of degree &gt;= 2 not to came back to the initial situation with the zero degree of the first vertex. If there is no such vertex, it is easy to check that there is no solution.</div></div></div></div></div></div></div></div></div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/65" class="notice" style="text-decoration: none;">Codeforces Beta Round 60</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-2326-1431").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "2326", blogEntryId: "1431", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=beta+round+%2360" class="tag notice" style="text-decoration: none;">beta round #60</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces" class="tag notice" style="text-decoration: none;">codeforces</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=tutorial" class="tag notice" style="text-decoration: none;">tutorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1431"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+33</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1431"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; 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top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26324" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="3858" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26324"> <div class="moveup"> <div class="ttypography">good analysis...</div> </div> </div> <div class="reply info"> <a class="comment-26324 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26324 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26324"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="26331" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/A.K.Goharshady" style="position: relative;"> <img src='https://userpic.codeforces.org/9153/avatar/358f1b75189ae870.jpg'/> </a> <div><a href="/profile/A.K.Goharshady" title="Candidate Master A.K.Goharshady" class="rated-user user-violet">A.K.Goharshady</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/06/2011 12:52">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26331" href="?#comment-26331" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26331" class="CommentVoteFrame" data-commentRating="2" data-commentUserId="9153" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+2</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26331"> <div class="moveup"> <div class="ttypography">Problem A was harder than D :D</div> </div> </div> <div class="reply info"> <a class="comment-26331 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26331 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26331"> <li> <div class="comment"> <table class="comment-table" commentId="26336" commentParentId="26331"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Alex_KPR" style="position: relative;"> <img src='https://userpic.codeforces.org/209/avatar/b403606b22dc5082.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/Alex_KPR" title="Master Alex_KPR" class="rated-user user-orange">Alex_KPR</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/06/2011 13:03">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26336" href="?#comment-26336" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-26331" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26336" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="209" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26336"> <div class="moveup"> <div class="ttypography">agree with you =)</div> </div> </div> <div class="reply info"> <a class="comment-26336 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26336 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26336"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="26374" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mR.ilchi" style="position: relative;"> <img src='https://userpic.codeforces.org/11753/avatar/b0675918b77546aa.jpg'/> </a> <div><a href="/profile/mR.ilchi" title="International Grandmaster mR.ilchi" class="rated-user user-red">mR.ilchi</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/06/2011 15:58">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26374" href="?#comment-26374" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="26374" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="26374" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="11753" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26374"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">please translate problem D and E too.</div><div class="from-renderer"><div>thank's for your nice contest!!!</div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-26374 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26374 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26374"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="26587" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/sunhaowen567" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/sunhaowen567" title="Expert sunhaowen567" class="rated-user user-blue">sunhaowen567</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/07/2011 07:43">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26587" href="?#comment-26587" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26587" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3232" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26587"> <div class="moveup"> <div class="ttypography">waiting for problem E......</div> </div> </div> <div class="reply info"> <a class="comment-26587 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26587 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26587"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="26588" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kang205" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/kang205" title="Expert kang205" class="rated-user user-blue">kang205</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/07/2011 08:13">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26588" href="?#comment-26588" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26588" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13097" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26588"> <div class="moveup"> <div class="ttypography">Problem D's proof is very NICE.<br /><br /><br /><br /></div> </div> </div> <div class="reply info"> <a class="comment-26588 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26588 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26588"> <li> <div class="comment"> <table class="comment-table" commentId="26589" commentParentId="26588"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kang205" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/kang205" title="Expert kang205" class="rated-user user-blue">kang205</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/07/2011 08:16">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26589" href="?#comment-26589" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-26588" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26589" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13097" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26589"> <div class="moveup"> <div class="ttypography">I use <b>random <b><b><b> generate permutations</b></b></b></b>,but the random times be set 10000,so I got TLE.<br /><br />If set 2000,I got AC....</div> </div> </div> <div class="reply info"> <a class="comment-26589 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26589 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26589"> <li> <div class="comment"> <table class="comment-table" commentId="194733" commentParentId="26589"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/wjh720" style="position: relative;"> <img src='https://userpic.codeforces.org/210352/avatar/d212772572283d08.jpg'/> </a> <div><a href="/profile/wjh720" title="International Grandmaster wjh720" class="rated-user user-red">wjh720</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Oct/30/2014 09:43">9 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-194733" href="?#comment-194733" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-26589" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="194733" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="210352" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-194733"> <div class="moveup"> <div class="ttypography"><p>You can have a try with {&quot;?HRS&quot;*2500} :)</p></div> </div> </div> <div class="reply info"> <a class="comment-194733 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-194733 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-194733"> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="310517" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/throwaways" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/throwaways" title="Unrated, throwaways" class="rated-user user-black">throwaways</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Aug/17/2016 00:08">7 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-310517" href="?#comment-310517" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="310517" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="310517" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="401734" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-310517"> <div class="moveup"> <div class="ttypography"><p>what might the time complexity of D be?</p></div> </div> </div> <div class="reply info"> <a class="comment-310517 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-310517 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-310517"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="555734" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/roll_no_1" style="position: relative;"> <img src='https://userpic.codeforces.org/631859/avatar/36d157f91f64fe7f.jpg'/> </a> <div><a href="/profile/roll_no_1" title="Master roll_no_1" class="rated-user user-orange">roll_no_1</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Nov/03/2019 08:56">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-555734" href="?#comment-555734" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="555734" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="631859" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-555734"> <div class="moveup"> <div class="ttypography"><p>Here are the 2 interpretations of problem A's solution as I understood them:</p><p><a href="/contest/65/submission/64128016" title="Submission 64128016 by roll_no_1">64128016</a></p><p><a href="/contest/65/submission/64128379" title="Submission 64128379 by roll_no_1">64128379</a></p></div> </div> </div> <div class="reply info"> <a class="comment-555734 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-555734 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-555734"> </ul> </div> <br/> <div id="editBox-1441" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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65C
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C. Harry Potter and the Golden Snitch
<div class="problem-statement"><div class="header"><div class="title">C. Harry Potter and the Golden Snitch</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Brothers Fred and George Weasley once got into the sporting goods store and opened a box of Quidditch balls. After long and painful experiments they found out that the Golden Snitch is not enchanted at all. It is simply a programmed device. It always moves along the same trajectory, which is a polyline with vertices at the points <span class="tex-span">(<i>x</i><sub class="lower-index">0</sub>, <i>y</i><sub class="lower-index">0</sub>, <i>z</i><sub class="lower-index">0</sub>)</span>, <span class="tex-span">(<i>x</i><sub class="lower-index">1</sub>, <i>y</i><sub class="lower-index">1</sub>, <i>z</i><sub class="lower-index">1</sub>)</span>, ..., <span class="tex-span">(<i>x</i><sub class="lower-index"><i>n</i></sub>, <i>y</i><sub class="lower-index"><i>n</i></sub>, <i>z</i><sub class="lower-index"><i>n</i></sub>)</span>. At the beginning of the game the snitch is positioned at the point <span class="tex-span">(<i>x</i><sub class="lower-index">0</sub>, <i>y</i><sub class="lower-index">0</sub>, <i>z</i><sub class="lower-index">0</sub>)</span>, and then moves along the polyline at the constant speed <span class="tex-span"><i>v</i><sub class="lower-index"><i>s</i></sub></span>. The twins have not yet found out how the snitch behaves then. Nevertheless, they hope that the retrieved information will help Harry Potter and his team in the upcoming match against Slytherin. Harry Potter learned that at the beginning the game he will be at the point <span class="tex-span">(<i>P</i><sub class="lower-index"><i>x</i></sub>, <i>P</i><sub class="lower-index"><i>y</i></sub>, <i>P</i><sub class="lower-index"><i>z</i></sub>)</span> and his super fast Nimbus 2011 broom allows him to move at the constant speed <span class="tex-span"><i>v</i><sub class="lower-index"><i>p</i></sub></span> in any direction or remain idle. <span class="tex-span"><i>v</i><sub class="lower-index"><i>p</i></sub></span> is not less than the speed of the snitch <span class="tex-span"><i>v</i><sub class="lower-index"><i>s</i></sub></span>. Harry Potter, of course, wants to catch the snitch as soon as possible. Or, if catching the snitch while it is moving along the polyline is impossible, he wants to hurry the Weasley brothers with their experiments. Harry Potter catches the snitch at the time when they are at the same point. Help Harry.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains a single integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10000</span>). The following <span class="tex-span"><i>n</i> + 1</span> lines contain the coordinates <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>z</i><sub class="lower-index"><i>i</i></sub></span>, separated by single spaces. The coordinates of any two consecutive points do not coincide. The next line contains the velocities <span class="tex-span"><i>v</i><sub class="lower-index"><i>p</i></sub></span> and <span class="tex-span"><i>v</i><sub class="lower-index"><i>s</i></sub></span>, the last line contains <span class="tex-span"><i>P</i><sub class="lower-index"><i>x</i></sub></span>, <span class="tex-span"><i>P</i><sub class="lower-index"><i>y</i></sub></span>, <span class="tex-span"><i>P</i><sub class="lower-index"><i>z</i></sub></span>, separated by single spaces. All the numbers in the input are integers, their absolute value does not exceed <span class="tex-span">10<sup class="upper-index">4</sup></span>. The speeds are strictly positive. It is guaranteed that <span class="tex-span"><i>v</i><sub class="lower-index"><i>s</i></sub> ≤ <i>v</i><sub class="lower-index"><i>p</i></sub></span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>If Harry Potter can catch the snitch while it is moving along the polyline (including the end <span class="tex-span">(<i>x</i><sub class="lower-index"><i>n</i></sub>, <i>y</i><sub class="lower-index"><i>n</i></sub>, <i>z</i><sub class="lower-index"><i>n</i></sub>)</span>), print "YES" in the first line (without the quotes). Print in the second line <span class="tex-span"><i>t</i></span>, which is the earliest moment of time, when Harry will be able to catch the snitch. On the third line print three numbers <span class="tex-span"><i>X</i></span>, <span class="tex-span"><i>Y</i></span>, <span class="tex-span"><i>Z</i></span>, the coordinates of the point at which this happens. The absolute or relative error in the answer should not exceed <span class="tex-span">10<sup class="upper-index"> - 6</sup></span>. If Harry is not able to catch the snitch during its moving along the described polyline, print "NO".</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>4<br/>0 0 0<br/>0 10 0<br/>10 10 0<br/>10 0 0<br/>0 0 0<br/>1 1<br/>5 5 25<br/></pre></div><div class="output"><div class="title">Output</div><pre>YES<br/>25.5000000000<br/>10.0000000000 4.5000000000 0.0000000000<br/></pre></div><div class="input"><div class="title">Input</div><pre>4<br/>0 0 0<br/>0 10 0<br/>10 10 0<br/>10 0 0<br/>0 0 0<br/>1 1<br/>5 5 50<br/></pre></div><div class="output"><div class="title">Output</div><pre>NO<br/></pre></div><div class="input"><div class="title">Input</div><pre>1<br/>1 2 3<br/>4 5 6<br/>20 10<br/>1 2 3<br/></pre></div><div class="output"><div class="title">Output</div><pre>YES<br/>0.0000000000<br/>1.0000000000 2.0000000000 3.0000000000<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="C" data-uuid="ps_e617f25c781b4bec4eaf10dc10c51593bf1da2fe"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. Harry Potter and the Golden Snitch</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Brothers Fred and George Weasley once got into the sporting goods store and opened a box of Quidditch balls. After long and painful experiments they found out that the Golden Snitch is not enchanted at all. It is simply a programmed device. It always moves along the same trajectory, which is a polyline with vertices at the points <span class="tex-span">(<i>x</i><sub class="lower-index">0</sub>, <i>y</i><sub class="lower-index">0</sub>, <i>z</i><sub class="lower-index">0</sub>)</span>, <span class="tex-span">(<i>x</i><sub class="lower-index">1</sub>, <i>y</i><sub class="lower-index">1</sub>, <i>z</i><sub class="lower-index">1</sub>)</span>, ..., <span class="tex-span">(<i>x</i><sub class="lower-index"><i>n</i></sub>, <i>y</i><sub class="lower-index"><i>n</i></sub>, <i>z</i><sub class="lower-index"><i>n</i></sub>)</span>. At the beginning of the game the snitch is positioned at the point <span class="tex-span">(<i>x</i><sub class="lower-index">0</sub>, <i>y</i><sub class="lower-index">0</sub>, <i>z</i><sub class="lower-index">0</sub>)</span>, and then moves along the polyline at the constant speed <span class="tex-span"><i>v</i><sub class="lower-index"><i>s</i></sub></span>. The twins have not yet found out how the snitch behaves then. Nevertheless, they hope that the retrieved information will help Harry Potter and his team in the upcoming match against Slytherin. Harry Potter learned that at the beginning the game he will be at the point <span class="tex-span">(<i>P</i><sub class="lower-index"><i>x</i></sub>, <i>P</i><sub class="lower-index"><i>y</i></sub>, <i>P</i><sub class="lower-index"><i>z</i></sub>)</span> and his super fast Nimbus 2011 broom allows him to move at the constant speed <span class="tex-span"><i>v</i><sub class="lower-index"><i>p</i></sub></span> in any direction or remain idle. <span class="tex-span"><i>v</i><sub class="lower-index"><i>p</i></sub></span> is not less than the speed of the snitch <span class="tex-span"><i>v</i><sub class="lower-index"><i>s</i></sub></span>. Harry Potter, of course, wants to catch the snitch as soon as possible. Or, if catching the snitch while it is moving along the polyline is impossible, he wants to hurry the Weasley brothers with their experiments. Harry Potter catches the snitch at the time when they are at the same point. Help Harry.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains a single integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10000</span>). The following <span class="tex-span"><i>n</i> + 1</span> lines contain the coordinates <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>z</i><sub class="lower-index"><i>i</i></sub></span>, separated by single spaces. The coordinates of any two consecutive points do not coincide. The next line contains the velocities <span class="tex-span"><i>v</i><sub class="lower-index"><i>p</i></sub></span> and <span class="tex-span"><i>v</i><sub class="lower-index"><i>s</i></sub></span>, the last line contains <span class="tex-span"><i>P</i><sub class="lower-index"><i>x</i></sub></span>, <span class="tex-span"><i>P</i><sub class="lower-index"><i>y</i></sub></span>, <span class="tex-span"><i>P</i><sub class="lower-index"><i>z</i></sub></span>, separated by single spaces. All the numbers in the input are integers, their absolute value does not exceed <span class="tex-span">10<sup class="upper-index">4</sup></span>. The speeds are strictly positive. It is guaranteed that <span class="tex-span"><i>v</i><sub class="lower-index"><i>s</i></sub> ≤ <i>v</i><sub class="lower-index"><i>p</i></sub></span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>If Harry Potter can catch the snitch while it is moving along the polyline (including the end <span class="tex-span">(<i>x</i><sub class="lower-index"><i>n</i></sub>, <i>y</i><sub class="lower-index"><i>n</i></sub>, <i>z</i><sub class="lower-index"><i>n</i></sub>)</span>), print &quot;YES&quot; in the first line (without the quotes). Print in the second line <span class="tex-span"><i>t</i></span>, which is the earliest moment of time, when Harry will be able to catch the snitch. On the third line print three numbers <span class="tex-span"><i>X</i></span>, <span class="tex-span"><i>Y</i></span>, <span class="tex-span"><i>Z</i></span>, the coordinates of the point at which this happens. The absolute or relative error in the answer should not exceed <span class="tex-span">10<sup class="upper-index"> - 6</sup></span>. If Harry is not able to catch the snitch during its moving along the described polyline, print &quot;NO&quot;.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>4<br />0 0 0<br />0 10 0<br />10 10 0<br />10 0 0<br />0 0 0<br />1 1<br />5 5 25<br /></pre></div><div class="output"><div class="title">Output</div><pre>YES<br />25.5000000000<br />10.0000000000 4.5000000000 0.0000000000<br /></pre></div><div class="input"><div class="title">Input</div><pre>4<br />0 0 0<br />0 10 0<br />10 10 0<br />10 0 0<br />0 0 0<br />1 1<br />5 5 50<br /></pre></div><div class="output"><div class="title">Output</div><pre>NO<br /></pre></div><div class="input"><div class="title">Input</div><pre>1<br />1 2 3<br />4 5 6<br />20 10<br />1 2 3<br /></pre></div><div class="output"><div class="title">Output</div><pre>YES<br />0.0000000000<br />1.0000000000 2.0000000000 3.0000000000<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=C]"); 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["Binary search", "Geometry, computational geometry"]
["binary search", "geometry", "*2100"]
https://codeforces.com/blog/entry/1431
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You can take a*c*e grams of sand, turn them into b*c*e grams of lead, and them turn into b*d*e grams of gold, and them turn into b*d*f grams of sand. If b*d*f &gt; a*c*e, you can infinitely increase the amount of sand and consequently the amount of gold. Otherwise, if b*d*f &lt;= a*c*e, it is impossible to get infinitely large amount of gold. The same is true when the fraction  (a*c*e)/(b*d*f) has zero numerator only or zero denuminator only. Otherwise there is 0/0, and  you have to check cases specially.</div><div><br /></div><div>I explain, why I make this problem to be problem A.</div><div><br /></div><div>1. Solution of the problem requires very little knowledge of programming (only &quot;if&quot;), so it was feasible for all participants.</div><div>2. Tricky cases really exist, but I hoped that &quot;<span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">stronger competitors will ... help newcomers to catch all bugs by their hacks&quot;. </span>And so it happened.</div><div><br /></div><div>Maybe I was wrong: this problem is too complex for A.</div><div><br /></div><div>A large number of hacks for this problem is a quite foreseen circumstance. I haven't include the special class of tests into the pretests intendently, to make hacking more interesting. In fairness I should note that Artem Rakhov was against this idea. Beause of this task the problem surfaced that Gassa writes about <a href="https://codeforces.com/comments/1432#comment-26176">here</a> in Russian: pretests cover some incomplete set of cases and it is not clear in advance what the event &quot;solution passed pretests&quot; means. I think it should be discussed, and strong principles of pretests development should be stated.</div></div><div><br /></div><div><b>Problem B</b></div><div> </div><div><br /></div><div>The problem has greedy solution. Change a digit in the first date to make it as small as possible. At each of the next steps try all one-digit exchanges in the current date and choose one that makes the date not less than the previous one and as small as possible at the same time. If the last year won't exceed 2011 - the answer is found. Otherwise there is no solution.</div><div><br /></div><div>How to prove that? Consider any correct answer. Clearly, if the first date in it is different from the smallest possible number that can be obtained from the first of given years, your can put the smallest number instead of it. The second date can be exchanged by the smallest possible number not exceeding the first number, etc.Ar a result you obtain a greedy solution that is built by the algorithm described above. If the greedy solution doesn't exist, solution doesn't esist too.</div><div><div><div><br /></div><div>The problem also has a dynamic solution.</div></div><div><br /></div><div><div><div><b>Problem C</b></div><div><div><br /></div><div>Check for each segment in the polyline if Harry can catch the snitch in it. Note that since <span class="tex-span"><i>v</i><sub class="lower-index"><i>p</i></sub> ≥ <i>v</i><sub class="lower-index"><i>s</i></sub></span>, if Harry can catch the snitch at some moment of time, he can catch it at any later moment. He can just follow snitch along its trajectory. So use binary search in each segment.</div><div><br /></div><div>About problems with EPS that participants got. The problems may be caused by</div><div>1) some EPS in the condition: while (leftTime + EPS &lt; rightTime) &lt;do binary search&gt;. The task was to output with a fixed accurancy not only the time, but also the point coordinates. If the difference between the time and the right one is less than EPS, the difference between coordinates may be significantly larger. In such cases you should compare not arguments of a function, but values of the function with EPS. Or the way that I usually follow and that once was not liked by the teacher of numerical methods - to implement some fixed number of iterations of the binary search (say, 60).  </div><div>2) EPS in comparison of time moments inside the binary search like this:</div><div>if (currentTime + addTime &gt; distance / potterSpeed - EPS)</div><div>                                                rightTime = currentTime;</div><div>                                        else</div><div>                                                leftTime = currentTime;</div><div>Here it is better to remove EPS at all. Or to put EPS significantly smaller than the required accurancy for printing the point.</div><div><br /></div><div>(Code fragments are from Egor's solution.)</div></div><div><br /></div><div>Thus, there was no crime with severe limitations. Probably for such problems extreme accurancy tests should be in pretests? It is about principles of pretests making again. </div><div><br /></div><div><b>UPD.</b> The problem has an analytical solution too. Consider the i-th segment. Let <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i></sub>, <i>y</i><sub class="lower-index"><i>i</i></sub>, <i>z</i><sub class="lower-index"><i>i</i></sub>)</span> and <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i> + 1</sub>, <i>y</i><sub class="lower-index"><i>i</i> + 1</sub>, <i>z</i><sub class="lower-index"><i>i</i> + 1</sub>)</span> be its ends, and let <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub></span> be the time required for the snitch to reach the beginning of the segment. Then at the moment t the snitch will be at the point (x, y, z), <span class="tex-span"><i>x</i> = <i>x</i><sub class="lower-index"><i>i</i></sub> + (<i>x</i><sub class="lower-index"><i>i</i> + 1</sub> - <i>x</i><sub class="lower-index"><i>i</i></sub>)(<i>t</i> - <i>t</i><sub class="lower-index"><i>i</i></sub>) / <i>T</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>y</i> = <i>y</i><sub class="lower-index"><i>i</i></sub> + (<i>y</i><sub class="lower-index"><i>i</i> + 1</sub> - <i>y</i><sub class="lower-index"><i>i</i></sub>)(<i>t</i> - <i>t</i><sub class="lower-index"><i>i</i></sub>) / <i>T</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>z</i> = <i>z</i><sub class="lower-index"><i>i</i></sub> + (<i>z</i><sub class="lower-index"><i>i</i> + 1</sub> - <i>z</i><sub class="lower-index"><i>i</i></sub>)(<i>t</i> - <i>t</i><sub class="lower-index"><i>i</i></sub>) / <i>T</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>T</i><sub class="lower-index"><i>i</i></sub></span> is a time necessary for snitch to overcome the segment. To catch the snitch at the point (x, y, z), Harry have to overcome the distance that squared is equal to <span class="tex-span">(<i>x</i> - <i>P</i><sub class="lower-index"><i>x</i></sub>)<sup class="upper-index">2</sup> + (<i>y</i> - <i>P</i><sub class="lower-index"><i>y</i></sub>)<sup class="upper-index">2</sup> + (<i>z</i> - <i>P</i><sub class="lower-index"><i>z</i></sub>)<sup class="upper-index">2</sup></span> for the time t. It is possible if <span class="tex-span">(<i>x</i> - <i>P</i><sub class="lower-index"><i>x</i></sub>)<sup class="upper-index">2</sup> + (<i>y</i> - <i>P</i><sub class="lower-index"><i>y</i></sub>)<sup class="upper-index">2</sup> + (<i>z</i> - <i>P</i><sub class="lower-index"><i>z</i></sub>)<sup class="upper-index">2</sup> ≤ (<i>tv</i><sub class="lower-index"><i>p</i></sub>)<sup class="upper-index">2</sup></span>. To find the minimal proper moment t, solve the corresponding quadratic equation.<br /></div><div><br /></div><div><div style="font-weight: normal;"><b>Problem D</b></div><div style="font-weight: normal;"><br /></div><div><div style="font-weight: normal;">Let <span class="tex-span"><i>S</i><sub class="lower-index"><i>i</i></sub></span> be a set of all possible assignments of the first <span class="tex-span"><i>i</i></span> students to the houses, that is a set of tuples <span class="tex-span">(<i>a</i><sub class="lower-index">1</sub>, <i>a</i><sub class="lower-index">2</sub>, <i>a</i><sub class="lower-index">3</sub>, <i>a</i><sub class="lower-index">4</sub>)</span>, where <span class="tex-span"><i>a</i><sub class="lower-index">1</sub></span> is a number of students sent to Gryffindor, <span class="tex-span"><i>a</i><sub class="lower-index">2</sub></span> - to Ravenclaw, etc. It's intuitively clear that these sets will not be large. So you can get <span class="tex-span"><i>S</i><sub class="lower-index"><i>i</i> - 1</sub></span> from <span class="tex-span"><i>S</i><sub class="lower-index"><i>i</i></sub></span> in a trivial way, and get finally <span class="tex-span"><i>S</i><sub class="lower-index"><i>n</i></sub></span>, and determine the answer from it. </div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"><br /></div></div></b></div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;">What is a rigorous proof of the algorithm? Let us have a set<b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"> <span class="tex-span"><i>S</i> = {(<i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">1</sub>, <i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">2</sub>, <i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">3</sub>, <i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">4</sub>)}<sub class="lower-index"><i>i</i> = 1, 2, ..., <i>k</i></sub></span>. Represent its elements as <span class="tex-span"><i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub> = <i>b</i><sub class="lower-index"><i>j</i></sub> + <i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub></span>, <span class="tex-span"><i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub> ≥ 0</span>, where <span class="tex-span"><i>b</i><sub class="lower-index"><i>j</i></sub></span> are maximal possible, i.e. there is i for each j such that <span class="tex-span"><i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub> = 0</span>. Let the tuple <span class="tex-span">(<i>b</i><sub class="lower-index">1</sub>, <i>b</i><sub class="lower-index">2</sub>, <i>b</i><sub class="lower-index">3</sub>, <i>b</i><sub class="lower-index">4</sub>)</span> be called the base part of S, and the set <span class="tex-span">{(<i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">1</sub>, <i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">2</sub>, <i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">3</sub>, <i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">4</sub>)}<sub class="lower-index"><i>i</i> = 1, 2, ..., <i>k</i></sub></span> be called the variant part of S. </div></div></b></div></div></b><br /></div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Initially for <span class="tex-span"><i>S</i><sub class="lower-index">0</sub></span> both base and variant parts are zeroes. Let us see how base and variant parts change when a current student is added. If a house is fixed for the student, only the base part changes. It increases by 1 at the position corresponding to the house. In particular, it follows that a set with every base part can be obtained (since the string given in the input can contain every combination of symbols G, H, R, S). If the current symbol in the string is '?', it can influence both base and variant parts.</div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">For example, for the string '????' we have:</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">0</sub> = {(0 + 0, 0 + 0, 0 + 0, 0 + 0)}</span>,</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">1</sub> = {(0 + 1, 0 + 0, 0 + 0, 0 + 0), (0 + 0, 0 + 1, 0 + 0, 0 + 0), (0 + 0, 0 + 0, 0 + 1, 0 + 0), (0 + 0, 0 + 0, 0 + 0, 0 + 1)}</span>,</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">2</sub> = {(0 + 1, 0 + 1, 0 + 0, 0 + 0), (0 + 1, 0 + 0, 0 + 1, 0 + 0), (0 + 1, 0 + 0, 0 + 0, 0 + 1), (0 + 0, 0 + 1, 0 + 1, 0 + 0), (0 + 0, 0 + 1, 0 + 0, 0 + 1), (0 + 0, 0 + 0, 0 + 1, 0 + 1)}</span>,</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">3</sub> = {(0 + 1, 0 + 1, 0 + 1, 0 + 0), (0 + 1, 0 + 1, 0 + 0, 0 + 1), (0 + 1, 0 + 0, 0 + 1, 0 + 1), (0 + 0, 0 + 1, 0 + 1, 0 + 1)}</span>,</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">4</sub> = {(1 + 0, 1 + 0, 1 + 0, 1 + 0)}</span>.</div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Let us investigate the question of what species a variant part may have. It can be analyzed independently from a base one, taking into account that a base part can be any. Consider a directed graph with vertices corresponding to variant parts and with edges determined by the existence of<b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"> at least one base part that let go from one variant part to another. We are interested only in vertices reachable from <span class="tex-span">{(0, 0, 0, 0)}</span>.</div></div></b></div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Proposition. For all the vertices reachable from zero the following properties hold</div><div style="font-weight: normal;">(1) <span class="tex-span"><i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub> ≤ 2</span>,</div><div style="font-weight: normal;">(2) <span class="tex-span"><i>k</i> ≤ 13</span>.</div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Let us prove that all the vertices not having the properties (1) and (2) are unreachable from zero. Consider a variant part with the property (1). To get all edges going from it you have to try all possible base parts. Note that base parts, that consist of the numbers 0, 1, 2, 3 and contain at lest one 0, are enough. Indeed, base part influence which elements are minimal, and 1 will be added to them. A base part can be always normed to contain at least one 0. If a base part contains numbers greater than 3, then the corresponding positions will never be minimal (since 4+0 &gt; 0+2) and they can be changed equivalently by 3 (3+0 &gt; 0+2).</div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Unfortunately, my attempts to deal with cases by hand were unsuccessful, so I wrote <a href="http://pastebin.com/p3sFKKya">the program</a> that traverse the described graph. Starting from 0, it builds edges trying only &quot;small&quot; base parts described in the previous paragraph. As a result, the program obtains all the reachable variant parts (there is a little more than 1000 of them) and check (1) and (2) for them. In addition, the program helps to construct a test with<b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"> <span class="tex-span"><i>k</i> = 13</span>.</div></div></b></div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"><br /></div></div></b></div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;">The problem was supposed to be a problem on intuition. Participants have another solution passed. Their solution generate all permutations and distribute students greedily with respect to each permutation.</div></div></b><b><div style="font-weight: normal;display: inline !important;"><b><div style="font-weight: normal;display: inline !important;">This solution was a complete surprise for me. Unfortunately, it is wrong. Test 66 against it was added. Of course, submissions accepted during the round won't be rejudged. If such a solution be expected, most likely I wouldn't give such a task. In terms of intuition this solution is not better and not worse than mine. I hope you will not judge me strictly: it is a beautiful problem, and it was interesting to see how it would be solved. </div></b></div></b></div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><b><div style="font-weight: normal;display: inline !important;"><br /></div></b></div></b></div><div><div style="display: inline !important;"><div style="display: inline !important;"><div style="font-weight: normal;"><b>Problem E</b></div><div style="font-weight: normal;"><b><br /></b></div><div><div><div><div style="display: inline !important;"><div style="display: inline !important;">Consider a graph with floors as vertices and staircases as edges. It is clear that Harry can visit the whole connected component in which he is currently located.<br /></div></div></div><div style="font-weight: normal;"><br /></div></div></div><div>Every edge can be used to reach a new vertex for not more than two times. If a connected component contains n vertices and m edges, only n - 1 edges are used to reach a new vertex during its traversal. The remaining m - n + 1 edges are not used to reach a new vertex in their initial placement. So they will be used to reach a new vertex not more than once.</div><div><div><br /></div><div>So using edges of only one connected component you can reach no more than n - m + 1 new vertices. Totally there are not more than  <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7fae5c87930e2f915b8c632872cc1662dd30fa09.png" style="max-width: 100.0%;max-height: 100.0%;" /> reachable vertices. If m &lt; k - 1, it is impossible to visit all the vertices.  </div><div><br /></div><div>We show that otherwise (m &gt;= k - 1), if the degree of the vertex 0 is different from zero, it is possible to visit all the vertices. In other words, there is such a traversal that every edge can be moved.  Use depth-first search for the current component. If a current edge goes to an already visited vertex, move it to a new component and traverse it recursively. If a current edge goes to a new vertex, after you visit this vertex and go back, you also can move this edge to a new component. As a result each edge can be moved and used again, if you reach all the components. If a component contains at least one edge, you can go from it to the next one. First visit components with edges, and you will visit them all and by the inequality (m &gt;= k - 1) there are enough edges to visit all the isolated vertices.  </div><div><br /></div><div>If the degree of the vertex 1 is zero, you can not start a traversal before you move some edge to it. After that you can go by this edge and remove it with the vertex 1 from the graph, becase you can not use this edge once more. If the chose edge is a bridge, you get k connected components and m - 1 egdes. If it is not a bridge, you get k - 1 components and m - 1 edges. In the first case the inequality m &gt;= k - 1 turns m &gt;= k. In the second case -  m &gt;= k - 1. So if not all the edges are bridges, you should not take a bridge. If they all are bridges, you should disconnect an edge from a vertex of degree &gt;= 2 not to came back to the initial situation with the zero degree of the first vertex. If there is no such vertex, it is easy to check that there is no solution.</div></div></div></div></div></div></div></div></div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/65" class="notice" style="text-decoration: none;">Codeforces Beta Round 60</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-2326-1431").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "2326", blogEntryId: "1431", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=beta+round+%2360" class="tag notice" style="text-decoration: none;">beta round #60</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces" class="tag notice" style="text-decoration: none;">codeforces</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=tutorial" class="tag notice" style="text-decoration: none;">tutorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1431"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+33</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1431"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; 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top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26324" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="3858" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26324"> <div class="moveup"> <div class="ttypography">good analysis...</div> </div> </div> <div class="reply info"> <a class="comment-26324 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26324 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26324"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="26331" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/A.K.Goharshady" style="position: relative;"> <img src='https://userpic.codeforces.org/9153/avatar/358f1b75189ae870.jpg'/> </a> <div><a href="/profile/A.K.Goharshady" title="Candidate Master A.K.Goharshady" class="rated-user user-violet">A.K.Goharshady</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/06/2011 12:52">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26331" href="?#comment-26331" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26331" class="CommentVoteFrame" data-commentRating="2" data-commentUserId="9153" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+2</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26331"> <div class="moveup"> <div class="ttypography">Problem A was harder than D :D</div> </div> </div> <div class="reply info"> <a class="comment-26331 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26331 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26331"> <li> <div class="comment"> <table class="comment-table" commentId="26336" commentParentId="26331"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Alex_KPR" style="position: relative;"> <img src='https://userpic.codeforces.org/209/avatar/b403606b22dc5082.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/Alex_KPR" title="Master Alex_KPR" class="rated-user user-orange">Alex_KPR</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/06/2011 13:03">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26336" href="?#comment-26336" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-26331" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26336" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="209" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26336"> <div class="moveup"> <div class="ttypography">agree with you =)</div> </div> </div> <div class="reply info"> <a class="comment-26336 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26336 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26336"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="26374" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mR.ilchi" style="position: relative;"> <img src='https://userpic.codeforces.org/11753/avatar/b0675918b77546aa.jpg'/> </a> <div><a href="/profile/mR.ilchi" title="International Grandmaster mR.ilchi" class="rated-user user-red">mR.ilchi</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/06/2011 15:58">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26374" href="?#comment-26374" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="26374" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="26374" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="11753" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26374"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">please translate problem D and E too.</div><div class="from-renderer"><div>thank's for your nice contest!!!</div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-26374 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26374 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26374"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="26587" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/sunhaowen567" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/sunhaowen567" title="Expert sunhaowen567" class="rated-user user-blue">sunhaowen567</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/07/2011 07:43">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26587" href="?#comment-26587" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26587" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3232" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26587"> <div class="moveup"> <div class="ttypography">waiting for problem E......</div> </div> </div> <div class="reply info"> <a class="comment-26587 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26587 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26587"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="26588" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kang205" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/kang205" title="Expert kang205" class="rated-user user-blue">kang205</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/07/2011 08:13">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26588" href="?#comment-26588" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26588" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13097" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26588"> <div class="moveup"> <div class="ttypography">Problem D's proof is very NICE.<br /><br /><br /><br /></div> </div> </div> <div class="reply info"> <a class="comment-26588 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26588 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26588"> <li> <div class="comment"> <table class="comment-table" commentId="26589" commentParentId="26588"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kang205" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/kang205" title="Expert kang205" class="rated-user user-blue">kang205</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/07/2011 08:16">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26589" href="?#comment-26589" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-26588" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26589" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13097" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26589"> <div class="moveup"> <div class="ttypography">I use <b>random <b><b><b> generate permutations</b></b></b></b>,but the random times be set 10000,so I got TLE.<br /><br />If set 2000,I got AC....</div> </div> </div> <div class="reply info"> <a class="comment-26589 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26589 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26589"> <li> <div class="comment"> <table class="comment-table" commentId="194733" commentParentId="26589"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/wjh720" style="position: relative;"> <img src='https://userpic.codeforces.org/210352/avatar/d212772572283d08.jpg'/> </a> <div><a href="/profile/wjh720" title="International Grandmaster wjh720" class="rated-user user-red">wjh720</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Oct/30/2014 09:43">9 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-194733" href="?#comment-194733" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-26589" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="194733" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="210352" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-194733"> <div class="moveup"> <div class="ttypography"><p>You can have a try with {&quot;?HRS&quot;*2500} :)</p></div> </div> </div> <div class="reply info"> <a class="comment-194733 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-194733 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-194733"> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="310517" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/throwaways" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/throwaways" title="Unrated, throwaways" class="rated-user user-black">throwaways</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Aug/17/2016 00:08">7 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-310517" href="?#comment-310517" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="310517" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="310517" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="401734" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-310517"> <div class="moveup"> <div class="ttypography"><p>what might the time complexity of D be?</p></div> </div> </div> <div class="reply info"> <a class="comment-310517 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-310517 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-310517"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="555734" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/roll_no_1" style="position: relative;"> <img src='https://userpic.codeforces.org/631859/avatar/36d157f91f64fe7f.jpg'/> </a> <div><a href="/profile/roll_no_1" title="Master roll_no_1" class="rated-user user-orange">roll_no_1</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Nov/03/2019 08:56">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-555734" href="?#comment-555734" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="555734" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="631859" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-555734"> <div class="moveup"> <div class="ttypography"><p>Here are the 2 interpretations of problem A's solution as I understood them:</p><p><a href="/contest/65/submission/64128016" title="Submission 64128016 by roll_no_1">64128016</a></p><p><a href="/contest/65/submission/64128379" title="Submission 64128379 by roll_no_1">64128379</a></p></div> </div> </div> <div class="reply info"> <a class="comment-555734 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-555734 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-555734"> </ul> </div> <br/> <div id="editBox-1441" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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D. Harry Potter and the Sorting Hat
<div class="problem-statement"><div class="header"><div class="title">D. Harry Potter and the Sorting Hat</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>As you know, Hogwarts has four houses: Gryffindor, Hufflepuff, Ravenclaw and Slytherin. The sorting of the first-years into houses is done by the Sorting Hat. The pupils are called one by one in the alphabetical order, each of them should put a hat on his head and, after some thought, the hat solemnly announces the name of the house the student should enter.</p><p>At that the Hat is believed to base its considerations on the student's personal qualities: it sends the brave and noble ones to Gryffindor, the smart and shrewd ones — to Ravenclaw, the persistent and honest ones — to Hufflepuff and the clever and cunning ones — to Slytherin. However, a first year student Hermione Granger got very concerned about the forthcoming sorting. She studied all the literature on the Sorting Hat and came to the conclusion that it is much simpler than that. If the relatives of the student have already studied at Hogwarts, the hat puts the student to the same house, where his family used to study. In controversial situations, when the relatives studied in different houses or when they were all Muggles like Hermione's parents, then the Hat sorts the student to the house, to which the least number of first years has been sent at that moment. If there are several such houses, the choice is given to the student himself. Then the student can choose any of the houses, to which the least number of first years has been sent so far. </p><p>Hermione has already asked the students that are on the list before her about their relatives. Now she and her new friends Harry Potter and Ron Weasley want to find out into what house the Hat will put Hermione.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first input line contains an integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10000</span>). It is the number of students who are in the list before Hermione. The next line contains <span class="tex-span"><i>n</i></span> symbols. If all the relatives of a student used to study in the same house, then the <span class="tex-span"><i>i</i></span>-th character in the string coincides with the first letter of the name of this house. Otherwise, the <span class="tex-span"><i>i</i></span>-th symbol is equal to "?".</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print all the possible houses where Hermione can be sent. The names of the houses should be printed in the alphabetical order, one per line.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>11<br/>G????SS???H<br/></pre></div><div class="output"><div class="title">Output</div><pre>Gryffindor<br/>Ravenclaw<br/></pre></div><div class="input"><div class="title">Input</div><pre>2<br/>H?<br/></pre></div><div class="output"><div class="title">Output</div><pre>Gryffindor<br/>Ravenclaw<br/>Slytherin<br/></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>Consider the second example. There are only two students before Hermione. The first student is sent to Hufflepuff. The second disciple is given the choice between the houses where the least number of students has been sent, i.e. Gryffindor, Slytherin and Ravenclaw. If he chooses Gryffindor, Hermione is forced to choose between Ravenclaw and Slytherin, if he chooses Ravenclaw, Hermione will choose between Gryffindor and Slytherin, if he chooses Slytherin, Hermione will choose between Gryffindor and Ravenclaw. In the end, the following situation is possible (it depends on the choice of the second student and Hermione). Hermione will end up 1) in Gryffindor, 2) in Ravenclaw, 3) in Slytherin. Note that, despite the fact that in neither case Hermione will be given a choice between all the three options, they are all possible and they should all be printed in the answer. Hermione will not, under any circumstances, end up in Hufflepuff.</p></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="D" data-uuid="ps_8ec279b4f26d9b2434104e7c054a2d4d108c531a"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">D. Harry Potter and the Sorting Hat</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>As you know, Hogwarts has four houses: Gryffindor, Hufflepuff, Ravenclaw and Slytherin. The sorting of the first-years into houses is done by the Sorting Hat. The pupils are called one by one in the alphabetical order, each of them should put a hat on his head and, after some thought, the hat solemnly announces the name of the house the student should enter.</p><p>At that the Hat is believed to base its considerations on the student's personal qualities: it sends the brave and noble ones to Gryffindor, the smart and shrewd ones — to Ravenclaw, the persistent and honest ones — to Hufflepuff and the clever and cunning ones — to Slytherin. However, a first year student Hermione Granger got very concerned about the forthcoming sorting. She studied all the literature on the Sorting Hat and came to the conclusion that it is much simpler than that. If the relatives of the student have already studied at Hogwarts, the hat puts the student to the same house, where his family used to study. In controversial situations, when the relatives studied in different houses or when they were all Muggles like Hermione's parents, then the Hat sorts the student to the house, to which the least number of first years has been sent at that moment. If there are several such houses, the choice is given to the student himself. Then the student can choose any of the houses, to which the least number of first years has been sent so far. </p><p>Hermione has already asked the students that are on the list before her about their relatives. Now she and her new friends Harry Potter and Ron Weasley want to find out into what house the Hat will put Hermione.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first input line contains an integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10000</span>). It is the number of students who are in the list before Hermione. The next line contains <span class="tex-span"><i>n</i></span> symbols. If all the relatives of a student used to study in the same house, then the <span class="tex-span"><i>i</i></span>-th character in the string coincides with the first letter of the name of this house. Otherwise, the <span class="tex-span"><i>i</i></span>-th symbol is equal to &quot;?&quot;.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print all the possible houses where Hermione can be sent. The names of the houses should be printed in the alphabetical order, one per line.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>11<br />G????SS???H<br /></pre></div><div class="output"><div class="title">Output</div><pre>Gryffindor<br />Ravenclaw<br /></pre></div><div class="input"><div class="title">Input</div><pre>2<br />H?<br /></pre></div><div class="output"><div class="title">Output</div><pre>Gryffindor<br />Ravenclaw<br />Slytherin<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>Consider the second example. There are only two students before Hermione. The first student is sent to Hufflepuff. The second disciple is given the choice between the houses where the least number of students has been sent, i.e. Gryffindor, Slytherin and Ravenclaw. If he chooses Gryffindor, Hermione is forced to choose between Ravenclaw and Slytherin, if he chooses Ravenclaw, Hermione will choose between Gryffindor and Slytherin, if he chooses Slytherin, Hermione will choose between Gryffindor and Ravenclaw. In the end, the following situation is possible (it depends on the choice of the second student and Hermione). Hermione will end up 1) in Gryffindor, 2) in Ravenclaw, 3) in Slytherin. Note that, despite the fact that in neither case Hermione will be given a choice between all the three options, they are all possible and they should all be printed in the answer. 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["Brute force", "Dfs and similar", "Hashing, hashtables"]
["brute force", "dfs and similar", "hashing", "*2200"]
https://codeforces.com/blog/entry/1431
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You can take a*c*e grams of sand, turn them into b*c*e grams of lead, and them turn into b*d*e grams of gold, and them turn into b*d*f grams of sand. If b*d*f &gt; a*c*e, you can infinitely increase the amount of sand and consequently the amount of gold. Otherwise, if b*d*f &lt;= a*c*e, it is impossible to get infinitely large amount of gold. The same is true when the fraction  (a*c*e)/(b*d*f) has zero numerator only or zero denuminator only. Otherwise there is 0/0, and  you have to check cases specially.</div><div><br /></div><div>I explain, why I make this problem to be problem A.</div><div><br /></div><div>1. Solution of the problem requires very little knowledge of programming (only &quot;if&quot;), so it was feasible for all participants.</div><div>2. Tricky cases really exist, but I hoped that &quot;<span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">stronger competitors will ... help newcomers to catch all bugs by their hacks&quot;. </span>And so it happened.</div><div><br /></div><div>Maybe I was wrong: this problem is too complex for A.</div><div><br /></div><div>A large number of hacks for this problem is a quite foreseen circumstance. I haven't include the special class of tests into the pretests intendently, to make hacking more interesting. In fairness I should note that Artem Rakhov was against this idea. Beause of this task the problem surfaced that Gassa writes about <a href="https://codeforces.com/comments/1432#comment-26176">here</a> in Russian: pretests cover some incomplete set of cases and it is not clear in advance what the event &quot;solution passed pretests&quot; means. I think it should be discussed, and strong principles of pretests development should be stated.</div></div><div><br /></div><div><b>Problem B</b></div><div> </div><div><br /></div><div>The problem has greedy solution. Change a digit in the first date to make it as small as possible. At each of the next steps try all one-digit exchanges in the current date and choose one that makes the date not less than the previous one and as small as possible at the same time. If the last year won't exceed 2011 - the answer is found. Otherwise there is no solution.</div><div><br /></div><div>How to prove that? Consider any correct answer. Clearly, if the first date in it is different from the smallest possible number that can be obtained from the first of given years, your can put the smallest number instead of it. The second date can be exchanged by the smallest possible number not exceeding the first number, etc.Ar a result you obtain a greedy solution that is built by the algorithm described above. If the greedy solution doesn't exist, solution doesn't esist too.</div><div><div><div><br /></div><div>The problem also has a dynamic solution.</div></div><div><br /></div><div><div><div><b>Problem C</b></div><div><div><br /></div><div>Check for each segment in the polyline if Harry can catch the snitch in it. Note that since <span class="tex-span"><i>v</i><sub class="lower-index"><i>p</i></sub> ≥ <i>v</i><sub class="lower-index"><i>s</i></sub></span>, if Harry can catch the snitch at some moment of time, he can catch it at any later moment. He can just follow snitch along its trajectory. So use binary search in each segment.</div><div><br /></div><div>About problems with EPS that participants got. The problems may be caused by</div><div>1) some EPS in the condition: while (leftTime + EPS &lt; rightTime) &lt;do binary search&gt;. The task was to output with a fixed accurancy not only the time, but also the point coordinates. If the difference between the time and the right one is less than EPS, the difference between coordinates may be significantly larger. In such cases you should compare not arguments of a function, but values of the function with EPS. Or the way that I usually follow and that once was not liked by the teacher of numerical methods - to implement some fixed number of iterations of the binary search (say, 60).  </div><div>2) EPS in comparison of time moments inside the binary search like this:</div><div>if (currentTime + addTime &gt; distance / potterSpeed - EPS)</div><div>                                                rightTime = currentTime;</div><div>                                        else</div><div>                                                leftTime = currentTime;</div><div>Here it is better to remove EPS at all. Or to put EPS significantly smaller than the required accurancy for printing the point.</div><div><br /></div><div>(Code fragments are from Egor's solution.)</div></div><div><br /></div><div>Thus, there was no crime with severe limitations. Probably for such problems extreme accurancy tests should be in pretests? It is about principles of pretests making again. </div><div><br /></div><div><b>UPD.</b> The problem has an analytical solution too. Consider the i-th segment. Let <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i></sub>, <i>y</i><sub class="lower-index"><i>i</i></sub>, <i>z</i><sub class="lower-index"><i>i</i></sub>)</span> and <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i> + 1</sub>, <i>y</i><sub class="lower-index"><i>i</i> + 1</sub>, <i>z</i><sub class="lower-index"><i>i</i> + 1</sub>)</span> be its ends, and let <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub></span> be the time required for the snitch to reach the beginning of the segment. Then at the moment t the snitch will be at the point (x, y, z), <span class="tex-span"><i>x</i> = <i>x</i><sub class="lower-index"><i>i</i></sub> + (<i>x</i><sub class="lower-index"><i>i</i> + 1</sub> - <i>x</i><sub class="lower-index"><i>i</i></sub>)(<i>t</i> - <i>t</i><sub class="lower-index"><i>i</i></sub>) / <i>T</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>y</i> = <i>y</i><sub class="lower-index"><i>i</i></sub> + (<i>y</i><sub class="lower-index"><i>i</i> + 1</sub> - <i>y</i><sub class="lower-index"><i>i</i></sub>)(<i>t</i> - <i>t</i><sub class="lower-index"><i>i</i></sub>) / <i>T</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>z</i> = <i>z</i><sub class="lower-index"><i>i</i></sub> + (<i>z</i><sub class="lower-index"><i>i</i> + 1</sub> - <i>z</i><sub class="lower-index"><i>i</i></sub>)(<i>t</i> - <i>t</i><sub class="lower-index"><i>i</i></sub>) / <i>T</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>T</i><sub class="lower-index"><i>i</i></sub></span> is a time necessary for snitch to overcome the segment. To catch the snitch at the point (x, y, z), Harry have to overcome the distance that squared is equal to <span class="tex-span">(<i>x</i> - <i>P</i><sub class="lower-index"><i>x</i></sub>)<sup class="upper-index">2</sup> + (<i>y</i> - <i>P</i><sub class="lower-index"><i>y</i></sub>)<sup class="upper-index">2</sup> + (<i>z</i> - <i>P</i><sub class="lower-index"><i>z</i></sub>)<sup class="upper-index">2</sup></span> for the time t. It is possible if <span class="tex-span">(<i>x</i> - <i>P</i><sub class="lower-index"><i>x</i></sub>)<sup class="upper-index">2</sup> + (<i>y</i> - <i>P</i><sub class="lower-index"><i>y</i></sub>)<sup class="upper-index">2</sup> + (<i>z</i> - <i>P</i><sub class="lower-index"><i>z</i></sub>)<sup class="upper-index">2</sup> ≤ (<i>tv</i><sub class="lower-index"><i>p</i></sub>)<sup class="upper-index">2</sup></span>. To find the minimal proper moment t, solve the corresponding quadratic equation.<br /></div><div><br /></div><div><div style="font-weight: normal;"><b>Problem D</b></div><div style="font-weight: normal;"><br /></div><div><div style="font-weight: normal;">Let <span class="tex-span"><i>S</i><sub class="lower-index"><i>i</i></sub></span> be a set of all possible assignments of the first <span class="tex-span"><i>i</i></span> students to the houses, that is a set of tuples <span class="tex-span">(<i>a</i><sub class="lower-index">1</sub>, <i>a</i><sub class="lower-index">2</sub>, <i>a</i><sub class="lower-index">3</sub>, <i>a</i><sub class="lower-index">4</sub>)</span>, where <span class="tex-span"><i>a</i><sub class="lower-index">1</sub></span> is a number of students sent to Gryffindor, <span class="tex-span"><i>a</i><sub class="lower-index">2</sub></span> - to Ravenclaw, etc. It's intuitively clear that these sets will not be large. So you can get <span class="tex-span"><i>S</i><sub class="lower-index"><i>i</i> - 1</sub></span> from <span class="tex-span"><i>S</i><sub class="lower-index"><i>i</i></sub></span> in a trivial way, and get finally <span class="tex-span"><i>S</i><sub class="lower-index"><i>n</i></sub></span>, and determine the answer from it. </div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"><br /></div></div></b></div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;">What is a rigorous proof of the algorithm? Let us have a set<b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"> <span class="tex-span"><i>S</i> = {(<i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">1</sub>, <i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">2</sub>, <i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">3</sub>, <i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">4</sub>)}<sub class="lower-index"><i>i</i> = 1, 2, ..., <i>k</i></sub></span>. Represent its elements as <span class="tex-span"><i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub> = <i>b</i><sub class="lower-index"><i>j</i></sub> + <i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub></span>, <span class="tex-span"><i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub> ≥ 0</span>, where <span class="tex-span"><i>b</i><sub class="lower-index"><i>j</i></sub></span> are maximal possible, i.e. there is i for each j such that <span class="tex-span"><i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub> = 0</span>. Let the tuple <span class="tex-span">(<i>b</i><sub class="lower-index">1</sub>, <i>b</i><sub class="lower-index">2</sub>, <i>b</i><sub class="lower-index">3</sub>, <i>b</i><sub class="lower-index">4</sub>)</span> be called the base part of S, and the set <span class="tex-span">{(<i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">1</sub>, <i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">2</sub>, <i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">3</sub>, <i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">4</sub>)}<sub class="lower-index"><i>i</i> = 1, 2, ..., <i>k</i></sub></span> be called the variant part of S. </div></div></b></div></div></b><br /></div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Initially for <span class="tex-span"><i>S</i><sub class="lower-index">0</sub></span> both base and variant parts are zeroes. Let us see how base and variant parts change when a current student is added. If a house is fixed for the student, only the base part changes. It increases by 1 at the position corresponding to the house. In particular, it follows that a set with every base part can be obtained (since the string given in the input can contain every combination of symbols G, H, R, S). If the current symbol in the string is '?', it can influence both base and variant parts.</div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">For example, for the string '????' we have:</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">0</sub> = {(0 + 0, 0 + 0, 0 + 0, 0 + 0)}</span>,</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">1</sub> = {(0 + 1, 0 + 0, 0 + 0, 0 + 0), (0 + 0, 0 + 1, 0 + 0, 0 + 0), (0 + 0, 0 + 0, 0 + 1, 0 + 0), (0 + 0, 0 + 0, 0 + 0, 0 + 1)}</span>,</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">2</sub> = {(0 + 1, 0 + 1, 0 + 0, 0 + 0), (0 + 1, 0 + 0, 0 + 1, 0 + 0), (0 + 1, 0 + 0, 0 + 0, 0 + 1), (0 + 0, 0 + 1, 0 + 1, 0 + 0), (0 + 0, 0 + 1, 0 + 0, 0 + 1), (0 + 0, 0 + 0, 0 + 1, 0 + 1)}</span>,</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">3</sub> = {(0 + 1, 0 + 1, 0 + 1, 0 + 0), (0 + 1, 0 + 1, 0 + 0, 0 + 1), (0 + 1, 0 + 0, 0 + 1, 0 + 1), (0 + 0, 0 + 1, 0 + 1, 0 + 1)}</span>,</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">4</sub> = {(1 + 0, 1 + 0, 1 + 0, 1 + 0)}</span>.</div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Let us investigate the question of what species a variant part may have. It can be analyzed independently from a base one, taking into account that a base part can be any. Consider a directed graph with vertices corresponding to variant parts and with edges determined by the existence of<b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"> at least one base part that let go from one variant part to another. We are interested only in vertices reachable from <span class="tex-span">{(0, 0, 0, 0)}</span>.</div></div></b></div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Proposition. For all the vertices reachable from zero the following properties hold</div><div style="font-weight: normal;">(1) <span class="tex-span"><i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub> ≤ 2</span>,</div><div style="font-weight: normal;">(2) <span class="tex-span"><i>k</i> ≤ 13</span>.</div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Let us prove that all the vertices not having the properties (1) and (2) are unreachable from zero. Consider a variant part with the property (1). To get all edges going from it you have to try all possible base parts. Note that base parts, that consist of the numbers 0, 1, 2, 3 and contain at lest one 0, are enough. Indeed, base part influence which elements are minimal, and 1 will be added to them. A base part can be always normed to contain at least one 0. If a base part contains numbers greater than 3, then the corresponding positions will never be minimal (since 4+0 &gt; 0+2) and they can be changed equivalently by 3 (3+0 &gt; 0+2).</div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Unfortunately, my attempts to deal with cases by hand were unsuccessful, so I wrote <a href="http://pastebin.com/p3sFKKya">the program</a> that traverse the described graph. Starting from 0, it builds edges trying only &quot;small&quot; base parts described in the previous paragraph. As a result, the program obtains all the reachable variant parts (there is a little more than 1000 of them) and check (1) and (2) for them. In addition, the program helps to construct a test with<b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"> <span class="tex-span"><i>k</i> = 13</span>.</div></div></b></div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"><br /></div></div></b></div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;">The problem was supposed to be a problem on intuition. Participants have another solution passed. Their solution generate all permutations and distribute students greedily with respect to each permutation.</div></div></b><b><div style="font-weight: normal;display: inline !important;"><b><div style="font-weight: normal;display: inline !important;">This solution was a complete surprise for me. Unfortunately, it is wrong. Test 66 against it was added. Of course, submissions accepted during the round won't be rejudged. If such a solution be expected, most likely I wouldn't give such a task. In terms of intuition this solution is not better and not worse than mine. I hope you will not judge me strictly: it is a beautiful problem, and it was interesting to see how it would be solved. </div></b></div></b></div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><b><div style="font-weight: normal;display: inline !important;"><br /></div></b></div></b></div><div><div style="display: inline !important;"><div style="display: inline !important;"><div style="font-weight: normal;"><b>Problem E</b></div><div style="font-weight: normal;"><b><br /></b></div><div><div><div><div style="display: inline !important;"><div style="display: inline !important;">Consider a graph with floors as vertices and staircases as edges. It is clear that Harry can visit the whole connected component in which he is currently located.<br /></div></div></div><div style="font-weight: normal;"><br /></div></div></div><div>Every edge can be used to reach a new vertex for not more than two times. If a connected component contains n vertices and m edges, only n - 1 edges are used to reach a new vertex during its traversal. The remaining m - n + 1 edges are not used to reach a new vertex in their initial placement. So they will be used to reach a new vertex not more than once.</div><div><div><br /></div><div>So using edges of only one connected component you can reach no more than n - m + 1 new vertices. Totally there are not more than  <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7fae5c87930e2f915b8c632872cc1662dd30fa09.png" style="max-width: 100.0%;max-height: 100.0%;" /> reachable vertices. If m &lt; k - 1, it is impossible to visit all the vertices.  </div><div><br /></div><div>We show that otherwise (m &gt;= k - 1), if the degree of the vertex 0 is different from zero, it is possible to visit all the vertices. In other words, there is such a traversal that every edge can be moved.  Use depth-first search for the current component. If a current edge goes to an already visited vertex, move it to a new component and traverse it recursively. If a current edge goes to a new vertex, after you visit this vertex and go back, you also can move this edge to a new component. As a result each edge can be moved and used again, if you reach all the components. If a component contains at least one edge, you can go from it to the next one. First visit components with edges, and you will visit them all and by the inequality (m &gt;= k - 1) there are enough edges to visit all the isolated vertices.  </div><div><br /></div><div>If the degree of the vertex 1 is zero, you can not start a traversal before you move some edge to it. After that you can go by this edge and remove it with the vertex 1 from the graph, becase you can not use this edge once more. If the chose edge is a bridge, you get k connected components and m - 1 egdes. If it is not a bridge, you get k - 1 components and m - 1 edges. In the first case the inequality m &gt;= k - 1 turns m &gt;= k. In the second case -  m &gt;= k - 1. So if not all the edges are bridges, you should not take a bridge. If they all are bridges, you should disconnect an edge from a vertex of degree &gt;= 2 not to came back to the initial situation with the zero degree of the first vertex. If there is no such vertex, it is easy to check that there is no solution.</div></div></div></div></div></div></div></div></div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/65" class="notice" style="text-decoration: none;">Codeforces Beta Round 60</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-2326-1431").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "2326", blogEntryId: "1431", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=beta+round+%2360" class="tag notice" style="text-decoration: none;">beta round #60</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces" class="tag notice" style="text-decoration: none;">codeforces</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=tutorial" class="tag notice" style="text-decoration: none;">tutorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1431"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+33</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1431"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/natalia"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/natalia"> natalia </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Mar/06/2011 08:27">13 years ago</span> </li> <li> <a href="/blog/entry/1431#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1431#comments"> 10 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1441"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (10)</a> </div> <div class="comments-actions-div"> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="26324" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/lyrics" style="position: relative;"> <img src='https://userpic.codeforces.org/3858/avatar/29787cdba9b12888.jpg'/> </a> <div><a href="/profile/lyrics" title="Expert lyrics" class="rated-user user-blue">lyrics</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/06/2011 12:30">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26324" href="?#comment-26324" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26324" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="3858" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26324"> <div class="moveup"> <div class="ttypography">good analysis...</div> </div> </div> <div class="reply info"> <a class="comment-26324 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26324 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26324"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="26331" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/A.K.Goharshady" style="position: relative;"> <img src='https://userpic.codeforces.org/9153/avatar/358f1b75189ae870.jpg'/> </a> <div><a href="/profile/A.K.Goharshady" title="Candidate Master A.K.Goharshady" class="rated-user user-violet">A.K.Goharshady</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/06/2011 12:52">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26331" href="?#comment-26331" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26331" class="CommentVoteFrame" data-commentRating="2" data-commentUserId="9153" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+2</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26331"> <div class="moveup"> <div class="ttypography">Problem A was harder than D :D</div> </div> </div> <div class="reply info"> <a class="comment-26331 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26331 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26331"> <li> <div class="comment"> <table class="comment-table" commentId="26336" commentParentId="26331"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Alex_KPR" style="position: relative;"> <img src='https://userpic.codeforces.org/209/avatar/b403606b22dc5082.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/Alex_KPR" title="Master Alex_KPR" class="rated-user user-orange">Alex_KPR</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/06/2011 13:03">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26336" href="?#comment-26336" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-26331" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26336" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="209" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26336"> <div class="moveup"> <div class="ttypography">agree with you =)</div> </div> </div> <div class="reply info"> <a class="comment-26336 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26336 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26336"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="26374" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mR.ilchi" style="position: relative;"> <img src='https://userpic.codeforces.org/11753/avatar/b0675918b77546aa.jpg'/> </a> <div><a href="/profile/mR.ilchi" title="International Grandmaster mR.ilchi" class="rated-user user-red">mR.ilchi</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/06/2011 15:58">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26374" href="?#comment-26374" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="26374" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="26374" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="11753" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26374"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">please translate problem D and E too.</div><div class="from-renderer"><div>thank's for your nice contest!!!</div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-26374 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26374 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26374"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="26587" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/sunhaowen567" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/sunhaowen567" title="Expert sunhaowen567" class="rated-user user-blue">sunhaowen567</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/07/2011 07:43">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26587" href="?#comment-26587" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26587" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3232" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26587"> <div class="moveup"> <div class="ttypography">waiting for problem E......</div> </div> </div> <div class="reply info"> <a class="comment-26587 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26587 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26587"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="26588" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kang205" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/kang205" title="Expert kang205" class="rated-user user-blue">kang205</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/07/2011 08:13">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26588" href="?#comment-26588" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26588" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13097" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26588"> <div class="moveup"> <div class="ttypography">Problem D's proof is very NICE.<br /><br /><br /><br /></div> </div> </div> <div class="reply info"> <a class="comment-26588 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26588 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26588"> <li> <div class="comment"> <table class="comment-table" commentId="26589" commentParentId="26588"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kang205" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/kang205" title="Expert kang205" class="rated-user user-blue">kang205</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/07/2011 08:16">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26589" href="?#comment-26589" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-26588" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26589" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13097" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26589"> <div class="moveup"> <div class="ttypography">I use <b>random <b><b><b> generate permutations</b></b></b></b>,but the random times be set 10000,so I got TLE.<br /><br />If set 2000,I got AC....</div> </div> </div> <div class="reply info"> <a class="comment-26589 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26589 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26589"> <li> <div class="comment"> <table class="comment-table" commentId="194733" commentParentId="26589"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/wjh720" style="position: relative;"> <img src='https://userpic.codeforces.org/210352/avatar/d212772572283d08.jpg'/> </a> <div><a href="/profile/wjh720" title="International Grandmaster wjh720" class="rated-user user-red">wjh720</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Oct/30/2014 09:43">9 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-194733" href="?#comment-194733" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-26589" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="194733" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="210352" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-194733"> <div class="moveup"> <div class="ttypography"><p>You can have a try with {&quot;?HRS&quot;*2500} :)</p></div> </div> </div> <div class="reply info"> <a class="comment-194733 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-194733 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-194733"> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="310517" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/throwaways" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/throwaways" title="Unrated, throwaways" class="rated-user user-black">throwaways</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Aug/17/2016 00:08">7 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-310517" href="?#comment-310517" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="310517" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="310517" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="401734" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-310517"> <div class="moveup"> <div class="ttypography"><p>what might the time complexity of D be?</p></div> </div> </div> <div class="reply info"> <a class="comment-310517 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-310517 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-310517"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="555734" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/roll_no_1" style="position: relative;"> <img src='https://userpic.codeforces.org/631859/avatar/36d157f91f64fe7f.jpg'/> </a> <div><a href="/profile/roll_no_1" title="Master roll_no_1" class="rated-user user-orange">roll_no_1</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Nov/03/2019 08:56">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-555734" href="?#comment-555734" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="555734" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="631859" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-555734"> <div class="moveup"> <div class="ttypography"><p>Here are the 2 interpretations of problem A's solution as I understood them:</p><p><a href="/contest/65/submission/64128016" title="Submission 64128016 by roll_no_1">64128016</a></p><p><a href="/contest/65/submission/64128379" title="Submission 64128379 by roll_no_1">64128379</a></p></div> </div> </div> <div class="reply info"> <a class="comment-555734 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-555734 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-555734"> </ul> </div> <br/> <div id="editBox-1441" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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E. Harry Potter and Moving Staircases
<div class="problem-statement"><div class="header"><div class="title">E. Harry Potter and Moving Staircases</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Harry Potter lost his Invisibility Cloak, running from the school caretaker Filch. Finding an invisible object is not an easy task. Fortunately, Harry has friends who are willing to help. Hermione Granger had read "The Invisibility Cloaks, and Everything about Them", as well as six volumes of "The Encyclopedia of Quick Search of Shortest Paths in Graphs, Network Flows, the Maximal Increasing Subsequences and Other Magical Objects". She has already developed a search algorithm for the invisibility cloak in complex dynamic systems (Hogwarts is one of them).</p><p>Hogwarts consists of <span class="tex-span"><i>n</i></span> floors, numbered by integers from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span>. Some pairs of floors are connected by staircases. The staircases may change its position, moving exactly one end. Formally the situation is like this: if a staircase connects the floors <span class="tex-span"><i>a</i></span> and <span class="tex-span"><i>b</i></span>, then in one move it may modify its position so as to connect the floors <span class="tex-span"><i>a</i></span> and <span class="tex-span"><i>c</i></span> or <span class="tex-span"><i>b</i></span> and <span class="tex-span"><i>c</i></span>, where <span class="tex-span"><i>c</i></span> is any floor different from <span class="tex-span"><i>a</i></span> and <span class="tex-span"><i>b</i></span>. Under no circumstances the staircase can connect a floor with itself. At the same time there can be multiple stairs between a pair of floors.</p><p>Initially, Harry is on the floor with the number <span class="tex-span">1</span>. He does not remember on what floor he has lost the cloak and wants to look for it on each of the floors. Therefore, his goal is to visit each of <span class="tex-span"><i>n</i></span> floors at least once. Harry can visit the floors in any order and finish the searching at any floor.</p><p>Nowadays the staircases move quite rarely. However, Ron and Hermione are willing to put a spell on any of them to help Harry find the cloak. To cause less suspicion, the three friends plan to move the staircases one by one, and no more than once for each staircase. In between shifting the staircases Harry will be able to move about the floors, reachable at the moment from the staircases, and look for his Invisibility Cloak. It is assumed that during all this time the staircases will not move spontaneously.</p><p>Help the three friends to compose a searching plan. If there are several variants to solve the problem, any valid option (not necessarily the optimal one) will be accepted.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>m</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 100000</span>, <span class="tex-span">0 ≤ <i>m</i> ≤ 200000</span>), which are the number of floors and staircases in Hogwarts, respectively. The following <span class="tex-span"><i>m</i></span> lines contain pairs of floors connected by staircases at the initial moment of time.</p></div><div class="output-specification"><div class="section-title">Output</div><p>In the first line print "YES" (without the quotes) if Harry is able to search all the floors, and "NO" otherwise. If the answer is positive, then print on the second line the number of staircases that Ron and Hermione will have to shift. Further output should look like this:</p><p><span class="tex-font-style-tt">Harry's moves</span> </p><p><span class="tex-font-style-tt">a staircase's move</span> </p><p><span class="tex-font-style-tt">Harry's moves</span></p><p><span class="tex-font-style-tt">a staircase's move</span></p><p>...</p><p><span class="tex-font-style-tt">a staircase's move</span></p><p><span class="tex-font-style-tt">Harry's moves</span></p><p>Each "<span class="tex-font-style-tt">Harry's move</span>" should be represented as a list of floors in the order in which they have been visited. <span class="tex-font-style-bf">The total amount of elements of these lists must not exceed</span> <span class="tex-span">10<sup class="upper-index">6</sup></span>. When you print each list, first print the number of elements in it, and then in the same line print the actual space-separated elements. The first number in the first list should be the number <span class="tex-span">1</span> (the floor, from which Harry begins to search). Any list except the first one might contain the zero number of elements. Note that Harry can visit some floors again, but must visit all <span class="tex-span"><i>n</i></span> floors at least once. Two consecutively visited floors must be directly connected by a staircase (at the time Harry goes from one of them to the other one). <span class="tex-font-style-bf">No two floors that are visited consequtively can be equal.</span></p><p>In the description of a "<span class="tex-font-style-tt">staircase's move</span>" indicate the number of staircase (the staircases are numbered from <span class="tex-span">1</span> to <span class="tex-span"><i>m</i></span> in the order in which they are given in the input data) and its new location (two numbers of the connected floors in any order).</p><p>Any staircase can be moved at most once. If there are several solutions, output any.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>6 4<br/>1 2<br/>1 3<br/>2 3<br/>4 5<br/></pre></div><div class="output"><div class="title">Output</div><pre>YES<br/>2<br/>3 1 2 3<br/>2 3 5<br/>3 5 4 5<br/>4 5 6<br/>3 6 5 3<br/></pre></div><div class="input"><div class="title">Input</div><pre>4 1<br/>1 2<br/></pre></div><div class="output"><div class="title">Output</div><pre>NO<br/></pre></div><div class="input"><div class="title">Input</div><pre>5 5<br/>1 2<br/>1 3<br/>3 4<br/>3 5<br/>4 5<br/></pre></div><div class="output"><div class="title">Output</div><pre>YES<br/>0<br/>6 1 2 1 3 4 5<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="E" data-uuid="ps_84dd42c0561ea43181bd23af90c59aa18096407c"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">E. Harry Potter and Moving Staircases</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Harry Potter lost his Invisibility Cloak, running from the school caretaker Filch. Finding an invisible object is not an easy task. Fortunately, Harry has friends who are willing to help. Hermione Granger had read &quot;The Invisibility Cloaks, and Everything about Them&quot;, as well as six volumes of &quot;The Encyclopedia of Quick Search of Shortest Paths in Graphs, Network Flows, the Maximal Increasing Subsequences and Other Magical Objects&quot;. She has already developed a search algorithm for the invisibility cloak in complex dynamic systems (Hogwarts is one of them).</p><p>Hogwarts consists of <span class="tex-span"><i>n</i></span> floors, numbered by integers from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span>. Some pairs of floors are connected by staircases. The staircases may change its position, moving exactly one end. Formally the situation is like this: if a staircase connects the floors <span class="tex-span"><i>a</i></span> and <span class="tex-span"><i>b</i></span>, then in one move it may modify its position so as to connect the floors <span class="tex-span"><i>a</i></span> and <span class="tex-span"><i>c</i></span> or <span class="tex-span"><i>b</i></span> and <span class="tex-span"><i>c</i></span>, where <span class="tex-span"><i>c</i></span> is any floor different from <span class="tex-span"><i>a</i></span> and <span class="tex-span"><i>b</i></span>. Under no circumstances the staircase can connect a floor with itself. At the same time there can be multiple stairs between a pair of floors.</p><p>Initially, Harry is on the floor with the number <span class="tex-span">1</span>. He does not remember on what floor he has lost the cloak and wants to look for it on each of the floors. Therefore, his goal is to visit each of <span class="tex-span"><i>n</i></span> floors at least once. Harry can visit the floors in any order and finish the searching at any floor.</p><p>Nowadays the staircases move quite rarely. However, Ron and Hermione are willing to put a spell on any of them to help Harry find the cloak. To cause less suspicion, the three friends plan to move the staircases one by one, and no more than once for each staircase. In between shifting the staircases Harry will be able to move about the floors, reachable at the moment from the staircases, and look for his Invisibility Cloak. It is assumed that during all this time the staircases will not move spontaneously.</p><p>Help the three friends to compose a searching plan. If there are several variants to solve the problem, any valid option (not necessarily the optimal one) will be accepted.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>m</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 100000</span>, <span class="tex-span">0 ≤ <i>m</i> ≤ 200000</span>), which are the number of floors and staircases in Hogwarts, respectively. The following <span class="tex-span"><i>m</i></span> lines contain pairs of floors connected by staircases at the initial moment of time.</p></div><div class="output-specification"><div class="section-title">Output</div><p>In the first line print &quot;YES&quot; (without the quotes) if Harry is able to search all the floors, and &quot;NO&quot; otherwise. If the answer is positive, then print on the second line the number of staircases that Ron and Hermione will have to shift. Further output should look like this:</p><p><span class="tex-font-style-tt">Harry's moves</span> </p><p><span class="tex-font-style-tt">a staircase's move</span> </p><p><span class="tex-font-style-tt">Harry's moves</span></p><p><span class="tex-font-style-tt">a staircase's move</span></p><p>...</p><p><span class="tex-font-style-tt">a staircase's move</span></p><p><span class="tex-font-style-tt">Harry's moves</span></p><p>Each &quot;<span class="tex-font-style-tt">Harry's move</span>&quot; should be represented as a list of floors in the order in which they have been visited. <span class="tex-font-style-bf">The total amount of elements of these lists must not exceed</span> <span class="tex-span">10<sup class="upper-index">6</sup></span>. When you print each list, first print the number of elements in it, and then in the same line print the actual space-separated elements. The first number in the first list should be the number <span class="tex-span">1</span> (the floor, from which Harry begins to search). Any list except the first one might contain the zero number of elements. Note that Harry can visit some floors again, but must visit all <span class="tex-span"><i>n</i></span> floors at least once. Two consecutively visited floors must be directly connected by a staircase (at the time Harry goes from one of them to the other one). <span class="tex-font-style-bf">No two floors that are visited consequtively can be equal.</span></p><p>In the description of a &quot;<span class="tex-font-style-tt">staircase's move</span>&quot; indicate the number of staircase (the staircases are numbered from <span class="tex-span">1</span> to <span class="tex-span"><i>m</i></span> in the order in which they are given in the input data) and its new location (two numbers of the connected floors in any order).</p><p>Any staircase can be moved at most once. If there are several solutions, output any.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>6 4<br />1 2<br />1 3<br />2 3<br />4 5<br /></pre></div><div class="output"><div class="title">Output</div><pre>YES<br />2<br />3 1 2 3<br />2 3 5<br />3 5 4 5<br />4 5 6<br />3 6 5 3<br /></pre></div><div class="input"><div class="title">Input</div><pre>4 1<br />1 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>NO<br /></pre></div><div class="input"><div class="title">Input</div><pre>5 5<br />1 2<br />1 3<br />3 4<br />3 5<br />4 5<br /></pre></div><div class="output"><div class="title">Output</div><pre>YES<br />0<br />6 1 2 1 3 4 5<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=E]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); 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["Dfs and similar", "Implementation problems, programming technics, simulation"]
["dfs and similar", "implementation", "*2900"]
https://codeforces.com/blog/entry/1431
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<a href="/blog/entry/120644">Codeforces Round 899 (Div. 2)</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/Misa-Misa" title="Expert Misa-Misa" class="rated-user user-blue">Misa-Misa</a> &rarr; <a href="/blog/entry/121157">Someone please help me understand this.</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/shivam565" title="Specialist shivam565" class="rated-user user-cyan">shivam565</a> &rarr; <a href="/blog/entry/108348">Total number of subarrays with sum atmost k</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> </ul> </div> <div class="bottom-links"> <table style="width:100%;"> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:right;"> <a href="/recent-actions">Detailed &rarr;</a> </td> </tr> </tbody> </table> </div> </div> </div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li><a href="/profile/natalia">natalia</a></li> <li class="current selectedLava"><a href="/blog/natalia">Blog</a></li> <li><a href="/teams/with/natalia">Teams</a></li> <li><a href="/submissions/natalia">Submissions</a></li> <li><a href="/groups/with/natalia">Groups</a></li> <li><a href="/contests/with/natalia">Contests</a></li> <li><a href="/contests/writer/natalia">Problemsetting</a></li> </ul> </div> <div style="margin-top:0;"> <div> <h3><a href="/blog/natalia" style="text-decoration:none;color:black !important;">natalia's blog</a></h3> </div> <div style="margin-top:2em;"> <div class="has-topic-id topic" topicId="1431"> <div class="title"> <a href="/blog/entry/1431"> Codeforces Beta Round #60: tutorial </a> </div> <div class="info" style="position:relative;"> By&nbsp;<a href="/profile/natalia" title="Master natalia" class="rated-user user-orange">natalia</a>, <span class="format-humantime" title="Mar/06/2011 08:27">13 years ago</span>, translation, <img style="position: relative;top: 5px;" src="//codeforces.org/s/81027/images/flags/24/gb.png" alt="In English" title="In English"/> <span style="position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;"> <div style="margin-top:0.25em;"> </div> </span> </div> <div class="content"> <div class="ttypography"><b>Problem A</b><div><br /></div><div><div>Fist, consider the case when all the numbers are non-zero. You can take a*c*e grams of sand, turn them into b*c*e grams of lead, and them turn into b*d*e grams of gold, and them turn into b*d*f grams of sand. If b*d*f &gt; a*c*e, you can infinitely increase the amount of sand and consequently the amount of gold. Otherwise, if b*d*f &lt;= a*c*e, it is impossible to get infinitely large amount of gold. The same is true when the fraction  (a*c*e)/(b*d*f) has zero numerator only or zero denuminator only. Otherwise there is 0/0, and  you have to check cases specially.</div><div><br /></div><div>I explain, why I make this problem to be problem A.</div><div><br /></div><div>1. Solution of the problem requires very little knowledge of programming (only &quot;if&quot;), so it was feasible for all participants.</div><div>2. Tricky cases really exist, but I hoped that &quot;<span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">stronger competitors will ... help newcomers to catch all bugs by their hacks&quot;. </span>And so it happened.</div><div><br /></div><div>Maybe I was wrong: this problem is too complex for A.</div><div><br /></div><div>A large number of hacks for this problem is a quite foreseen circumstance. I haven't include the special class of tests into the pretests intendently, to make hacking more interesting. In fairness I should note that Artem Rakhov was against this idea. Beause of this task the problem surfaced that Gassa writes about <a href="https://codeforces.com/comments/1432#comment-26176">here</a> in Russian: pretests cover some incomplete set of cases and it is not clear in advance what the event &quot;solution passed pretests&quot; means. I think it should be discussed, and strong principles of pretests development should be stated.</div></div><div><br /></div><div><b>Problem B</b></div><div> </div><div><br /></div><div>The problem has greedy solution. Change a digit in the first date to make it as small as possible. At each of the next steps try all one-digit exchanges in the current date and choose one that makes the date not less than the previous one and as small as possible at the same time. If the last year won't exceed 2011 - the answer is found. Otherwise there is no solution.</div><div><br /></div><div>How to prove that? Consider any correct answer. Clearly, if the first date in it is different from the smallest possible number that can be obtained from the first of given years, your can put the smallest number instead of it. The second date can be exchanged by the smallest possible number not exceeding the first number, etc.Ar a result you obtain a greedy solution that is built by the algorithm described above. If the greedy solution doesn't exist, solution doesn't esist too.</div><div><div><div><br /></div><div>The problem also has a dynamic solution.</div></div><div><br /></div><div><div><div><b>Problem C</b></div><div><div><br /></div><div>Check for each segment in the polyline if Harry can catch the snitch in it. Note that since <span class="tex-span"><i>v</i><sub class="lower-index"><i>p</i></sub> ≥ <i>v</i><sub class="lower-index"><i>s</i></sub></span>, if Harry can catch the snitch at some moment of time, he can catch it at any later moment. He can just follow snitch along its trajectory. So use binary search in each segment.</div><div><br /></div><div>About problems with EPS that participants got. The problems may be caused by</div><div>1) some EPS in the condition: while (leftTime + EPS &lt; rightTime) &lt;do binary search&gt;. The task was to output with a fixed accurancy not only the time, but also the point coordinates. If the difference between the time and the right one is less than EPS, the difference between coordinates may be significantly larger. In such cases you should compare not arguments of a function, but values of the function with EPS. Or the way that I usually follow and that once was not liked by the teacher of numerical methods - to implement some fixed number of iterations of the binary search (say, 60).  </div><div>2) EPS in comparison of time moments inside the binary search like this:</div><div>if (currentTime + addTime &gt; distance / potterSpeed - EPS)</div><div>                                                rightTime = currentTime;</div><div>                                        else</div><div>                                                leftTime = currentTime;</div><div>Here it is better to remove EPS at all. Or to put EPS significantly smaller than the required accurancy for printing the point.</div><div><br /></div><div>(Code fragments are from Egor's solution.)</div></div><div><br /></div><div>Thus, there was no crime with severe limitations. Probably for such problems extreme accurancy tests should be in pretests? It is about principles of pretests making again. </div><div><br /></div><div><b>UPD.</b> The problem has an analytical solution too. Consider the i-th segment. Let <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i></sub>, <i>y</i><sub class="lower-index"><i>i</i></sub>, <i>z</i><sub class="lower-index"><i>i</i></sub>)</span> and <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i> + 1</sub>, <i>y</i><sub class="lower-index"><i>i</i> + 1</sub>, <i>z</i><sub class="lower-index"><i>i</i> + 1</sub>)</span> be its ends, and let <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub></span> be the time required for the snitch to reach the beginning of the segment. Then at the moment t the snitch will be at the point (x, y, z), <span class="tex-span"><i>x</i> = <i>x</i><sub class="lower-index"><i>i</i></sub> + (<i>x</i><sub class="lower-index"><i>i</i> + 1</sub> - <i>x</i><sub class="lower-index"><i>i</i></sub>)(<i>t</i> - <i>t</i><sub class="lower-index"><i>i</i></sub>) / <i>T</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>y</i> = <i>y</i><sub class="lower-index"><i>i</i></sub> + (<i>y</i><sub class="lower-index"><i>i</i> + 1</sub> - <i>y</i><sub class="lower-index"><i>i</i></sub>)(<i>t</i> - <i>t</i><sub class="lower-index"><i>i</i></sub>) / <i>T</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>z</i> = <i>z</i><sub class="lower-index"><i>i</i></sub> + (<i>z</i><sub class="lower-index"><i>i</i> + 1</sub> - <i>z</i><sub class="lower-index"><i>i</i></sub>)(<i>t</i> - <i>t</i><sub class="lower-index"><i>i</i></sub>) / <i>T</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>T</i><sub class="lower-index"><i>i</i></sub></span> is a time necessary for snitch to overcome the segment. To catch the snitch at the point (x, y, z), Harry have to overcome the distance that squared is equal to <span class="tex-span">(<i>x</i> - <i>P</i><sub class="lower-index"><i>x</i></sub>)<sup class="upper-index">2</sup> + (<i>y</i> - <i>P</i><sub class="lower-index"><i>y</i></sub>)<sup class="upper-index">2</sup> + (<i>z</i> - <i>P</i><sub class="lower-index"><i>z</i></sub>)<sup class="upper-index">2</sup></span> for the time t. It is possible if <span class="tex-span">(<i>x</i> - <i>P</i><sub class="lower-index"><i>x</i></sub>)<sup class="upper-index">2</sup> + (<i>y</i> - <i>P</i><sub class="lower-index"><i>y</i></sub>)<sup class="upper-index">2</sup> + (<i>z</i> - <i>P</i><sub class="lower-index"><i>z</i></sub>)<sup class="upper-index">2</sup> ≤ (<i>tv</i><sub class="lower-index"><i>p</i></sub>)<sup class="upper-index">2</sup></span>. To find the minimal proper moment t, solve the corresponding quadratic equation.<br /></div><div><br /></div><div><div style="font-weight: normal;"><b>Problem D</b></div><div style="font-weight: normal;"><br /></div><div><div style="font-weight: normal;">Let <span class="tex-span"><i>S</i><sub class="lower-index"><i>i</i></sub></span> be a set of all possible assignments of the first <span class="tex-span"><i>i</i></span> students to the houses, that is a set of tuples <span class="tex-span">(<i>a</i><sub class="lower-index">1</sub>, <i>a</i><sub class="lower-index">2</sub>, <i>a</i><sub class="lower-index">3</sub>, <i>a</i><sub class="lower-index">4</sub>)</span>, where <span class="tex-span"><i>a</i><sub class="lower-index">1</sub></span> is a number of students sent to Gryffindor, <span class="tex-span"><i>a</i><sub class="lower-index">2</sub></span> - to Ravenclaw, etc. It's intuitively clear that these sets will not be large. So you can get <span class="tex-span"><i>S</i><sub class="lower-index"><i>i</i> - 1</sub></span> from <span class="tex-span"><i>S</i><sub class="lower-index"><i>i</i></sub></span> in a trivial way, and get finally <span class="tex-span"><i>S</i><sub class="lower-index"><i>n</i></sub></span>, and determine the answer from it. </div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"><br /></div></div></b></div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;">What is a rigorous proof of the algorithm? Let us have a set<b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"> <span class="tex-span"><i>S</i> = {(<i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">1</sub>, <i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">2</sub>, <i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">3</sub>, <i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">4</sub>)}<sub class="lower-index"><i>i</i> = 1, 2, ..., <i>k</i></sub></span>. Represent its elements as <span class="tex-span"><i>a</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub> = <i>b</i><sub class="lower-index"><i>j</i></sub> + <i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub></span>, <span class="tex-span"><i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub> ≥ 0</span>, where <span class="tex-span"><i>b</i><sub class="lower-index"><i>j</i></sub></span> are maximal possible, i.e. there is i for each j such that <span class="tex-span"><i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub> = 0</span>. Let the tuple <span class="tex-span">(<i>b</i><sub class="lower-index">1</sub>, <i>b</i><sub class="lower-index">2</sub>, <i>b</i><sub class="lower-index">3</sub>, <i>b</i><sub class="lower-index">4</sub>)</span> be called the base part of S, and the set <span class="tex-span">{(<i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">1</sub>, <i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">2</sub>, <i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">3</sub>, <i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index">4</sub>)}<sub class="lower-index"><i>i</i> = 1, 2, ..., <i>k</i></sub></span> be called the variant part of S. </div></div></b></div></div></b><br /></div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Initially for <span class="tex-span"><i>S</i><sub class="lower-index">0</sub></span> both base and variant parts are zeroes. Let us see how base and variant parts change when a current student is added. If a house is fixed for the student, only the base part changes. It increases by 1 at the position corresponding to the house. In particular, it follows that a set with every base part can be obtained (since the string given in the input can contain every combination of symbols G, H, R, S). If the current symbol in the string is '?', it can influence both base and variant parts.</div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">For example, for the string '????' we have:</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">0</sub> = {(0 + 0, 0 + 0, 0 + 0, 0 + 0)}</span>,</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">1</sub> = {(0 + 1, 0 + 0, 0 + 0, 0 + 0), (0 + 0, 0 + 1, 0 + 0, 0 + 0), (0 + 0, 0 + 0, 0 + 1, 0 + 0), (0 + 0, 0 + 0, 0 + 0, 0 + 1)}</span>,</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">2</sub> = {(0 + 1, 0 + 1, 0 + 0, 0 + 0), (0 + 1, 0 + 0, 0 + 1, 0 + 0), (0 + 1, 0 + 0, 0 + 0, 0 + 1), (0 + 0, 0 + 1, 0 + 1, 0 + 0), (0 + 0, 0 + 1, 0 + 0, 0 + 1), (0 + 0, 0 + 0, 0 + 1, 0 + 1)}</span>,</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">3</sub> = {(0 + 1, 0 + 1, 0 + 1, 0 + 0), (0 + 1, 0 + 1, 0 + 0, 0 + 1), (0 + 1, 0 + 0, 0 + 1, 0 + 1), (0 + 0, 0 + 1, 0 + 1, 0 + 1)}</span>,</div><div style="font-weight: normal;"><span class="tex-span"><i>S</i><sub class="lower-index">4</sub> = {(1 + 0, 1 + 0, 1 + 0, 1 + 0)}</span>.</div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Let us investigate the question of what species a variant part may have. It can be analyzed independently from a base one, taking into account that a base part can be any. Consider a directed graph with vertices corresponding to variant parts and with edges determined by the existence of<b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"> at least one base part that let go from one variant part to another. We are interested only in vertices reachable from <span class="tex-span">{(0, 0, 0, 0)}</span>.</div></div></b></div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Proposition. For all the vertices reachable from zero the following properties hold</div><div style="font-weight: normal;">(1) <span class="tex-span"><i>x</i><sup class="upper-index"><i>i</i></sup><sub class="lower-index"><i>j</i></sub> ≤ 2</span>,</div><div style="font-weight: normal;">(2) <span class="tex-span"><i>k</i> ≤ 13</span>.</div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Let us prove that all the vertices not having the properties (1) and (2) are unreachable from zero. Consider a variant part with the property (1). To get all edges going from it you have to try all possible base parts. Note that base parts, that consist of the numbers 0, 1, 2, 3 and contain at lest one 0, are enough. Indeed, base part influence which elements are minimal, and 1 will be added to them. A base part can be always normed to contain at least one 0. If a base part contains numbers greater than 3, then the corresponding positions will never be minimal (since 4+0 &gt; 0+2) and they can be changed equivalently by 3 (3+0 &gt; 0+2).</div><div style="font-weight: normal;"><br /></div><div style="font-weight: normal;">Unfortunately, my attempts to deal with cases by hand were unsuccessful, so I wrote <a href="http://pastebin.com/p3sFKKya">the program</a> that traverse the described graph. Starting from 0, it builds edges trying only &quot;small&quot; base parts described in the previous paragraph. As a result, the program obtains all the reachable variant parts (there is a little more than 1000 of them) and check (1) and (2) for them. In addition, the program helps to construct a test with<b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"> <span class="tex-span"><i>k</i> = 13</span>.</div></div></b></div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;"><br /></div></div></b></div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><div style="display: inline !important;">The problem was supposed to be a problem on intuition. Participants have another solution passed. Their solution generate all permutations and distribute students greedily with respect to each permutation.</div></div></b><b><div style="font-weight: normal;display: inline !important;"><b><div style="font-weight: normal;display: inline !important;">This solution was a complete surprise for me. Unfortunately, it is wrong. Test 66 against it was added. Of course, submissions accepted during the round won't be rejudged. If such a solution be expected, most likely I wouldn't give such a task. In terms of intuition this solution is not better and not worse than mine. I hope you will not judge me strictly: it is a beautiful problem, and it was interesting to see how it would be solved. </div></b></div></b></div><div style="font-weight: normal;"><b><div style="font-weight: normal;display: inline !important;"><b><div style="font-weight: normal;display: inline !important;"><br /></div></b></div></b></div><div><div style="display: inline !important;"><div style="display: inline !important;"><div style="font-weight: normal;"><b>Problem E</b></div><div style="font-weight: normal;"><b><br /></b></div><div><div><div><div style="display: inline !important;"><div style="display: inline !important;">Consider a graph with floors as vertices and staircases as edges. It is clear that Harry can visit the whole connected component in which he is currently located.<br /></div></div></div><div style="font-weight: normal;"><br /></div></div></div><div>Every edge can be used to reach a new vertex for not more than two times. If a connected component contains n vertices and m edges, only n - 1 edges are used to reach a new vertex during its traversal. The remaining m - n + 1 edges are not used to reach a new vertex in their initial placement. So they will be used to reach a new vertex not more than once.</div><div><div><br /></div><div>So using edges of only one connected component you can reach no more than n - m + 1 new vertices. Totally there are not more than  <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7fae5c87930e2f915b8c632872cc1662dd30fa09.png" style="max-width: 100.0%;max-height: 100.0%;" /> reachable vertices. If m &lt; k - 1, it is impossible to visit all the vertices.  </div><div><br /></div><div>We show that otherwise (m &gt;= k - 1), if the degree of the vertex 0 is different from zero, it is possible to visit all the vertices. In other words, there is such a traversal that every edge can be moved.  Use depth-first search for the current component. If a current edge goes to an already visited vertex, move it to a new component and traverse it recursively. If a current edge goes to a new vertex, after you visit this vertex and go back, you also can move this edge to a new component. As a result each edge can be moved and used again, if you reach all the components. If a component contains at least one edge, you can go from it to the next one. First visit components with edges, and you will visit them all and by the inequality (m &gt;= k - 1) there are enough edges to visit all the isolated vertices.  </div><div><br /></div><div>If the degree of the vertex 1 is zero, you can not start a traversal before you move some edge to it. After that you can go by this edge and remove it with the vertex 1 from the graph, becase you can not use this edge once more. If the chose edge is a bridge, you get k connected components and m - 1 egdes. If it is not a bridge, you get k - 1 components and m - 1 edges. In the first case the inequality m &gt;= k - 1 turns m &gt;= k. In the second case -  m &gt;= k - 1. So if not all the edges are bridges, you should not take a bridge. If they all are bridges, you should disconnect an edge from a vertex of degree &gt;= 2 not to came back to the initial situation with the zero degree of the first vertex. If there is no such vertex, it is easy to check that there is no solution.</div></div></div></div></div></div></div></div></div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/65" class="notice" style="text-decoration: none;">Codeforces Beta Round 60</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-2326-1431").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "2326", blogEntryId: "1431", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=beta+round+%2360" class="tag notice" style="text-decoration: none;">beta round #60</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces" class="tag notice" style="text-decoration: none;">codeforces</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=tutorial" class="tag notice" style="text-decoration: none;">tutorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1431"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+33</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1431"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/natalia"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/natalia"> natalia </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Mar/06/2011 08:27">13 years ago</span> </li> <li> <a href="/blog/entry/1431#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1431#comments"> 10 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1441"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (10)</a> </div> <div class="comments-actions-div"> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="26324" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/lyrics" style="position: relative;"> <img src='https://userpic.codeforces.org/3858/avatar/29787cdba9b12888.jpg'/> </a> <div><a href="/profile/lyrics" title="Expert lyrics" class="rated-user user-blue">lyrics</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/06/2011 12:30">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26324" href="?#comment-26324" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26324" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="3858" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26324"> <div class="moveup"> <div class="ttypography">good analysis...</div> </div> </div> <div class="reply info"> <a class="comment-26324 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26324 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26324"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="26331" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/A.K.Goharshady" style="position: relative;"> <img src='https://userpic.codeforces.org/9153/avatar/358f1b75189ae870.jpg'/> </a> <div><a href="/profile/A.K.Goharshady" title="Candidate Master A.K.Goharshady" class="rated-user user-violet">A.K.Goharshady</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/06/2011 12:52">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26331" href="?#comment-26331" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26331" class="CommentVoteFrame" data-commentRating="2" data-commentUserId="9153" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+2</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26331"> <div class="moveup"> <div class="ttypography">Problem A was harder than D :D</div> </div> </div> <div class="reply info"> <a class="comment-26331 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26331 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26331"> <li> <div class="comment"> <table class="comment-table" commentId="26336" commentParentId="26331"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Alex_KPR" style="position: relative;"> <img src='https://userpic.codeforces.org/209/avatar/b403606b22dc5082.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/Alex_KPR" title="Master Alex_KPR" class="rated-user user-orange">Alex_KPR</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/06/2011 13:03">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26336" href="?#comment-26336" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-26331" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26336" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="209" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26336"> <div class="moveup"> <div class="ttypography">agree with you =)</div> </div> </div> <div class="reply info"> <a class="comment-26336 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26336 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26336"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="26374" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mR.ilchi" style="position: relative;"> <img src='https://userpic.codeforces.org/11753/avatar/b0675918b77546aa.jpg'/> </a> <div><a href="/profile/mR.ilchi" title="International Grandmaster mR.ilchi" class="rated-user user-red">mR.ilchi</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/06/2011 15:58">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26374" href="?#comment-26374" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="26374" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="26374" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="11753" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26374"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">please translate problem D and E too.</div><div class="from-renderer"><div>thank's for your nice contest!!!</div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-26374 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26374 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26374"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="26587" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/sunhaowen567" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/sunhaowen567" title="Expert sunhaowen567" class="rated-user user-blue">sunhaowen567</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/07/2011 07:43">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26587" href="?#comment-26587" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26587" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3232" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26587"> <div class="moveup"> <div class="ttypography">waiting for problem E......</div> </div> </div> <div class="reply info"> <a class="comment-26587 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26587 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26587"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="26588" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kang205" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/kang205" title="Expert kang205" class="rated-user user-blue">kang205</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/07/2011 08:13">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26588" href="?#comment-26588" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26588" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13097" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26588"> <div class="moveup"> <div class="ttypography">Problem D's proof is very NICE.<br /><br /><br /><br /></div> </div> </div> <div class="reply info"> <a class="comment-26588 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26588 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26588"> <li> <div class="comment"> <table class="comment-table" commentId="26589" commentParentId="26588"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kang205" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/kang205" title="Expert kang205" class="rated-user user-blue">kang205</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/07/2011 08:16">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-26589" href="?#comment-26589" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-26588" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="26589" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13097" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-26589"> <div class="moveup"> <div class="ttypography">I use <b>random <b><b><b> generate permutations</b></b></b></b>,but the random times be set 10000,so I got TLE.<br /><br />If set 2000,I got AC....</div> </div> </div> <div class="reply info"> <a class="comment-26589 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-26589 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-26589"> <li> <div class="comment"> <table class="comment-table" commentId="194733" commentParentId="26589"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/wjh720" style="position: relative;"> <img src='https://userpic.codeforces.org/210352/avatar/d212772572283d08.jpg'/> </a> <div><a href="/profile/wjh720" title="International Grandmaster wjh720" class="rated-user user-red">wjh720</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Oct/30/2014 09:43">9 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-194733" href="?#comment-194733" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-26589" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="194733" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="210352" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-194733"> <div class="moveup"> <div class="ttypography"><p>You can have a try with {&quot;?HRS&quot;*2500} :)</p></div> </div> </div> <div class="reply info"> <a class="comment-194733 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-194733 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-194733"> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="310517" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/throwaways" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/throwaways" title="Unrated, throwaways" class="rated-user user-black">throwaways</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Aug/17/2016 00:08">7 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-310517" href="?#comment-310517" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="310517" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="310517" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="401734" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-310517"> <div class="moveup"> <div class="ttypography"><p>what might the time complexity of D be?</p></div> </div> </div> <div class="reply info"> <a class="comment-310517 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-310517 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-310517"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="555734" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/roll_no_1" style="position: relative;"> <img src='https://userpic.codeforces.org/631859/avatar/36d157f91f64fe7f.jpg'/> </a> <div><a href="/profile/roll_no_1" title="Master roll_no_1" class="rated-user user-orange">roll_no_1</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Nov/03/2019 08:56">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-555734" href="?#comment-555734" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="555734" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="631859" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-555734"> <div class="moveup"> <div class="ttypography"><p>Here are the 2 interpretations of problem A's solution as I understood them:</p><p><a href="/contest/65/submission/64128016" title="Submission 64128016 by roll_no_1">64128016</a></p><p><a href="/contest/65/submission/64128379" title="Submission 64128379 by roll_no_1">64128379</a></p></div> </div> </div> <div class="reply info"> <a class="comment-555734 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-555734 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-555734"> </ul> </div> <br/> <div id="editBox-1441" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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A. Petya and Java
<div class="problem-statement"><div class="header"><div class="title">A. Petya and Java</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Little Petya has recently started attending a programming club. Naturally he is facing the problem of choosing a programming language. After long considerations he realized that Java is the best choice. The main argument in favor of choosing Java was that it has a very large integer data type, called BigInteger.</p><p>But having attended several classes of the club, Petya realized that not all tasks require using the BigInteger type. It turned out that in some tasks it is much easier to use small data types. That's why a question arises: "Which integer type to use if one wants to store a positive integer <span class="tex-span"><i>n</i></span>?"</p><p>Petya knows only 5 integer types:</p><p>1) <span class="tex-font-style-bf">byte</span> occupies 1 byte and allows you to store numbers from <span class="tex-span"> - 128</span> to <span class="tex-span">127</span></p><p>2) <span class="tex-font-style-bf">short</span> occupies 2 bytes and allows you to store numbers from <span class="tex-span"> - 32768</span> to <span class="tex-span">32767</span></p><p>3) <span class="tex-font-style-bf">int</span> occupies 4 bytes and allows you to store numbers from <span class="tex-span"> - 2147483648</span> to <span class="tex-span">2147483647</span></p><p>4) <span class="tex-font-style-bf">long</span> occupies 8 bytes and allows you to store numbers from <span class="tex-span"> - 9223372036854775808</span> to <span class="tex-span">9223372036854775807</span></p><p>5) <span class="tex-font-style-bf">BigInteger</span> can store any integer number, but at that it is not a primitive type, and operations with it are much slower.</p><p>For all the types given above the boundary values are included in the value range.</p><p>From this list, Petya wants to choose the smallest type that can store a positive integer <span class="tex-span"><i>n</i></span>. Since BigInteger works much slower, Peter regards it last. Help him.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains a positive number <span class="tex-span"><i>n</i></span>. It consists of no more than <span class="tex-span">100</span> digits and doesn't contain any leading zeros. The number <span class="tex-span"><i>n</i></span> can't be represented as an empty string.</p><p>Please, do not use <span class="tex-font-style-tt">%lld</span> specificator to read or write 64-bit integers in C++. It is preffered to use <span class="tex-font-style-tt">cout</span> (also you may use <span class="tex-font-style-tt">%I64d</span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print the first type from the list "<span class="tex-font-style-tt">byte</span>, <span class="tex-font-style-tt">short</span>, <span class="tex-font-style-tt">int</span>, <span class="tex-font-style-tt">long</span>, <span class="tex-font-style-tt">BigInteger</span>", that can store the natural number <span class="tex-span"><i>n</i></span>, in accordance with the data given above.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>127<br/></pre></div><div class="output"><div class="title">Output</div><pre>byte<br/></pre></div><div class="input"><div class="title">Input</div><pre>130<br/></pre></div><div class="output"><div class="title">Output</div><pre>short<br/></pre></div><div class="input"><div class="title">Input</div><pre>123456789101112131415161718192021222324<br/></pre></div><div class="output"><div class="title">Output</div><pre>BigInteger<br/></pre></div></div></div></div>
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If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="A" data-uuid="ps_1a63e11e8567c006bdde0c43fb0769222d6771a8"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">A. Petya and Java</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Little Petya has recently started attending a programming club. Naturally he is facing the problem of choosing a programming language. After long considerations he realized that Java is the best choice. The main argument in favor of choosing Java was that it has a very large integer data type, called BigInteger.</p><p>But having attended several classes of the club, Petya realized that not all tasks require using the BigInteger type. It turned out that in some tasks it is much easier to use small data types. That's why a question arises: &quot;Which integer type to use if one wants to store a positive integer <span class="tex-span"><i>n</i></span>?&quot;</p><p>Petya knows only 5 integer types:</p><p>1) <span class="tex-font-style-bf">byte</span> occupies 1 byte and allows you to store numbers from <span class="tex-span"> - 128</span> to <span class="tex-span">127</span></p><p>2) <span class="tex-font-style-bf">short</span> occupies 2 bytes and allows you to store numbers from <span class="tex-span"> - 32768</span> to <span class="tex-span">32767</span></p><p>3) <span class="tex-font-style-bf">int</span> occupies 4 bytes and allows you to store numbers from <span class="tex-span"> - 2147483648</span> to <span class="tex-span">2147483647</span></p><p>4) <span class="tex-font-style-bf">long</span> occupies 8 bytes and allows you to store numbers from <span class="tex-span"> - 9223372036854775808</span> to <span class="tex-span">9223372036854775807</span></p><p>5) <span class="tex-font-style-bf">BigInteger</span> can store any integer number, but at that it is not a primitive type, and operations with it are much slower.</p><p>For all the types given above the boundary values are included in the value range.</p><p>From this list, Petya wants to choose the smallest type that can store a positive integer <span class="tex-span"><i>n</i></span>. Since BigInteger works much slower, Peter regards it last. Help him.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains a positive number <span class="tex-span"><i>n</i></span>. It consists of no more than <span class="tex-span">100</span> digits and doesn't contain any leading zeros. The number <span class="tex-span"><i>n</i></span> can't be represented as an empty string.</p><p>Please, do not use <span class="tex-font-style-tt">%lld</span> specificator to read or write 64-bit integers in C++. It is preffered to use <span class="tex-font-style-tt">cout</span> (also you may use <span class="tex-font-style-tt">%I64d</span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print the first type from the list &quot;<span class="tex-font-style-tt">byte</span>, <span class="tex-font-style-tt">short</span>, <span class="tex-font-style-tt">int</span>, <span class="tex-font-style-tt">long</span>, <span class="tex-font-style-tt">BigInteger</span>&quot;, that can store the natural number <span class="tex-span"><i>n</i></span>, in accordance with the data given above.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>127<br /></pre></div><div class="output"><div class="title">Output</div><pre>byte<br /></pre></div><div class="input"><div class="title">Input</div><pre>130<br /></pre></div><div class="output"><div class="title">Output</div><pre>short<br /></pre></div><div class="input"><div class="title">Input</div><pre>123456789101112131415161718192021222324<br /></pre></div><div class="output"><div class="title">Output</div><pre>BigInteger<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=A]"); 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["Implementation problems, programming technics, simulation", "Prefix- and Z-functions, suffix structures, Knuth\u2013Morris\u2013Pratt algorithm, etc"]
["implementation", "strings", "*1300"]
https://codeforces.com/blog/entry/1452
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<a href="/blog/entry/120644">Codeforces Round 899 (Div. 2)</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/Misa-Misa" title="Expert Misa-Misa" class="rated-user user-blue">Misa-Misa</a> &rarr; <a href="/blog/entry/121157">Someone please help me understand this.</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/shivam565" title="Specialist shivam565" class="rated-user user-cyan">shivam565</a> &rarr; <a href="/blog/entry/108348">Total number of subarrays with sum atmost k</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> </ul> </div> <div class="bottom-links"> <table style="width:100%;"> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:right;"> <a href="/recent-actions">Detailed &rarr;</a> </td> </tr> </tbody> </table> </div> </div> </div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li><a href="/profile/Seyaua">Seyaua</a></li> <li class="current selectedLava"><a href="/blog/Seyaua">Blog</a></li> <li><a href="/teams/with/Seyaua">Teams</a></li> <li><a href="/submissions/Seyaua">Submissions</a></li> <li><a href="/contests/with/Seyaua">Contests</a></li> <li><a href="/contests/writer/Seyaua">Problemsetting</a></li> </ul> </div> <div style="margin-top:0;"> <div> <h3><a href="/blog/Seyaua" style="text-decoration:none;color:black !important;">Seyaua's blog</a></h3> </div> <div style="margin-top:2em;"> <div class="has-topic-id topic" topicId="1452"> <div class="title"> <a href="/blog/entry/1452"> <p>Codeforces Beta Round #61 (Div. 2): Editorial</p> </a> </div> <div class="info" style="position:relative;"> By&nbsp;<a href="/profile/Seyaua" title="Master Seyaua" class="rated-user user-orange">Seyaua</a>, <span class="format-humantime" title="Mar/07/2011 21:01">13 years ago</span>, translation, <img style="position: relative;top: 5px;" src="//codeforces.org/s/81027/images/flags/24/gb.png" alt="In English" title="In English"/> <span style="position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;"> <div style="margin-top:0.25em;"> </div> </span> </div> <div class="content"> <div class="ttypography"><p><font face="Arial"></font></p><p style=""><font face="Arial"><span><span style="font-family: Arial;color: black;">Here you can find the editorial for the past round. You can ask questions in the comments below. Special thank you goes to </span></span><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;"><a class="rated-user user-red" href="//codeforces.com/profile/sdya" style="font-family: arial;text-decoration: none !important;font-weight: bold;color: rgb(0,0,204);" title="Colonel sdya">sdya</a> </span>who prepared editorials for problems D and E, which I used here.</font></p> <h3><span lang="EN-US">Problem A</span></h3> <p><span lang="EN-US">In this problem you should answer to 4 questions:</span></p> <p style="margin-left: 42.75pt;"><span lang="EN-US">1)<span style="font: 7.0pt &quot;Times New Roman&quot;;">       </span></span><span lang="EN-US">Can we use type byte to store N?</span></p> <p style="margin-left: 42.75pt;"><span lang="EN-US">2)<span style="font: 7.0pt &quot;Times New Roman&quot;;">       </span></span><span lang="EN-US">Can we use type short to store N?</span></p> <p style="margin-left: 42.75pt;"><span lang="EN-US">3)<span style="font: 7.0pt &quot;Times New Roman&quot;;">       </span></span><span lang="EN-US">Can we use type int to store N?</span></p> <p style="margin-left: 42.75pt;"><span lang="EN-US">4)<span style="font: 7.0pt &quot;Times New Roman&quot;;">       </span></span><span lang="EN-US">Can we use type long to store N?</span></p> <p><span lang="EN-US">We should check these conditions in the given order. If all these conditions are wrong, the answer is BigInteger.</span></p> <p><span lang="EN-US">The simplest way to check these conditions is to store numbers as strings and write a function to compare such strings. In Java you can use type BigInteger.</span></p> <h3><span lang="EN-US">Problem B</span></h3> <p><span lang="EN-US">Try to check all possibilities for creation artificial rain and calculate how many sections contain water. The maximal answer from all these possibilities is the answer for the problem. To calculate the answer for the given position we should check how many sections are to the left and to the right of the given section receive water. The complexity of this algorithm is O(N^2).</span></p> <h3><span lang="EN-US">Problem C</span></h3> <p>Will be published later. </p> <h3><span lang="EN-US">Problem D</span></h3> <p><span lang="EN-US">Consider N distinct prime numbers: p1, p2, …, pn. </span></p> <p><span lang="EN-US">Let A=p1*p2*…*pn. Then, easy to see, that the numbers A/p1, A/p2, …, A/pn can be considered as the answer.</span></p> <p><span lang="EN-US">The special case is when N=2. In this case there is no answer. We can see that this solution needs long arithmetic. If we choose first n prime numbers as p1, p2, …, pn then the maximal number in the answer for all N&lt;=50 contains less than 100 digits.</span></p> <p><span lang="EN-US"> </span></p> <p><span lang="EN-US">Of course, there are other solutions. For example, if N=3 numbers 15, 10, 6 are the answer, and for N&gt;3 numbers 15, 10, 6, 6*2, 6*3, …, 6*(N-2) are the answer.</span></p> <h3><span lang="EN-US">Problem E</span></h3> <p><span lang="EN-US">First of all we divide our problem into 2 parts: consider stations from which we can start if we are moving in the clockwise direction and stations from which we can start if we are moving in the counterclockwise direction.</span></p> <p><span lang="EN-US">Obviously, if we know the solution of one of these problems, we know the solution of another problem.</span></p> <p><span lang="EN-US">So, we may assume that stations are located in the counterclockwise order and we are moving in the counterclockwise direction.</span></p> <p><span lang="EN-US">Consider the following differences:</span></p> <p><span lang="EN-US">D1=a1-b1,</span></p> <p><span lang="EN-US">D2=(a1+a2)-(b1+b2),</span></p> <p><span lang="EN-US">D3=(a1+a2+a3)-(b1+b2+b3),</span></p> <p><span lang="EN-US">…</span></p> <p><span lang="EN-US">Dn=(a1+a2+…+an)-(b1+b2+…+bn);</span></p> <p><span lang="EN-US">Obviously if one of Di’s is less than a zero, then we cannot drive one round along the road. Let D = min(Di) – we will use it later.</span></p> <p><span lang="EN-US">Obviously, if D&lt;0 then the first station cannot be the start station.</span></p> <p><span lang="EN-US">Now, we can check with complexity O(n) whether the first station can be used as the starting point. Next, we want to show how we can check this for the second station with complexity O(1).<br /> To show this, consider:</span></p> <p><span lang="EN-US">E1=D1-(a1-b1),</span></p> <p><span lang="EN-US">E2=D2-(a1-b1),</span></p> <p><span lang="EN-US">…</span></p> <p><span lang="EN-US">En=Dn-(a1-b1).</span></p> <p><span lang="EN-US">Next, substitute Di in these equalities. We get the following:</span></p> <p><span lang="EN-US">E1=(a1-b1)-(a1-b1)=0=(a2+a3+…+an+a1)-(b2+b3+…+bn+b1) – (a1+…+an=b1+…+bn=X)</span></p> <p><span lang="EN-US">E2=(a1+a2)-(b1+b2)-(a1-b1)=a2-b2</span></p> <p><span lang="EN-US">E3=(a1+a2+a3)-(b1+b2+b3)-(a1-b1)=(a2+a3)-(b2+b3)</span></p> <p><span lang="EN-US">…</span></p> <p><span lang="EN-US">En=(a1+a2+…+an)-(b1+b2+…+bn)-(a1-b1)=(a2+…+an)-(b2+…+bn)</span></p> <p><span lang="EN-US">But it’s easy to see that number E1 has the same meaning for the second station as number D1 for the first one. So, we just have to check min(Ei)&gt;=0. But Ei=Di-(a1-b1), so we have to check min(Di-(a1-b1))&gt;=0. Now, we can see that if min(Di)=Dk, then min(Di-(a1-b1))=Dk-(a1-b1). So, if we know Dk, that we can check whether the second station can be the starting point with complexity O(1). Similarly, we can check this for the third, the fourth, …, the nth stations.</span></p> <p><span lang="EN-US">Now we should check the same things but assuming that the car is moving in the clockwise direction.<font></font></span></p></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/66" class="notice" style="text-decoration: none;">Codeforces Beta Round 61 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-140-1452").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "140", blogEntryId: "1452", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces+round+%2361" class="tag notice" style="text-decoration: none;">codeforces round #61</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=editorial" class="tag notice" style="text-decoration: none;">editorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1452"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+57</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1452"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/Seyaua"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/Seyaua"> Seyaua </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Mar/07/2011 21:01">13 years ago</span> </li> <li> <a href="/blog/entry/1452#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1452#comments"> 17 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1462"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (10)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="27331" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/fura2" style="position: relative;"> <img src='https://userpic.codeforces.org/4118/avatar/98f7ddceb1dac755.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/fura2" title="Master fura2" class="rated-user user-orange">fura2</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/11/2011 23:44">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-27331" href="?#comment-27331" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="27331" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4118" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-27331"> <div class="moveup"> <div class="ttypography">Elegant solutions!<br />In particular, problem E!!</div> </div> </div> <div class="reply info"> <a class="comment-27331 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-27331 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-27331"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="27953" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/seen" style="position: relative;"> <img src='https://userpic.codeforces.org/13855/avatar/8d25f30f74ce6c29.jpg'/> </a> <div><a href="/profile/seen" title="Expert seen" class="rated-user user-blue">seen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/14/2011 12:28">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-27953" href="?#comment-27953" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="27953" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13855" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-27953"> <div class="moveup"> <div class="ttypography"><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;">problem E!</span></div> </div> </div> <div class="reply info"> <a class="comment-27953 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-27953 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-27953"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29796" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/wil93" style="position: relative;"> <img src='https://userpic.codeforces.org/14356/avatar/897f1996dfb7343b.jpg'/> </a> <div><a href="/profile/wil93" title="Expert wil93" class="rated-user user-blue">wil93</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/24/2011 23:24">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29796" href="?#comment-29796" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29796" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14356" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29796"> <div class="moveup"> <div class="ttypography">Will problem C be published?</div> </div> </div> <div class="reply info"> <a class="comment-29796 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29796 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29796"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="305792" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/haleyk100198" style="position: relative;"> <img src='https://userpic.codeforces.org/416324/avatar/f2d97d505af17e9d.jpg'/> </a> <div><a href="/profile/haleyk100198" title="Candidate Master haleyk100198" class="rated-user user-violet">haleyk100198</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jul/19/2016 07:49">7 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-305792" href="?#comment-305792" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="305792" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="416324" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-305792"> <div class="moveup"> <div class="ttypography"><p>What is test case 14 for problem C? I tried to simulate the file system yet it ended up in a RE.</p><p><a href="//codeforces.com/contest/66/submission/19224146">http://codeforces.com/contest/66/submission/19224146</a></p></div> </div> </div> <div class="reply info"> <a class="comment-305792 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-305792 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-305792"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="317215" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/XenoAmess" style="position: relative;"> <img src='https://userpic.codeforces.org/361918/avatar/e575f783daf72fba.jpg'/> </a> <div><a href="/profile/XenoAmess" title="Expert XenoAmess" class="rated-user user-blue">XenoAmess</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Sep/26/2016 03:09">7 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-317215" href="?#comment-317215" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="317215" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="361918" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-317215"> <div class="moveup"> <div class="ttypography"><p>well...I don't need it myself but, problem C's Editorial has been delayed for 6 years...</p></div> </div> </div> <div class="reply info"> <a class="comment-317215 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-317215 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-317215"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="415288" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/ghoshsai5000" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/ghoshsai5000" title="Pupil ghoshsai5000" class="rated-user user-green">ghoshsai5000</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/18/2018 12:28">6 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-415288" href="?#comment-415288" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="415288" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="415288" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="543439" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-415288"> <div class="moveup"> <div class="ttypography"><p>For whoever is interested, here is an outstanding and creative approach taught to me by IOI silver medalist, ICPC world Finalist and my teacher <a class="rated-user user-violet" href="/profile/razimantv" title="Candidate Master razimantv">razimantv</a> to problem D. It does not require big integers and teaches an important fact about binary numbers. </p><p>First, let us consider all the numbers (from 1 to N) in binary.</p><p>For each bit position, associate two primes — P[i], Q[i]. Multiply all numbers which have the i-th bit set by P[i]. Multiply all numbers which have the i-th bit unset by Q[i]. </p><p>Now, all pairs of numbers which have a common bit set have a common factor. We only have to deal with those numbers which don't have any common bit (i.e. ... Those numbers who's XOR gives a string of all 1s).</p><p>We give all pairs of numbers (i, X) a common prime factor if i^X gives a string of all 1s.</p><p>Now, we have ensured that any two numbers have a common prime factor and no prime divides all numbers, We are done !</p><p><a href="//codeforces.com/contest/66/submission/35441406">Here</a> is code for this approach and here is some <a href="https://github.com/MathProgrammer/CodeForces/blob/master/C%20Programs/C%20Programs%2020/Petya%20and%20His%20Friends%20Alternate%20Solution%20Explanation.txt">explanation</a>.</p><p>(<a href="https://github.com/MathProgrammer/CodeForces/blob/master/C%20Programs/C%20Programs%2020/Petya%20and%20His%20Friends%20Alternate%20Solution.cpp">Here</a>'s the same code on GitHub)</p></div> </div> </div> <div class="reply info"> <a class="comment-415288 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-415288 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-415288"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="429734" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/ghoshsai5000" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/ghoshsai5000" title="Pupil ghoshsai5000" class="rated-user user-green">ghoshsai5000</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/10/2018 15:48">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-429734" href="?#comment-429734" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="429734" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="543439" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-429734"> <div class="moveup"> <div class="ttypography"><p>In case, anybody requires more explanation for Problem D, I have written a post about it <a href="https://qr.ae/TUTYGd">here</a>.</p></div> </div> </div> <div class="reply info"> <a class="comment-429734 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-429734 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-429734"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="525312" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/vjvjain0" style="position: relative;"> <img src='https://userpic.codeforces.org/699621/avatar/e27ffdf24b4ccf7b.jpg'/> </a> <div><a href="/profile/vjvjain0" title="Expert vjvjain0" class="rated-user user-blue">vjvjain0</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jul/06/2019 16:21">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-525312" href="?#comment-525312" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="525312" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="699621" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-525312"> <div class="moveup"> <div class="ttypography"><p>My solution for D is like this: </p> <ul> <li><p>First element will always be $$$2\times3$$$ and fill $$$n/2$$$ elements with $$$2$$$ while fill remaining elements with $$$3$$$. It will ensure that $$$n/2$$$ and $$$n-n/2$$$ groups have pairwise $$$gcd&gt;1$$$ inside their groups. This also means that $$$gcd$$$ of all elements is $$$1$$$.</p></li> <li><p>Now for every element from $$$2$$$ to $$$n$$$ multiply it by 5. This ensures that each pair has $$$gcd&gt;1$$$.</p></li> <li><p>Now for elements to be distinct, multiply elements with unique prime numbers.</p></li> </ul><p><strong>Note</strong>: It will not work for $$$n=3$$$.</p><p><a href="https://codeforces.com/contest/66/submission/56623956">Solution link</a></p></div> </div> </div> <div class="reply info"> <a class="comment-525312 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-525312 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-525312"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="828502" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/deepansh10" style="position: relative;"> <img src='https://userpic.codeforces.org/2028719/avatar/4366b653cd30d59b.jpg'/> </a> <div><a href="/profile/deepansh10" title="Expert deepansh10" class="rated-user user-blue">deepansh10</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Aug/14/2021 11:05">2 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-828502" href="?#comment-828502" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="828502" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2028719" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-828502"> <div class="moveup"> <div class="ttypography"><p>Can anyone suggest how to deal with the overflow in C++? Long long is not sufficient for storing the answer and trying to perform multiplication with strings is very complex.</p></div> </div> </div> <div class="reply info"> <a class="comment-828502 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-828502 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-828502"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="1067844" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Billy_Nguyen" style="position: relative;"> <img src='https://userpic.codeforces.org/3379746/avatar/dd0e8cc957d07897.jpg'/> </a> <div><a href="/profile/Billy_Nguyen" title="Newbie Billy_Nguyen" class="rated-user user-gray">Billy_Nguyen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Sep/12/2023 06:15">4 weeks ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-1067844" href="?#comment-1067844" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="1067844" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3379746" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-1067844"> <div class="moveup"> <div class="ttypography"><p>I found way to solve problem B with time complexity O(n)</p><p><a href="/contest/66/submission/223024612" title="Submission 223024612 by Billy_Nguyen">223024612</a></p><p>Hope someone find it useful, I am not necroposting or flexing ( i am just a grey ), I comment this just with the intention of helping so that someone who has seeked out a more efficient solution could see this because actually I have thought of the editorial solution and tbh I dont think it would be the solution since it is kinda too inefficient, thats why I wasted so much time thinking and coming up with this solution. Tbh if I knew the solution is just this brute force I would have done it</p></div> </div> </div> <div class="reply info"> <a class="comment-1067844 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-1067844 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-1067844"> </ul> </div> <br/> <div id="editBox-1462" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In Russian</span> </div> <textarea data-drafts-id="CommentReplyFrame" class="wysiwyg" name="editContent" rows="20" style="width:99%;"></textarea> <div class="error error__content"></div> <div style="text-align:center;"> <input type="button" name="preview" style="padding: 0.25em 1em; 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66B
66
B
en
B. Petya and Countryside
<div class="problem-statement"><div class="header"><div class="title">B. Petya and Countryside</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Little Petya often travels to his grandmother in the countryside. The grandmother has a large garden, which can be represented as a rectangle <span class="tex-span">1 × <i>n</i></span> in size, when viewed from above. This rectangle is divided into <span class="tex-span"><i>n</i></span> equal square sections. The garden is very unusual as each of the square sections possesses its own fixed height and due to the newest irrigation system we can create artificial rain above each section.</p><p>Creating artificial rain is an expensive operation. That's why we limit ourselves to creating the artificial rain only above one section. At that, the water from each watered section will flow into its neighbouring sections if their height does not exceed the height of the section. That is, for example, the garden can be represented by a <span class="tex-span">1 × 5</span> rectangle, where the section heights are equal to 4, 2, 3, 3, 2. Then if we create an artificial rain over any of the sections with the height of 3, the water will flow over all the sections, except the ones with the height of 4. See the illustration of this example at the picture:</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/9a76a52a71905a2651ba09ebbc571d25a9f9fe07.png" style="max-width: 100.0%;max-height: 100.0%;"/> </center><p>As Petya is keen on programming, he decided to find such a section that if we create artificial rain above it, the number of watered sections will be maximal. Help him. </p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains a positive integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 1000</span>). The second line contains <span class="tex-span"><i>n</i></span> positive integers which are the height of the sections. All the numbers are no less than 1 and not more than 1000.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single number, the maximal number of watered sections if we create artificial rain above exactly one section.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>1<br/>2<br/></pre></div><div class="output"><div class="title">Output</div><pre>1<br/></pre></div><div class="input"><div class="title">Input</div><pre>5<br/>1 2 1 2 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>3<br/></pre></div><div class="input"><div class="title">Input</div><pre>8<br/>1 2 1 1 1 3 3 4<br/></pre></div><div class="output"><div class="title">Output</div><pre>6<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="B" data-uuid="ps_18f4d9da1ab08318702937430190c2717511b950"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">B. Petya and Countryside</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Little Petya often travels to his grandmother in the countryside. The grandmother has a large garden, which can be represented as a rectangle <span class="tex-span">1 × <i>n</i></span> in size, when viewed from above. This rectangle is divided into <span class="tex-span"><i>n</i></span> equal square sections. The garden is very unusual as each of the square sections possesses its own fixed height and due to the newest irrigation system we can create artificial rain above each section.</p><p>Creating artificial rain is an expensive operation. That's why we limit ourselves to creating the artificial rain only above one section. At that, the water from each watered section will flow into its neighbouring sections if their height does not exceed the height of the section. That is, for example, the garden can be represented by a <span class="tex-span">1 × 5</span> rectangle, where the section heights are equal to 4, 2, 3, 3, 2. Then if we create an artificial rain over any of the sections with the height of 3, the water will flow over all the sections, except the ones with the height of 4. See the illustration of this example at the picture:</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/9a76a52a71905a2651ba09ebbc571d25a9f9fe07.png" style="max-width: 100.0%;max-height: 100.0%;" /> </center><p>As Petya is keen on programming, he decided to find such a section that if we create artificial rain above it, the number of watered sections will be maximal. Help him. </p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains a positive integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 1000</span>). The second line contains <span class="tex-span"><i>n</i></span> positive integers which are the height of the sections. All the numbers are no less than 1 and not more than 1000.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single number, the maximal number of watered sections if we create artificial rain above exactly one section.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>1<br />2<br /></pre></div><div class="output"><div class="title">Output</div><pre>1<br /></pre></div><div class="input"><div class="title">Input</div><pre>5<br />1 2 1 2 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>3<br /></pre></div><div class="input"><div class="title">Input</div><pre>8<br />1 2 1 1 1 3 3 4<br /></pre></div><div class="output"><div class="title">Output</div><pre>6<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=B]"); let uuid = $problem.attr("data-uuid"); 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["Brute force", "Implementation problems, programming technics, simulation"]
["brute force", "implementation", "*1100"]
https://codeforces.com/blog/entry/1452
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<a href="/blog/entry/120644">Codeforces Round 899 (Div. 2)</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/Misa-Misa" title="Expert Misa-Misa" class="rated-user user-blue">Misa-Misa</a> &rarr; <a href="/blog/entry/121157">Someone please help me understand this.</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/shivam565" title="Specialist shivam565" class="rated-user user-cyan">shivam565</a> &rarr; <a href="/blog/entry/108348">Total number of subarrays with sum atmost k</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> </ul> </div> <div class="bottom-links"> <table style="width:100%;"> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:right;"> <a href="/recent-actions">Detailed &rarr;</a> </td> </tr> </tbody> </table> </div> </div> </div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li><a href="/profile/Seyaua">Seyaua</a></li> <li class="current selectedLava"><a href="/blog/Seyaua">Blog</a></li> <li><a href="/teams/with/Seyaua">Teams</a></li> <li><a href="/submissions/Seyaua">Submissions</a></li> <li><a href="/contests/with/Seyaua">Contests</a></li> <li><a href="/contests/writer/Seyaua">Problemsetting</a></li> </ul> </div> <div style="margin-top:0;"> <div> <h3><a href="/blog/Seyaua" style="text-decoration:none;color:black !important;">Seyaua's blog</a></h3> </div> <div style="margin-top:2em;"> <div class="has-topic-id topic" topicId="1452"> <div class="title"> <a href="/blog/entry/1452"> <p>Codeforces Beta Round #61 (Div. 2): Editorial</p> </a> </div> <div class="info" style="position:relative;"> By&nbsp;<a href="/profile/Seyaua" title="Master Seyaua" class="rated-user user-orange">Seyaua</a>, <span class="format-humantime" title="Mar/07/2011 21:01">13 years ago</span>, translation, <img style="position: relative;top: 5px;" src="//codeforces.org/s/81027/images/flags/24/gb.png" alt="In English" title="In English"/> <span style="position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;"> <div style="margin-top:0.25em;"> </div> </span> </div> <div class="content"> <div class="ttypography"><p><font face="Arial"></font></p><p style=""><font face="Arial"><span><span style="font-family: Arial;color: black;">Here you can find the editorial for the past round. You can ask questions in the comments below. Special thank you goes to </span></span><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;"><a class="rated-user user-red" href="//codeforces.com/profile/sdya" style="font-family: arial;text-decoration: none !important;font-weight: bold;color: rgb(0,0,204);" title="Colonel sdya">sdya</a> </span>who prepared editorials for problems D and E, which I used here.</font></p> <h3><span lang="EN-US">Problem A</span></h3> <p><span lang="EN-US">In this problem you should answer to 4 questions:</span></p> <p style="margin-left: 42.75pt;"><span lang="EN-US">1)<span style="font: 7.0pt &quot;Times New Roman&quot;;">       </span></span><span lang="EN-US">Can we use type byte to store N?</span></p> <p style="margin-left: 42.75pt;"><span lang="EN-US">2)<span style="font: 7.0pt &quot;Times New Roman&quot;;">       </span></span><span lang="EN-US">Can we use type short to store N?</span></p> <p style="margin-left: 42.75pt;"><span lang="EN-US">3)<span style="font: 7.0pt &quot;Times New Roman&quot;;">       </span></span><span lang="EN-US">Can we use type int to store N?</span></p> <p style="margin-left: 42.75pt;"><span lang="EN-US">4)<span style="font: 7.0pt &quot;Times New Roman&quot;;">       </span></span><span lang="EN-US">Can we use type long to store N?</span></p> <p><span lang="EN-US">We should check these conditions in the given order. If all these conditions are wrong, the answer is BigInteger.</span></p> <p><span lang="EN-US">The simplest way to check these conditions is to store numbers as strings and write a function to compare such strings. In Java you can use type BigInteger.</span></p> <h3><span lang="EN-US">Problem B</span></h3> <p><span lang="EN-US">Try to check all possibilities for creation artificial rain and calculate how many sections contain water. The maximal answer from all these possibilities is the answer for the problem. To calculate the answer for the given position we should check how many sections are to the left and to the right of the given section receive water. The complexity of this algorithm is O(N^2).</span></p> <h3><span lang="EN-US">Problem C</span></h3> <p>Will be published later. </p> <h3><span lang="EN-US">Problem D</span></h3> <p><span lang="EN-US">Consider N distinct prime numbers: p1, p2, …, pn. </span></p> <p><span lang="EN-US">Let A=p1*p2*…*pn. Then, easy to see, that the numbers A/p1, A/p2, …, A/pn can be considered as the answer.</span></p> <p><span lang="EN-US">The special case is when N=2. In this case there is no answer. We can see that this solution needs long arithmetic. If we choose first n prime numbers as p1, p2, …, pn then the maximal number in the answer for all N&lt;=50 contains less than 100 digits.</span></p> <p><span lang="EN-US"> </span></p> <p><span lang="EN-US">Of course, there are other solutions. For example, if N=3 numbers 15, 10, 6 are the answer, and for N&gt;3 numbers 15, 10, 6, 6*2, 6*3, …, 6*(N-2) are the answer.</span></p> <h3><span lang="EN-US">Problem E</span></h3> <p><span lang="EN-US">First of all we divide our problem into 2 parts: consider stations from which we can start if we are moving in the clockwise direction and stations from which we can start if we are moving in the counterclockwise direction.</span></p> <p><span lang="EN-US">Obviously, if we know the solution of one of these problems, we know the solution of another problem.</span></p> <p><span lang="EN-US">So, we may assume that stations are located in the counterclockwise order and we are moving in the counterclockwise direction.</span></p> <p><span lang="EN-US">Consider the following differences:</span></p> <p><span lang="EN-US">D1=a1-b1,</span></p> <p><span lang="EN-US">D2=(a1+a2)-(b1+b2),</span></p> <p><span lang="EN-US">D3=(a1+a2+a3)-(b1+b2+b3),</span></p> <p><span lang="EN-US">…</span></p> <p><span lang="EN-US">Dn=(a1+a2+…+an)-(b1+b2+…+bn);</span></p> <p><span lang="EN-US">Obviously if one of Di’s is less than a zero, then we cannot drive one round along the road. Let D = min(Di) – we will use it later.</span></p> <p><span lang="EN-US">Obviously, if D&lt;0 then the first station cannot be the start station.</span></p> <p><span lang="EN-US">Now, we can check with complexity O(n) whether the first station can be used as the starting point. Next, we want to show how we can check this for the second station with complexity O(1).<br /> To show this, consider:</span></p> <p><span lang="EN-US">E1=D1-(a1-b1),</span></p> <p><span lang="EN-US">E2=D2-(a1-b1),</span></p> <p><span lang="EN-US">…</span></p> <p><span lang="EN-US">En=Dn-(a1-b1).</span></p> <p><span lang="EN-US">Next, substitute Di in these equalities. We get the following:</span></p> <p><span lang="EN-US">E1=(a1-b1)-(a1-b1)=0=(a2+a3+…+an+a1)-(b2+b3+…+bn+b1) – (a1+…+an=b1+…+bn=X)</span></p> <p><span lang="EN-US">E2=(a1+a2)-(b1+b2)-(a1-b1)=a2-b2</span></p> <p><span lang="EN-US">E3=(a1+a2+a3)-(b1+b2+b3)-(a1-b1)=(a2+a3)-(b2+b3)</span></p> <p><span lang="EN-US">…</span></p> <p><span lang="EN-US">En=(a1+a2+…+an)-(b1+b2+…+bn)-(a1-b1)=(a2+…+an)-(b2+…+bn)</span></p> <p><span lang="EN-US">But it’s easy to see that number E1 has the same meaning for the second station as number D1 for the first one. So, we just have to check min(Ei)&gt;=0. But Ei=Di-(a1-b1), so we have to check min(Di-(a1-b1))&gt;=0. Now, we can see that if min(Di)=Dk, then min(Di-(a1-b1))=Dk-(a1-b1). So, if we know Dk, that we can check whether the second station can be the starting point with complexity O(1). Similarly, we can check this for the third, the fourth, …, the nth stations.</span></p> <p><span lang="EN-US">Now we should check the same things but assuming that the car is moving in the clockwise direction.<font></font></span></p></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/66" class="notice" style="text-decoration: none;">Codeforces Beta Round 61 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-140-1452").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "140", blogEntryId: "1452", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces+round+%2361" class="tag notice" style="text-decoration: none;">codeforces round #61</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=editorial" class="tag notice" style="text-decoration: none;">editorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1452"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+57</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1452"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/Seyaua"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/Seyaua"> Seyaua </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Mar/07/2011 21:01">13 years ago</span> </li> <li> <a href="/blog/entry/1452#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1452#comments"> 17 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1462"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (10)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="27331" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/fura2" style="position: relative;"> <img src='https://userpic.codeforces.org/4118/avatar/98f7ddceb1dac755.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/fura2" title="Master fura2" class="rated-user user-orange">fura2</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/11/2011 23:44">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-27331" href="?#comment-27331" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="27331" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4118" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-27331"> <div class="moveup"> <div class="ttypography">Elegant solutions!<br />In particular, problem E!!</div> </div> </div> <div class="reply info"> <a class="comment-27331 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-27331 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-27331"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="27953" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/seen" style="position: relative;"> <img src='https://userpic.codeforces.org/13855/avatar/8d25f30f74ce6c29.jpg'/> </a> <div><a href="/profile/seen" title="Expert seen" class="rated-user user-blue">seen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/14/2011 12:28">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-27953" href="?#comment-27953" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="27953" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13855" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-27953"> <div class="moveup"> <div class="ttypography"><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;">problem E!</span></div> </div> </div> <div class="reply info"> <a class="comment-27953 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-27953 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-27953"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29796" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/wil93" style="position: relative;"> <img src='https://userpic.codeforces.org/14356/avatar/897f1996dfb7343b.jpg'/> </a> <div><a href="/profile/wil93" title="Expert wil93" class="rated-user user-blue">wil93</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/24/2011 23:24">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29796" href="?#comment-29796" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29796" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14356" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29796"> <div class="moveup"> <div class="ttypography">Will problem C be published?</div> </div> </div> <div class="reply info"> <a class="comment-29796 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29796 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29796"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="305792" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/haleyk100198" style="position: relative;"> <img src='https://userpic.codeforces.org/416324/avatar/f2d97d505af17e9d.jpg'/> </a> <div><a href="/profile/haleyk100198" title="Candidate Master haleyk100198" class="rated-user user-violet">haleyk100198</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jul/19/2016 07:49">7 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-305792" href="?#comment-305792" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="305792" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="416324" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-305792"> <div class="moveup"> <div class="ttypography"><p>What is test case 14 for problem C? I tried to simulate the file system yet it ended up in a RE.</p><p><a href="//codeforces.com/contest/66/submission/19224146">http://codeforces.com/contest/66/submission/19224146</a></p></div> </div> </div> <div class="reply info"> <a class="comment-305792 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-305792 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-305792"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="317215" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/XenoAmess" style="position: relative;"> <img src='https://userpic.codeforces.org/361918/avatar/e575f783daf72fba.jpg'/> </a> <div><a href="/profile/XenoAmess" title="Expert XenoAmess" class="rated-user user-blue">XenoAmess</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Sep/26/2016 03:09">7 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-317215" href="?#comment-317215" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="317215" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="361918" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-317215"> <div class="moveup"> <div class="ttypography"><p>well...I don't need it myself but, problem C's Editorial has been delayed for 6 years...</p></div> </div> </div> <div class="reply info"> <a class="comment-317215 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-317215 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-317215"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="415288" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/ghoshsai5000" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/ghoshsai5000" title="Pupil ghoshsai5000" class="rated-user user-green">ghoshsai5000</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/18/2018 12:28">6 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-415288" href="?#comment-415288" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="415288" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="415288" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="543439" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-415288"> <div class="moveup"> <div class="ttypography"><p>For whoever is interested, here is an outstanding and creative approach taught to me by IOI silver medalist, ICPC world Finalist and my teacher <a class="rated-user user-violet" href="/profile/razimantv" title="Candidate Master razimantv">razimantv</a> to problem D. It does not require big integers and teaches an important fact about binary numbers. </p><p>First, let us consider all the numbers (from 1 to N) in binary.</p><p>For each bit position, associate two primes — P[i], Q[i]. Multiply all numbers which have the i-th bit set by P[i]. Multiply all numbers which have the i-th bit unset by Q[i]. </p><p>Now, all pairs of numbers which have a common bit set have a common factor. We only have to deal with those numbers which don't have any common bit (i.e. ... Those numbers who's XOR gives a string of all 1s).</p><p>We give all pairs of numbers (i, X) a common prime factor if i^X gives a string of all 1s.</p><p>Now, we have ensured that any two numbers have a common prime factor and no prime divides all numbers, We are done !</p><p><a href="//codeforces.com/contest/66/submission/35441406">Here</a> is code for this approach and here is some <a href="https://github.com/MathProgrammer/CodeForces/blob/master/C%20Programs/C%20Programs%2020/Petya%20and%20His%20Friends%20Alternate%20Solution%20Explanation.txt">explanation</a>.</p><p>(<a href="https://github.com/MathProgrammer/CodeForces/blob/master/C%20Programs/C%20Programs%2020/Petya%20and%20His%20Friends%20Alternate%20Solution.cpp">Here</a>'s the same code on GitHub)</p></div> </div> </div> <div class="reply info"> <a class="comment-415288 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-415288 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-415288"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="429734" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/ghoshsai5000" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/ghoshsai5000" title="Pupil ghoshsai5000" class="rated-user user-green">ghoshsai5000</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/10/2018 15:48">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-429734" href="?#comment-429734" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="429734" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="543439" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-429734"> <div class="moveup"> <div class="ttypography"><p>In case, anybody requires more explanation for Problem D, I have written a post about it <a href="https://qr.ae/TUTYGd">here</a>.</p></div> </div> </div> <div class="reply info"> <a class="comment-429734 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-429734 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-429734"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="525312" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/vjvjain0" style="position: relative;"> <img src='https://userpic.codeforces.org/699621/avatar/e27ffdf24b4ccf7b.jpg'/> </a> <div><a href="/profile/vjvjain0" title="Expert vjvjain0" class="rated-user user-blue">vjvjain0</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jul/06/2019 16:21">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-525312" href="?#comment-525312" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="525312" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="699621" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-525312"> <div class="moveup"> <div class="ttypography"><p>My solution for D is like this: </p> <ul> <li><p>First element will always be $$$2\times3$$$ and fill $$$n/2$$$ elements with $$$2$$$ while fill remaining elements with $$$3$$$. It will ensure that $$$n/2$$$ and $$$n-n/2$$$ groups have pairwise $$$gcd&gt;1$$$ inside their groups. This also means that $$$gcd$$$ of all elements is $$$1$$$.</p></li> <li><p>Now for every element from $$$2$$$ to $$$n$$$ multiply it by 5. This ensures that each pair has $$$gcd&gt;1$$$.</p></li> <li><p>Now for elements to be distinct, multiply elements with unique prime numbers.</p></li> </ul><p><strong>Note</strong>: It will not work for $$$n=3$$$.</p><p><a href="https://codeforces.com/contest/66/submission/56623956">Solution link</a></p></div> </div> </div> <div class="reply info"> <a class="comment-525312 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-525312 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-525312"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="828502" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/deepansh10" style="position: relative;"> <img src='https://userpic.codeforces.org/2028719/avatar/4366b653cd30d59b.jpg'/> </a> <div><a href="/profile/deepansh10" title="Expert deepansh10" class="rated-user user-blue">deepansh10</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Aug/14/2021 11:05">2 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-828502" href="?#comment-828502" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="828502" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2028719" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-828502"> <div class="moveup"> <div class="ttypography"><p>Can anyone suggest how to deal with the overflow in C++? Long long is not sufficient for storing the answer and trying to perform multiplication with strings is very complex.</p></div> </div> </div> <div class="reply info"> <a class="comment-828502 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-828502 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-828502"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="1067844" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Billy_Nguyen" style="position: relative;"> <img src='https://userpic.codeforces.org/3379746/avatar/dd0e8cc957d07897.jpg'/> </a> <div><a href="/profile/Billy_Nguyen" title="Newbie Billy_Nguyen" class="rated-user user-gray">Billy_Nguyen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Sep/12/2023 06:15">4 weeks ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-1067844" href="?#comment-1067844" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="1067844" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3379746" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-1067844"> <div class="moveup"> <div class="ttypography"><p>I found way to solve problem B with time complexity O(n)</p><p><a href="/contest/66/submission/223024612" title="Submission 223024612 by Billy_Nguyen">223024612</a></p><p>Hope someone find it useful, I am not necroposting or flexing ( i am just a grey ), I comment this just with the intention of helping so that someone who has seeked out a more efficient solution could see this because actually I have thought of the editorial solution and tbh I dont think it would be the solution since it is kinda too inefficient, thats why I wasted so much time thinking and coming up with this solution. Tbh if I knew the solution is just this brute force I would have done it</p></div> </div> </div> <div class="reply info"> <a class="comment-1067844 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-1067844 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-1067844"> </ul> </div> <br/> <div id="editBox-1462" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In Russian</span> </div> <textarea data-drafts-id="CommentReplyFrame" class="wysiwyg" name="editContent" rows="20" style="width:99%;"></textarea> <div class="error error__content"></div> <div style="text-align:center;"> <input type="button" name="preview" style="padding: 0.25em 1em; 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C. Petya and File System
<div class="problem-statement"><div class="header"><div class="title">C. Petya and File System</div><div class="time-limit"><div class="property-title">time limit per test</div>3 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Recently, on a programming lesson little Petya showed how quickly he can create files and folders on the computer. But he got soon fed up with this activity, and he decided to do a much more useful thing. He decided to calculate what folder contains most subfolders (including nested folders, nested folders of nested folders, and so on) and what folder contains most files (including the files in the subfolders).</p><p>More formally, the subfolders of the folder are all its directly nested folders and the subfolders of these nested folders. The given folder is not considered the subfolder of itself. A file is regarded as lying in a folder, if and only if it either lies directly in this folder, or lies in some subfolder of the folder.</p><p>For a better understanding of how to count subfolders and files for calculating the answer, see notes and answers to the samples.</p><p>You are given a few files that Petya has managed to create. The path to each file looks as follows:</p><p><span class="tex-span"><i>diskName</i></span>:<span class="tex-span">\</span><span class="tex-span"><i>folder</i><sub class="lower-index">1</sub></span><span class="tex-span">\</span><span class="tex-span"><i>folder</i><sub class="lower-index">2</sub></span><span class="tex-span">\...\</span> <span class="tex-span"><i>folder</i><sub class="lower-index"><i>n</i></sub></span><span class="tex-span">\</span><span class="tex-span"><i>fileName</i></span> </p><ul><li> <span class="tex-span"><i>diskName</i></span> is single capital letter from the set {<span class="tex-font-style-tt">C,D,E,F,G</span>}.</li><li> <span class="tex-span"><i>folder</i><sub class="lower-index">1</sub></span>, ..., <span class="tex-span"><i>folder</i><sub class="lower-index"><i>n</i></sub></span> are folder names. Each folder name is nonempty sequence of lowercase Latin letters and digits from 0 to 9. (<span class="tex-span"><i>n</i> ≥ 1</span>)</li><li> <span class="tex-span"><i>fileName</i></span> is a file name in the form of <span class="tex-span"><i>name</i></span>.<span class="tex-span"><i>extension</i></span>, where the <span class="tex-span"><i>name</i></span> and the <span class="tex-span"><i>extension</i></span> are nonempty sequences of lowercase Latin letters and digits from 0 to 9. </li></ul><p>It is also known that there is no file whose path looks like <span class="tex-span"><i>diskName</i></span>:<span class="tex-span">\</span><span class="tex-span"><i>fileName</i></span>. That is, each file is stored in some folder, but there are no files directly in the root. Also let us assume that the disk root is not a folder.</p><p>Help Petya to find the largest number of subfolders, which can be in some folder, and the largest number of files that can be in some folder, counting all its subfolders.</p></div><div class="input-specification"><div class="section-title">Input</div><p>Each line of input data contains the description of one file path. The length of each line does not exceed 100, and overall there are no more than 100 lines. It is guaranteed, that all the paths are correct and meet the above rules. It is also guaranteed, that there are no two completely equal lines. That is, each file is described exactly once.</p><p>There is at least one line in the input data.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print two space-separated numbers. The first one is the maximal number of possible subfolders in a folder (including nested folders, nested folders of nested folders, and so on). The second one is the maximal number of files in a folder (including nested files in subfolders). Note that the disks are not regarded as folders.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>C:<span class="tex-span">\</span>folder1<span class="tex-span">\</span>file1.txt</pre></div><div class="output"><div class="title">Output</div><pre>0 1</pre></div><div class="input"><div class="title">Input</div><pre>C:<span class="tex-span">\</span>folder1<span class="tex-span">\</span>folder2<span class="tex-span">\</span>folder3<span class="tex-span">\</span>file1.txt<br/>C:<span class="tex-span">\</span>folder1<span class="tex-span">\</span>folder2<span class="tex-span">\</span>folder4<span class="tex-span">\</span>file1.txt<br/>D:<span class="tex-span">\</span>folder1<span class="tex-span">\</span>file1.txt<br/></pre></div><div class="output"><div class="title">Output</div><pre>3 2</pre></div><div class="input"><div class="title">Input</div><pre>C:<span class="tex-span">\</span>file<span class="tex-span">\</span>file<span class="tex-span">\</span>file<span class="tex-span">\</span>file<span class="tex-span">\</span>file.txt<br/>C:<span class="tex-span">\</span>file<span class="tex-span">\</span>file<span class="tex-span">\</span>file<span class="tex-span">\</span>file2<span class="tex-span">\</span>file.txt</pre></div><div class="output"><div class="title">Output</div><pre>4 2</pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first sample we have one folder on the "<span class="tex-font-style-tt">C</span>" disk. It has no subfolders, which is why the first number in the answer is <span class="tex-span">0</span>. But this folder contains one file, so the second number of the answer is <span class="tex-span">1</span>.</p><p>In the second sample we have several different folders. Consider the "<span class="tex-font-style-tt">folder1</span>" folder on the "<span class="tex-font-style-tt">C</span>" disk. This folder directly contains one folder, "<span class="tex-font-style-tt">folder2</span>". The "<span class="tex-font-style-tt">folder2</span>" folder contains two more folders — "<span class="tex-font-style-tt">folder3</span>" and "<span class="tex-font-style-tt">folder4</span>". Thus, the "<span class="tex-font-style-tt">folder1</span>" folder on the "<span class="tex-font-style-tt">C</span>" drive has exactly <span class="tex-span">3</span> subfolders. Also this folder contains two files, even though they do not lie directly in the folder, but they are located in subfolders of "<span class="tex-font-style-tt">folder1</span>".</p><p>In the third example we see that the names of some folders and some subfolders are identical. Consider the "<span class="tex-font-style-tt">file</span>" folder, which lies directly on the "<span class="tex-font-style-tt">C</span>" disk. That folder contains another "<span class="tex-font-style-tt">file</span>" folder, which in turn contains another "<span class="tex-font-style-tt">file</span>" folder, which contains two more folders, "<span class="tex-font-style-tt">file</span>" and "<span class="tex-font-style-tt">file2</span>". Thus, the "<span class="tex-font-style-tt">file</span>" folder, which lies directly on the "<span class="tex-font-style-tt">C</span>" disk, contains <span class="tex-span">4</span> subfolders.</p></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="C" data-uuid="ps_1bfecfd3a1b2afdbc2d655234993f1cb57612ed7"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. Petya and File System</div><div class="time-limit"><div class="property-title">time limit per test</div>3 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Recently, on a programming lesson little Petya showed how quickly he can create files and folders on the computer. But he got soon fed up with this activity, and he decided to do a much more useful thing. He decided to calculate what folder contains most subfolders (including nested folders, nested folders of nested folders, and so on) and what folder contains most files (including the files in the subfolders).</p><p>More formally, the subfolders of the folder are all its directly nested folders and the subfolders of these nested folders. The given folder is not considered the subfolder of itself. A file is regarded as lying in a folder, if and only if it either lies directly in this folder, or lies in some subfolder of the folder.</p><p>For a better understanding of how to count subfolders and files for calculating the answer, see notes and answers to the samples.</p><p>You are given a few files that Petya has managed to create. The path to each file looks as follows:</p><p><span class="tex-span"><i>diskName</i></span>:<span class="tex-span">\</span><span class="tex-span"><i>folder</i><sub class="lower-index">1</sub></span><span class="tex-span">\</span><span class="tex-span"><i>folder</i><sub class="lower-index">2</sub></span><span class="tex-span">\...\</span> <span class="tex-span"><i>folder</i><sub class="lower-index"><i>n</i></sub></span><span class="tex-span">\</span><span class="tex-span"><i>fileName</i></span> </p><ul><li> <span class="tex-span"><i>diskName</i></span> is single capital letter from the set {<span class="tex-font-style-tt">C,D,E,F,G</span>}.</li><li> <span class="tex-span"><i>folder</i><sub class="lower-index">1</sub></span>, ..., <span class="tex-span"><i>folder</i><sub class="lower-index"><i>n</i></sub></span> are folder names. Each folder name is nonempty sequence of lowercase Latin letters and digits from 0 to 9. (<span class="tex-span"><i>n</i> ≥ 1</span>)</li><li> <span class="tex-span"><i>fileName</i></span> is a file name in the form of <span class="tex-span"><i>name</i></span>.<span class="tex-span"><i>extension</i></span>, where the <span class="tex-span"><i>name</i></span> and the <span class="tex-span"><i>extension</i></span> are nonempty sequences of lowercase Latin letters and digits from 0 to 9. </li></ul><p>It is also known that there is no file whose path looks like <span class="tex-span"><i>diskName</i></span>:<span class="tex-span">\</span><span class="tex-span"><i>fileName</i></span>. That is, each file is stored in some folder, but there are no files directly in the root. Also let us assume that the disk root is not a folder.</p><p>Help Petya to find the largest number of subfolders, which can be in some folder, and the largest number of files that can be in some folder, counting all its subfolders.</p></div><div class="input-specification"><div class="section-title">Input</div><p>Each line of input data contains the description of one file path. The length of each line does not exceed 100, and overall there are no more than 100 lines. It is guaranteed, that all the paths are correct and meet the above rules. It is also guaranteed, that there are no two completely equal lines. That is, each file is described exactly once.</p><p>There is at least one line in the input data.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print two space-separated numbers. The first one is the maximal number of possible subfolders in a folder (including nested folders, nested folders of nested folders, and so on). The second one is the maximal number of files in a folder (including nested files in subfolders). Note that the disks are not regarded as folders.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>C:<span class="tex-span">\</span>folder1<span class="tex-span">\</span>file1.txt</pre></div><div class="output"><div class="title">Output</div><pre>0 1</pre></div><div class="input"><div class="title">Input</div><pre>C:<span class="tex-span">\</span>folder1<span class="tex-span">\</span>folder2<span class="tex-span">\</span>folder3<span class="tex-span">\</span>file1.txt<br />C:<span class="tex-span">\</span>folder1<span class="tex-span">\</span>folder2<span class="tex-span">\</span>folder4<span class="tex-span">\</span>file1.txt<br />D:<span class="tex-span">\</span>folder1<span class="tex-span">\</span>file1.txt<br /></pre></div><div class="output"><div class="title">Output</div><pre>3 2</pre></div><div class="input"><div class="title">Input</div><pre>C:<span class="tex-span">\</span>file<span class="tex-span">\</span>file<span class="tex-span">\</span>file<span class="tex-span">\</span>file<span class="tex-span">\</span>file.txt<br />C:<span class="tex-span">\</span>file<span class="tex-span">\</span>file<span class="tex-span">\</span>file<span class="tex-span">\</span>file2<span class="tex-span">\</span>file.txt</pre></div><div class="output"><div class="title">Output</div><pre>4 2</pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first sample we have one folder on the &quot;<span class="tex-font-style-tt">C</span>&quot; disk. It has no subfolders, which is why the first number in the answer is <span class="tex-span">0</span>. But this folder contains one file, so the second number of the answer is <span class="tex-span">1</span>.</p><p>In the second sample we have several different folders. Consider the &quot;<span class="tex-font-style-tt">folder1</span>&quot; folder on the &quot;<span class="tex-font-style-tt">C</span>&quot; disk. This folder directly contains one folder, &quot;<span class="tex-font-style-tt">folder2</span>&quot;. The &quot;<span class="tex-font-style-tt">folder2</span>&quot; folder contains two more folders — &quot;<span class="tex-font-style-tt">folder3</span>&quot; and &quot;<span class="tex-font-style-tt">folder4</span>&quot;. Thus, the &quot;<span class="tex-font-style-tt">folder1</span>&quot; folder on the &quot;<span class="tex-font-style-tt">C</span>&quot; drive has exactly <span class="tex-span">3</span> subfolders. Also this folder contains two files, even though they do not lie directly in the folder, but they are located in subfolders of &quot;<span class="tex-font-style-tt">folder1</span>&quot;.</p><p>In the third example we see that the names of some folders and some subfolders are identical. Consider the &quot;<span class="tex-font-style-tt">file</span>&quot; folder, which lies directly on the &quot;<span class="tex-font-style-tt">C</span>&quot; disk. That folder contains another &quot;<span class="tex-font-style-tt">file</span>&quot; folder, which in turn contains another &quot;<span class="tex-font-style-tt">file</span>&quot; folder, which contains two more folders, &quot;<span class="tex-font-style-tt">file</span>&quot; and &quot;<span class="tex-font-style-tt">file2</span>&quot;. 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["Heaps, binary search trees, segment trees, hash tables, etc", "Implementation problems, programming technics, simulation"]
["data structures", "implementation", "*1800"]
https://codeforces.com/blog/entry/1452
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<a href="/blog/entry/120644">Codeforces Round 899 (Div. 2)</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/Misa-Misa" title="Expert Misa-Misa" class="rated-user user-blue">Misa-Misa</a> &rarr; <a href="/blog/entry/121157">Someone please help me understand this.</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/shivam565" title="Specialist shivam565" class="rated-user user-cyan">shivam565</a> &rarr; <a href="/blog/entry/108348">Total number of subarrays with sum atmost k</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> </ul> </div> <div class="bottom-links"> <table style="width:100%;"> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:right;"> <a href="/recent-actions">Detailed &rarr;</a> </td> </tr> </tbody> </table> </div> </div> </div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li><a href="/profile/Seyaua">Seyaua</a></li> <li class="current selectedLava"><a href="/blog/Seyaua">Blog</a></li> <li><a href="/teams/with/Seyaua">Teams</a></li> <li><a href="/submissions/Seyaua">Submissions</a></li> <li><a href="/contests/with/Seyaua">Contests</a></li> <li><a href="/contests/writer/Seyaua">Problemsetting</a></li> </ul> </div> <div style="margin-top:0;"> <div> <h3><a href="/blog/Seyaua" style="text-decoration:none;color:black !important;">Seyaua's blog</a></h3> </div> <div style="margin-top:2em;"> <div class="has-topic-id topic" topicId="1452"> <div class="title"> <a href="/blog/entry/1452"> <p>Codeforces Beta Round #61 (Div. 2): Editorial</p> </a> </div> <div class="info" style="position:relative;"> By&nbsp;<a href="/profile/Seyaua" title="Master Seyaua" class="rated-user user-orange">Seyaua</a>, <span class="format-humantime" title="Mar/07/2011 21:01">13 years ago</span>, translation, <img style="position: relative;top: 5px;" src="//codeforces.org/s/81027/images/flags/24/gb.png" alt="In English" title="In English"/> <span style="position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;"> <div style="margin-top:0.25em;"> </div> </span> </div> <div class="content"> <div class="ttypography"><p><font face="Arial"></font></p><p style=""><font face="Arial"><span><span style="font-family: Arial;color: black;">Here you can find the editorial for the past round. You can ask questions in the comments below. Special thank you goes to </span></span><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;"><a class="rated-user user-red" href="//codeforces.com/profile/sdya" style="font-family: arial;text-decoration: none !important;font-weight: bold;color: rgb(0,0,204);" title="Colonel sdya">sdya</a> </span>who prepared editorials for problems D and E, which I used here.</font></p> <h3><span lang="EN-US">Problem A</span></h3> <p><span lang="EN-US">In this problem you should answer to 4 questions:</span></p> <p style="margin-left: 42.75pt;"><span lang="EN-US">1)<span style="font: 7.0pt &quot;Times New Roman&quot;;">       </span></span><span lang="EN-US">Can we use type byte to store N?</span></p> <p style="margin-left: 42.75pt;"><span lang="EN-US">2)<span style="font: 7.0pt &quot;Times New Roman&quot;;">       </span></span><span lang="EN-US">Can we use type short to store N?</span></p> <p style="margin-left: 42.75pt;"><span lang="EN-US">3)<span style="font: 7.0pt &quot;Times New Roman&quot;;">       </span></span><span lang="EN-US">Can we use type int to store N?</span></p> <p style="margin-left: 42.75pt;"><span lang="EN-US">4)<span style="font: 7.0pt &quot;Times New Roman&quot;;">       </span></span><span lang="EN-US">Can we use type long to store N?</span></p> <p><span lang="EN-US">We should check these conditions in the given order. If all these conditions are wrong, the answer is BigInteger.</span></p> <p><span lang="EN-US">The simplest way to check these conditions is to store numbers as strings and write a function to compare such strings. In Java you can use type BigInteger.</span></p> <h3><span lang="EN-US">Problem B</span></h3> <p><span lang="EN-US">Try to check all possibilities for creation artificial rain and calculate how many sections contain water. The maximal answer from all these possibilities is the answer for the problem. To calculate the answer for the given position we should check how many sections are to the left and to the right of the given section receive water. The complexity of this algorithm is O(N^2).</span></p> <h3><span lang="EN-US">Problem C</span></h3> <p>Will be published later. </p> <h3><span lang="EN-US">Problem D</span></h3> <p><span lang="EN-US">Consider N distinct prime numbers: p1, p2, …, pn. </span></p> <p><span lang="EN-US">Let A=p1*p2*…*pn. Then, easy to see, that the numbers A/p1, A/p2, …, A/pn can be considered as the answer.</span></p> <p><span lang="EN-US">The special case is when N=2. In this case there is no answer. We can see that this solution needs long arithmetic. If we choose first n prime numbers as p1, p2, …, pn then the maximal number in the answer for all N&lt;=50 contains less than 100 digits.</span></p> <p><span lang="EN-US"> </span></p> <p><span lang="EN-US">Of course, there are other solutions. For example, if N=3 numbers 15, 10, 6 are the answer, and for N&gt;3 numbers 15, 10, 6, 6*2, 6*3, …, 6*(N-2) are the answer.</span></p> <h3><span lang="EN-US">Problem E</span></h3> <p><span lang="EN-US">First of all we divide our problem into 2 parts: consider stations from which we can start if we are moving in the clockwise direction and stations from which we can start if we are moving in the counterclockwise direction.</span></p> <p><span lang="EN-US">Obviously, if we know the solution of one of these problems, we know the solution of another problem.</span></p> <p><span lang="EN-US">So, we may assume that stations are located in the counterclockwise order and we are moving in the counterclockwise direction.</span></p> <p><span lang="EN-US">Consider the following differences:</span></p> <p><span lang="EN-US">D1=a1-b1,</span></p> <p><span lang="EN-US">D2=(a1+a2)-(b1+b2),</span></p> <p><span lang="EN-US">D3=(a1+a2+a3)-(b1+b2+b3),</span></p> <p><span lang="EN-US">…</span></p> <p><span lang="EN-US">Dn=(a1+a2+…+an)-(b1+b2+…+bn);</span></p> <p><span lang="EN-US">Obviously if one of Di’s is less than a zero, then we cannot drive one round along the road. Let D = min(Di) – we will use it later.</span></p> <p><span lang="EN-US">Obviously, if D&lt;0 then the first station cannot be the start station.</span></p> <p><span lang="EN-US">Now, we can check with complexity O(n) whether the first station can be used as the starting point. Next, we want to show how we can check this for the second station with complexity O(1).<br /> To show this, consider:</span></p> <p><span lang="EN-US">E1=D1-(a1-b1),</span></p> <p><span lang="EN-US">E2=D2-(a1-b1),</span></p> <p><span lang="EN-US">…</span></p> <p><span lang="EN-US">En=Dn-(a1-b1).</span></p> <p><span lang="EN-US">Next, substitute Di in these equalities. We get the following:</span></p> <p><span lang="EN-US">E1=(a1-b1)-(a1-b1)=0=(a2+a3+…+an+a1)-(b2+b3+…+bn+b1) – (a1+…+an=b1+…+bn=X)</span></p> <p><span lang="EN-US">E2=(a1+a2)-(b1+b2)-(a1-b1)=a2-b2</span></p> <p><span lang="EN-US">E3=(a1+a2+a3)-(b1+b2+b3)-(a1-b1)=(a2+a3)-(b2+b3)</span></p> <p><span lang="EN-US">…</span></p> <p><span lang="EN-US">En=(a1+a2+…+an)-(b1+b2+…+bn)-(a1-b1)=(a2+…+an)-(b2+…+bn)</span></p> <p><span lang="EN-US">But it’s easy to see that number E1 has the same meaning for the second station as number D1 for the first one. So, we just have to check min(Ei)&gt;=0. But Ei=Di-(a1-b1), so we have to check min(Di-(a1-b1))&gt;=0. Now, we can see that if min(Di)=Dk, then min(Di-(a1-b1))=Dk-(a1-b1). So, if we know Dk, that we can check whether the second station can be the starting point with complexity O(1). Similarly, we can check this for the third, the fourth, …, the nth stations.</span></p> <p><span lang="EN-US">Now we should check the same things but assuming that the car is moving in the clockwise direction.<font></font></span></p></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/66" class="notice" style="text-decoration: none;">Codeforces Beta Round 61 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-140-1452").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "140", blogEntryId: "1452", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces+round+%2361" class="tag notice" style="text-decoration: none;">codeforces round #61</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=editorial" class="tag notice" style="text-decoration: none;">editorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1452"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+57</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1452"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/Seyaua"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/Seyaua"> Seyaua </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Mar/07/2011 21:01">13 years ago</span> </li> <li> <a href="/blog/entry/1452#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1452#comments"> 17 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1462"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (10)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="27331" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/fura2" style="position: relative;"> <img src='https://userpic.codeforces.org/4118/avatar/98f7ddceb1dac755.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/fura2" title="Master fura2" class="rated-user user-orange">fura2</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/11/2011 23:44">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-27331" href="?#comment-27331" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="27331" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4118" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-27331"> <div class="moveup"> <div class="ttypography">Elegant solutions!<br />In particular, problem E!!</div> </div> </div> <div class="reply info"> <a class="comment-27331 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-27331 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-27331"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="27953" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/seen" style="position: relative;"> <img src='https://userpic.codeforces.org/13855/avatar/8d25f30f74ce6c29.jpg'/> </a> <div><a href="/profile/seen" title="Expert seen" class="rated-user user-blue">seen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/14/2011 12:28">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-27953" href="?#comment-27953" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="27953" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13855" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-27953"> <div class="moveup"> <div class="ttypography"><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;">problem E!</span></div> </div> </div> <div class="reply info"> <a class="comment-27953 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-27953 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-27953"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29796" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/wil93" style="position: relative;"> <img src='https://userpic.codeforces.org/14356/avatar/897f1996dfb7343b.jpg'/> </a> <div><a href="/profile/wil93" title="Expert wil93" class="rated-user user-blue">wil93</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/24/2011 23:24">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29796" href="?#comment-29796" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29796" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14356" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29796"> <div class="moveup"> <div class="ttypography">Will problem C be published?</div> </div> </div> <div class="reply info"> <a class="comment-29796 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29796 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29796"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="305792" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/haleyk100198" style="position: relative;"> <img src='https://userpic.codeforces.org/416324/avatar/f2d97d505af17e9d.jpg'/> </a> <div><a href="/profile/haleyk100198" title="Candidate Master haleyk100198" class="rated-user user-violet">haleyk100198</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jul/19/2016 07:49">7 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-305792" href="?#comment-305792" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="305792" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="416324" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-305792"> <div class="moveup"> <div class="ttypography"><p>What is test case 14 for problem C? I tried to simulate the file system yet it ended up in a RE.</p><p><a href="//codeforces.com/contest/66/submission/19224146">http://codeforces.com/contest/66/submission/19224146</a></p></div> </div> </div> <div class="reply info"> <a class="comment-305792 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-305792 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-305792"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="317215" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/XenoAmess" style="position: relative;"> <img src='https://userpic.codeforces.org/361918/avatar/e575f783daf72fba.jpg'/> </a> <div><a href="/profile/XenoAmess" title="Expert XenoAmess" class="rated-user user-blue">XenoAmess</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Sep/26/2016 03:09">7 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-317215" href="?#comment-317215" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="317215" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="361918" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-317215"> <div class="moveup"> <div class="ttypography"><p>well...I don't need it myself but, problem C's Editorial has been delayed for 6 years...</p></div> </div> </div> <div class="reply info"> <a class="comment-317215 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-317215 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-317215"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="415288" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/ghoshsai5000" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/ghoshsai5000" title="Pupil ghoshsai5000" class="rated-user user-green">ghoshsai5000</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/18/2018 12:28">6 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-415288" href="?#comment-415288" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="415288" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="415288" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="543439" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-415288"> <div class="moveup"> <div class="ttypography"><p>For whoever is interested, here is an outstanding and creative approach taught to me by IOI silver medalist, ICPC world Finalist and my teacher <a class="rated-user user-violet" href="/profile/razimantv" title="Candidate Master razimantv">razimantv</a> to problem D. It does not require big integers and teaches an important fact about binary numbers. </p><p>First, let us consider all the numbers (from 1 to N) in binary.</p><p>For each bit position, associate two primes — P[i], Q[i]. Multiply all numbers which have the i-th bit set by P[i]. Multiply all numbers which have the i-th bit unset by Q[i]. </p><p>Now, all pairs of numbers which have a common bit set have a common factor. We only have to deal with those numbers which don't have any common bit (i.e. ... Those numbers who's XOR gives a string of all 1s).</p><p>We give all pairs of numbers (i, X) a common prime factor if i^X gives a string of all 1s.</p><p>Now, we have ensured that any two numbers have a common prime factor and no prime divides all numbers, We are done !</p><p><a href="//codeforces.com/contest/66/submission/35441406">Here</a> is code for this approach and here is some <a href="https://github.com/MathProgrammer/CodeForces/blob/master/C%20Programs/C%20Programs%2020/Petya%20and%20His%20Friends%20Alternate%20Solution%20Explanation.txt">explanation</a>.</p><p>(<a href="https://github.com/MathProgrammer/CodeForces/blob/master/C%20Programs/C%20Programs%2020/Petya%20and%20His%20Friends%20Alternate%20Solution.cpp">Here</a>'s the same code on GitHub)</p></div> </div> </div> <div class="reply info"> <a class="comment-415288 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-415288 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-415288"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="429734" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/ghoshsai5000" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/ghoshsai5000" title="Pupil ghoshsai5000" class="rated-user user-green">ghoshsai5000</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/10/2018 15:48">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-429734" href="?#comment-429734" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="429734" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="543439" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-429734"> <div class="moveup"> <div class="ttypography"><p>In case, anybody requires more explanation for Problem D, I have written a post about it <a href="https://qr.ae/TUTYGd">here</a>.</p></div> </div> </div> <div class="reply info"> <a class="comment-429734 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-429734 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-429734"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="525312" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/vjvjain0" style="position: relative;"> <img src='https://userpic.codeforces.org/699621/avatar/e27ffdf24b4ccf7b.jpg'/> </a> <div><a href="/profile/vjvjain0" title="Expert vjvjain0" class="rated-user user-blue">vjvjain0</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jul/06/2019 16:21">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-525312" href="?#comment-525312" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="525312" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="699621" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-525312"> <div class="moveup"> <div class="ttypography"><p>My solution for D is like this: </p> <ul> <li><p>First element will always be $$$2\times3$$$ and fill $$$n/2$$$ elements with $$$2$$$ while fill remaining elements with $$$3$$$. It will ensure that $$$n/2$$$ and $$$n-n/2$$$ groups have pairwise $$$gcd&gt;1$$$ inside their groups. This also means that $$$gcd$$$ of all elements is $$$1$$$.</p></li> <li><p>Now for every element from $$$2$$$ to $$$n$$$ multiply it by 5. This ensures that each pair has $$$gcd&gt;1$$$.</p></li> <li><p>Now for elements to be distinct, multiply elements with unique prime numbers.</p></li> </ul><p><strong>Note</strong>: It will not work for $$$n=3$$$.</p><p><a href="https://codeforces.com/contest/66/submission/56623956">Solution link</a></p></div> </div> </div> <div class="reply info"> <a class="comment-525312 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-525312 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-525312"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="828502" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/deepansh10" style="position: relative;"> <img src='https://userpic.codeforces.org/2028719/avatar/4366b653cd30d59b.jpg'/> </a> <div><a href="/profile/deepansh10" title="Expert deepansh10" class="rated-user user-blue">deepansh10</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Aug/14/2021 11:05">2 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-828502" href="?#comment-828502" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="828502" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2028719" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-828502"> <div class="moveup"> <div class="ttypography"><p>Can anyone suggest how to deal with the overflow in C++? Long long is not sufficient for storing the answer and trying to perform multiplication with strings is very complex.</p></div> </div> </div> <div class="reply info"> <a class="comment-828502 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-828502 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-828502"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="1067844" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Billy_Nguyen" style="position: relative;"> <img src='https://userpic.codeforces.org/3379746/avatar/dd0e8cc957d07897.jpg'/> </a> <div><a href="/profile/Billy_Nguyen" title="Newbie Billy_Nguyen" class="rated-user user-gray">Billy_Nguyen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Sep/12/2023 06:15">4 weeks ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-1067844" href="?#comment-1067844" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="1067844" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3379746" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-1067844"> <div class="moveup"> <div class="ttypography"><p>I found way to solve problem B with time complexity O(n)</p><p><a href="/contest/66/submission/223024612" title="Submission 223024612 by Billy_Nguyen">223024612</a></p><p>Hope someone find it useful, I am not necroposting or flexing ( i am just a grey ), I comment this just with the intention of helping so that someone who has seeked out a more efficient solution could see this because actually I have thought of the editorial solution and tbh I dont think it would be the solution since it is kinda too inefficient, thats why I wasted so much time thinking and coming up with this solution. Tbh if I knew the solution is just this brute force I would have done it</p></div> </div> </div> <div class="reply info"> <a class="comment-1067844 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-1067844 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-1067844"> </ul> </div> <br/> <div id="editBox-1462" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In Russian</span> </div> <textarea data-drafts-id="CommentReplyFrame" class="wysiwyg" name="editContent" rows="20" style="width:99%;"></textarea> <div class="error error__content"></div> <div style="text-align:center;"> <input type="button" name="preview" style="padding: 0.25em 1em; 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D. Petya and His Friends
<div class="problem-statement"><div class="header"><div class="title">D. Petya and His Friends</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Little Petya has a birthday soon. Due this wonderful event, Petya's friends decided to give him sweets. The total number of Petya's friends equals to <span class="tex-span"><i>n</i></span>.</p><p>Let us remind you the definition of the greatest common divisor: <span class="tex-span"><i>GCD</i>(<i>a</i><sub class="lower-index">1</sub>, ..., <i>a</i><sub class="lower-index"><i>k</i></sub>) = <i>d</i></span>, where <span class="tex-span"><i>d</i></span> represents such a maximal positive number that each <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>k</i></span>) is evenly divisible by <span class="tex-span"><i>d</i></span>. At that, we assume that all <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span>'s are greater than zero.</p><p>Knowing that Petya is keen on programming, his friends has agreed beforehand that the <span class="tex-span">1</span>-st friend gives <span class="tex-span"><i>a</i><sub class="lower-index">1</sub></span> sweets, the <span class="tex-span">2</span>-nd one gives <span class="tex-span"><i>a</i><sub class="lower-index">2</sub></span> sweets, ..., the <span class="tex-span"><i>n</i></span>-th one gives <span class="tex-span"><i>a</i><sub class="lower-index"><i>n</i></sub></span> sweets. At the same time, for any <span class="tex-span"><i>i</i></span> and <span class="tex-span"><i>j</i></span> (<span class="tex-span">1 ≤ <i>i</i>, <i>j</i> ≤ <i>n</i></span>) they want the <span class="tex-span"><i>GCD</i>(<i>a</i><sub class="lower-index"><i>i</i></sub>, <i>a</i><sub class="lower-index"><i>j</i></sub>)</span> not to be equal to <span class="tex-span">1</span>. However, they also want the following condition to be satisfied: <span class="tex-span"><i>GCD</i>(<i>a</i><sub class="lower-index">1</sub>, <i>a</i><sub class="lower-index">2</sub>, ..., <i>a</i><sub class="lower-index"><i>n</i></sub>) = 1</span>. One more: all the <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> should be distinct.</p><p>Help the friends to choose the suitable numbers <span class="tex-span"><i>a</i><sub class="lower-index">1</sub>, ..., <i>a</i><sub class="lower-index"><i>n</i></sub></span>.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains an integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">2 ≤ <i>n</i> ≤ 50</span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>If there is no answer, print "<span class="tex-font-style-tt">-1</span>" without quotes. Otherwise print a set of <span class="tex-span"><i>n</i></span> distinct positive numbers <span class="tex-span"><i>a</i><sub class="lower-index">1</sub>, <i>a</i><sub class="lower-index">2</sub>, ..., <i>a</i><sub class="lower-index"><i>n</i></sub></span>. Each line must contain one number. Each number must consist of not more than <span class="tex-span">100</span> digits, and must not contain any leading zeros. If there are several solutions to that problem, print any of them.</p><p>Do not forget, please, that all of the following conditions must be true:</p><ul><li> For every <span class="tex-span"><i>i</i></span> and <span class="tex-span"><i>j</i></span> (<span class="tex-span">1 ≤ <i>i</i>, <i>j</i> ≤ <i>n</i></span>): <span class="tex-span"><i>GCD</i>(<i>a</i><sub class="lower-index"><i>i</i></sub>, <i>a</i><sub class="lower-index"><i>j</i></sub>) ≠ 1</span></li><li> <span class="tex-span"><i>GCD</i>(<i>a</i><sub class="lower-index">1</sub>, <i>a</i><sub class="lower-index">2</sub>, ..., <i>a</i><sub class="lower-index"><i>n</i></sub>) = 1</span></li><li> For every <span class="tex-span"><i>i</i></span> and <span class="tex-span"><i>j</i></span> (<span class="tex-span">1 ≤ <i>i</i>, <i>j</i> ≤ <i>n</i>, <i>i</i> ≠ <i>j</i></span>): <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub> ≠ <i>a</i><sub class="lower-index"><i>j</i></sub></span> </li></ul><p>Please, do not use <span class="tex-font-style-tt">%lld</span> specificator to read or write 64-bit integers in C++. It is preffered to use <span class="tex-font-style-tt">cout</span> (also you may use <span class="tex-font-style-tt">%I64d</span>).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br/></pre></div><div class="output"><div class="title">Output</div><pre>99<br/>55<br/>11115<br/></pre></div><div class="input"><div class="title">Input</div><pre>4<br/></pre></div><div class="output"><div class="title">Output</div><pre>385<br/>360<br/>792<br/>8360<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="D" data-uuid="ps_456101bfe671c80b9777da980840227c03ceed7b"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">D. Petya and His Friends</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Little Petya has a birthday soon. Due this wonderful event, Petya's friends decided to give him sweets. The total number of Petya's friends equals to <span class="tex-span"><i>n</i></span>.</p><p>Let us remind you the definition of the greatest common divisor: <span class="tex-span"><i>GCD</i>(<i>a</i><sub class="lower-index">1</sub>, ..., <i>a</i><sub class="lower-index"><i>k</i></sub>) = <i>d</i></span>, where <span class="tex-span"><i>d</i></span> represents such a maximal positive number that each <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>k</i></span>) is evenly divisible by <span class="tex-span"><i>d</i></span>. At that, we assume that all <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span>'s are greater than zero.</p><p>Knowing that Petya is keen on programming, his friends has agreed beforehand that the <span class="tex-span">1</span>-st friend gives <span class="tex-span"><i>a</i><sub class="lower-index">1</sub></span> sweets, the <span class="tex-span">2</span>-nd one gives <span class="tex-span"><i>a</i><sub class="lower-index">2</sub></span> sweets, ..., the <span class="tex-span"><i>n</i></span>-th one gives <span class="tex-span"><i>a</i><sub class="lower-index"><i>n</i></sub></span> sweets. At the same time, for any <span class="tex-span"><i>i</i></span> and <span class="tex-span"><i>j</i></span> (<span class="tex-span">1 ≤ <i>i</i>, <i>j</i> ≤ <i>n</i></span>) they want the <span class="tex-span"><i>GCD</i>(<i>a</i><sub class="lower-index"><i>i</i></sub>, <i>a</i><sub class="lower-index"><i>j</i></sub>)</span> not to be equal to <span class="tex-span">1</span>. However, they also want the following condition to be satisfied: <span class="tex-span"><i>GCD</i>(<i>a</i><sub class="lower-index">1</sub>, <i>a</i><sub class="lower-index">2</sub>, ..., <i>a</i><sub class="lower-index"><i>n</i></sub>) = 1</span>. One more: all the <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> should be distinct.</p><p>Help the friends to choose the suitable numbers <span class="tex-span"><i>a</i><sub class="lower-index">1</sub>, ..., <i>a</i><sub class="lower-index"><i>n</i></sub></span>.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains an integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">2 ≤ <i>n</i> ≤ 50</span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>If there is no answer, print &quot;<span class="tex-font-style-tt">-1</span>&quot; without quotes. Otherwise print a set of <span class="tex-span"><i>n</i></span> distinct positive numbers <span class="tex-span"><i>a</i><sub class="lower-index">1</sub>, <i>a</i><sub class="lower-index">2</sub>, ..., <i>a</i><sub class="lower-index"><i>n</i></sub></span>. Each line must contain one number. Each number must consist of not more than <span class="tex-span">100</span> digits, and must not contain any leading zeros. If there are several solutions to that problem, print any of them.</p><p>Do not forget, please, that all of the following conditions must be true:</p><ul><li> For every <span class="tex-span"><i>i</i></span> and <span class="tex-span"><i>j</i></span> (<span class="tex-span">1 ≤ <i>i</i>, <i>j</i> ≤ <i>n</i></span>): <span class="tex-span"><i>GCD</i>(<i>a</i><sub class="lower-index"><i>i</i></sub>, <i>a</i><sub class="lower-index"><i>j</i></sub>) ≠ 1</span></li><li> <span class="tex-span"><i>GCD</i>(<i>a</i><sub class="lower-index">1</sub>, <i>a</i><sub class="lower-index">2</sub>, ..., <i>a</i><sub class="lower-index"><i>n</i></sub>) = 1</span></li><li> For every <span class="tex-span"><i>i</i></span> and <span class="tex-span"><i>j</i></span> (<span class="tex-span">1 ≤ <i>i</i>, <i>j</i> ≤ <i>n</i>, <i>i</i> ≠ <i>j</i></span>): <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub> ≠ <i>a</i><sub class="lower-index"><i>j</i></sub></span> </li></ul><p>Please, do not use <span class="tex-font-style-tt">%lld</span> specificator to read or write 64-bit integers in C++. It is preffered to use <span class="tex-font-style-tt">cout</span> (also you may use <span class="tex-font-style-tt">%I64d</span>).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br /></pre></div><div class="output"><div class="title">Output</div><pre>99<br />55<br />11115<br /></pre></div><div class="input"><div class="title">Input</div><pre>4<br /></pre></div><div class="output"><div class="title">Output</div><pre>385<br />360<br />792<br />8360<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=D]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); if (previousStatementText) { if (previousStatementText !== statementText) { $problem.find(".diff-notifier").show(); 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["Constructive algorithms", "Mathematics including integration, differential equations, etc", "Number theory: Euler function, GCD, divisibility, etc"]
["constructive algorithms", "math", "number theory", "*1700"]
https://codeforces.com/blog/entry/1452
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<a href="/blog/entry/120644">Codeforces Round 899 (Div. 2)</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/Misa-Misa" title="Expert Misa-Misa" class="rated-user user-blue">Misa-Misa</a> &rarr; <a href="/blog/entry/121157">Someone please help me understand this.</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/shivam565" title="Specialist shivam565" class="rated-user user-cyan">shivam565</a> &rarr; <a href="/blog/entry/108348">Total number of subarrays with sum atmost k</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> </ul> </div> <div class="bottom-links"> <table style="width:100%;"> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:right;"> <a href="/recent-actions">Detailed &rarr;</a> </td> </tr> </tbody> </table> </div> </div> </div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li><a href="/profile/Seyaua">Seyaua</a></li> <li class="current selectedLava"><a href="/blog/Seyaua">Blog</a></li> <li><a href="/teams/with/Seyaua">Teams</a></li> <li><a href="/submissions/Seyaua">Submissions</a></li> <li><a href="/contests/with/Seyaua">Contests</a></li> <li><a href="/contests/writer/Seyaua">Problemsetting</a></li> </ul> </div> <div style="margin-top:0;"> <div> <h3><a href="/blog/Seyaua" style="text-decoration:none;color:black !important;">Seyaua's blog</a></h3> </div> <div style="margin-top:2em;"> <div class="has-topic-id topic" topicId="1452"> <div class="title"> <a href="/blog/entry/1452"> <p>Codeforces Beta Round #61 (Div. 2): Editorial</p> </a> </div> <div class="info" style="position:relative;"> By&nbsp;<a href="/profile/Seyaua" title="Master Seyaua" class="rated-user user-orange">Seyaua</a>, <span class="format-humantime" title="Mar/07/2011 21:01">13 years ago</span>, translation, <img style="position: relative;top: 5px;" src="//codeforces.org/s/81027/images/flags/24/gb.png" alt="In English" title="In English"/> <span style="position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;"> <div style="margin-top:0.25em;"> </div> </span> </div> <div class="content"> <div class="ttypography"><p><font face="Arial"></font></p><p style=""><font face="Arial"><span><span style="font-family: Arial;color: black;">Here you can find the editorial for the past round. You can ask questions in the comments below. Special thank you goes to </span></span><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;"><a class="rated-user user-red" href="//codeforces.com/profile/sdya" style="font-family: arial;text-decoration: none !important;font-weight: bold;color: rgb(0,0,204);" title="Colonel sdya">sdya</a> </span>who prepared editorials for problems D and E, which I used here.</font></p> <h3><span lang="EN-US">Problem A</span></h3> <p><span lang="EN-US">In this problem you should answer to 4 questions:</span></p> <p style="margin-left: 42.75pt;"><span lang="EN-US">1)<span style="font: 7.0pt &quot;Times New Roman&quot;;">       </span></span><span lang="EN-US">Can we use type byte to store N?</span></p> <p style="margin-left: 42.75pt;"><span lang="EN-US">2)<span style="font: 7.0pt &quot;Times New Roman&quot;;">       </span></span><span lang="EN-US">Can we use type short to store N?</span></p> <p style="margin-left: 42.75pt;"><span lang="EN-US">3)<span style="font: 7.0pt &quot;Times New Roman&quot;;">       </span></span><span lang="EN-US">Can we use type int to store N?</span></p> <p style="margin-left: 42.75pt;"><span lang="EN-US">4)<span style="font: 7.0pt &quot;Times New Roman&quot;;">       </span></span><span lang="EN-US">Can we use type long to store N?</span></p> <p><span lang="EN-US">We should check these conditions in the given order. If all these conditions are wrong, the answer is BigInteger.</span></p> <p><span lang="EN-US">The simplest way to check these conditions is to store numbers as strings and write a function to compare such strings. In Java you can use type BigInteger.</span></p> <h3><span lang="EN-US">Problem B</span></h3> <p><span lang="EN-US">Try to check all possibilities for creation artificial rain and calculate how many sections contain water. The maximal answer from all these possibilities is the answer for the problem. To calculate the answer for the given position we should check how many sections are to the left and to the right of the given section receive water. The complexity of this algorithm is O(N^2).</span></p> <h3><span lang="EN-US">Problem C</span></h3> <p>Will be published later. </p> <h3><span lang="EN-US">Problem D</span></h3> <p><span lang="EN-US">Consider N distinct prime numbers: p1, p2, …, pn. </span></p> <p><span lang="EN-US">Let A=p1*p2*…*pn. Then, easy to see, that the numbers A/p1, A/p2, …, A/pn can be considered as the answer.</span></p> <p><span lang="EN-US">The special case is when N=2. In this case there is no answer. We can see that this solution needs long arithmetic. If we choose first n prime numbers as p1, p2, …, pn then the maximal number in the answer for all N&lt;=50 contains less than 100 digits.</span></p> <p><span lang="EN-US"> </span></p> <p><span lang="EN-US">Of course, there are other solutions. For example, if N=3 numbers 15, 10, 6 are the answer, and for N&gt;3 numbers 15, 10, 6, 6*2, 6*3, …, 6*(N-2) are the answer.</span></p> <h3><span lang="EN-US">Problem E</span></h3> <p><span lang="EN-US">First of all we divide our problem into 2 parts: consider stations from which we can start if we are moving in the clockwise direction and stations from which we can start if we are moving in the counterclockwise direction.</span></p> <p><span lang="EN-US">Obviously, if we know the solution of one of these problems, we know the solution of another problem.</span></p> <p><span lang="EN-US">So, we may assume that stations are located in the counterclockwise order and we are moving in the counterclockwise direction.</span></p> <p><span lang="EN-US">Consider the following differences:</span></p> <p><span lang="EN-US">D1=a1-b1,</span></p> <p><span lang="EN-US">D2=(a1+a2)-(b1+b2),</span></p> <p><span lang="EN-US">D3=(a1+a2+a3)-(b1+b2+b3),</span></p> <p><span lang="EN-US">…</span></p> <p><span lang="EN-US">Dn=(a1+a2+…+an)-(b1+b2+…+bn);</span></p> <p><span lang="EN-US">Obviously if one of Di’s is less than a zero, then we cannot drive one round along the road. Let D = min(Di) – we will use it later.</span></p> <p><span lang="EN-US">Obviously, if D&lt;0 then the first station cannot be the start station.</span></p> <p><span lang="EN-US">Now, we can check with complexity O(n) whether the first station can be used as the starting point. Next, we want to show how we can check this for the second station with complexity O(1).<br /> To show this, consider:</span></p> <p><span lang="EN-US">E1=D1-(a1-b1),</span></p> <p><span lang="EN-US">E2=D2-(a1-b1),</span></p> <p><span lang="EN-US">…</span></p> <p><span lang="EN-US">En=Dn-(a1-b1).</span></p> <p><span lang="EN-US">Next, substitute Di in these equalities. We get the following:</span></p> <p><span lang="EN-US">E1=(a1-b1)-(a1-b1)=0=(a2+a3+…+an+a1)-(b2+b3+…+bn+b1) – (a1+…+an=b1+…+bn=X)</span></p> <p><span lang="EN-US">E2=(a1+a2)-(b1+b2)-(a1-b1)=a2-b2</span></p> <p><span lang="EN-US">E3=(a1+a2+a3)-(b1+b2+b3)-(a1-b1)=(a2+a3)-(b2+b3)</span></p> <p><span lang="EN-US">…</span></p> <p><span lang="EN-US">En=(a1+a2+…+an)-(b1+b2+…+bn)-(a1-b1)=(a2+…+an)-(b2+…+bn)</span></p> <p><span lang="EN-US">But it’s easy to see that number E1 has the same meaning for the second station as number D1 for the first one. So, we just have to check min(Ei)&gt;=0. But Ei=Di-(a1-b1), so we have to check min(Di-(a1-b1))&gt;=0. Now, we can see that if min(Di)=Dk, then min(Di-(a1-b1))=Dk-(a1-b1). So, if we know Dk, that we can check whether the second station can be the starting point with complexity O(1). Similarly, we can check this for the third, the fourth, …, the nth stations.</span></p> <p><span lang="EN-US">Now we should check the same things but assuming that the car is moving in the clockwise direction.<font></font></span></p></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/66" class="notice" style="text-decoration: none;">Codeforces Beta Round 61 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-140-1452").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "140", blogEntryId: "1452", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces+round+%2361" class="tag notice" style="text-decoration: none;">codeforces round #61</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=editorial" class="tag notice" style="text-decoration: none;">editorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1452"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+57</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1452"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/Seyaua"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/Seyaua"> Seyaua </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Mar/07/2011 21:01">13 years ago</span> </li> <li> <a href="/blog/entry/1452#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1452#comments"> 17 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1462"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (10)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="27331" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/fura2" style="position: relative;"> <img src='https://userpic.codeforces.org/4118/avatar/98f7ddceb1dac755.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/fura2" title="Master fura2" class="rated-user user-orange">fura2</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/11/2011 23:44">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-27331" href="?#comment-27331" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="27331" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4118" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-27331"> <div class="moveup"> <div class="ttypography">Elegant solutions!<br />In particular, problem E!!</div> </div> </div> <div class="reply info"> <a class="comment-27331 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-27331 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-27331"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="27953" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/seen" style="position: relative;"> <img src='https://userpic.codeforces.org/13855/avatar/8d25f30f74ce6c29.jpg'/> </a> <div><a href="/profile/seen" title="Expert seen" class="rated-user user-blue">seen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/14/2011 12:28">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-27953" href="?#comment-27953" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="27953" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13855" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-27953"> <div class="moveup"> <div class="ttypography"><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;">problem E!</span></div> </div> </div> <div class="reply info"> <a class="comment-27953 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-27953 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-27953"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29796" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/wil93" style="position: relative;"> <img src='https://userpic.codeforces.org/14356/avatar/897f1996dfb7343b.jpg'/> </a> <div><a href="/profile/wil93" title="Expert wil93" class="rated-user user-blue">wil93</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/24/2011 23:24">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29796" href="?#comment-29796" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29796" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14356" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29796"> <div class="moveup"> <div class="ttypography">Will problem C be published?</div> </div> </div> <div class="reply info"> <a class="comment-29796 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29796 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29796"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="305792" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/haleyk100198" style="position: relative;"> <img src='https://userpic.codeforces.org/416324/avatar/f2d97d505af17e9d.jpg'/> </a> <div><a href="/profile/haleyk100198" title="Candidate Master haleyk100198" class="rated-user user-violet">haleyk100198</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jul/19/2016 07:49">7 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-305792" href="?#comment-305792" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="305792" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="416324" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-305792"> <div class="moveup"> <div class="ttypography"><p>What is test case 14 for problem C? I tried to simulate the file system yet it ended up in a RE.</p><p><a href="//codeforces.com/contest/66/submission/19224146">http://codeforces.com/contest/66/submission/19224146</a></p></div> </div> </div> <div class="reply info"> <a class="comment-305792 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-305792 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-305792"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="317215" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/XenoAmess" style="position: relative;"> <img src='https://userpic.codeforces.org/361918/avatar/e575f783daf72fba.jpg'/> </a> <div><a href="/profile/XenoAmess" title="Expert XenoAmess" class="rated-user user-blue">XenoAmess</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Sep/26/2016 03:09">7 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-317215" href="?#comment-317215" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="317215" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="361918" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-317215"> <div class="moveup"> <div class="ttypography"><p>well...I don't need it myself but, problem C's Editorial has been delayed for 6 years...</p></div> </div> </div> <div class="reply info"> <a class="comment-317215 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-317215 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-317215"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="415288" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/ghoshsai5000" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/ghoshsai5000" title="Pupil ghoshsai5000" class="rated-user user-green">ghoshsai5000</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/18/2018 12:28">6 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-415288" href="?#comment-415288" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="415288" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="415288" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="543439" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-415288"> <div class="moveup"> <div class="ttypography"><p>For whoever is interested, here is an outstanding and creative approach taught to me by IOI silver medalist, ICPC world Finalist and my teacher <a class="rated-user user-violet" href="/profile/razimantv" title="Candidate Master razimantv">razimantv</a> to problem D. It does not require big integers and teaches an important fact about binary numbers. </p><p>First, let us consider all the numbers (from 1 to N) in binary.</p><p>For each bit position, associate two primes — P[i], Q[i]. Multiply all numbers which have the i-th bit set by P[i]. Multiply all numbers which have the i-th bit unset by Q[i]. </p><p>Now, all pairs of numbers which have a common bit set have a common factor. We only have to deal with those numbers which don't have any common bit (i.e. ... Those numbers who's XOR gives a string of all 1s).</p><p>We give all pairs of numbers (i, X) a common prime factor if i^X gives a string of all 1s.</p><p>Now, we have ensured that any two numbers have a common prime factor and no prime divides all numbers, We are done !</p><p><a href="//codeforces.com/contest/66/submission/35441406">Here</a> is code for this approach and here is some <a href="https://github.com/MathProgrammer/CodeForces/blob/master/C%20Programs/C%20Programs%2020/Petya%20and%20His%20Friends%20Alternate%20Solution%20Explanation.txt">explanation</a>.</p><p>(<a href="https://github.com/MathProgrammer/CodeForces/blob/master/C%20Programs/C%20Programs%2020/Petya%20and%20His%20Friends%20Alternate%20Solution.cpp">Here</a>'s the same code on GitHub)</p></div> </div> </div> <div class="reply info"> <a class="comment-415288 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-415288 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-415288"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="429734" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/ghoshsai5000" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/ghoshsai5000" title="Pupil ghoshsai5000" class="rated-user user-green">ghoshsai5000</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/10/2018 15:48">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-429734" href="?#comment-429734" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="429734" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="543439" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-429734"> <div class="moveup"> <div class="ttypography"><p>In case, anybody requires more explanation for Problem D, I have written a post about it <a href="https://qr.ae/TUTYGd">here</a>.</p></div> </div> </div> <div class="reply info"> <a class="comment-429734 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-429734 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-429734"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="525312" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/vjvjain0" style="position: relative;"> <img src='https://userpic.codeforces.org/699621/avatar/e27ffdf24b4ccf7b.jpg'/> </a> <div><a href="/profile/vjvjain0" title="Expert vjvjain0" class="rated-user user-blue">vjvjain0</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jul/06/2019 16:21">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-525312" href="?#comment-525312" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="525312" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="699621" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-525312"> <div class="moveup"> <div class="ttypography"><p>My solution for D is like this: </p> <ul> <li><p>First element will always be $$$2\times3$$$ and fill $$$n/2$$$ elements with $$$2$$$ while fill remaining elements with $$$3$$$. It will ensure that $$$n/2$$$ and $$$n-n/2$$$ groups have pairwise $$$gcd&gt;1$$$ inside their groups. This also means that $$$gcd$$$ of all elements is $$$1$$$.</p></li> <li><p>Now for every element from $$$2$$$ to $$$n$$$ multiply it by 5. This ensures that each pair has $$$gcd&gt;1$$$.</p></li> <li><p>Now for elements to be distinct, multiply elements with unique prime numbers.</p></li> </ul><p><strong>Note</strong>: It will not work for $$$n=3$$$.</p><p><a href="https://codeforces.com/contest/66/submission/56623956">Solution link</a></p></div> </div> </div> <div class="reply info"> <a class="comment-525312 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-525312 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-525312"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="828502" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/deepansh10" style="position: relative;"> <img src='https://userpic.codeforces.org/2028719/avatar/4366b653cd30d59b.jpg'/> </a> <div><a href="/profile/deepansh10" title="Expert deepansh10" class="rated-user user-blue">deepansh10</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Aug/14/2021 11:05">2 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-828502" href="?#comment-828502" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="828502" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2028719" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-828502"> <div class="moveup"> <div class="ttypography"><p>Can anyone suggest how to deal with the overflow in C++? Long long is not sufficient for storing the answer and trying to perform multiplication with strings is very complex.</p></div> </div> </div> <div class="reply info"> <a class="comment-828502 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-828502 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-828502"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="1067844" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Billy_Nguyen" style="position: relative;"> <img src='https://userpic.codeforces.org/3379746/avatar/dd0e8cc957d07897.jpg'/> </a> <div><a href="/profile/Billy_Nguyen" title="Newbie Billy_Nguyen" class="rated-user user-gray">Billy_Nguyen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Sep/12/2023 06:15">4 weeks ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-1067844" href="?#comment-1067844" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="1067844" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3379746" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-1067844"> <div class="moveup"> <div class="ttypography"><p>I found way to solve problem B with time complexity O(n)</p><p><a href="/contest/66/submission/223024612" title="Submission 223024612 by Billy_Nguyen">223024612</a></p><p>Hope someone find it useful, I am not necroposting or flexing ( i am just a grey ), I comment this just with the intention of helping so that someone who has seeked out a more efficient solution could see this because actually I have thought of the editorial solution and tbh I dont think it would be the solution since it is kinda too inefficient, thats why I wasted so much time thinking and coming up with this solution. Tbh if I knew the solution is just this brute force I would have done it</p></div> </div> </div> <div class="reply info"> <a class="comment-1067844 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-1067844 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-1067844"> </ul> </div> <br/> <div id="editBox-1462" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In Russian</span> </div> <textarea data-drafts-id="CommentReplyFrame" class="wysiwyg" name="editContent" rows="20" style="width:99%;"></textarea> <div class="error error__content"></div> <div style="text-align:center;"> <input type="button" name="preview" style="padding: 0.25em 1em; 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66E
66
E
en
E. Petya and Post
<div class="problem-statement"><div class="header"><div class="title">E. Petya and Post</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Little Vasya's uncle is a postman. The post offices are located on one circular road. Besides, each post office has its own gas station located next to it. Petya's uncle works as follows: in the morning he should leave the house and go to some post office. In the office he receives a portion of letters and a car. Then he must drive in the given car exactly one round along the circular road and return to the starting post office (the uncle can drive along the circle in any direction, counterclockwise or clockwise). Besides, since the car belongs to the city post, it should also be fuelled with gasoline only at the Post Office stations. </p><p>The total number of stations equals to <span class="tex-span"><i>n</i></span>. One can fuel the car at the <span class="tex-span"><i>i</i></span>-th station with no more than <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> liters of gasoline. Besides, one can fuel the car no more than once at each station. Also, the distance between the <span class="tex-span">1</span>-st and the <span class="tex-span">2</span>-nd station is <span class="tex-span"><i>b</i><sub class="lower-index">1</sub></span> kilometers, the distance between the <span class="tex-span">2</span>-nd and the <span class="tex-span">3</span>-rd one is <span class="tex-span"><i>b</i><sub class="lower-index">2</sub></span> kilometers, ..., between the <span class="tex-span">(<i>n</i> - 1)</span>-th and the <span class="tex-span"><i>n</i></span>-th ones the distance is <span class="tex-span"><i>b</i><sub class="lower-index"><i>n</i> - 1</sub></span> kilometers and between the <span class="tex-span"><i>n</i></span>-th and the <span class="tex-span">1</span>-st one the distance is <span class="tex-span"><i>b</i><sub class="lower-index"><i>n</i></sub></span> kilometers. Petya's uncle's high-tech car uses only one liter of gasoline per kilometer. It is known that the stations are located so that the sum of all <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> is equal to the sum of all <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span>. The <span class="tex-span"><i>i</i></span>-th gas station and <span class="tex-span"><i>i</i></span>-th post office are very close, so the distance between them is <span class="tex-span">0</span> kilometers.</p><p>Thus, it becomes clear that if we start from some post offices, then it is not always possible to drive one round along a circular road. The uncle faces the following problem: to what stations can he go in the morning to be able to ride exactly one circle along the circular road and visit all the post offices that are on it?</p><p>Petya, who used to attend programming classes, has volunteered to help his uncle, but his knowledge turned out to be not enough, so he asks you to help him write the program that will solve the posed problem.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup></span>). The second line contains <span class="tex-span"><i>n</i></span> integers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> — amount of gasoline on the <span class="tex-span"><i>i</i></span>-th station. The third line contains <span class="tex-span"><i>n</i></span> integers <span class="tex-span"><i>b</i><sub class="lower-index">1</sub>, <i>b</i><sub class="lower-index">2</sub>, ..., <i>b</i><sub class="lower-index"><i>n</i></sub></span>. They are the distances between the <span class="tex-span">1</span>-st and the <span class="tex-span">2</span>-nd gas stations, between the <span class="tex-span">2</span>-nd and the <span class="tex-span">3</span>-rd ones, ..., between the <span class="tex-span"><i>n</i></span>-th and the <span class="tex-span">1</span>-st ones, respectively. The sum of all <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> equals to the sum of all <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> and is no more than <span class="tex-span">10<sup class="upper-index">9</sup></span>. Each of the numbers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> is no less than <span class="tex-span">1</span> and no more than <span class="tex-span">10<sup class="upper-index">9</sup></span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print on the first line the number <span class="tex-span"><i>k</i></span> — the number of possible post offices, from which the car can drive one circle along a circular road. Print on the second line <span class="tex-span"><i>k</i></span> numbers in the ascending order — the numbers of offices, from which the car can start.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>4<br/>1 7 2 3<br/>8 1 1 3<br/></pre></div><div class="output"><div class="title">Output</div><pre>2<br/>2 4<br/></pre></div><div class="input"><div class="title">Input</div><pre>8<br/>1 2 1 2 1 2 1 2<br/>2 1 2 1 2 1 2 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>8<br/>1 2 3 4 5 6 7 8<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="E" data-uuid="ps_52a49adf4a23b64dac7e6e27df1e9a8d71685b53"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">E. Petya and Post</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Little Vasya's uncle is a postman. The post offices are located on one circular road. Besides, each post office has its own gas station located next to it. Petya's uncle works as follows: in the morning he should leave the house and go to some post office. In the office he receives a portion of letters and a car. Then he must drive in the given car exactly one round along the circular road and return to the starting post office (the uncle can drive along the circle in any direction, counterclockwise or clockwise). Besides, since the car belongs to the city post, it should also be fuelled with gasoline only at the Post Office stations. </p><p>The total number of stations equals to <span class="tex-span"><i>n</i></span>. One can fuel the car at the <span class="tex-span"><i>i</i></span>-th station with no more than <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> liters of gasoline. Besides, one can fuel the car no more than once at each station. Also, the distance between the <span class="tex-span">1</span>-st and the <span class="tex-span">2</span>-nd station is <span class="tex-span"><i>b</i><sub class="lower-index">1</sub></span> kilometers, the distance between the <span class="tex-span">2</span>-nd and the <span class="tex-span">3</span>-rd one is <span class="tex-span"><i>b</i><sub class="lower-index">2</sub></span> kilometers, ..., between the <span class="tex-span">(<i>n</i> - 1)</span>-th and the <span class="tex-span"><i>n</i></span>-th ones the distance is <span class="tex-span"><i>b</i><sub class="lower-index"><i>n</i> - 1</sub></span> kilometers and between the <span class="tex-span"><i>n</i></span>-th and the <span class="tex-span">1</span>-st one the distance is <span class="tex-span"><i>b</i><sub class="lower-index"><i>n</i></sub></span> kilometers. Petya's uncle's high-tech car uses only one liter of gasoline per kilometer. It is known that the stations are located so that the sum of all <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> is equal to the sum of all <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span>. The <span class="tex-span"><i>i</i></span>-th gas station and <span class="tex-span"><i>i</i></span>-th post office are very close, so the distance between them is <span class="tex-span">0</span> kilometers.</p><p>Thus, it becomes clear that if we start from some post offices, then it is not always possible to drive one round along a circular road. The uncle faces the following problem: to what stations can he go in the morning to be able to ride exactly one circle along the circular road and visit all the post offices that are on it?</p><p>Petya, who used to attend programming classes, has volunteered to help his uncle, but his knowledge turned out to be not enough, so he asks you to help him write the program that will solve the posed problem.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup></span>). The second line contains <span class="tex-span"><i>n</i></span> integers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> — amount of gasoline on the <span class="tex-span"><i>i</i></span>-th station. The third line contains <span class="tex-span"><i>n</i></span> integers <span class="tex-span"><i>b</i><sub class="lower-index">1</sub>, <i>b</i><sub class="lower-index">2</sub>, ..., <i>b</i><sub class="lower-index"><i>n</i></sub></span>. They are the distances between the <span class="tex-span">1</span>-st and the <span class="tex-span">2</span>-nd gas stations, between the <span class="tex-span">2</span>-nd and the <span class="tex-span">3</span>-rd ones, ..., between the <span class="tex-span"><i>n</i></span>-th and the <span class="tex-span">1</span>-st ones, respectively. The sum of all <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> equals to the sum of all <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> and is no more than <span class="tex-span">10<sup class="upper-index">9</sup></span>. Each of the numbers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> is no less than <span class="tex-span">1</span> and no more than <span class="tex-span">10<sup class="upper-index">9</sup></span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print on the first line the number <span class="tex-span"><i>k</i></span> — the number of possible post offices, from which the car can drive one circle along a circular road. Print on the second line <span class="tex-span"><i>k</i></span> numbers in the ascending order — the numbers of offices, from which the car can start.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>4<br />1 7 2 3<br />8 1 1 3<br /></pre></div><div class="output"><div class="title">Output</div><pre>2<br />2 4<br /></pre></div><div class="input"><div class="title">Input</div><pre>8<br />1 2 1 2 1 2 1 2<br />2 1 2 1 2 1 2 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>8<br />1 2 3 4 5 6 7 8<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=E]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); if (previousStatementText) { if (previousStatementText !== statementText) { $problem.find(".diff-notifier").show(); 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["Heaps, binary search trees, segment trees, hash tables, etc", "Dynamic programming"]
["data structures", "dp", "*2000"]
https://codeforces.com/blog/entry/1452
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<a href="/blog/entry/120644">Codeforces Round 899 (Div. 2)</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/Misa-Misa" title="Expert Misa-Misa" class="rated-user user-blue">Misa-Misa</a> &rarr; <a href="/blog/entry/121157">Someone please help me understand this.</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/shivam565" title="Specialist shivam565" class="rated-user user-cyan">shivam565</a> &rarr; <a href="/blog/entry/108348">Total number of subarrays with sum atmost k</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> </ul> </div> <div class="bottom-links"> <table style="width:100%;"> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:right;"> <a href="/recent-actions">Detailed &rarr;</a> </td> </tr> </tbody> </table> </div> </div> </div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li><a href="/profile/Seyaua">Seyaua</a></li> <li class="current selectedLava"><a href="/blog/Seyaua">Blog</a></li> <li><a href="/teams/with/Seyaua">Teams</a></li> <li><a href="/submissions/Seyaua">Submissions</a></li> <li><a href="/contests/with/Seyaua">Contests</a></li> <li><a href="/contests/writer/Seyaua">Problemsetting</a></li> </ul> </div> <div style="margin-top:0;"> <div> <h3><a href="/blog/Seyaua" style="text-decoration:none;color:black !important;">Seyaua's blog</a></h3> </div> <div style="margin-top:2em;"> <div class="has-topic-id topic" topicId="1452"> <div class="title"> <a href="/blog/entry/1452"> <p>Codeforces Beta Round #61 (Div. 2): Editorial</p> </a> </div> <div class="info" style="position:relative;"> By&nbsp;<a href="/profile/Seyaua" title="Master Seyaua" class="rated-user user-orange">Seyaua</a>, <span class="format-humantime" title="Mar/07/2011 21:01">13 years ago</span>, translation, <img style="position: relative;top: 5px;" src="//codeforces.org/s/81027/images/flags/24/gb.png" alt="In English" title="In English"/> <span style="position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;"> <div style="margin-top:0.25em;"> </div> </span> </div> <div class="content"> <div class="ttypography"><p><font face="Arial"></font></p><p style=""><font face="Arial"><span><span style="font-family: Arial;color: black;">Here you can find the editorial for the past round. You can ask questions in the comments below. Special thank you goes to </span></span><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;"><a class="rated-user user-red" href="//codeforces.com/profile/sdya" style="font-family: arial;text-decoration: none !important;font-weight: bold;color: rgb(0,0,204);" title="Colonel sdya">sdya</a> </span>who prepared editorials for problems D and E, which I used here.</font></p> <h3><span lang="EN-US">Problem A</span></h3> <p><span lang="EN-US">In this problem you should answer to 4 questions:</span></p> <p style="margin-left: 42.75pt;"><span lang="EN-US">1)<span style="font: 7.0pt &quot;Times New Roman&quot;;">       </span></span><span lang="EN-US">Can we use type byte to store N?</span></p> <p style="margin-left: 42.75pt;"><span lang="EN-US">2)<span style="font: 7.0pt &quot;Times New Roman&quot;;">       </span></span><span lang="EN-US">Can we use type short to store N?</span></p> <p style="margin-left: 42.75pt;"><span lang="EN-US">3)<span style="font: 7.0pt &quot;Times New Roman&quot;;">       </span></span><span lang="EN-US">Can we use type int to store N?</span></p> <p style="margin-left: 42.75pt;"><span lang="EN-US">4)<span style="font: 7.0pt &quot;Times New Roman&quot;;">       </span></span><span lang="EN-US">Can we use type long to store N?</span></p> <p><span lang="EN-US">We should check these conditions in the given order. If all these conditions are wrong, the answer is BigInteger.</span></p> <p><span lang="EN-US">The simplest way to check these conditions is to store numbers as strings and write a function to compare such strings. In Java you can use type BigInteger.</span></p> <h3><span lang="EN-US">Problem B</span></h3> <p><span lang="EN-US">Try to check all possibilities for creation artificial rain and calculate how many sections contain water. The maximal answer from all these possibilities is the answer for the problem. To calculate the answer for the given position we should check how many sections are to the left and to the right of the given section receive water. The complexity of this algorithm is O(N^2).</span></p> <h3><span lang="EN-US">Problem C</span></h3> <p>Will be published later. </p> <h3><span lang="EN-US">Problem D</span></h3> <p><span lang="EN-US">Consider N distinct prime numbers: p1, p2, …, pn. </span></p> <p><span lang="EN-US">Let A=p1*p2*…*pn. Then, easy to see, that the numbers A/p1, A/p2, …, A/pn can be considered as the answer.</span></p> <p><span lang="EN-US">The special case is when N=2. In this case there is no answer. We can see that this solution needs long arithmetic. If we choose first n prime numbers as p1, p2, …, pn then the maximal number in the answer for all N&lt;=50 contains less than 100 digits.</span></p> <p><span lang="EN-US"> </span></p> <p><span lang="EN-US">Of course, there are other solutions. For example, if N=3 numbers 15, 10, 6 are the answer, and for N&gt;3 numbers 15, 10, 6, 6*2, 6*3, …, 6*(N-2) are the answer.</span></p> <h3><span lang="EN-US">Problem E</span></h3> <p><span lang="EN-US">First of all we divide our problem into 2 parts: consider stations from which we can start if we are moving in the clockwise direction and stations from which we can start if we are moving in the counterclockwise direction.</span></p> <p><span lang="EN-US">Obviously, if we know the solution of one of these problems, we know the solution of another problem.</span></p> <p><span lang="EN-US">So, we may assume that stations are located in the counterclockwise order and we are moving in the counterclockwise direction.</span></p> <p><span lang="EN-US">Consider the following differences:</span></p> <p><span lang="EN-US">D1=a1-b1,</span></p> <p><span lang="EN-US">D2=(a1+a2)-(b1+b2),</span></p> <p><span lang="EN-US">D3=(a1+a2+a3)-(b1+b2+b3),</span></p> <p><span lang="EN-US">…</span></p> <p><span lang="EN-US">Dn=(a1+a2+…+an)-(b1+b2+…+bn);</span></p> <p><span lang="EN-US">Obviously if one of Di’s is less than a zero, then we cannot drive one round along the road. Let D = min(Di) – we will use it later.</span></p> <p><span lang="EN-US">Obviously, if D&lt;0 then the first station cannot be the start station.</span></p> <p><span lang="EN-US">Now, we can check with complexity O(n) whether the first station can be used as the starting point. Next, we want to show how we can check this for the second station with complexity O(1).<br /> To show this, consider:</span></p> <p><span lang="EN-US">E1=D1-(a1-b1),</span></p> <p><span lang="EN-US">E2=D2-(a1-b1),</span></p> <p><span lang="EN-US">…</span></p> <p><span lang="EN-US">En=Dn-(a1-b1).</span></p> <p><span lang="EN-US">Next, substitute Di in these equalities. We get the following:</span></p> <p><span lang="EN-US">E1=(a1-b1)-(a1-b1)=0=(a2+a3+…+an+a1)-(b2+b3+…+bn+b1) – (a1+…+an=b1+…+bn=X)</span></p> <p><span lang="EN-US">E2=(a1+a2)-(b1+b2)-(a1-b1)=a2-b2</span></p> <p><span lang="EN-US">E3=(a1+a2+a3)-(b1+b2+b3)-(a1-b1)=(a2+a3)-(b2+b3)</span></p> <p><span lang="EN-US">…</span></p> <p><span lang="EN-US">En=(a1+a2+…+an)-(b1+b2+…+bn)-(a1-b1)=(a2+…+an)-(b2+…+bn)</span></p> <p><span lang="EN-US">But it’s easy to see that number E1 has the same meaning for the second station as number D1 for the first one. So, we just have to check min(Ei)&gt;=0. But Ei=Di-(a1-b1), so we have to check min(Di-(a1-b1))&gt;=0. Now, we can see that if min(Di)=Dk, then min(Di-(a1-b1))=Dk-(a1-b1). So, if we know Dk, that we can check whether the second station can be the starting point with complexity O(1). Similarly, we can check this for the third, the fourth, …, the nth stations.</span></p> <p><span lang="EN-US">Now we should check the same things but assuming that the car is moving in the clockwise direction.<font></font></span></p></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/66" class="notice" style="text-decoration: none;">Codeforces Beta Round 61 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-140-1452").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "140", blogEntryId: "1452", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces+round+%2361" class="tag notice" style="text-decoration: none;">codeforces round #61</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=editorial" class="tag notice" style="text-decoration: none;">editorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1452"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+57</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1452"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/Seyaua"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/Seyaua"> Seyaua </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Mar/07/2011 21:01">13 years ago</span> </li> <li> <a href="/blog/entry/1452#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1452#comments"> 17 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1462"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (10)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="27331" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/fura2" style="position: relative;"> <img src='https://userpic.codeforces.org/4118/avatar/98f7ddceb1dac755.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/fura2" title="Master fura2" class="rated-user user-orange">fura2</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/11/2011 23:44">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-27331" href="?#comment-27331" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="27331" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4118" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-27331"> <div class="moveup"> <div class="ttypography">Elegant solutions!<br />In particular, problem E!!</div> </div> </div> <div class="reply info"> <a class="comment-27331 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-27331 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-27331"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="27953" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/seen" style="position: relative;"> <img src='https://userpic.codeforces.org/13855/avatar/8d25f30f74ce6c29.jpg'/> </a> <div><a href="/profile/seen" title="Expert seen" class="rated-user user-blue">seen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/14/2011 12:28">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-27953" href="?#comment-27953" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="27953" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13855" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-27953"> <div class="moveup"> <div class="ttypography"><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;">problem E!</span></div> </div> </div> <div class="reply info"> <a class="comment-27953 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-27953 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-27953"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29796" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/wil93" style="position: relative;"> <img src='https://userpic.codeforces.org/14356/avatar/897f1996dfb7343b.jpg'/> </a> <div><a href="/profile/wil93" title="Expert wil93" class="rated-user user-blue">wil93</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/24/2011 23:24">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29796" href="?#comment-29796" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29796" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14356" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29796"> <div class="moveup"> <div class="ttypography">Will problem C be published?</div> </div> </div> <div class="reply info"> <a class="comment-29796 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29796 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29796"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="305792" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/haleyk100198" style="position: relative;"> <img src='https://userpic.codeforces.org/416324/avatar/f2d97d505af17e9d.jpg'/> </a> <div><a href="/profile/haleyk100198" title="Candidate Master haleyk100198" class="rated-user user-violet">haleyk100198</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jul/19/2016 07:49">7 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-305792" href="?#comment-305792" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="305792" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="416324" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-305792"> <div class="moveup"> <div class="ttypography"><p>What is test case 14 for problem C? I tried to simulate the file system yet it ended up in a RE.</p><p><a href="//codeforces.com/contest/66/submission/19224146">http://codeforces.com/contest/66/submission/19224146</a></p></div> </div> </div> <div class="reply info"> <a class="comment-305792 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-305792 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-305792"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="317215" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/XenoAmess" style="position: relative;"> <img src='https://userpic.codeforces.org/361918/avatar/e575f783daf72fba.jpg'/> </a> <div><a href="/profile/XenoAmess" title="Expert XenoAmess" class="rated-user user-blue">XenoAmess</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Sep/26/2016 03:09">7 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-317215" href="?#comment-317215" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="317215" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="361918" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-317215"> <div class="moveup"> <div class="ttypography"><p>well...I don't need it myself but, problem C's Editorial has been delayed for 6 years...</p></div> </div> </div> <div class="reply info"> <a class="comment-317215 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-317215 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-317215"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="415288" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/ghoshsai5000" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/ghoshsai5000" title="Pupil ghoshsai5000" class="rated-user user-green">ghoshsai5000</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/18/2018 12:28">6 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-415288" href="?#comment-415288" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="415288" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="415288" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="543439" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-415288"> <div class="moveup"> <div class="ttypography"><p>For whoever is interested, here is an outstanding and creative approach taught to me by IOI silver medalist, ICPC world Finalist and my teacher <a class="rated-user user-violet" href="/profile/razimantv" title="Candidate Master razimantv">razimantv</a> to problem D. It does not require big integers and teaches an important fact about binary numbers. </p><p>First, let us consider all the numbers (from 1 to N) in binary.</p><p>For each bit position, associate two primes — P[i], Q[i]. Multiply all numbers which have the i-th bit set by P[i]. Multiply all numbers which have the i-th bit unset by Q[i]. </p><p>Now, all pairs of numbers which have a common bit set have a common factor. We only have to deal with those numbers which don't have any common bit (i.e. ... Those numbers who's XOR gives a string of all 1s).</p><p>We give all pairs of numbers (i, X) a common prime factor if i^X gives a string of all 1s.</p><p>Now, we have ensured that any two numbers have a common prime factor and no prime divides all numbers, We are done !</p><p><a href="//codeforces.com/contest/66/submission/35441406">Here</a> is code for this approach and here is some <a href="https://github.com/MathProgrammer/CodeForces/blob/master/C%20Programs/C%20Programs%2020/Petya%20and%20His%20Friends%20Alternate%20Solution%20Explanation.txt">explanation</a>.</p><p>(<a href="https://github.com/MathProgrammer/CodeForces/blob/master/C%20Programs/C%20Programs%2020/Petya%20and%20His%20Friends%20Alternate%20Solution.cpp">Here</a>'s the same code on GitHub)</p></div> </div> </div> <div class="reply info"> <a class="comment-415288 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-415288 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-415288"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="429734" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/ghoshsai5000" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/ghoshsai5000" title="Pupil ghoshsai5000" class="rated-user user-green">ghoshsai5000</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/10/2018 15:48">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-429734" href="?#comment-429734" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="429734" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="543439" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-429734"> <div class="moveup"> <div class="ttypography"><p>In case, anybody requires more explanation for Problem D, I have written a post about it <a href="https://qr.ae/TUTYGd">here</a>.</p></div> </div> </div> <div class="reply info"> <a class="comment-429734 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-429734 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-429734"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="525312" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/vjvjain0" style="position: relative;"> <img src='https://userpic.codeforces.org/699621/avatar/e27ffdf24b4ccf7b.jpg'/> </a> <div><a href="/profile/vjvjain0" title="Expert vjvjain0" class="rated-user user-blue">vjvjain0</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jul/06/2019 16:21">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-525312" href="?#comment-525312" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="525312" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="699621" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-525312"> <div class="moveup"> <div class="ttypography"><p>My solution for D is like this: </p> <ul> <li><p>First element will always be $$$2\times3$$$ and fill $$$n/2$$$ elements with $$$2$$$ while fill remaining elements with $$$3$$$. It will ensure that $$$n/2$$$ and $$$n-n/2$$$ groups have pairwise $$$gcd&gt;1$$$ inside their groups. This also means that $$$gcd$$$ of all elements is $$$1$$$.</p></li> <li><p>Now for every element from $$$2$$$ to $$$n$$$ multiply it by 5. This ensures that each pair has $$$gcd&gt;1$$$.</p></li> <li><p>Now for elements to be distinct, multiply elements with unique prime numbers.</p></li> </ul><p><strong>Note</strong>: It will not work for $$$n=3$$$.</p><p><a href="https://codeforces.com/contest/66/submission/56623956">Solution link</a></p></div> </div> </div> <div class="reply info"> <a class="comment-525312 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-525312 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-525312"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="828502" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/deepansh10" style="position: relative;"> <img src='https://userpic.codeforces.org/2028719/avatar/4366b653cd30d59b.jpg'/> </a> <div><a href="/profile/deepansh10" title="Expert deepansh10" class="rated-user user-blue">deepansh10</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Aug/14/2021 11:05">2 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-828502" href="?#comment-828502" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="828502" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2028719" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-828502"> <div class="moveup"> <div class="ttypography"><p>Can anyone suggest how to deal with the overflow in C++? Long long is not sufficient for storing the answer and trying to perform multiplication with strings is very complex.</p></div> </div> </div> <div class="reply info"> <a class="comment-828502 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-828502 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-828502"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="1067844" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Billy_Nguyen" style="position: relative;"> <img src='https://userpic.codeforces.org/3379746/avatar/dd0e8cc957d07897.jpg'/> </a> <div><a href="/profile/Billy_Nguyen" title="Newbie Billy_Nguyen" class="rated-user user-gray">Billy_Nguyen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Sep/12/2023 06:15">4 weeks ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-1067844" href="?#comment-1067844" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="1067844" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3379746" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-1067844"> <div class="moveup"> <div class="ttypography"><p>I found way to solve problem B with time complexity O(n)</p><p><a href="/contest/66/submission/223024612" title="Submission 223024612 by Billy_Nguyen">223024612</a></p><p>Hope someone find it useful, I am not necroposting or flexing ( i am just a grey ), I comment this just with the intention of helping so that someone who has seeked out a more efficient solution could see this because actually I have thought of the editorial solution and tbh I dont think it would be the solution since it is kinda too inefficient, thats why I wasted so much time thinking and coming up with this solution. Tbh if I knew the solution is just this brute force I would have done it</p></div> </div> </div> <div class="reply info"> <a class="comment-1067844 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-1067844 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-1067844"> </ul> </div> <br/> <div id="editBox-1462" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In Russian</span> </div> <textarea data-drafts-id="CommentReplyFrame" class="wysiwyg" name="editContent" rows="20" style="width:99%;"></textarea> <div class="error error__content"></div> <div style="text-align:center;"> <input type="button" name="preview" style="padding: 0.25em 1em; 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67A
67
A
en
A. Partial Teacher
<div class="problem-statement"><div class="header"><div class="title">A. Partial Teacher</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>A teacher decides to give toffees to his students. He asks <span class="tex-span"><i>n</i></span> students to stand in a queue. Since the teacher is very partial, he follows the following rule to distribute toffees.</p><p>He looks at the first two students and gives more toffees to the student having higher marks than the other one. If they have the same marks they get the same number of toffees. The same procedure is followed for each pair of adjacent students starting from the first one to the last one.</p><p>It is given that each student receives at least one toffee. You have to find the number of toffees given to each student by the teacher such that the total number of toffees is minimum.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of input contains the number of students <span class="tex-span"><i>n</i></span> (<span class="tex-span">2 ≤ <i>n</i> ≤ 1000</span>). The second line gives (<span class="tex-span"><i>n</i> - 1</span>) characters consisting of "<span class="tex-font-style-tt">L</span>", "<span class="tex-font-style-tt">R</span>" and "<span class="tex-font-style-tt">=</span>". For each pair of adjacent students "<span class="tex-font-style-tt">L</span>" means that the left student has higher marks, "<span class="tex-font-style-tt">R</span>" means that the right student has higher marks and "<span class="tex-font-style-tt">=</span>" means that both have equal marks. </p></div><div class="output-specification"><div class="section-title">Output</div><p>Output consists of <span class="tex-span"><i>n</i></span> integers separated by a space representing the number of toffees each student receives in the queue starting from the first one to the last one.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>5<br/>LRLR<br/></pre></div><div class="output"><div class="title">Output</div><pre>2 1 2 1 2<br/></pre></div><div class="input"><div class="title">Input</div><pre>5<br/>=RRR<br/></pre></div><div class="output"><div class="title">Output</div><pre>1 1 2 3 4<br/></pre></div></div></div></div>
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} </style> <div class="roundbox sidebox sidebar-menu borderTopRound " style=""> <div class="caption titled">&rarr; Contest materials <div class="top-links"> </div> </div> <ul> <li> <span> <a href="/blog/entry/1475" title="Manthan 2011" target="_blank">Manthan 2011</a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="580:581" resourceName="Announcement" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> </ul> </div></div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li class="current selectedLava"><a href="/contest/67">Problems</a></li> <li><a href="/contest/67/submit">Submit Code</a></li> <li><a href="/contest/67/my">My Submissions</a></li> <li><a href="/contest/67/status">Status</a></li> <li><a href="/contest/67/hacks">Hacks</a></li> <li><a href="/contest/67/room/1">Room</a></li> <li><a href="/contest/67/standings">Standings</a></li> <li><a href="/contest/67/customtest">Custom Invocation</a></li> </ul> </div> <style> #facebox .content:has(.diff-popup) { width: 90vw; 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="A" data-uuid="ps_4e7dbc9fc7ba7e9a1625265e24060f4dfcbf385e"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">A. Partial Teacher</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>A teacher decides to give toffees to his students. He asks <span class="tex-span"><i>n</i></span> students to stand in a queue. Since the teacher is very partial, he follows the following rule to distribute toffees.</p><p>He looks at the first two students and gives more toffees to the student having higher marks than the other one. If they have the same marks they get the same number of toffees. The same procedure is followed for each pair of adjacent students starting from the first one to the last one.</p><p>It is given that each student receives at least one toffee. You have to find the number of toffees given to each student by the teacher such that the total number of toffees is minimum.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of input contains the number of students <span class="tex-span"><i>n</i></span> (<span class="tex-span">2 ≤ <i>n</i> ≤ 1000</span>). The second line gives (<span class="tex-span"><i>n</i> - 1</span>) characters consisting of &quot;<span class="tex-font-style-tt">L</span>&quot;, &quot;<span class="tex-font-style-tt">R</span>&quot; and &quot;<span class="tex-font-style-tt">=</span>&quot;. For each pair of adjacent students &quot;<span class="tex-font-style-tt">L</span>&quot; means that the left student has higher marks, &quot;<span class="tex-font-style-tt">R</span>&quot; means that the right student has higher marks and &quot;<span class="tex-font-style-tt">=</span>&quot; means that both have equal marks. </p></div><div class="output-specification"><div class="section-title">Output</div><p>Output consists of <span class="tex-span"><i>n</i></span> integers separated by a space representing the number of toffees each student receives in the queue starting from the first one to the last one.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>5<br />LRLR<br /></pre></div><div class="output"><div class="title">Output</div><pre>2 1 2 1 2<br /></pre></div><div class="input"><div class="title">Input</div><pre>5<br />=RRR<br /></pre></div><div class="output"><div class="title">Output</div><pre>1 1 2 3 4<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=A]"); 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["Dynamic programming", "Graphs", "Greedy algorithms", "Implementation problems, programming technics, simulation"]
["dp", "graphs", "greedy", "implementation", "*1800"]
67B
67
B
en
B. Restoration of the Permutation
<div class="problem-statement"><div class="header"><div class="title">B. Restoration of the Permutation</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Let <span class="tex-span"><i>A</i> = {<i>a</i><sub class="lower-index">1</sub>, <i>a</i><sub class="lower-index">2</sub>, ..., <i>a</i><sub class="lower-index"><i>n</i></sub>}</span> be any permutation of the first <span class="tex-span"><i>n</i></span> natural numbers <span class="tex-span">{1, 2, ..., <i>n</i>}</span>. You are given a positive integer <span class="tex-span"><i>k</i></span> and another sequence <span class="tex-span"><i>B</i> = {<i>b</i><sub class="lower-index">1</sub>, <i>b</i><sub class="lower-index">2</sub>, ..., <i>b</i><sub class="lower-index"><i>n</i></sub>}</span>, where <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> is the number of elements <span class="tex-span"><i>a</i><sub class="lower-index"><i>j</i></sub></span> in <span class="tex-span"><i>A</i></span> to the left of the element <span class="tex-span"><i>a</i><sub class="lower-index"><i>t</i></sub> = <i>i</i></span> such that <span class="tex-span"><i>a</i><sub class="lower-index"><i>j</i></sub> ≥ (<i>i</i> + <i>k</i>)</span>.</p><p>For example, if <span class="tex-span"><i>n</i> = 5</span>, a possible <span class="tex-span"><i>A</i></span> is <span class="tex-span">{5, 1, 4, 2, 3}</span>. For <span class="tex-span"><i>k</i> = 2</span>, <span class="tex-span"><i>B</i></span> is given by <span class="tex-span">{1, 2, 1, 0, 0}</span>. But if <span class="tex-span"><i>k</i> = 3</span>, then <span class="tex-span"><i>B</i> = {1, 1, 0, 0, 0}</span>.</p><p>For two sequences <span class="tex-span"><i>X</i> = {<i>x</i><sub class="lower-index">1</sub>, <i>x</i><sub class="lower-index">2</sub>, ..., <i>x</i><sub class="lower-index"><i>n</i></sub>}</span> and <span class="tex-span"><i>Y</i> = {<i>y</i><sub class="lower-index">1</sub>, <i>y</i><sub class="lower-index">2</sub>, ..., <i>y</i><sub class="lower-index"><i>n</i></sub>}</span>, let <span class="tex-span"><i>i</i></span>-th elements be the first elements such that <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub> ≠ <i>y</i><sub class="lower-index"><i>i</i></sub></span>. If <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub> &lt; <i>y</i><sub class="lower-index"><i>i</i></sub></span>, then <span class="tex-span"><i>X</i></span> is lexicographically smaller than <span class="tex-span"><i>Y</i></span>, while if <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub> &gt; <i>y</i><sub class="lower-index"><i>i</i></sub></span>, then <span class="tex-span"><i>X</i></span> is lexicographically greater than <span class="tex-span"><i>Y</i></span>.</p><p>Given <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>k</i></span> and <span class="tex-span"><i>B</i></span>, you need to determine the lexicographically smallest <span class="tex-span"><i>A</i></span>.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two space separated integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 1000</span>, <span class="tex-span">1 ≤ <i>k</i> ≤ <i>n</i></span>). On the second line are <span class="tex-span"><i>n</i></span> integers specifying the values of <span class="tex-span"><i>B</i> = {<i>b</i><sub class="lower-index">1</sub>, <i>b</i><sub class="lower-index">2</sub>, ..., <i>b</i><sub class="lower-index"><i>n</i></sub>}</span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print on a single line <span class="tex-span"><i>n</i></span> integers of <span class="tex-span"><i>A</i> = {<i>a</i><sub class="lower-index">1</sub>, <i>a</i><sub class="lower-index">2</sub>, ..., <i>a</i><sub class="lower-index"><i>n</i></sub>}</span> such that <span class="tex-span"><i>A</i></span> is lexicographically minimal. It is guaranteed that the solution exists.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>5 2<br/>1 2 1 0 0<br/></pre></div><div class="output"><div class="title">Output</div><pre>4 1 5 2 3 </pre></div><div class="input"><div class="title">Input</div><pre>4 2<br/>1 0 0 0<br/></pre></div><div class="output"><div class="title">Output</div><pre>2 3 1 4 </pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="B" data-uuid="ps_53df125d7865d97bd0e9431e0b2ffcdd5d04a5aa"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">B. Restoration of the Permutation</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Let <span class="tex-span"><i>A</i> = {<i>a</i><sub class="lower-index">1</sub>, <i>a</i><sub class="lower-index">2</sub>, ..., <i>a</i><sub class="lower-index"><i>n</i></sub>}</span> be any permutation of the first <span class="tex-span"><i>n</i></span> natural numbers <span class="tex-span">{1, 2, ..., <i>n</i>}</span>. You are given a positive integer <span class="tex-span"><i>k</i></span> and another sequence <span class="tex-span"><i>B</i> = {<i>b</i><sub class="lower-index">1</sub>, <i>b</i><sub class="lower-index">2</sub>, ..., <i>b</i><sub class="lower-index"><i>n</i></sub>}</span>, where <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> is the number of elements <span class="tex-span"><i>a</i><sub class="lower-index"><i>j</i></sub></span> in <span class="tex-span"><i>A</i></span> to the left of the element <span class="tex-span"><i>a</i><sub class="lower-index"><i>t</i></sub> = <i>i</i></span> such that <span class="tex-span"><i>a</i><sub class="lower-index"><i>j</i></sub> ≥ (<i>i</i> + <i>k</i>)</span>.</p><p>For example, if <span class="tex-span"><i>n</i> = 5</span>, a possible <span class="tex-span"><i>A</i></span> is <span class="tex-span">{5, 1, 4, 2, 3}</span>. For <span class="tex-span"><i>k</i> = 2</span>, <span class="tex-span"><i>B</i></span> is given by <span class="tex-span">{1, 2, 1, 0, 0}</span>. But if <span class="tex-span"><i>k</i> = 3</span>, then <span class="tex-span"><i>B</i> = {1, 1, 0, 0, 0}</span>.</p><p>For two sequences <span class="tex-span"><i>X</i> = {<i>x</i><sub class="lower-index">1</sub>, <i>x</i><sub class="lower-index">2</sub>, ..., <i>x</i><sub class="lower-index"><i>n</i></sub>}</span> and <span class="tex-span"><i>Y</i> = {<i>y</i><sub class="lower-index">1</sub>, <i>y</i><sub class="lower-index">2</sub>, ..., <i>y</i><sub class="lower-index"><i>n</i></sub>}</span>, let <span class="tex-span"><i>i</i></span>-th elements be the first elements such that <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub> ≠ <i>y</i><sub class="lower-index"><i>i</i></sub></span>. If <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub> &lt; <i>y</i><sub class="lower-index"><i>i</i></sub></span>, then <span class="tex-span"><i>X</i></span> is lexicographically smaller than <span class="tex-span"><i>Y</i></span>, while if <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub> &gt; <i>y</i><sub class="lower-index"><i>i</i></sub></span>, then <span class="tex-span"><i>X</i></span> is lexicographically greater than <span class="tex-span"><i>Y</i></span>.</p><p>Given <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>k</i></span> and <span class="tex-span"><i>B</i></span>, you need to determine the lexicographically smallest <span class="tex-span"><i>A</i></span>.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two space separated integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 1000</span>, <span class="tex-span">1 ≤ <i>k</i> ≤ <i>n</i></span>). On the second line are <span class="tex-span"><i>n</i></span> integers specifying the values of <span class="tex-span"><i>B</i> = {<i>b</i><sub class="lower-index">1</sub>, <i>b</i><sub class="lower-index">2</sub>, ..., <i>b</i><sub class="lower-index"><i>n</i></sub>}</span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print on a single line <span class="tex-span"><i>n</i></span> integers of <span class="tex-span"><i>A</i> = {<i>a</i><sub class="lower-index">1</sub>, <i>a</i><sub class="lower-index">2</sub>, ..., <i>a</i><sub class="lower-index"><i>n</i></sub>}</span> such that <span class="tex-span"><i>A</i></span> is lexicographically minimal. It is guaranteed that the solution exists.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>5 2<br />1 2 1 0 0<br /></pre></div><div class="output"><div class="title">Output</div><pre>4 1 5 2 3 </pre></div><div class="input"><div class="title">Input</div><pre>4 2<br />1 0 0 0<br /></pre></div><div class="output"><div class="title">Output</div><pre>2 3 1 4 </pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=B]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); if (previousStatementText) { if (previousStatementText !== statementText) { $problem.find(".diff-notifier").show(); $problem.find(".diff-notifier-close").click(function() { Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60); 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["Greedy algorithms"]
["greedy", "*1800"]
67C
67
C
en
C. Sequence of Balls
<div class="problem-statement"><div class="header"><div class="title">C. Sequence of Balls</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>You are given a sequence of balls <span class="tex-span"><i>A</i></span> by your teacher, each labeled with a lowercase Latin letter 'a'-'z'. You don't like the given sequence. You want to change it into a new sequence, <span class="tex-span"><i>B</i></span> that suits you better. So, you allow yourself four operations:</p><ul> <li> You can insert any ball with any label into the sequence at any position. </li><li> You can delete (remove) any ball from any position. </li><li> You can replace any ball with any other ball. </li><li> You can exchange (swap) two adjacent balls. </li></ul><p>Your teacher now places time constraints on each operation, meaning that an operation can only be performed in certain time. So, the first operation takes time <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub></span>, the second one takes <span class="tex-span"><i>t</i><sub class="lower-index"><i>d</i></sub></span>, the third one takes <span class="tex-span"><i>t</i><sub class="lower-index"><i>r</i></sub></span> and the fourth one takes <span class="tex-span"><i>t</i><sub class="lower-index"><i>e</i></sub></span>. Also, it is given that <span class="tex-span">2·<i>t</i><sub class="lower-index"><i>e</i></sub> ≥ <i>t</i><sub class="lower-index"><i>i</i></sub> + <i>t</i><sub class="lower-index"><i>d</i></sub></span>.</p><p>Find the minimal time to convert the sequence <span class="tex-span"><i>A</i></span> to the sequence <span class="tex-span"><i>B</i></span>.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains four space-separated integers <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub>, <i>t</i><sub class="lower-index"><i>d</i></sub>, <i>t</i><sub class="lower-index"><i>r</i></sub>, <i>t</i><sub class="lower-index"><i>e</i></sub></span> (<span class="tex-span">0 &lt; <i>t</i><sub class="lower-index"><i>i</i></sub>, <i>t</i><sub class="lower-index"><i>d</i></sub>, <i>t</i><sub class="lower-index"><i>r</i></sub>, <i>t</i><sub class="lower-index"><i>e</i></sub> ≤ 100</span>). The following two lines contain sequences <span class="tex-span"><i>A</i></span> and <span class="tex-span"><i>B</i></span> on separate lines. The length of each line is between 1 and 4000 characters inclusive.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single integer representing minimum time to convert <span class="tex-span"><i>A</i></span> into <span class="tex-span"><i>B</i></span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>1 1 1 1<br/>youshouldnot<br/>thoushaltnot<br/></pre></div><div class="output"><div class="title">Output</div><pre>5<br/></pre></div><div class="input"><div class="title">Input</div><pre>2 4 10 3<br/>ab<br/>ba<br/></pre></div><div class="output"><div class="title">Output</div><pre>3<br/></pre></div><div class="input"><div class="title">Input</div><pre>1 10 20 30<br/>a<br/>za<br/></pre></div><div class="output"><div class="title">Output</div><pre>1<br/></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the second sample, you could delete the ball labeled 'a' from the first position and then insert another 'a' at the new second position with total time 6. However exchanging the balls give total time 3.</p></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/67">Manthan 2011</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? 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If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="C" data-uuid="ps_d30789c8560f1b2eac71b1b9cfc1406e4773ffb9"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. Sequence of Balls</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>You are given a sequence of balls <span class="tex-span"><i>A</i></span> by your teacher, each labeled with a lowercase Latin letter 'a'-'z'. You don't like the given sequence. You want to change it into a new sequence, <span class="tex-span"><i>B</i></span> that suits you better. So, you allow yourself four operations:</p><ul> <li> You can insert any ball with any label into the sequence at any position. </li><li> You can delete (remove) any ball from any position. </li><li> You can replace any ball with any other ball. </li><li> You can exchange (swap) two adjacent balls. </li></ul><p>Your teacher now places time constraints on each operation, meaning that an operation can only be performed in certain time. So, the first operation takes time <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub></span>, the second one takes <span class="tex-span"><i>t</i><sub class="lower-index"><i>d</i></sub></span>, the third one takes <span class="tex-span"><i>t</i><sub class="lower-index"><i>r</i></sub></span> and the fourth one takes <span class="tex-span"><i>t</i><sub class="lower-index"><i>e</i></sub></span>. Also, it is given that <span class="tex-span">2·<i>t</i><sub class="lower-index"><i>e</i></sub> ≥ <i>t</i><sub class="lower-index"><i>i</i></sub> + <i>t</i><sub class="lower-index"><i>d</i></sub></span>.</p><p>Find the minimal time to convert the sequence <span class="tex-span"><i>A</i></span> to the sequence <span class="tex-span"><i>B</i></span>.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains four space-separated integers <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub>, <i>t</i><sub class="lower-index"><i>d</i></sub>, <i>t</i><sub class="lower-index"><i>r</i></sub>, <i>t</i><sub class="lower-index"><i>e</i></sub></span> (<span class="tex-span">0 &lt; <i>t</i><sub class="lower-index"><i>i</i></sub>, <i>t</i><sub class="lower-index"><i>d</i></sub>, <i>t</i><sub class="lower-index"><i>r</i></sub>, <i>t</i><sub class="lower-index"><i>e</i></sub> ≤ 100</span>). The following two lines contain sequences <span class="tex-span"><i>A</i></span> and <span class="tex-span"><i>B</i></span> on separate lines. The length of each line is between 1 and 4000 characters inclusive.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single integer representing minimum time to convert <span class="tex-span"><i>A</i></span> into <span class="tex-span"><i>B</i></span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>1 1 1 1<br />youshouldnot<br />thoushaltnot<br /></pre></div><div class="output"><div class="title">Output</div><pre>5<br /></pre></div><div class="input"><div class="title">Input</div><pre>2 4 10 3<br />ab<br />ba<br /></pre></div><div class="output"><div class="title">Output</div><pre>3<br /></pre></div><div class="input"><div class="title">Input</div><pre>1 10 20 30<br />a<br />za<br /></pre></div><div class="output"><div class="title">Output</div><pre>1<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the second sample, you could delete the ball labeled 'a' from the first position and then insert another 'a' at the new second position with total time 6. 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["Dynamic programming"]
["dp", "*2600"]
67D
67
D
en
D. Optical Experiment
<div class="problem-statement"><div class="header"><div class="title">D. Optical Experiment</div><div class="time-limit"><div class="property-title">time limit per test</div>5 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Professor Phunsuk Wangdu has performed some experiments on rays. The setup for <span class="tex-span"><i>n</i></span> rays is as follows.</p><p>There is a rectangular box having exactly <span class="tex-span"><i>n</i></span> holes on the opposite faces. All rays enter from the holes of the first side and exit from the holes of the other side of the box. Exactly one ray can enter or exit from each hole. The holes are in a straight line.</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/28583bedfa0495c0d7b4821b0712ee974a30bb9e.png" style="max-width: 100.0%;max-height: 100.0%;"/> </center><p>Professor Wangdu is showing his experiment to his students. He shows that there are cases, when all the rays are intersected by every other ray. A curious student asked the professor: "Sir, there are some groups of rays such that all rays in that group intersect every other ray in that group. Can we determine the number of rays in the largest of such groups?".</p><p>Professor Wangdu now is in trouble and knowing your intellect he asks you to help him.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">6</sup></span>), the number of rays. The second line contains <span class="tex-span"><i>n</i></span> distinct integers. The <span class="tex-span"><i>i</i></span>-th integer <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>x</i><sub class="lower-index"><i>i</i></sub> ≤ <i>n</i></span>) shows that the <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span>-th ray enters from the <span class="tex-span"><i>i</i></span>-th hole. Similarly, third line contains <span class="tex-span"><i>n</i></span> distinct integers. The <span class="tex-span"><i>i</i></span>-th integer <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>y</i><sub class="lower-index"><i>i</i></sub> ≤ <i>n</i></span>) shows that the <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span>-th ray exits from the <span class="tex-span"><i>i</i></span>-th hole. All rays are numbered from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span>. </p></div><div class="output-specification"><div class="section-title">Output</div><p>Output contains the only integer which is the number of rays in the largest group of rays all of which intersect each other.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>5<br/>1 4 5 2 3<br/>3 4 2 1 5<br/></pre></div><div class="output"><div class="title">Output</div><pre>3<br/></pre></div><div class="input"><div class="title">Input</div><pre>3<br/>3 1 2<br/>2 3 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>2<br/></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>For the first test case, the figure is shown above. The output of the first test case is 3, since the rays number 1, 4 and 3 are the ones which are intersected by each other one i.e. 1 is intersected by 4 and 3, 3 is intersected by 4 and 1, and 4 is intersected by 1 and 3. Hence every ray in this group is intersected by each other one. There does not exist any group containing more than 3 rays satisfying the above-mentioned constraint.</p></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="D" data-uuid="ps_c3f0792bd3c3addd79b1cf4c714216da265af705"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">D. Optical Experiment</div><div class="time-limit"><div class="property-title">time limit per test</div>5 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Professor Phunsuk Wangdu has performed some experiments on rays. The setup for <span class="tex-span"><i>n</i></span> rays is as follows.</p><p>There is a rectangular box having exactly <span class="tex-span"><i>n</i></span> holes on the opposite faces. All rays enter from the holes of the first side and exit from the holes of the other side of the box. Exactly one ray can enter or exit from each hole. The holes are in a straight line.</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/28583bedfa0495c0d7b4821b0712ee974a30bb9e.png" style="max-width: 100.0%;max-height: 100.0%;" /> </center><p>Professor Wangdu is showing his experiment to his students. He shows that there are cases, when all the rays are intersected by every other ray. A curious student asked the professor: &quot;Sir, there are some groups of rays such that all rays in that group intersect every other ray in that group. Can we determine the number of rays in the largest of such groups?&quot;.</p><p>Professor Wangdu now is in trouble and knowing your intellect he asks you to help him.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">6</sup></span>), the number of rays. The second line contains <span class="tex-span"><i>n</i></span> distinct integers. The <span class="tex-span"><i>i</i></span>-th integer <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>x</i><sub class="lower-index"><i>i</i></sub> ≤ <i>n</i></span>) shows that the <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span>-th ray enters from the <span class="tex-span"><i>i</i></span>-th hole. Similarly, third line contains <span class="tex-span"><i>n</i></span> distinct integers. The <span class="tex-span"><i>i</i></span>-th integer <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>y</i><sub class="lower-index"><i>i</i></sub> ≤ <i>n</i></span>) shows that the <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span>-th ray exits from the <span class="tex-span"><i>i</i></span>-th hole. All rays are numbered from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span>. </p></div><div class="output-specification"><div class="section-title">Output</div><p>Output contains the only integer which is the number of rays in the largest group of rays all of which intersect each other.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>5<br />1 4 5 2 3<br />3 4 2 1 5<br /></pre></div><div class="output"><div class="title">Output</div><pre>3<br /></pre></div><div class="input"><div class="title">Input</div><pre>3<br />3 1 2<br />2 3 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>2<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>For the first test case, the figure is shown above. The output of the first test case is 3, since the rays number 1, 4 and 3 are the ones which are intersected by each other one i.e. 1 is intersected by 4 and 3, 3 is intersected by 4 and 1, and 4 is intersected by 1 and 3. Hence every ray in this group is intersected by each other one. 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["Binary search", "Heaps, binary search trees, segment trees, hash tables, etc", "Dynamic programming"]
["binary search", "data structures", "dp", "*1900"]
67E
67
E
en
E. Save the City!
<div class="problem-statement"><div class="header"><div class="title">E. Save the City!</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>In the town of Aalam-Aara (meaning the Light of the Earth), previously there was no crime, no criminals but as the time progressed, sins started creeping into the hearts of once righteous people. Seeking solution to the problem, some of the elders found that as long as the corrupted part of population was kept away from the uncorrupted part, the crimes could be stopped. So, they are trying to set up a compound where they can keep the corrupted people. To ensure that the criminals don't escape the compound, a watchtower needs to be set up, so that they can be watched.</p><p>Since the people of Aalam-Aara aren't very rich, they met up with a merchant from some rich town who agreed to sell them a land-plot which has already a straight line fence <span class="tex-span"><i>AB</i></span> along which a few points are set up where they can put up a watchtower. Your task is to help them find out the number of points on that fence where the tower can be put up, so that all the criminals can be watched from there. Only one watchtower can be set up. A criminal is watchable from the watchtower if the line of visibility from the watchtower to him doesn't cross the plot-edges at any point between him and the tower i.e. as shown in figure 1 below, points <span class="tex-span"><i>X</i></span>, <span class="tex-span"><i>Y</i></span>, <span class="tex-span"><i>C</i></span> and <span class="tex-span"><i>A</i></span> are visible from point <span class="tex-span"><i>B</i></span> but the points <span class="tex-span"><i>E</i></span> and <span class="tex-span"><i>D</i></span> are not.</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/41ba551d817de9b5b014eca15c734435101517c0.png" style="max-width: 100.0%;max-height: 100.0%;"/> Figure 1 </center><center> <img class="tex-graphics" src="https://espresso.codeforces.com/26a7fa87bcc974229c12dbd4338a4ad20f93cdc7.png" style="max-width: 100.0%;max-height: 100.0%;"/> Figure 2 </center><p>Assume that the land plot is in the shape of a polygon and coordinate axes have been setup such that the fence <span class="tex-span"><i>AB</i></span> is parallel to <span class="tex-span"><i>x</i></span>-axis and the points where the watchtower can be set up are the integer points on the line. For example, in given figure 2, watchtower can be setup on any of five integer points on <span class="tex-span"><i>AB</i></span> i.e. <span class="tex-span">(4, 8)</span>, <span class="tex-span">(5, 8)</span>, <span class="tex-span">(6, 8)</span>, <span class="tex-span">(7, 8)</span> or <span class="tex-span">(8, 8)</span>. You can assume that no three consecutive points are collinear and all the corner points other than <span class="tex-span"><i>A</i></span> and <span class="tex-span"><i>B</i></span>, lie towards same side of fence <span class="tex-span"><i>AB</i></span>. The given polygon doesn't contain self-intersections.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of the test case will consist of the number of vertices <span class="tex-span"><i>n</i></span> (<span class="tex-span">3 ≤ <i>n</i> ≤ 1000</span>).</p><p>Next <span class="tex-span"><i>n</i></span> lines will contain the coordinates of the vertices in the clockwise order of the polygon. On the <span class="tex-span"><i>i</i></span>-th line are integers <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">0 ≤ <i>x</i><sub class="lower-index"><i>i</i></sub>, <i>y</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">6</sup></span>) separated by a space.</p><p>The endpoints of the fence <span class="tex-span"><i>AB</i></span> are the first two points, <span class="tex-span">(<i>x</i><sub class="lower-index">1</sub>, <i>y</i><sub class="lower-index">1</sub>)</span> and <span class="tex-span">(<i>x</i><sub class="lower-index">2</sub>, <i>y</i><sub class="lower-index">2</sub>)</span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Output consists of a single line containing the number of points where the watchtower can be set up.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>5<br/>4 8<br/>8 8<br/>9 4<br/>4 0<br/>0 4<br/></pre></div><div class="output"><div class="title">Output</div><pre>5<br/></pre></div><div class="input"><div class="title">Input</div><pre>5<br/>4 8<br/>5 8<br/>5 4<br/>7 4<br/>2 2<br/></pre></div><div class="output"><div class="title">Output</div><pre>0<br/></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>Figure 2 shows the first test case. All the points in the figure are watchable from any point on fence <span class="tex-span"><i>AB</i></span>. Since, <span class="tex-span"><i>AB</i></span> has <span class="tex-span">5</span> integer coordinates, so answer is <span class="tex-span">5</span>.</p><p>For case two, fence <span class="tex-span"><i>CD</i></span> and <span class="tex-span"><i>DE</i></span> are not completely visible, thus answer is <span class="tex-span">0</span>.</p></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/67">Manthan 2011</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? 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If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="E" data-uuid="ps_42ec3ed197e43a2797bb91d204af42ade22cfb39"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">E. Save the City!</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>In the town of Aalam-Aara (meaning the Light of the Earth), previously there was no crime, no criminals but as the time progressed, sins started creeping into the hearts of once righteous people. Seeking solution to the problem, some of the elders found that as long as the corrupted part of population was kept away from the uncorrupted part, the crimes could be stopped. So, they are trying to set up a compound where they can keep the corrupted people. To ensure that the criminals don't escape the compound, a watchtower needs to be set up, so that they can be watched.</p><p>Since the people of Aalam-Aara aren't very rich, they met up with a merchant from some rich town who agreed to sell them a land-plot which has already a straight line fence <span class="tex-span"><i>AB</i></span> along which a few points are set up where they can put up a watchtower. Your task is to help them find out the number of points on that fence where the tower can be put up, so that all the criminals can be watched from there. Only one watchtower can be set up. A criminal is watchable from the watchtower if the line of visibility from the watchtower to him doesn't cross the plot-edges at any point between him and the tower i.e. as shown in figure 1 below, points <span class="tex-span"><i>X</i></span>, <span class="tex-span"><i>Y</i></span>, <span class="tex-span"><i>C</i></span> and <span class="tex-span"><i>A</i></span> are visible from point <span class="tex-span"><i>B</i></span> but the points <span class="tex-span"><i>E</i></span> and <span class="tex-span"><i>D</i></span> are not.</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/41ba551d817de9b5b014eca15c734435101517c0.png" style="max-width: 100.0%;max-height: 100.0%;" /> Figure 1 </center><center> <img class="tex-graphics" src="https://espresso.codeforces.com/26a7fa87bcc974229c12dbd4338a4ad20f93cdc7.png" style="max-width: 100.0%;max-height: 100.0%;" /> Figure 2 </center><p>Assume that the land plot is in the shape of a polygon and coordinate axes have been setup such that the fence <span class="tex-span"><i>AB</i></span> is parallel to <span class="tex-span"><i>x</i></span>-axis and the points where the watchtower can be set up are the integer points on the line. For example, in given figure 2, watchtower can be setup on any of five integer points on <span class="tex-span"><i>AB</i></span> i.e. <span class="tex-span">(4, 8)</span>, <span class="tex-span">(5, 8)</span>, <span class="tex-span">(6, 8)</span>, <span class="tex-span">(7, 8)</span> or <span class="tex-span">(8, 8)</span>. You can assume that no three consecutive points are collinear and all the corner points other than <span class="tex-span"><i>A</i></span> and <span class="tex-span"><i>B</i></span>, lie towards same side of fence <span class="tex-span"><i>AB</i></span>. The given polygon doesn't contain self-intersections.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of the test case will consist of the number of vertices <span class="tex-span"><i>n</i></span> (<span class="tex-span">3 ≤ <i>n</i> ≤ 1000</span>).</p><p>Next <span class="tex-span"><i>n</i></span> lines will contain the coordinates of the vertices in the clockwise order of the polygon. On the <span class="tex-span"><i>i</i></span>-th line are integers <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">0 ≤ <i>x</i><sub class="lower-index"><i>i</i></sub>, <i>y</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">6</sup></span>) separated by a space.</p><p>The endpoints of the fence <span class="tex-span"><i>AB</i></span> are the first two points, <span class="tex-span">(<i>x</i><sub class="lower-index">1</sub>, <i>y</i><sub class="lower-index">1</sub>)</span> and <span class="tex-span">(<i>x</i><sub class="lower-index">2</sub>, <i>y</i><sub class="lower-index">2</sub>)</span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Output consists of a single line containing the number of points where the watchtower can be set up.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>5<br />4 8<br />8 8<br />9 4<br />4 0<br />0 4<br /></pre></div><div class="output"><div class="title">Output</div><pre>5<br /></pre></div><div class="input"><div class="title">Input</div><pre>5<br />4 8<br />5 8<br />5 4<br />7 4<br />2 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>0<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>Figure 2 shows the first test case. All the points in the figure are watchable from any point on fence <span class="tex-span"><i>AB</i></span>. Since, <span class="tex-span"><i>AB</i></span> has <span class="tex-span">5</span> integer coordinates, so answer is <span class="tex-span">5</span>.</p><p>For case two, fence <span class="tex-span"><i>CD</i></span> and <span class="tex-span"><i>DE</i></span> are not completely visible, thus answer is <span class="tex-span">0</span>.</p></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=E]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); if (previousStatementText) { if (previousStatementText !== statementText) { $problem.find(".diff-notifier").show(); $problem.find(".diff-notifier-close").click(function() { Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60); $problem.find(".diff-notifier").hide(); }); $problem.find("a.view-changes").click(function() { $.post("/data/diff", {action: "getDiff", a: previousStatementText, b: statementText}, function (result) { if (result["success"] === "true") { Codeforces.facebox(".diff-popup", "//codeforces.org/s/73366"); 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["Geometry, computational geometry"]
["geometry", "*2500"]
68A
68
A
en
A. Irrational problem
<div class="problem-statement"><div class="header"><div class="title">A. Irrational problem</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Little Petya was given this problem for homework:</p><p>You are given function <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/22d161d4a5bc6cfd41667ca591d56973abfe8655.png" style="max-width: 100.0%;max-height: 100.0%;"/> (here <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/e91a39ad64cd7a33e8f1b67cd60e5b40257de950.png" style="max-width: 100.0%;max-height: 100.0%;"/> represents the operation of taking the remainder). His task is to count the number of integers <span class="tex-span"><i>x</i></span> in range <span class="tex-span">[<i>a</i>;<i>b</i>]</span> with property <span class="tex-span"><i>f</i>(<i>x</i>) = <i>x</i></span>.</p><p>It is a pity that Petya forgot the order in which the remainders should be taken and wrote down only 4 numbers. Each of 24 possible orders of taking the remainder has equal probability of being chosen. For example, if Petya has numbers 1, 2, 3, 4 then he can take remainders in that order or first take remainder modulo 4, then modulo 2, 3, 1. There also are 22 other permutations of these numbers that represent orders in which remainder can be taken. In this problem 4 numbers wrote down by Petya will be pairwise distinct.</p><p>Now it is impossible for Petya to complete the task given by teacher but just for fun he decided to find the number of integers <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/66564024af56fb327f06ed6542f6badc5c851715.png" style="max-width: 100.0%;max-height: 100.0%;"/> with property that probability that <span class="tex-span"><i>f</i>(<i>x</i>) = <i>x</i></span> is not less than <span class="tex-span">31.4159265352718281828459045%</span>. In other words, Petya will pick up the number <span class="tex-span"><i>x</i></span> if there exist at least <span class="tex-span">7</span> permutations of numbers <span class="tex-span"><i>p</i><sub class="lower-index">1</sub>, <i>p</i><sub class="lower-index">2</sub>, <i>p</i><sub class="lower-index">3</sub>, <i>p</i><sub class="lower-index">4</sub></span>, for which <span class="tex-span"><i>f</i>(<i>x</i>) = <i>x</i></span>.</p></div><div class="input-specification"><div class="section-title">Input</div><p>First line of the input will contain 6 integers, separated by spaces: <span class="tex-span"><i>p</i><sub class="lower-index">1</sub>, <i>p</i><sub class="lower-index">2</sub>, <i>p</i><sub class="lower-index">3</sub>, <i>p</i><sub class="lower-index">4</sub>, <i>a</i>, <i>b</i></span> (<span class="tex-span">1 ≤ <i>p</i><sub class="lower-index">1</sub>, <i>p</i><sub class="lower-index">2</sub>, <i>p</i><sub class="lower-index">3</sub>, <i>p</i><sub class="lower-index">4</sub> ≤ 1000, 0 ≤ <i>a</i> ≤ <i>b</i> ≤ 31415</span>). </p><p>It is guaranteed that numbers <span class="tex-span"><i>p</i><sub class="lower-index">1</sub>, <i>p</i><sub class="lower-index">2</sub>, <i>p</i><sub class="lower-index">3</sub>, <i>p</i><sub class="lower-index">4</sub></span> will be pairwise distinct.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Output the number of integers in the given range that have the given property.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2 7 1 8 2 8<br/></pre></div><div class="output"><div class="title">Output</div><pre>0<br/></pre></div><div class="input"><div class="title">Input</div><pre>20 30 40 50 0 100<br/></pre></div><div class="output"><div class="title">Output</div><pre>20<br/></pre></div><div class="input"><div class="title">Input</div><pre>31 41 59 26 17 43<br/></pre></div><div class="output"><div class="title">Output</div><pre>9<br/></pre></div></div></div></div>
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Irrational problem</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Little Petya was given this problem for homework:</p><p>You are given function <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/22d161d4a5bc6cfd41667ca591d56973abfe8655.png" style="max-width: 100.0%;max-height: 100.0%;" /> (here <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/e91a39ad64cd7a33e8f1b67cd60e5b40257de950.png" style="max-width: 100.0%;max-height: 100.0%;" /> represents the operation of taking the remainder). His task is to count the number of integers <span class="tex-span"><i>x</i></span> in range <span class="tex-span">[<i>a</i>;<i>b</i>]</span> with property <span class="tex-span"><i>f</i>(<i>x</i>) = <i>x</i></span>.</p><p>It is a pity that Petya forgot the order in which the remainders should be taken and wrote down only 4 numbers. Each of 24 possible orders of taking the remainder has equal probability of being chosen. For example, if Petya has numbers 1, 2, 3, 4 then he can take remainders in that order or first take remainder modulo 4, then modulo 2, 3, 1. There also are 22 other permutations of these numbers that represent orders in which remainder can be taken. In this problem 4 numbers wrote down by Petya will be pairwise distinct.</p><p>Now it is impossible for Petya to complete the task given by teacher but just for fun he decided to find the number of integers <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/66564024af56fb327f06ed6542f6badc5c851715.png" style="max-width: 100.0%;max-height: 100.0%;" /> with property that probability that <span class="tex-span"><i>f</i>(<i>x</i>) = <i>x</i></span> is not less than <span class="tex-span">31.4159265352718281828459045%</span>. In other words, Petya will pick up the number <span class="tex-span"><i>x</i></span> if there exist at least <span class="tex-span">7</span> permutations of numbers <span class="tex-span"><i>p</i><sub class="lower-index">1</sub>, <i>p</i><sub class="lower-index">2</sub>, <i>p</i><sub class="lower-index">3</sub>, <i>p</i><sub class="lower-index">4</sub></span>, for which <span class="tex-span"><i>f</i>(<i>x</i>) = <i>x</i></span>.</p></div><div class="input-specification"><div class="section-title">Input</div><p>First line of the input will contain 6 integers, separated by spaces: <span class="tex-span"><i>p</i><sub class="lower-index">1</sub>, <i>p</i><sub class="lower-index">2</sub>, <i>p</i><sub class="lower-index">3</sub>, <i>p</i><sub class="lower-index">4</sub>, <i>a</i>, <i>b</i></span> (<span class="tex-span">1 ≤ <i>p</i><sub class="lower-index">1</sub>, <i>p</i><sub class="lower-index">2</sub>, <i>p</i><sub class="lower-index">3</sub>, <i>p</i><sub class="lower-index">4</sub> ≤ 1000, 0 ≤ <i>a</i> ≤ <i>b</i> ≤ 31415</span>). </p><p>It is guaranteed that numbers <span class="tex-span"><i>p</i><sub class="lower-index">1</sub>, <i>p</i><sub class="lower-index">2</sub>, <i>p</i><sub class="lower-index">3</sub>, <i>p</i><sub class="lower-index">4</sub></span> will be pairwise distinct.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Output the number of integers in the given range that have the given property.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2 7 1 8 2 8<br /></pre></div><div class="output"><div class="title">Output</div><pre>0<br /></pre></div><div class="input"><div class="title">Input</div><pre>20 30 40 50 0 100<br /></pre></div><div class="output"><div class="title">Output</div><pre>20<br /></pre></div><div class="input"><div class="title">Input</div><pre>31 41 59 26 17 43<br /></pre></div><div class="output"><div class="title">Output</div><pre>9<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=A]"); 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["Implementation problems, programming technics, simulation", "Number theory: Euler function, GCD, divisibility, etc"]
["implementation", "number theory", "*1100"]
68B
68
B
en
B. Energy exchange
<div class="problem-statement"><div class="header"><div class="title">B. Energy exchange</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>It is well known that the planet suffers from the energy crisis. Little Petya doesn't like that and wants to save the world. For this purpose he needs every accumulator to contain the same amount of energy. Initially every accumulator has some amount of energy: the <span class="tex-span"><i>i</i></span>-th accumulator has <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> units of energy. Energy can be transferred from one accumulator to the other. Every time <span class="tex-span"><i>x</i></span> units of energy are transferred (<span class="tex-span"><i>x</i></span> is not necessarily an integer) <span class="tex-span"><i>k</i></span> percent of it is lost. That is, if <span class="tex-span"><i>x</i></span> units were transferred from one accumulator to the other, amount of energy in the first one decreased by <span class="tex-span"><i>x</i></span> units and in other increased by <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5da936c833914e398476bcdcd55a9583860c2e5c.png" style="max-width: 100.0%;max-height: 100.0%;"/> units.</p><p>Your task is to help Petya find what maximum equal amount of energy can be stored in each accumulator after the transfers.</p></div><div class="input-specification"><div class="section-title">Input</div><p>First line of the input contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10000, 0 ≤ <i>k</i> ≤ 99</span>) — number of accumulators and the percent of energy that is lost during transfers.</p><p>Next line contains <span class="tex-span"><i>n</i></span> integers <span class="tex-span"><i>a</i><sub class="lower-index">1</sub>, <i>a</i><sub class="lower-index">2</sub>, ... , <i>a</i><sub class="lower-index"><i>n</i></sub></span> — amounts of energy in the first, second, .., <span class="tex-span"><i>n</i></span>-th accumulator respectively (<span class="tex-span">0 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 1000, 1 ≤ <i>i</i> ≤ <i>n</i></span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Output maximum possible amount of energy that can remain in each of accumulators after the transfers of energy.</p><p>The absolute or relative error in the answer should not exceed <span class="tex-span">10<sup class="upper-index"> - 6</sup></span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3 50<br/>4 2 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>2.000000000<br/></pre></div><div class="input"><div class="title">Input</div><pre>2 90<br/>1 11<br/></pre></div><div class="output"><div class="title">Output</div><pre>1.909090909<br/></pre></div></div></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/68">Codeforces Beta Round 62</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? 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Energy exchange</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>It is well known that the planet suffers from the energy crisis. Little Petya doesn't like that and wants to save the world. For this purpose he needs every accumulator to contain the same amount of energy. Initially every accumulator has some amount of energy: the <span class="tex-span"><i>i</i></span>-th accumulator has <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> units of energy. Energy can be transferred from one accumulator to the other. Every time <span class="tex-span"><i>x</i></span> units of energy are transferred (<span class="tex-span"><i>x</i></span> is not necessarily an integer) <span class="tex-span"><i>k</i></span> percent of it is lost. That is, if <span class="tex-span"><i>x</i></span> units were transferred from one accumulator to the other, amount of energy in the first one decreased by <span class="tex-span"><i>x</i></span> units and in other increased by <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5da936c833914e398476bcdcd55a9583860c2e5c.png" style="max-width: 100.0%;max-height: 100.0%;" /> units.</p><p>Your task is to help Petya find what maximum equal amount of energy can be stored in each accumulator after the transfers.</p></div><div class="input-specification"><div class="section-title">Input</div><p>First line of the input contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10000, 0 ≤ <i>k</i> ≤ 99</span>) — number of accumulators and the percent of energy that is lost during transfers.</p><p>Next line contains <span class="tex-span"><i>n</i></span> integers <span class="tex-span"><i>a</i><sub class="lower-index">1</sub>, <i>a</i><sub class="lower-index">2</sub>, ... , <i>a</i><sub class="lower-index"><i>n</i></sub></span> — amounts of energy in the first, second, .., <span class="tex-span"><i>n</i></span>-th accumulator respectively (<span class="tex-span">0 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 1000, 1 ≤ <i>i</i> ≤ <i>n</i></span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Output maximum possible amount of energy that can remain in each of accumulators after the transfers of energy.</p><p>The absolute or relative error in the answer should not exceed <span class="tex-span">10<sup class="upper-index"> - 6</sup></span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3 50<br />4 2 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>2.000000000<br /></pre></div><div class="input"><div class="title">Input</div><pre>2 90<br />1 11<br /></pre></div><div class="output"><div class="title">Output</div><pre>1.909090909<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=B]"); 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["Binary search"]
["binary search", "*1600"]
68C
68
C
en
C. Synchrophasotron
<div class="problem-statement"><div class="header"><div class="title">C. Synchrophasotron</div><div class="time-limit"><div class="property-title">time limit per test</div>3 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>For some experiments little Petya needs a synchrophasotron. He has already got the device, all that's left is to set the fuel supply. Fuel comes through a system of nodes numbered from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span> and connected by pipes. Pipes go from every node with smaller number to every node with greater number. Fuel can only flow through pipes in direction from node with smaller number to node with greater number. Any amount of fuel can enter through the first node and the last node is connected directly to the synchrophasotron. It is known that every pipe has three attributes: the minimum amount of fuel that should go through it, the maximum amount of fuel that can possibly go through it and the cost of pipe activation. If <span class="tex-span"><i>c</i><sub class="lower-index"><i>ij</i></sub></span> units of fuel (<span class="tex-span"><i>c</i><sub class="lower-index"><i>ij</i></sub> &gt; 0</span>) flow from node <span class="tex-span"><i>i</i></span> to node <span class="tex-span"><i>j</i></span>, it will cost <span class="tex-span"><i>a</i><sub class="lower-index"><i>ij</i></sub> + <i>c</i><sub class="lower-index"><i>ij</i></sub><sup class="upper-index">2</sup></span> tugriks (<span class="tex-span"><i>a</i><sub class="lower-index"><i>ij</i></sub></span> is the cost of pipe activation), and if fuel doesn't flow through the pipe, it doesn't cost anything. Only integer number of units of fuel can flow through each pipe.</p><p>Constraints on the minimal and the maximal fuel capacity of a pipe take place <span class="tex-font-style-bf">always</span>, not only if it is active. You may assume that the pipe is active if and only if the flow through it is strictly greater than zero.</p><p>Petya doesn't want the pipe system to be overloaded, so he wants to find the minimal amount of fuel, that, having entered the first node, can reach the synchrophasotron. Besides that he wants to impress the sponsors, so the sum of money needed to be paid for fuel to go through each pipe, must be as big as possible.</p></div><div class="input-specification"><div class="section-title">Input</div><p>First line contains integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">2 ≤ <i>n</i> ≤ 6</span>), which represents the number of nodes. Each of the next <span class="tex-span"><i>n</i>(<i>n</i> - 1) / 2</span> lines contains five integers <span class="tex-span"><i>s</i>, <i>f</i>, <i>l</i>, <i>h</i>, <i>a</i></span> that describe pipes — the first node of the pipe, the second node of the pipe, the minimum and the maximum amount of fuel that can flow through the pipe and the the activation cost, respectively. (<span class="tex-span">1 ≤ <i>s</i> &lt; <i>f</i> ≤ <i>n</i>, 0 ≤ <i>l</i> ≤ <i>h</i> ≤ 5, 0 ≤ <i>a</i> ≤ 6</span>). It is guaranteed that for each pair of nodes with distinct numbers there will be exactly one pipe between them described in the input.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Output in the first line two space-separated numbers: the minimum possible amount of fuel that can flow into the synchrophasotron, and the maximum possible sum that needs to be paid in order for that amount of fuel to reach synchrophasotron. If there is no amount of fuel that can reach synchrophasotron, output "<span class="tex-font-style-tt">-1 -1</span>".</p><p>The amount of fuel which will flow into synchrophasotron is not neccessary positive. It could be equal to zero if the minimum constraint of every pipe is equal to zero.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2<br/>1 2 1 2 3<br/></pre></div><div class="output"><div class="title">Output</div><pre>1 4<br/></pre></div><div class="input"><div class="title">Input</div><pre>3<br/>1 2 1 2 3<br/>1 3 0 0 0<br/>2 3 3 4 5<br/></pre></div><div class="output"><div class="title">Output</div><pre>-1 -1<br/></pre></div><div class="input"><div class="title">Input</div><pre>4<br/>1 2 0 2 1<br/>2 3 0 2 1<br/>1 3 0 2 6<br/>1 4 0 0 1<br/>2 4 0 0 0<br/>3 4 2 3 0<br/></pre></div><div class="output"><div class="title">Output</div><pre>2 15<br/></pre></div><div class="input"><div class="title">Input</div><pre>3<br/>1 2 0 2 1<br/>1 3 1 2 1<br/>2 3 1 2 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>2 6<br/></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first test, we can either pass 1 or 2 units of fuel from node 1 to node 2. The minimum possible amount is 1, it costs <span class="tex-span"><i>a</i><sub class="lower-index">12</sub> + 1<sup class="upper-index">2</sup> = 4</span>.</p><p>In the second test, you can pass at most 2 units from node 1 to node 2, and at you have to pass at least 3 units from node 2 to node 3. It is impossible.</p><p>In the third test, the minimum possible amount is 2. You can pass each unit of fuel through two different paths: either 1-&gt;2-&gt;3-&gt;4 or 1-&gt;3-&gt;4. If you use the first path twice, it will cost <span class="tex-span"><i>a</i><sub class="lower-index">12</sub> + 2<sup class="upper-index">2</sup> + <i>a</i><sub class="lower-index">23</sub> + 2<sup class="upper-index">2</sup> + <i>a</i><sub class="lower-index">34</sub> + 2<sup class="upper-index">2</sup></span>=14. If you use the second path twice, it will cost <span class="tex-span"><i>a</i><sub class="lower-index">13</sub> + 2<sup class="upper-index">2</sup> + <i>a</i><sub class="lower-index">34</sub> + 2<sup class="upper-index">2</sup></span>=14. However, if you use each path (allowing one unit of fuel go through pipes 1-&gt;2, 2-&gt;3, 1-&gt;3, and two units go through 3-&gt;4) it will cost <span class="tex-span"><i>a</i><sub class="lower-index">12</sub> + 1<sup class="upper-index">2</sup> + <i>a</i><sub class="lower-index">23</sub> + 1<sup class="upper-index">2</sup> + <i>a</i><sub class="lower-index">13</sub> + 1<sup class="upper-index">2</sup> + <i>a</i><sub class="lower-index">34</sub> + 2<sup class="upper-index">2</sup></span>=15 and it is the maximum possible cost.</p><p>Also note that since no fuel flows from node 1 to node 4, activation cost for that pipe is not added to the answer.</p></div></div>
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Synchrophasotron</div><div class="time-limit"><div class="property-title">time limit per test</div>3 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>For some experiments little Petya needs a synchrophasotron. He has already got the device, all that's left is to set the fuel supply. Fuel comes through a system of nodes numbered from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span> and connected by pipes. Pipes go from every node with smaller number to every node with greater number. Fuel can only flow through pipes in direction from node with smaller number to node with greater number. Any amount of fuel can enter through the first node and the last node is connected directly to the synchrophasotron. It is known that every pipe has three attributes: the minimum amount of fuel that should go through it, the maximum amount of fuel that can possibly go through it and the cost of pipe activation. If <span class="tex-span"><i>c</i><sub class="lower-index"><i>ij</i></sub></span> units of fuel (<span class="tex-span"><i>c</i><sub class="lower-index"><i>ij</i></sub> &gt; 0</span>) flow from node <span class="tex-span"><i>i</i></span> to node <span class="tex-span"><i>j</i></span>, it will cost <span class="tex-span"><i>a</i><sub class="lower-index"><i>ij</i></sub> + <i>c</i><sub class="lower-index"><i>ij</i></sub><sup class="upper-index">2</sup></span> tugriks (<span class="tex-span"><i>a</i><sub class="lower-index"><i>ij</i></sub></span> is the cost of pipe activation), and if fuel doesn't flow through the pipe, it doesn't cost anything. Only integer number of units of fuel can flow through each pipe.</p><p>Constraints on the minimal and the maximal fuel capacity of a pipe take place <span class="tex-font-style-bf">always</span>, not only if it is active. You may assume that the pipe is active if and only if the flow through it is strictly greater than zero.</p><p>Petya doesn't want the pipe system to be overloaded, so he wants to find the minimal amount of fuel, that, having entered the first node, can reach the synchrophasotron. Besides that he wants to impress the sponsors, so the sum of money needed to be paid for fuel to go through each pipe, must be as big as possible.</p></div><div class="input-specification"><div class="section-title">Input</div><p>First line contains integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">2 ≤ <i>n</i> ≤ 6</span>), which represents the number of nodes. Each of the next <span class="tex-span"><i>n</i>(<i>n</i> - 1) / 2</span> lines contains five integers <span class="tex-span"><i>s</i>, <i>f</i>, <i>l</i>, <i>h</i>, <i>a</i></span> that describe pipes — the first node of the pipe, the second node of the pipe, the minimum and the maximum amount of fuel that can flow through the pipe and the the activation cost, respectively. (<span class="tex-span">1 ≤ <i>s</i> &lt; <i>f</i> ≤ <i>n</i>, 0 ≤ <i>l</i> ≤ <i>h</i> ≤ 5, 0 ≤ <i>a</i> ≤ 6</span>). It is guaranteed that for each pair of nodes with distinct numbers there will be exactly one pipe between them described in the input.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Output in the first line two space-separated numbers: the minimum possible amount of fuel that can flow into the synchrophasotron, and the maximum possible sum that needs to be paid in order for that amount of fuel to reach synchrophasotron. If there is no amount of fuel that can reach synchrophasotron, output &quot;<span class="tex-font-style-tt">-1 -1</span>&quot;.</p><p>The amount of fuel which will flow into synchrophasotron is not neccessary positive. It could be equal to zero if the minimum constraint of every pipe is equal to zero.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2<br />1 2 1 2 3<br /></pre></div><div class="output"><div class="title">Output</div><pre>1 4<br /></pre></div><div class="input"><div class="title">Input</div><pre>3<br />1 2 1 2 3<br />1 3 0 0 0<br />2 3 3 4 5<br /></pre></div><div class="output"><div class="title">Output</div><pre>-1 -1<br /></pre></div><div class="input"><div class="title">Input</div><pre>4<br />1 2 0 2 1<br />2 3 0 2 1<br />1 3 0 2 6<br />1 4 0 0 1<br />2 4 0 0 0<br />3 4 2 3 0<br /></pre></div><div class="output"><div class="title">Output</div><pre>2 15<br /></pre></div><div class="input"><div class="title">Input</div><pre>3<br />1 2 0 2 1<br />1 3 1 2 1<br />2 3 1 2 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>2 6<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first test, we can either pass 1 or 2 units of fuel from node 1 to node 2. The minimum possible amount is 1, it costs <span class="tex-span"><i>a</i><sub class="lower-index">12</sub> + 1<sup class="upper-index">2</sup> = 4</span>.</p><p>In the second test, you can pass at most 2 units from node 1 to node 2, and at you have to pass at least 3 units from node 2 to node 3. It is impossible.</p><p>In the third test, the minimum possible amount is 2. You can pass each unit of fuel through two different paths: either 1-&gt;2-&gt;3-&gt;4 or 1-&gt;3-&gt;4. If you use the first path twice, it will cost <span class="tex-span"><i>a</i><sub class="lower-index">12</sub> + 2<sup class="upper-index">2</sup> + <i>a</i><sub class="lower-index">23</sub> + 2<sup class="upper-index">2</sup> + <i>a</i><sub class="lower-index">34</sub> + 2<sup class="upper-index">2</sup></span>=14. If you use the second path twice, it will cost <span class="tex-span"><i>a</i><sub class="lower-index">13</sub> + 2<sup class="upper-index">2</sup> + <i>a</i><sub class="lower-index">34</sub> + 2<sup class="upper-index">2</sup></span>=14. However, if you use each path (allowing one unit of fuel go through pipes 1-&gt;2, 2-&gt;3, 1-&gt;3, and two units go through 3-&gt;4) it will cost <span class="tex-span"><i>a</i><sub class="lower-index">12</sub> + 1<sup class="upper-index">2</sup> + <i>a</i><sub class="lower-index">23</sub> + 1<sup class="upper-index">2</sup> + <i>a</i><sub class="lower-index">13</sub> + 1<sup class="upper-index">2</sup> + <i>a</i><sub class="lower-index">34</sub> + 2<sup class="upper-index">2</sup></span>=15 and it is the maximum possible cost.</p><p>Also note that since no fuel flows from node 1 to node 4, activation cost for that pipe is not added to the answer.</p></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=C]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); if (previousStatementText) { if (previousStatementText !== statementText) { $problem.find(".diff-notifier").show(); 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["Brute force"]
["brute force", "*2200"]
68D
68
D
en
D. Half-decay tree
<div class="problem-statement"><div class="header"><div class="title">D. Half-decay tree</div><div class="time-limit"><div class="property-title">time limit per test</div>3 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Recently Petya has become keen on physics. Anna V., his teacher noticed Petya's interest and gave him a fascinating physical puzzle — a half-decay tree. </p><p>A half-decay tree is a complete binary tree with the height <span class="tex-span"><i>h</i></span>. The height of a tree is the length of the path (in edges) from the root to a leaf in the tree. While studying the tree Petya can add electrons to vertices or induce random decay with synchrophasotron. Random decay is a process during which the edges of some path from the root to the random leaf of the tree are deleted. All the leaves are equiprobable. As the half-decay tree is the school property, Petya will return back the deleted edges into the tree after each decay.</p><p>After being desintegrated, the tree decomposes into connected components. Charge of each component is the total quantity of electrons placed in vertices of the component. Potential of desintegerated tree is the maximum from the charges of its connected components. Each time before inducing random decay Petya is curious about the mathematical expectation of potential of the tree after being desintegrated. </p></div><div class="input-specification"><div class="section-title">Input</div><p>First line will contain two integers <span class="tex-span"><i>h</i></span> and <span class="tex-span"><i>q</i></span> (<span class="tex-span">1 ≤ <i>h</i> ≤ 30, 1 ≤ <i>q</i> ≤ 10<sup class="upper-index">5</sup></span>). Next <span class="tex-span"><i>q</i></span> lines will contain a query of one of two types: </p><ul><li> <span class="tex-font-style-tt">add</span> <span class="tex-span"><i>v</i></span> <span class="tex-span"><i>e</i></span><p>Petya adds <span class="tex-span"><i>e</i></span> electrons to vertex number <span class="tex-span"><i>v</i></span> (<span class="tex-span">1 ≤ <i>v</i> ≤ 2<sup class="upper-index"><i>h</i> + 1</sup> - 1, 0 ≤ <i>e</i> ≤ 10<sup class="upper-index">4</sup></span>). <span class="tex-span"><i>v</i></span> and <span class="tex-span"><i>e</i></span> are integers.</p><p>The vertices of the tree are numbered in the following way: the root is numbered with 1, the children of the vertex with number <span class="tex-span"><i>x</i></span> are numbered with <span class="tex-span">2<i>x</i></span> and <span class="tex-span">2<i>x</i> + 1</span>.</p></li><li> <span class="tex-font-style-tt">decay</span><p>Petya induces tree decay. </p></li></ul></div><div class="output-specification"><div class="section-title">Output</div><p>For each query <span class="tex-font-style-tt">decay</span> solution you should output the mathematical expectation of potential of the tree after being desintegrated. The absolute or relative error in the answer should not exceed <span class="tex-span">10<sup class="upper-index"> - 4</sup></span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>1 4<br/>add 1 3<br/>add 2 10<br/>add 3 11<br/>decay<br/></pre></div><div class="output"><div class="title">Output</div><pre>13.50000000<br/></pre></div></div></div></div>
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Half-decay tree</div><div class="time-limit"><div class="property-title">time limit per test</div>3 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Recently Petya has become keen on physics. Anna V., his teacher noticed Petya's interest and gave him a fascinating physical puzzle — a half-decay tree. </p><p>A half-decay tree is a complete binary tree with the height <span class="tex-span"><i>h</i></span>. The height of a tree is the length of the path (in edges) from the root to a leaf in the tree. While studying the tree Petya can add electrons to vertices or induce random decay with synchrophasotron. Random decay is a process during which the edges of some path from the root to the random leaf of the tree are deleted. All the leaves are equiprobable. As the half-decay tree is the school property, Petya will return back the deleted edges into the tree after each decay.</p><p>After being desintegrated, the tree decomposes into connected components. Charge of each component is the total quantity of electrons placed in vertices of the component. Potential of desintegerated tree is the maximum from the charges of its connected components. Each time before inducing random decay Petya is curious about the mathematical expectation of potential of the tree after being desintegrated. </p></div><div class="input-specification"><div class="section-title">Input</div><p>First line will contain two integers <span class="tex-span"><i>h</i></span> and <span class="tex-span"><i>q</i></span> (<span class="tex-span">1 ≤ <i>h</i> ≤ 30, 1 ≤ <i>q</i> ≤ 10<sup class="upper-index">5</sup></span>). Next <span class="tex-span"><i>q</i></span> lines will contain a query of one of two types: </p><ul><li> <span class="tex-font-style-tt">add</span> <span class="tex-span"><i>v</i></span> <span class="tex-span"><i>e</i></span><p>Petya adds <span class="tex-span"><i>e</i></span> electrons to vertex number <span class="tex-span"><i>v</i></span> (<span class="tex-span">1 ≤ <i>v</i> ≤ 2<sup class="upper-index"><i>h</i> + 1</sup> - 1, 0 ≤ <i>e</i> ≤ 10<sup class="upper-index">4</sup></span>). <span class="tex-span"><i>v</i></span> and <span class="tex-span"><i>e</i></span> are integers.</p><p>The vertices of the tree are numbered in the following way: the root is numbered with 1, the children of the vertex with number <span class="tex-span"><i>x</i></span> are numbered with <span class="tex-span">2<i>x</i></span> and <span class="tex-span">2<i>x</i> + 1</span>.</p></li><li> <span class="tex-font-style-tt">decay</span><p>Petya induces tree decay. </p></li></ul></div><div class="output-specification"><div class="section-title">Output</div><p>For each query <span class="tex-font-style-tt">decay</span> solution you should output the mathematical expectation of potential of the tree after being desintegrated. 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["Heaps, binary search trees, segment trees, hash tables, etc", "Divide and Conquer", "Dynamic programming", "Mathematics including integration, differential equations, etc", "Probabilities, expected values, statistics, random variables, etc"]
["data structures", "divide and conquer", "dp", "math", "probabilities", "*2500"]
68E
68
E
en
E. Contact
<div class="problem-statement"><div class="header"><div class="title">E. Contact</div><div class="time-limit"><div class="property-title">time limit per test</div>3 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Little Petya is preparing for the first contact with aliens. He knows that alien spaceships have shapes of non-degenerate triangles and there will be exactly 4 ships. Landing platform for a ship can be made of 3 special columns located at some points of a Cartesian plane such that these 3 points form a triangle equal to the ship with respect to rotations, translations (parallel shifts along some vector) and reflections (symmetries along the edges). The ships can overlap after the landing.</p><p>Each column can be used to land more than one ship, for example, if there are two equal ships, we don't need to build 6 columns to land both ships, 3 will be enough. Petya wants to know what minimum number of columns will be enough to land all ships. </p></div><div class="input-specification"><div class="section-title">Input</div><p>Each of 4 lines will contain 6 integers <span class="tex-span"><i>x</i><sub class="lower-index">1</sub></span> <span class="tex-span"><i>y</i><sub class="lower-index">1</sub></span> <span class="tex-span"><i>x</i><sub class="lower-index">2</sub></span> <span class="tex-span"><i>y</i><sub class="lower-index">2</sub></span> <span class="tex-span"><i>x</i><sub class="lower-index">3</sub></span> <span class="tex-span"><i>y</i><sub class="lower-index">3</sub></span> (<span class="tex-span">0 ≤ <i>x</i><sub class="lower-index">1</sub>, <i>y</i><sub class="lower-index">1</sub>, <i>x</i><sub class="lower-index">2</sub>, <i>y</i><sub class="lower-index">2</sub>, <i>x</i><sub class="lower-index">3</sub>, <i>y</i><sub class="lower-index">3</sub> ≤ 20</span>), representing 3 points that describe the shape of each of 4 ships. It is guaranteed that 3 points in each line will represent a non-degenerate triangle.</p></div><div class="output-specification"><div class="section-title">Output</div><p>First line should contain minimum number of columns enough to land all spaceships.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>0 0 1 0 1 2<br/>0 0 0 2 2 2<br/>0 0 3 0 1 2<br/>0 0 3 0 2 2<br/></pre></div><div class="output"><div class="title">Output</div><pre>4<br/></pre></div><div class="input"><div class="title">Input</div><pre>0 0 0 1 1 1<br/>0 0 0 2 2 2<br/>0 0 0 5 5 5<br/>0 0 0 17 17 17<br/></pre></div><div class="output"><div class="title">Output</div><pre>9<br/></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first test case columns can be put in these points: <span class="tex-span">(0, 0), (1, 0), (3, 0), (1, 2)</span>. Note that the second ship can land using last 3 columns.</p><p>In the second test case following points can be chosen: <span class="tex-span">(0, 0), (0, 1), (1, 0), (0, 2), (2, 0), (0, 5), (5, 0), (0, 17), (17, 0)</span>. It is impossible to use less than 9 columns.</p></div></div>
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Contact</div><div class="time-limit"><div class="property-title">time limit per test</div>3 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Little Petya is preparing for the first contact with aliens. He knows that alien spaceships have shapes of non-degenerate triangles and there will be exactly 4 ships. Landing platform for a ship can be made of 3 special columns located at some points of a Cartesian plane such that these 3 points form a triangle equal to the ship with respect to rotations, translations (parallel shifts along some vector) and reflections (symmetries along the edges). The ships can overlap after the landing.</p><p>Each column can be used to land more than one ship, for example, if there are two equal ships, we don't need to build 6 columns to land both ships, 3 will be enough. Petya wants to know what minimum number of columns will be enough to land all ships. </p></div><div class="input-specification"><div class="section-title">Input</div><p>Each of 4 lines will contain 6 integers <span class="tex-span"><i>x</i><sub class="lower-index">1</sub></span> <span class="tex-span"><i>y</i><sub class="lower-index">1</sub></span> <span class="tex-span"><i>x</i><sub class="lower-index">2</sub></span> <span class="tex-span"><i>y</i><sub class="lower-index">2</sub></span> <span class="tex-span"><i>x</i><sub class="lower-index">3</sub></span> <span class="tex-span"><i>y</i><sub class="lower-index">3</sub></span> (<span class="tex-span">0 ≤ <i>x</i><sub class="lower-index">1</sub>, <i>y</i><sub class="lower-index">1</sub>, <i>x</i><sub class="lower-index">2</sub>, <i>y</i><sub class="lower-index">2</sub>, <i>x</i><sub class="lower-index">3</sub>, <i>y</i><sub class="lower-index">3</sub> ≤ 20</span>), representing 3 points that describe the shape of each of 4 ships. It is guaranteed that 3 points in each line will represent a non-degenerate triangle.</p></div><div class="output-specification"><div class="section-title">Output</div><p>First line should contain minimum number of columns enough to land all spaceships.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>0 0 1 0 1 2<br />0 0 0 2 2 2<br />0 0 3 0 1 2<br />0 0 3 0 2 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>4<br /></pre></div><div class="input"><div class="title">Input</div><pre>0 0 0 1 1 1<br />0 0 0 2 2 2<br />0 0 0 5 5 5<br />0 0 0 17 17 17<br /></pre></div><div class="output"><div class="title">Output</div><pre>9<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first test case columns can be put in these points: <span class="tex-span">(0, 0), (1, 0), (3, 0), (1, 2)</span>. Note that the second ship can land using last 3 columns.</p><p>In the second test case following points can be chosen: <span class="tex-span">(0, 0), (0, 1), (1, 0), (0, 2), (2, 0), (0, 5), (5, 0), (0, 17), (17, 0)</span>. 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["Geometry, computational geometry"]
["geometry", "*2900"]
69A
69
A
en
A. Young Physicist
<div class="problem-statement"><div class="header"><div class="title">A. Young Physicist</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>A guy named Vasya attends the final grade of a high school. One day Vasya decided to watch a match of his favorite hockey team. And, as the boy loves hockey very much, even more than physics, he forgot to do the homework. Specifically, he forgot to complete his physics tasks. Next day the teacher got very angry at Vasya and decided to teach him a lesson. He gave the lazy student a seemingly easy task: You are given an idle body in space and the forces that affect it. The body can be considered as a material point with coordinates (0; 0; 0). Vasya had only to answer whether it is in equilibrium. "Piece of cake" — thought Vasya, we need only to check if the sum of all vectors is equal to 0. So, Vasya began to solve the problem. But later it turned out that there can be lots and lots of these forces, and Vasya can not cope without your help. Help him. Write a program that determines whether a body is idle or is moving by the given vectors of forces.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains a positive integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 100</span>), then follow <span class="tex-span"><i>n</i></span> lines containing three integers each: the <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> coordinate, the <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span> coordinate and the <span class="tex-span"><i>z</i><sub class="lower-index"><i>i</i></sub></span> coordinate of the force vector, applied to the body (<span class="tex-span"> - 100 ≤ <i>x</i><sub class="lower-index"><i>i</i></sub>, <i>y</i><sub class="lower-index"><i>i</i></sub>, <i>z</i><sub class="lower-index"><i>i</i></sub> ≤ 100</span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print the word "<span class="tex-font-style-tt">YES</span>" if the body is in equilibrium, or the word "<span class="tex-font-style-tt">NO</span>" if it is not.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br/>4 1 7<br/>-2 4 -1<br/>1 -5 -3<br/></pre></div><div class="output"><div class="title">Output</div><pre>NO</pre></div><div class="input"><div class="title">Input</div><pre>3<br/>3 -1 7<br/>-5 2 -4<br/>2 -1 -3<br/></pre></div><div class="output"><div class="title">Output</div><pre>YES</pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="A" data-uuid="ps_65b352353955cae453fcc56bc1f9abc9cac8e7ee"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">A. Young Physicist</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>A guy named Vasya attends the final grade of a high school. One day Vasya decided to watch a match of his favorite hockey team. And, as the boy loves hockey very much, even more than physics, he forgot to do the homework. Specifically, he forgot to complete his physics tasks. Next day the teacher got very angry at Vasya and decided to teach him a lesson. He gave the lazy student a seemingly easy task: You are given an idle body in space and the forces that affect it. The body can be considered as a material point with coordinates (0; 0; 0). Vasya had only to answer whether it is in equilibrium. &quot;Piece of cake&quot; — thought Vasya, we need only to check if the sum of all vectors is equal to 0. So, Vasya began to solve the problem. But later it turned out that there can be lots and lots of these forces, and Vasya can not cope without your help. Help him. Write a program that determines whether a body is idle or is moving by the given vectors of forces.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains a positive integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 100</span>), then follow <span class="tex-span"><i>n</i></span> lines containing three integers each: the <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> coordinate, the <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span> coordinate and the <span class="tex-span"><i>z</i><sub class="lower-index"><i>i</i></sub></span> coordinate of the force vector, applied to the body (<span class="tex-span"> - 100 ≤ <i>x</i><sub class="lower-index"><i>i</i></sub>, <i>y</i><sub class="lower-index"><i>i</i></sub>, <i>z</i><sub class="lower-index"><i>i</i></sub> ≤ 100</span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print the word &quot;<span class="tex-font-style-tt">YES</span>&quot; 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["Implementation problems, programming technics, simulation", "Mathematics including integration, differential equations, etc"]
["implementation", "math", "*1000"]
https://codeforces.com/blog/entry/1571
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<a href="/blog/entry/120644">Codeforces Round 899 (Div. 2)</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/Misa-Misa" title="Expert Misa-Misa" class="rated-user user-blue">Misa-Misa</a> &rarr; <a href="/blog/entry/121157">Someone please help me understand this.</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/shivam565" title="Specialist shivam565" class="rated-user user-cyan">shivam565</a> &rarr; <a href="/blog/entry/108348">Total number of subarrays with sum atmost k</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> </ul> </div> <div class="bottom-links"> <table style="width:100%;"> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:right;"> <a href="/recent-actions">Detailed &rarr;</a> </td> </tr> </tbody> </table> </div> </div> </div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li><a href="/profile/map">map</a></li> <li class="current selectedLava"><a href="/blog/map">Blog</a></li> <li><a href="/teams/with/map">Teams</a></li> <li><a href="/submissions/map">Submissions</a></li> <li><a href="/groups/with/map">Groups</a></li> <li><a href="/contests/with/map">Contests</a></li> <li><a href="/contests/writer/map">Problemsetting</a></li> </ul> </div> <div style="margin-top:0;"> <div> <h3><a href="/blog/map" style="text-decoration:none;color:black !important;">map's blog</a></h3> </div> <div style="margin-top:2em;"> <div class="has-topic-id topic" topicId="1571"> <div class="title"> <a href="/blog/entry/1571"> Analysis Codeforces Beta Round #63 (Div. 2) </a> </div> <div class="info" style="position:relative;"> By&nbsp;<a href="/profile/map" title="International Master map" class="rated-user user-orange">map</a>, <span class="format-humantime" title="Mar/22/2011 21:02">13 years ago</span>, translation, <img style="position: relative;top: 5px;" src="//codeforces.org/s/81027/images/flags/24/gb.png" alt="In English" title="In English"/> <span style="position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;"> <div style="margin-top:0.25em;"> </div> </span> </div> <div class="content"> <div class="ttypography"><div><div><div><p></p><p></p><p><span lang="EN-US" style="">Problem A.</span></p> <p><span lang="EN-US" style="">In this task all you had to do was to make sure that the sum of all </span>Σ<span lang="EN-US" style="">x<sub>i</sub> is 0, the sum of all </span>Σ<span lang="EN-US" style="">y<span style="font-size: 13.0px;"><sub>i</sub></span> is 0 and that the sum of all </span>Σ<span lang="EN-US" style="">z<sub>i</sub> - 0 . </span><br /> <span lang="X-NONE" style="">We have not written that condition evidently in order that participants will have a chance to break a solution.</span><span lang="EN-US" style=""></span></p> <p><span lang="EN-US" style=""> </span></p><p><span lang="EN-US" style=""></span>Problem B.</p><p></p><p>In this problem, in fact, you should find a winner at every section. For each section, you must do a full search of all competitors to find a competitor with a minimum section time, which ran that section. Asymptotic of the solution is O(nm).</p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">Problem C.</span></p> <p><span lang="EN-US" style="">In this task, you had to update the collection of artifacts, which belong to Kostya’s friends, after each purchase . You had to set<span style="">  </span>a matrix c[i][j] - number of the j-th basic artifact that is required in order to collect the i-th component artifact. Further, one can make a matrix of composite artifacts, where a[i][j] is number of the j-th basic artifact of the i-th friend and a similar matrix b of composite artifacts, and<span style="">  </span>check whether i-th friend has any a composite artifact of O (MN) after each<span style="">  </span>i-th friend’s<span style="">  </span>purchase. Check whether one component of the artifact assembles for O (N): while checking whether the i-th friend is able to collect the j-th artifact you have to check, if there is such u, that c[j [u]&gt; a[i][u], if so, the j-th artefact will not be collected, if not, then you have to increase the b[i][j] and update the values in a[i]). </span></p> <p><span lang="EN-US" style="">So.the asymptotics of the processing of all purchases will be O (NQM). Then, we need<span style="">  </span>to make a list of artifacts for each person, keeping their quantity(a total of O (KN + KM), and sort it (a total of O (QlogQ)).</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">Problem D.</span></p> <p><span lang="EN-US" style="">This game is over, because except for a finite number (2) of reflections about the line y = x,the coordinates are changed to non-negative integer (and at least one coordinate is changed to a positive number).</span></p> <p><span lang="EN-US" style="">Algorithm for solving this problem<span style="">  </span>is DFS / BFS (states) where the state is a pair of coordinates, and two logical variables, which denote if the 1 (2) player had reflected a point about the line y = x.</span></p> <p><span lang="EN-US" style="">Total number of states is obtained by S &lt;= 4D^2 (pairs of coordinates) * 4 (Boolean variables).</span></p> <p><span lang="EN-US" style="">Processing of one state takes O (N) actions (do not forget to try to reflect the point about the line y = x, if the player had not made it earlier in the game). Thereby, we have the overall asymptotic O (ND^2), which works on C + + in less than 200ms.</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">Problem E</span></p> <p><span lang="EN-US" style="">To solve this problem you have to do a &quot;move&quot; subsegment and know :</span></p> <p><span lang="EN-US" style=""><span style=""> </span>1. The set B of numbers, meeting once, with the function of extracting the maximum for O (logN) </span></p> <p><span lang="EN-US" style="">2.The set of numbers appearing on this subsegments with keeping the number of times,that this number is found on this subsegments, with function of verifying how many times the number in this subsegments for O (logN).</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">While moving a segment from (a[i] .. a[i + k - 1]) for 1 item left (a[I + 1] .. a[I + k]) you have to:</span></p> <p><span lang="EN-US" style="">1) Check whether a[i] with a[I + k]. If yes, then there is no need to modify the set, otherwise proceed to item 2 and 3.</span></p> <p><span lang="EN-US" style="">2) Check how many times we have a[i] in the set A: if 2, then add a[i] to B, if 1, then remove it from<span style="">  </span>A and B. Do not forget to reduce the corresponding number of occurrences of a[i] in the current segment 1.</span></p> <p><span lang="EN-US" style="">3) Check, how many times we have a[I + k] in the set A: if 0, then add a[i] in the B and A, if 1, then remove it from B. Do not forget to increase the corresponding number of occurrences of a[i] the current interval to 1.</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">After that, if the set is not empty, we should take peak from it.</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">So the asymptotics of this process will be O(NlogN).</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">As such data structures<span style="">  </span>set / map(for those who use C + +) and the Cartesian tree are suitable.</span></p><p></p></div></div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/69" class="notice" style="text-decoration: none;">Codeforces Beta Round 63 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-3346-1571").click(function() { var that = this; 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line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/map"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/map"> map </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Mar/22/2011 21:02">13 years ago</span> </li> <li> <a href="/blog/entry/1571#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1571#comments"> 29 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1581"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (20)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="29594" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/P___" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/P___" title="Expert P___" class="rated-user user-blue">P___</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:40">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29594" href="?#comment-29594" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29594" class="CommentVoteFrame" data-commentRating="4" data-commentUserId="333" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+4</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29594"> <div class="moveup"> <div class="ttypography">You don't have to check reflections at all in task D. If player is in loosing position he can reflect coordinates, but the opponent (who had winnig strategy, so didn't use the reflection) also reflects.</div> </div> </div> <div class="reply info"> <a class="comment-29594 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29594 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29594"> <li> <div class="comment"> <table class="comment-table" commentId="29608" commentParentId="29594"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/rizwanhudda" style="position: relative;"> <img src='https://userpic.codeforces.org/616/avatar/255f41799f0df297.jpg'/> </a> <div><a href="/profile/rizwanhudda" title="Expert rizwanhudda" class="rated-user user-blue">rizwanhudda</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:43">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29608" href="?#comment-29608" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29594" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29608" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="616" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29608"> <div class="moveup"> <div class="ttypography">Can you please explain this?</div> </div> </div> <div class="reply info"> <a class="comment-29608 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29608 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29608"> <li> <div class="comment"> <table class="comment-table" commentId="29613" commentParentId="29608"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/riadwaw" style="position: relative;"> <img src='https://userpic.codeforces.org/8452/avatar/7b374574b05a50df.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/riadwaw" title="International Master riadwaw" class="rated-user user-orange">riadwaw</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:47">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29613" href="?#comment-29613" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29608" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29613" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="8452" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29613"> <div class="moveup"> <div class="ttypography">Lets see on game without reflects. Somebody have win strategy.<div><br /></div><div>So, in this game he should use it only after opp's reflection ad win</div></div> </div> </div> <div class="reply info"> <a class="comment-29613 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29613 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29613"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="29616" commentParentId="29608"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/P___" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/P___" title="Expert P___" class="rated-user user-blue">P___</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:50">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29616" href="?#comment-29616" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29608" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="29616" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="29616" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="333" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29616"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">Suppose that we can't make reflections, so for each reachable position you can determine whether player who starts at this position has a winning strategy (no matter what his opponent does) or he must lose no matter what he does. Suppose that the player starts in losing position, so the only rescue for him is to reflect coordinates and then his opponent starts at losing position (if a position is losing/winning, then reflected position has the same state). But since his opponent has a winning strategy without using reflections, you know that he didn't need to use reflection and can use this reflection now to make his opponent start in losing position again.</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-29616 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29616 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29616"> <li> <div class="comment"> <table class="comment-table" commentId="29637" commentParentId="29616"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/rizwanhudda" style="position: relative;"> <img src='https://userpic.codeforces.org/616/avatar/255f41799f0df297.jpg'/> </a> <div><a href="/profile/rizwanhudda" title="Expert rizwanhudda" class="rated-user user-blue">rizwanhudda</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 22:08">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29637" href="?#comment-29637" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29616" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29637" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="616" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29637"> <div class="moveup"> <div class="ttypography">Great explanation..:)</div> </div> </div> <div class="reply info"> <a class="comment-29637 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29637 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29637"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29598" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cauchyk" style="position: relative;"> <img src='https://userpic.codeforces.org/6307/avatar/1be12bd76cca6bd4.jpg'/> </a> <div><a href="/profile/cauchyk" title="Expert cauchyk" class="rated-user user-blue">cauchyk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:41">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29598" href="?#comment-29598" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="29598" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="29598" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6307" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29598"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"></div></div> </div> </div> <div class="reply info"> <a class="comment-29598 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29598 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29598"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29602" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/map" style="position: relative;"> <img src='https://userpic.codeforces.org/8362/avatar/5def203e6aa044bf.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/map" title="International Master map" class="rated-user user-orange">map</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:42">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29602" href="?#comment-29602" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29602" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="8362" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29602"> <div class="moveup"> <div class="ttypography">Yes, of course. You are absolutely right.</div> </div> </div> <div class="reply info"> <a class="comment-29602 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29602 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29602"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29614" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Anurag" style="position: relative;"> <img src='https://userpic.codeforces.org/1040/avatar/83f11106d57a9eef.jpg'/> </a> <div><a href="/profile/Anurag" title="Newbie Anurag" class="rated-user user-gray">Anurag</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:48">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29614" href="?#comment-29614" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29614" class="CommentVoteFrame" data-commentRating="5" data-commentUserId="1040" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+5</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29614"> <div class="moveup"> <div class="ttypography">For problem E , if my solution was O(n<sup>2</sup>) then it would have led to TLE?</div> </div> </div> <div class="reply info"> <a class="comment-29614 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29614 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29614"> <li> <div class="comment"> <table class="comment-table" commentId="29620" commentParentId="29614"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/logic_max" style="position: relative;"> <img src='https://userpic.codeforces.org/6829/avatar/abbf50e9dcdf31d9.jpg'/> </a> <div><a href="/profile/logic_max" title="Expert logic_max" class="rated-user user-blue">logic_max</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:53">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29620" href="?#comment-29620" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29614" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29620" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29620"> <div class="moveup"> <div class="ttypography">Yes.</div> </div> </div> <div class="reply info"> <a class="comment-29620 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29620 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29620"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="29703" commentParentId="29614"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Shafaet" style="position: relative;"> <img src='https://userpic.codeforces.org/5137/avatar/bcd103c3d3c35548.jpg'/> </a> <div><a href="/profile/Shafaet" title="Expert Shafaet" class="rated-user user-blue">Shafaet</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/23/2011 15:06">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29703" href="?#comment-29703" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29614" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29703" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5137" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29703"> <div class="moveup"> <div class="ttypography">n=10^5,so n^2 will certainly lead to TLE. <br />Here is my approach:<br /><br />Process first K numbers at once. Store frequencies of each number in hash table and maintain a set which contain values which occurred only once. then process rest of the numbers while taking input. reduce frequency of i-K th number, modify the set according to frequency. <br /><br />Suppose input is:<br />6 3<br />1<br />1<br />2<br />6<br />6<br />First i will process first 3 numbers. so the set will be {2} and map will be freq[1]=2,freq[2]=1. <br />When i get 4th number 6,i will reduce freq of 1st number. freq[1] will become 1 from 2. as it has become 1,the set will be {1,2,6}(as i got 6 for the first time). <br /><br />Then i get 5th number 6,i will reduce freq of 2nd number. freq[1] is now 0. as it went 0 from 1, i need to remove it from set too. so the set becomes{2}(i will remove 6 too as i got it 2 times now).<br /><br />Every time print the largest number from set. If the set is empty print &quot;nothing&quot;. i've used c++ stl &lt;set&gt;.</div> </div> </div> <div class="reply info"> <a class="comment-29703 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29703 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29703"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29632" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cauchyk" style="position: relative;"> <img src='https://userpic.codeforces.org/6307/avatar/1be12bd76cca6bd4.jpg'/> </a> <div><a href="/profile/cauchyk" title="Expert cauchyk" class="rated-user user-blue">cauchyk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 22:02">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29632" href="?#comment-29632" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29632" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6307" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29632"> <div class="moveup"> <div class="ttypography"><div style="text-align: left;"><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 13.0px;">please check my submission for problem C id: 350527 it says answer mismatch in line 2 but it does not...</span></div></div> </div> </div> <div class="reply info"> <a class="comment-29632 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29632 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29632"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29642" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/VladBelous" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/VladBelous" title="Expert VladBelous" class="rated-user user-blue">VladBelous</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 22:14">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29642" href="?#comment-29642" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29642" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3894" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29642"> <div class="moveup"> <div class="ttypography"><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">About D:</span><div><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">&quot;Thereby, we have the overall asymptotic O (ND^2), which works on C + + in less than 600ms&quot;</span><div><font face="verdana, arial, sans-serif"><span style="font-size: 12.0px;line-height: 20.0px;"><br /></span></font></div></span></div><div><font face="verdana, arial, sans-serif"><span style="font-size: 12.0px;line-height: 20.0px;">My solution used the same complexity, but ran in 80ms. Reason (I think) is that once I find a move to a losing position, I declare current position as winning and return (i.e. no need to look at other moves).</span></font></div><div><font face="verdana, arial, sans-serif"><span style="font-size: 12.0px;line-height: 20.0px;">This is trivial optimization, but I think an important one, because some Java solutions with </span></font><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">O(ND^2) failed due to TLE. (600ms in C++ does not leave a good margin)</span></div><div><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><br /></span></div></div> </div> </div> <div class="reply info"> <a class="comment-29642 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29642 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29642"> <li> <div class="comment"> <table class="comment-table" commentId="29644" commentParentId="29642"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/map" style="position: relative;"> <img src='https://userpic.codeforces.org/8362/avatar/5def203e6aa044bf.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/map" title="International Master map" class="rated-user user-orange">map</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 22:18">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29644" href="?#comment-29644" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29642" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29644" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="8362" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29644"> <div class="moveup"> <div class="ttypography">200ms. T<span style="font-family: arial , sans-serif;font-size: 13.0px;white-space: nowrap;">yping error. We have same correct JAVA solution.</span></div> </div> </div> <div class="reply info"> <a class="comment-29644 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29644 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29644"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29738" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cornflow" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/cornflow" title="Expert cornflow" class="rated-user user-blue">cornflow</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/23/2011 20:09">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29738" href="?#comment-29738" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="29738" revisionCount="3" revision="3"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">3</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="29738" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14075" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29738"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><p>When I changed &quot;double&quot; to &quot;int&quot; in task E, I've got AC (with double - WA). But I can't find any words in problem statement about representation of numbers in answer. Also I can't find nothing in problem statement to determine if numbers are integers or not...</p></div> </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-29738 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29738 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29738"> <li> <div class="comment"> <table class="comment-table" commentId="29834" commentParentId="29738"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/timmy" style="position: relative;"> <img src='https://userpic.codeforces.org/2446/avatar/d9bd36d3627fc50e.jpg'/> </a> <div><a href="/profile/timmy" title="Expert timmy" class="rated-user user-blue">timmy</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/25/2011 15:27">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29834" href="?#comment-29834" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29738" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29834" class="CommentVoteFrame" class="negative-comment-vote" data-commentRating="-11" data-commentUserId="2446" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">-11</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29834"> <div class="moveup"> <div class="ttypography"><p>ATTENTION! THIS CONTEST SHOULD BE UNRATED!</p><p>Maybe now you will read my message carefully :) I think that Corny is right. His solution works just after replacing &quot;double&quot; to &quot;int&quot;.</p></div> </div> </div> <div class="reply info"> <a class="comment-29834 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29834 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29834"> <li> <div class="comment"> <table class="comment-table" commentId="29903" commentParentId="29834"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cornflow" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/cornflow" title="Expert cornflow" class="rated-user user-blue">cornflow</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/26/2011 11:01">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29903" href="?#comment-29903" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29834" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29903" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14075" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29903"> <div class="moveup"> <div class="ttypography">I've found problem. It with presentation, but it's my fault. When answer is 994790178 I write 9.9479e+008. I should be more careful next time.</div> </div> </div> <div class="reply info"> <a class="comment-29903 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29903 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29903"> <li> <div class="comment"> <table class="comment-table" commentId="29907" commentParentId="29903"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/timmy" style="position: relative;"> <img src='https://userpic.codeforces.org/2446/avatar/d9bd36d3627fc50e.jpg'/> </a> <div><a href="/profile/timmy" title="Expert timmy" class="rated-user user-blue">timmy</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/26/2011 12:19">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29907" href="?#comment-29907" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29903" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29907" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2446" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29907"> <div class="moveup"> <div class="ttypography"><p>Really? Ok, try to output floating-point numbers with 1e-10 precision.</p><p>I think result would be the same :) </p></div> </div> </div> <div class="reply info"> <a class="comment-29907 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29907 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29907"> <li> <div class="comment"> <table class="comment-table" commentId="29946" commentParentId="29907"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cornflow" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/cornflow" title="Expert cornflow" class="rated-user user-blue">cornflow</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/26/2011 18:38">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29946" href="?#comment-29946" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29907" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29946" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14075" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29946"> <div class="moveup"> <div class="ttypography">I've tried to output correct floating-point numbers. It got WA. So maybe statement should be more precise.</div> </div> </div> <div class="reply info"> <a class="comment-29946 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29946 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29946"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29748" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mostafa_fahim" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/mostafa_fahim" title="Expert mostafa_fahim" class="rated-user user-blue">mostafa_fahim</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/23/2011 21:57">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29748" href="?#comment-29748" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29748" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5382" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29748"> <div class="moveup"> <div class="ttypography">About Task C <div>for this input </div><div><span style="font-family: verdana , arial , sans-serif;font-size: 11.0px;"><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">1 1 2 2 a b: a 2 c: a 1 1 a 1 a  </pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">I am printing </pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><span style="font-family: verdana , arial , sans-serif;white-space: normal;"><pre class="output" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">1 </pre></span>b 1</pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">while the answer is</pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><span style="font-family: verdana , arial , sans-serif;white-space: normal;"><pre class="answer" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">1 </pre></span>c 2</pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">I can't see why my output is wrong (I think both outputs are correct in this case) <br /></pre></span></div></div> </div> </div> <div class="reply info"> <a class="comment-29748 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29748 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29748"> <li> <div class="comment"> <table class="comment-table" commentId="29774" commentParentId="29748"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/adavydow" style="position: relative;"> <img src='https://userpic.codeforces.org/2385/avatar/11fa80222a24e45c.jpg'/> </a> <div><a href="/profile/adavydow" title="Master adavydow" class="rated-user user-orange">adavydow</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/23/2011 22:55">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29774" href="?#comment-29774" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29748" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29774" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="2385" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29774"> <div class="moveup"> <div class="ttypography">&quot;It is guaranteed that after the <span class="tex-span"><i>i</i></span>-th purchase no more than one opportunity to collect the composite artifact appears. If such an opportunity arose, the hero must take advantage of it.&quot;<br />So your solution is wrong. After buyin first 'a' artifact player has oportunity to build artifact 'c' but in your solution he didn't take advantage of it, he waited for the second 'a' to compose 'b'</div> </div> </div> <div class="reply info"> <a class="comment-29774 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29774 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29774"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1581" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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69B
69
B
en
B. Bets
<div class="problem-statement"><div class="header"><div class="title">B. Bets</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>In Chelyabinsk lives a much respected businessman Nikita with a strange nickname "Boss". Once Nikita decided to go with his friend Alex to the Summer Biathlon World Cup. Nikita, as a very important person, received a token which allows to place bets on each section no more than on one competitor.</p><p>To begin with friends learned the rules: in the race there are <span class="tex-span"><i>n</i></span> sections of equal length and <span class="tex-span"><i>m</i></span> participants. The participants numbered from <span class="tex-span">1</span> to <span class="tex-span"><i>m</i></span>. About each participant the following is known:</p><ul><li> <span class="tex-span"><i>l</i><sub class="lower-index"><i>i</i></sub></span> — the number of the starting section, </li><li> <span class="tex-span"><i>r</i><sub class="lower-index"><i>i</i></sub></span> — the number of the finishing section (<span class="tex-span"><i>l</i><sub class="lower-index"><i>i</i></sub> ≤ <i>r</i><sub class="lower-index"><i>i</i></sub></span>),</li><li> <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub></span> — the time a biathlete needs to complete an section of the path,</li><li> <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span> — the profit in roubles. If the <span class="tex-span"><i>i</i></span>-th sportsman wins on one of the sections, the profit will be given to the man who had placed a bet on that sportsman.</li></ul> <p>The <span class="tex-span"><i>i</i></span>-th biathlete passes the sections from <span class="tex-span"><i>l</i><sub class="lower-index"><i>i</i></sub></span> to <span class="tex-span"><i>r</i><sub class="lower-index"><i>i</i></sub></span> inclusive. The competitor runs the whole way in <span class="tex-span">(<i>r</i><sub class="lower-index"><i>i</i></sub> - <i>l</i><sub class="lower-index"><i>i</i></sub> + 1)·<i>t</i><sub class="lower-index"><i>i</i></sub></span> time units. It takes him exactly <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub></span> time units to pass each section. In case of the athlete's victory on <span class="tex-span"><i>k</i></span> sections the man who has betted on him receives <span class="tex-span"><i>k</i>·<i>c</i><sub class="lower-index"><i>i</i></sub></span> roubles.</p><p>In each section the winner is determined <span class="tex-font-style-bf">independently</span> as follows: if there is at least one biathlete running this in this section, then among all of them the winner is the one who has ran this section in minimum time (spent minimum time passing this section). In case of equality of times the athlete with the smaller index number wins. If there are no participants in this section, then the winner in this section in not determined. We have to say that in the summer biathlon all the participants are moving at a constant speed.</p><p>We should also add that Nikita can bet on each section and on any contestant running in this section.</p><p>Help the friends find the maximum possible profit.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>m</i></span> (<span class="tex-span">1 ≤ <i>n</i>, <i>m</i> ≤ 100</span>). Then follow <span class="tex-span"><i>m</i></span> lines, each containing 4 integers <span class="tex-span"><i>l</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>r</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>l</i><sub class="lower-index"><i>i</i></sub> ≤ <i>r</i><sub class="lower-index"><i>i</i></sub> ≤ <i>n</i></span>, <span class="tex-span">1 ≤ <i>t</i><sub class="lower-index"><i>i</i></sub>, <i>c</i><sub class="lower-index"><i>i</i></sub> ≤ 1000</span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single integer, the maximal profit in roubles that the friends can get. In each of <span class="tex-span"><i>n</i></span> sections it is not allowed to place bets on more than one sportsman.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>4 4<br/>1 4 20 5<br/>1 3 21 10<br/>3 3 4 30<br/>3 4 4 20<br/></pre></div><div class="output"><div class="title">Output</div><pre>60</pre></div><div class="input"><div class="title">Input</div><pre>8 4<br/>1 5 24 10<br/>2 4 6 15<br/>4 6 30 50<br/>6 7 4 20<br/></pre></div><div class="output"><div class="title">Output</div><pre>105</pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first test the optimal bet is: in the 1-2 sections on biathlete 1, in section 3 on biathlete 3, in section 4 on biathlete 4. Total: profit of 5 rubles for 1 section, the profit of 5 rubles for 2 section, profit of 30 rubles for a 3 section, profit of 20 rubles for 4 section. Total profit 60 rubles.</p><p>In the second test the optimal bet is: on 1 and 5 sections on biathlete 1, in the 2-4 sections on biathlete 2, in the 6-7 sections on athlete 4. There is no winner in the 8 section. Total: profit of 10 rubles for 1 section, the profit of 15 rubles for 2,3,4 section, profit of 10 rubles for a 5 section, profit of 20 rubles for 6, 7 section. Total profit 105 rubles.</p></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/69">Codeforces Beta Round 63 (Div. 2)</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? Just register for practice and you will be able to submit solutions. </div> <div style="text-align:center;margin:1em;"> <form action="" method="post"><input type='hidden' name='csrf_token' value='39fe9a17ce4bd0d197dc66bcf199b61b'/> <input type="hidden" name="action" value="registerForPractice"/> <input type="submit" name="submit" value="Register for practice" style="padding:0 0.5em;"> </form> </div> </div> </div> <div class="roundbox sidebox ContestVirtualFrame borderTopRound " style=""> <div class="caption titled">&rarr; Virtual participation <i class="sidebar-caption-icon las la-angle-down"></i> <div class="top-links"> </div> </div> <div style=" " data-page-url="/data/sidebarFrames" > <div style="margin:1em;font-size:0.8em;"> Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests. If you've seen these problems, a virtual contest is not for you - solve these problems in the archive. If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="B" data-uuid="ps_fb2018e99680d9ce97dd6cd0b345d3f5602be7e1"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">B. Bets</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>In Chelyabinsk lives a much respected businessman Nikita with a strange nickname &quot;Boss&quot;. Once Nikita decided to go with his friend Alex to the Summer Biathlon World Cup. Nikita, as a very important person, received a token which allows to place bets on each section no more than on one competitor.</p><p>To begin with friends learned the rules: in the race there are <span class="tex-span"><i>n</i></span> sections of equal length and <span class="tex-span"><i>m</i></span> participants. The participants numbered from <span class="tex-span">1</span> to <span class="tex-span"><i>m</i></span>. About each participant the following is known:</p><ul><li> <span class="tex-span"><i>l</i><sub class="lower-index"><i>i</i></sub></span> — the number of the starting section, </li><li> <span class="tex-span"><i>r</i><sub class="lower-index"><i>i</i></sub></span> — the number of the finishing section (<span class="tex-span"><i>l</i><sub class="lower-index"><i>i</i></sub> ≤ <i>r</i><sub class="lower-index"><i>i</i></sub></span>),</li><li> <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub></span> — the time a biathlete needs to complete an section of the path,</li><li> <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span> — the profit in roubles. If the <span class="tex-span"><i>i</i></span>-th sportsman wins on one of the sections, the profit will be given to the man who had placed a bet on that sportsman.</li></ul> <p>The <span class="tex-span"><i>i</i></span>-th biathlete passes the sections from <span class="tex-span"><i>l</i><sub class="lower-index"><i>i</i></sub></span> to <span class="tex-span"><i>r</i><sub class="lower-index"><i>i</i></sub></span> inclusive. The competitor runs the whole way in <span class="tex-span">(<i>r</i><sub class="lower-index"><i>i</i></sub> - <i>l</i><sub class="lower-index"><i>i</i></sub> + 1)·<i>t</i><sub class="lower-index"><i>i</i></sub></span> time units. It takes him exactly <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub></span> time units to pass each section. In case of the athlete's victory on <span class="tex-span"><i>k</i></span> sections the man who has betted on him receives <span class="tex-span"><i>k</i>·<i>c</i><sub class="lower-index"><i>i</i></sub></span> roubles.</p><p>In each section the winner is determined <span class="tex-font-style-bf">independently</span> as follows: if there is at least one biathlete running this in this section, then among all of them the winner is the one who has ran this section in minimum time (spent minimum time passing this section). In case of equality of times the athlete with the smaller index number wins. If there are no participants in this section, then the winner in this section in not determined. We have to say that in the summer biathlon all the participants are moving at a constant speed.</p><p>We should also add that Nikita can bet on each section and on any contestant running in this section.</p><p>Help the friends find the maximum possible profit.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>m</i></span> (<span class="tex-span">1 ≤ <i>n</i>, <i>m</i> ≤ 100</span>). Then follow <span class="tex-span"><i>m</i></span> lines, each containing 4 integers <span class="tex-span"><i>l</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>r</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>l</i><sub class="lower-index"><i>i</i></sub> ≤ <i>r</i><sub class="lower-index"><i>i</i></sub> ≤ <i>n</i></span>, <span class="tex-span">1 ≤ <i>t</i><sub class="lower-index"><i>i</i></sub>, <i>c</i><sub class="lower-index"><i>i</i></sub> ≤ 1000</span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single integer, the maximal profit in roubles that the friends can get. In each of <span class="tex-span"><i>n</i></span> sections it is not allowed to place bets on more than one sportsman.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>4 4<br />1 4 20 5<br />1 3 21 10<br />3 3 4 30<br />3 4 4 20<br /></pre></div><div class="output"><div class="title">Output</div><pre>60</pre></div><div class="input"><div class="title">Input</div><pre>8 4<br />1 5 24 10<br />2 4 6 15<br />4 6 30 50<br />6 7 4 20<br /></pre></div><div class="output"><div class="title">Output</div><pre>105</pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first test the optimal bet is: in the 1-2 sections on biathlete 1, in section 3 on biathlete 3, in section 4 on biathlete 4. Total: profit of 5 rubles for 1 section, the profit of 5 rubles for 2 section, profit of 30 rubles for a 3 section, profit of 20 rubles for 4 section. Total profit 60 rubles.</p><p>In the second test the optimal bet is: on 1 and 5 sections on biathlete 1, in the 2-4 sections on biathlete 2, in the 6-7 sections on athlete 4. There is no winner in the 8 section. Total: profit of 10 rubles for 1 section, the profit of 15 rubles for 2,3,4 section, profit of 10 rubles for a 5 section, profit of 20 rubles for 6, 7 section. 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["Greedy algorithms", "Implementation problems, programming technics, simulation"]
["greedy", "implementation", "*1200"]
https://codeforces.com/blog/entry/1571
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<a href="/blog/entry/120644">Codeforces Round 899 (Div. 2)</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/Misa-Misa" title="Expert Misa-Misa" class="rated-user user-blue">Misa-Misa</a> &rarr; <a href="/blog/entry/121157">Someone please help me understand this.</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/shivam565" title="Specialist shivam565" class="rated-user user-cyan">shivam565</a> &rarr; <a href="/blog/entry/108348">Total number of subarrays with sum atmost k</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> </ul> </div> <div class="bottom-links"> <table style="width:100%;"> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:right;"> <a href="/recent-actions">Detailed &rarr;</a> </td> </tr> </tbody> </table> </div> </div> </div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li><a href="/profile/map">map</a></li> <li class="current selectedLava"><a href="/blog/map">Blog</a></li> <li><a href="/teams/with/map">Teams</a></li> <li><a href="/submissions/map">Submissions</a></li> <li><a href="/groups/with/map">Groups</a></li> <li><a href="/contests/with/map">Contests</a></li> <li><a href="/contests/writer/map">Problemsetting</a></li> </ul> </div> <div style="margin-top:0;"> <div> <h3><a href="/blog/map" style="text-decoration:none;color:black !important;">map's blog</a></h3> </div> <div style="margin-top:2em;"> <div class="has-topic-id topic" topicId="1571"> <div class="title"> <a href="/blog/entry/1571"> Analysis Codeforces Beta Round #63 (Div. 2) </a> </div> <div class="info" style="position:relative;"> By&nbsp;<a href="/profile/map" title="International Master map" class="rated-user user-orange">map</a>, <span class="format-humantime" title="Mar/22/2011 21:02">13 years ago</span>, translation, <img style="position: relative;top: 5px;" src="//codeforces.org/s/81027/images/flags/24/gb.png" alt="In English" title="In English"/> <span style="position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;"> <div style="margin-top:0.25em;"> </div> </span> </div> <div class="content"> <div class="ttypography"><div><div><div><p></p><p></p><p><span lang="EN-US" style="">Problem A.</span></p> <p><span lang="EN-US" style="">In this task all you had to do was to make sure that the sum of all </span>Σ<span lang="EN-US" style="">x<sub>i</sub> is 0, the sum of all </span>Σ<span lang="EN-US" style="">y<span style="font-size: 13.0px;"><sub>i</sub></span> is 0 and that the sum of all </span>Σ<span lang="EN-US" style="">z<sub>i</sub> - 0 . </span><br /> <span lang="X-NONE" style="">We have not written that condition evidently in order that participants will have a chance to break a solution.</span><span lang="EN-US" style=""></span></p> <p><span lang="EN-US" style=""> </span></p><p><span lang="EN-US" style=""></span>Problem B.</p><p></p><p>In this problem, in fact, you should find a winner at every section. For each section, you must do a full search of all competitors to find a competitor with a minimum section time, which ran that section. Asymptotic of the solution is O(nm).</p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">Problem C.</span></p> <p><span lang="EN-US" style="">In this task, you had to update the collection of artifacts, which belong to Kostya’s friends, after each purchase . You had to set<span style="">  </span>a matrix c[i][j] - number of the j-th basic artifact that is required in order to collect the i-th component artifact. Further, one can make a matrix of composite artifacts, where a[i][j] is number of the j-th basic artifact of the i-th friend and a similar matrix b of composite artifacts, and<span style="">  </span>check whether i-th friend has any a composite artifact of O (MN) after each<span style="">  </span>i-th friend’s<span style="">  </span>purchase. Check whether one component of the artifact assembles for O (N): while checking whether the i-th friend is able to collect the j-th artifact you have to check, if there is such u, that c[j [u]&gt; a[i][u], if so, the j-th artefact will not be collected, if not, then you have to increase the b[i][j] and update the values in a[i]). </span></p> <p><span lang="EN-US" style="">So.the asymptotics of the processing of all purchases will be O (NQM). Then, we need<span style="">  </span>to make a list of artifacts for each person, keeping their quantity(a total of O (KN + KM), and sort it (a total of O (QlogQ)).</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">Problem D.</span></p> <p><span lang="EN-US" style="">This game is over, because except for a finite number (2) of reflections about the line y = x,the coordinates are changed to non-negative integer (and at least one coordinate is changed to a positive number).</span></p> <p><span lang="EN-US" style="">Algorithm for solving this problem<span style="">  </span>is DFS / BFS (states) where the state is a pair of coordinates, and two logical variables, which denote if the 1 (2) player had reflected a point about the line y = x.</span></p> <p><span lang="EN-US" style="">Total number of states is obtained by S &lt;= 4D^2 (pairs of coordinates) * 4 (Boolean variables).</span></p> <p><span lang="EN-US" style="">Processing of one state takes O (N) actions (do not forget to try to reflect the point about the line y = x, if the player had not made it earlier in the game). Thereby, we have the overall asymptotic O (ND^2), which works on C + + in less than 200ms.</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">Problem E</span></p> <p><span lang="EN-US" style="">To solve this problem you have to do a &quot;move&quot; subsegment and know :</span></p> <p><span lang="EN-US" style=""><span style=""> </span>1. The set B of numbers, meeting once, with the function of extracting the maximum for O (logN) </span></p> <p><span lang="EN-US" style="">2.The set of numbers appearing on this subsegments with keeping the number of times,that this number is found on this subsegments, with function of verifying how many times the number in this subsegments for O (logN).</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">While moving a segment from (a[i] .. a[i + k - 1]) for 1 item left (a[I + 1] .. a[I + k]) you have to:</span></p> <p><span lang="EN-US" style="">1) Check whether a[i] with a[I + k]. If yes, then there is no need to modify the set, otherwise proceed to item 2 and 3.</span></p> <p><span lang="EN-US" style="">2) Check how many times we have a[i] in the set A: if 2, then add a[i] to B, if 1, then remove it from<span style="">  </span>A and B. Do not forget to reduce the corresponding number of occurrences of a[i] in the current segment 1.</span></p> <p><span lang="EN-US" style="">3) Check, how many times we have a[I + k] in the set A: if 0, then add a[i] in the B and A, if 1, then remove it from B. Do not forget to increase the corresponding number of occurrences of a[i] the current interval to 1.</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">After that, if the set is not empty, we should take peak from it.</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">So the asymptotics of this process will be O(NlogN).</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">As such data structures<span style="">  </span>set / map(for those who use C + +) and the Cartesian tree are suitable.</span></p><p></p></div></div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/69" class="notice" style="text-decoration: none;">Codeforces Beta Round 63 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-3346-1571").click(function() { var that = this; 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line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/map"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/map"> map </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Mar/22/2011 21:02">13 years ago</span> </li> <li> <a href="/blog/entry/1571#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1571#comments"> 29 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1581"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (20)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="29594" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/P___" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/P___" title="Expert P___" class="rated-user user-blue">P___</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:40">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29594" href="?#comment-29594" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29594" class="CommentVoteFrame" data-commentRating="4" data-commentUserId="333" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+4</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29594"> <div class="moveup"> <div class="ttypography">You don't have to check reflections at all in task D. If player is in loosing position he can reflect coordinates, but the opponent (who had winnig strategy, so didn't use the reflection) also reflects.</div> </div> </div> <div class="reply info"> <a class="comment-29594 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29594 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29594"> <li> <div class="comment"> <table class="comment-table" commentId="29608" commentParentId="29594"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/rizwanhudda" style="position: relative;"> <img src='https://userpic.codeforces.org/616/avatar/255f41799f0df297.jpg'/> </a> <div><a href="/profile/rizwanhudda" title="Expert rizwanhudda" class="rated-user user-blue">rizwanhudda</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:43">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29608" href="?#comment-29608" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29594" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29608" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="616" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29608"> <div class="moveup"> <div class="ttypography">Can you please explain this?</div> </div> </div> <div class="reply info"> <a class="comment-29608 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29608 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29608"> <li> <div class="comment"> <table class="comment-table" commentId="29613" commentParentId="29608"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/riadwaw" style="position: relative;"> <img src='https://userpic.codeforces.org/8452/avatar/7b374574b05a50df.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/riadwaw" title="International Master riadwaw" class="rated-user user-orange">riadwaw</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:47">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29613" href="?#comment-29613" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29608" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29613" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="8452" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29613"> <div class="moveup"> <div class="ttypography">Lets see on game without reflects. Somebody have win strategy.<div><br /></div><div>So, in this game he should use it only after opp's reflection ad win</div></div> </div> </div> <div class="reply info"> <a class="comment-29613 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29613 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29613"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="29616" commentParentId="29608"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/P___" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/P___" title="Expert P___" class="rated-user user-blue">P___</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:50">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29616" href="?#comment-29616" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29608" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="29616" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="29616" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="333" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29616"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">Suppose that we can't make reflections, so for each reachable position you can determine whether player who starts at this position has a winning strategy (no matter what his opponent does) or he must lose no matter what he does. Suppose that the player starts in losing position, so the only rescue for him is to reflect coordinates and then his opponent starts at losing position (if a position is losing/winning, then reflected position has the same state). But since his opponent has a winning strategy without using reflections, you know that he didn't need to use reflection and can use this reflection now to make his opponent start in losing position again.</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-29616 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29616 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29616"> <li> <div class="comment"> <table class="comment-table" commentId="29637" commentParentId="29616"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/rizwanhudda" style="position: relative;"> <img src='https://userpic.codeforces.org/616/avatar/255f41799f0df297.jpg'/> </a> <div><a href="/profile/rizwanhudda" title="Expert rizwanhudda" class="rated-user user-blue">rizwanhudda</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 22:08">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29637" href="?#comment-29637" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29616" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29637" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="616" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29637"> <div class="moveup"> <div class="ttypography">Great explanation..:)</div> </div> </div> <div class="reply info"> <a class="comment-29637 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29637 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29637"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29598" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cauchyk" style="position: relative;"> <img src='https://userpic.codeforces.org/6307/avatar/1be12bd76cca6bd4.jpg'/> </a> <div><a href="/profile/cauchyk" title="Expert cauchyk" class="rated-user user-blue">cauchyk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:41">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29598" href="?#comment-29598" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="29598" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="29598" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6307" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29598"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"></div></div> </div> </div> <div class="reply info"> <a class="comment-29598 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29598 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29598"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29602" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/map" style="position: relative;"> <img src='https://userpic.codeforces.org/8362/avatar/5def203e6aa044bf.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/map" title="International Master map" class="rated-user user-orange">map</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:42">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29602" href="?#comment-29602" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29602" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="8362" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29602"> <div class="moveup"> <div class="ttypography">Yes, of course. You are absolutely right.</div> </div> </div> <div class="reply info"> <a class="comment-29602 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29602 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29602"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29614" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Anurag" style="position: relative;"> <img src='https://userpic.codeforces.org/1040/avatar/83f11106d57a9eef.jpg'/> </a> <div><a href="/profile/Anurag" title="Newbie Anurag" class="rated-user user-gray">Anurag</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:48">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29614" href="?#comment-29614" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29614" class="CommentVoteFrame" data-commentRating="5" data-commentUserId="1040" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+5</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29614"> <div class="moveup"> <div class="ttypography">For problem E , if my solution was O(n<sup>2</sup>) then it would have led to TLE?</div> </div> </div> <div class="reply info"> <a class="comment-29614 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29614 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29614"> <li> <div class="comment"> <table class="comment-table" commentId="29620" commentParentId="29614"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/logic_max" style="position: relative;"> <img src='https://userpic.codeforces.org/6829/avatar/abbf50e9dcdf31d9.jpg'/> </a> <div><a href="/profile/logic_max" title="Expert logic_max" class="rated-user user-blue">logic_max</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:53">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29620" href="?#comment-29620" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29614" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29620" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29620"> <div class="moveup"> <div class="ttypography">Yes.</div> </div> </div> <div class="reply info"> <a class="comment-29620 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29620 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29620"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="29703" commentParentId="29614"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Shafaet" style="position: relative;"> <img src='https://userpic.codeforces.org/5137/avatar/bcd103c3d3c35548.jpg'/> </a> <div><a href="/profile/Shafaet" title="Expert Shafaet" class="rated-user user-blue">Shafaet</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/23/2011 15:06">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29703" href="?#comment-29703" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29614" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29703" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5137" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29703"> <div class="moveup"> <div class="ttypography">n=10^5,so n^2 will certainly lead to TLE. <br />Here is my approach:<br /><br />Process first K numbers at once. Store frequencies of each number in hash table and maintain a set which contain values which occurred only once. then process rest of the numbers while taking input. reduce frequency of i-K th number, modify the set according to frequency. <br /><br />Suppose input is:<br />6 3<br />1<br />1<br />2<br />6<br />6<br />First i will process first 3 numbers. so the set will be {2} and map will be freq[1]=2,freq[2]=1. <br />When i get 4th number 6,i will reduce freq of 1st number. freq[1] will become 1 from 2. as it has become 1,the set will be {1,2,6}(as i got 6 for the first time). <br /><br />Then i get 5th number 6,i will reduce freq of 2nd number. freq[1] is now 0. as it went 0 from 1, i need to remove it from set too. so the set becomes{2}(i will remove 6 too as i got it 2 times now).<br /><br />Every time print the largest number from set. If the set is empty print &quot;nothing&quot;. i've used c++ stl &lt;set&gt;.</div> </div> </div> <div class="reply info"> <a class="comment-29703 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29703 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29703"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29632" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cauchyk" style="position: relative;"> <img src='https://userpic.codeforces.org/6307/avatar/1be12bd76cca6bd4.jpg'/> </a> <div><a href="/profile/cauchyk" title="Expert cauchyk" class="rated-user user-blue">cauchyk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 22:02">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29632" href="?#comment-29632" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29632" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6307" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29632"> <div class="moveup"> <div class="ttypography"><div style="text-align: left;"><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 13.0px;">please check my submission for problem C id: 350527 it says answer mismatch in line 2 but it does not...</span></div></div> </div> </div> <div class="reply info"> <a class="comment-29632 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29632 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29632"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29642" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/VladBelous" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/VladBelous" title="Expert VladBelous" class="rated-user user-blue">VladBelous</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 22:14">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29642" href="?#comment-29642" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29642" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3894" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29642"> <div class="moveup"> <div class="ttypography"><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">About D:</span><div><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">&quot;Thereby, we have the overall asymptotic O (ND^2), which works on C + + in less than 600ms&quot;</span><div><font face="verdana, arial, sans-serif"><span style="font-size: 12.0px;line-height: 20.0px;"><br /></span></font></div></span></div><div><font face="verdana, arial, sans-serif"><span style="font-size: 12.0px;line-height: 20.0px;">My solution used the same complexity, but ran in 80ms. Reason (I think) is that once I find a move to a losing position, I declare current position as winning and return (i.e. no need to look at other moves).</span></font></div><div><font face="verdana, arial, sans-serif"><span style="font-size: 12.0px;line-height: 20.0px;">This is trivial optimization, but I think an important one, because some Java solutions with </span></font><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">O(ND^2) failed due to TLE. (600ms in C++ does not leave a good margin)</span></div><div><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><br /></span></div></div> </div> </div> <div class="reply info"> <a class="comment-29642 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29642 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29642"> <li> <div class="comment"> <table class="comment-table" commentId="29644" commentParentId="29642"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/map" style="position: relative;"> <img src='https://userpic.codeforces.org/8362/avatar/5def203e6aa044bf.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/map" title="International Master map" class="rated-user user-orange">map</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 22:18">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29644" href="?#comment-29644" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29642" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29644" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="8362" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29644"> <div class="moveup"> <div class="ttypography">200ms. T<span style="font-family: arial , sans-serif;font-size: 13.0px;white-space: nowrap;">yping error. We have same correct JAVA solution.</span></div> </div> </div> <div class="reply info"> <a class="comment-29644 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29644 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29644"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29738" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cornflow" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/cornflow" title="Expert cornflow" class="rated-user user-blue">cornflow</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/23/2011 20:09">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29738" href="?#comment-29738" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="29738" revisionCount="3" revision="3"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">3</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="29738" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14075" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29738"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><p>When I changed &quot;double&quot; to &quot;int&quot; in task E, I've got AC (with double - WA). But I can't find any words in problem statement about representation of numbers in answer. Also I can't find nothing in problem statement to determine if numbers are integers or not...</p></div> </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-29738 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29738 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29738"> <li> <div class="comment"> <table class="comment-table" commentId="29834" commentParentId="29738"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/timmy" style="position: relative;"> <img src='https://userpic.codeforces.org/2446/avatar/d9bd36d3627fc50e.jpg'/> </a> <div><a href="/profile/timmy" title="Expert timmy" class="rated-user user-blue">timmy</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/25/2011 15:27">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29834" href="?#comment-29834" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29738" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29834" class="CommentVoteFrame" class="negative-comment-vote" data-commentRating="-11" data-commentUserId="2446" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">-11</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29834"> <div class="moveup"> <div class="ttypography"><p>ATTENTION! THIS CONTEST SHOULD BE UNRATED!</p><p>Maybe now you will read my message carefully :) I think that Corny is right. His solution works just after replacing &quot;double&quot; to &quot;int&quot;.</p></div> </div> </div> <div class="reply info"> <a class="comment-29834 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29834 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29834"> <li> <div class="comment"> <table class="comment-table" commentId="29903" commentParentId="29834"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cornflow" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/cornflow" title="Expert cornflow" class="rated-user user-blue">cornflow</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/26/2011 11:01">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29903" href="?#comment-29903" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29834" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29903" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14075" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29903"> <div class="moveup"> <div class="ttypography">I've found problem. It with presentation, but it's my fault. When answer is 994790178 I write 9.9479e+008. I should be more careful next time.</div> </div> </div> <div class="reply info"> <a class="comment-29903 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29903 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29903"> <li> <div class="comment"> <table class="comment-table" commentId="29907" commentParentId="29903"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/timmy" style="position: relative;"> <img src='https://userpic.codeforces.org/2446/avatar/d9bd36d3627fc50e.jpg'/> </a> <div><a href="/profile/timmy" title="Expert timmy" class="rated-user user-blue">timmy</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/26/2011 12:19">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29907" href="?#comment-29907" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29903" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29907" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2446" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29907"> <div class="moveup"> <div class="ttypography"><p>Really? Ok, try to output floating-point numbers with 1e-10 precision.</p><p>I think result would be the same :) </p></div> </div> </div> <div class="reply info"> <a class="comment-29907 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29907 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29907"> <li> <div class="comment"> <table class="comment-table" commentId="29946" commentParentId="29907"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cornflow" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/cornflow" title="Expert cornflow" class="rated-user user-blue">cornflow</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/26/2011 18:38">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29946" href="?#comment-29946" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29907" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29946" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14075" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29946"> <div class="moveup"> <div class="ttypography">I've tried to output correct floating-point numbers. It got WA. So maybe statement should be more precise.</div> </div> </div> <div class="reply info"> <a class="comment-29946 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29946 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29946"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29748" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mostafa_fahim" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/mostafa_fahim" title="Expert mostafa_fahim" class="rated-user user-blue">mostafa_fahim</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/23/2011 21:57">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29748" href="?#comment-29748" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29748" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5382" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29748"> <div class="moveup"> <div class="ttypography">About Task C <div>for this input </div><div><span style="font-family: verdana , arial , sans-serif;font-size: 11.0px;"><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">1 1 2 2 a b: a 2 c: a 1 1 a 1 a  </pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">I am printing </pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><span style="font-family: verdana , arial , sans-serif;white-space: normal;"><pre class="output" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">1 </pre></span>b 1</pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">while the answer is</pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><span style="font-family: verdana , arial , sans-serif;white-space: normal;"><pre class="answer" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">1 </pre></span>c 2</pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">I can't see why my output is wrong (I think both outputs are correct in this case) <br /></pre></span></div></div> </div> </div> <div class="reply info"> <a class="comment-29748 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29748 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29748"> <li> <div class="comment"> <table class="comment-table" commentId="29774" commentParentId="29748"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/adavydow" style="position: relative;"> <img src='https://userpic.codeforces.org/2385/avatar/11fa80222a24e45c.jpg'/> </a> <div><a href="/profile/adavydow" title="Master adavydow" class="rated-user user-orange">adavydow</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/23/2011 22:55">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29774" href="?#comment-29774" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29748" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29774" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="2385" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29774"> <div class="moveup"> <div class="ttypography">&quot;It is guaranteed that after the <span class="tex-span"><i>i</i></span>-th purchase no more than one opportunity to collect the composite artifact appears. If such an opportunity arose, the hero must take advantage of it.&quot;<br />So your solution is wrong. After buyin first 'a' artifact player has oportunity to build artifact 'c' but in your solution he didn't take advantage of it, he waited for the second 'a' to compose 'b'</div> </div> </div> <div class="reply info"> <a class="comment-29774 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29774 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29774"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1581" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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69C
69
C
en
C. Game
<div class="problem-statement"><div class="header"><div class="title">C. Game</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>In one school with Vasya there is a student Kostya. Kostya does not like physics, he likes different online games. Every day, having come home, Kostya throws his bag in the farthest corner and sits down at his beloved computer. Kostya even eats glued to the game. A few days ago Kostya bought a new RPG game "HaresButtle", which differs from all other games in this genre. It has a huge number of artifacts. As we know, artifacts are divided into basic and composite ones. Only the basic artifacts are available on sale. More powerful composite artifacts are collected from some number of basic artifacts.</p><p>After the composing composite artifact, all the components disappear.</p><p>Kostya is the head of the alliance, so he has to remember, what artifacts has not only himself, but also his allies. You must identify by sequence of artifacts purchased by Kostya and his allies, how many and which artifacts has been collected by each of them. It is believed that initially no one has any artifacts. </p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line has 4 natural numbers: <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>k</i> ≤ 100</span>) — the number of Kostya's allies, <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 50</span>) — the number of basic artifacts, <span class="tex-span"><i>m</i></span> (<span class="tex-span">0 ≤ <i>m</i> ≤ 50</span>) — the number of composite artifacts, <span class="tex-span"><i>q</i></span> (<span class="tex-span">1 ≤ <i>q</i> ≤ 500</span>) — the number of his friends' purchases. The following <span class="tex-span"><i>n</i></span> lines contain the names of basic artifacts. After them <span class="tex-span"><i>m</i></span> lines contain the descriptions of composite artifacts in the following format:</p><p><span class="tex-font-style-tt">&lt;Art. Name&gt;: &lt;Art. №1&gt; &lt;Art. №1 Number&gt;, &lt;Art. №2&gt; &lt;Art. №2 Number&gt;, ... &lt;Art. №X&gt; &lt;Art. №Х Number&gt;</span></p><p>All the numbers are natural numbers not exceeding 100 (<span class="tex-span">1 ≤ <i>X</i> ≤ <i>n</i></span>).</p><p>The names of all artifacts are different, they are composed of lowercase Latin letters, and the length of each name is from 1 to 100 characters inclusive. All the words in the format of the description of a composite artifact are separated by exactly one space. It is guaranteed that all components of the new artifact are different and have already been met in the input data as the names of basic artifacts. </p><p>Next, each of the following <span class="tex-span"><i>q</i></span> lines is characterized by the number <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span>, the number of a friend who has bought the artifact (<span class="tex-span">1 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ <i>k</i></span>), and the name of the purchased basic artifact. Let's assume that the backpacks of the heroes are infinitely large and any artifact bought later can fit in there.</p><p>It is guaranteed that after the <span class="tex-span"><i>i</i></span>-th purchase no more than one opportunity to collect the composite artifact appears. If such an opportunity arose, the hero must take advantage of it.</p></div><div class="output-specification"><div class="section-title">Output</div><p>The output file should consist of <span class="tex-span"><i>k</i></span> blocks. The first line should contain number <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> — the number of different artifacts the <span class="tex-span"><i>i</i></span>-th ally has. Then the block should contain <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> lines with the names of these artifacts and the number of these artifacts. At that the lines should be printed in accordance with the lexicographical order of the names of the artifacts. In each block all the artifacts must be different, and all the numbers except the <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> should be positive.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2 3 2 5<br/>desolator<br/>refresher<br/>perseverance<br/>vanguard: desolator 1, refresher 1<br/>maelstorm: perseverance 2<br/>1 desolator<br/>2 perseverance<br/>1 refresher<br/>2 desolator<br/>2 perseverance<br/></pre></div><div class="output"><div class="title">Output</div><pre>1<br/>vanguard 1<br/>2<br/>desolator 1<br/>maelstorm 1<br/></pre></div></div></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/69">Codeforces Beta Round 63 (Div. 2)</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? 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If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="C" data-uuid="ps_74e6f449e34b43bf73298ec48ddeb4fe18d2d661"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. Game</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>In one school with Vasya there is a student Kostya. Kostya does not like physics, he likes different online games. Every day, having come home, Kostya throws his bag in the farthest corner and sits down at his beloved computer. Kostya even eats glued to the game. A few days ago Kostya bought a new RPG game &quot;HaresButtle&quot;, which differs from all other games in this genre. It has a huge number of artifacts. As we know, artifacts are divided into basic and composite ones. Only the basic artifacts are available on sale. More powerful composite artifacts are collected from some number of basic artifacts.</p><p>After the composing composite artifact, all the components disappear.</p><p>Kostya is the head of the alliance, so he has to remember, what artifacts has not only himself, but also his allies. You must identify by sequence of artifacts purchased by Kostya and his allies, how many and which artifacts has been collected by each of them. It is believed that initially no one has any artifacts. </p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line has 4 natural numbers: <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>k</i> ≤ 100</span>) — the number of Kostya's allies, <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 50</span>) — the number of basic artifacts, <span class="tex-span"><i>m</i></span> (<span class="tex-span">0 ≤ <i>m</i> ≤ 50</span>) — the number of composite artifacts, <span class="tex-span"><i>q</i></span> (<span class="tex-span">1 ≤ <i>q</i> ≤ 500</span>) — the number of his friends' purchases. The following <span class="tex-span"><i>n</i></span> lines contain the names of basic artifacts. After them <span class="tex-span"><i>m</i></span> lines contain the descriptions of composite artifacts in the following format:</p><p><span class="tex-font-style-tt">&lt;Art. Name&gt;: &lt;Art. №1&gt; &lt;Art. №1 Number&gt;, &lt;Art. №2&gt; &lt;Art. №2 Number&gt;, ... &lt;Art. №X&gt; &lt;Art. №Х Number&gt;</span></p><p>All the numbers are natural numbers not exceeding 100 (<span class="tex-span">1 ≤ <i>X</i> ≤ <i>n</i></span>).</p><p>The names of all artifacts are different, they are composed of lowercase Latin letters, and the length of each name is from 1 to 100 characters inclusive. All the words in the format of the description of a composite artifact are separated by exactly one space. It is guaranteed that all components of the new artifact are different and have already been met in the input data as the names of basic artifacts. </p><p>Next, each of the following <span class="tex-span"><i>q</i></span> lines is characterized by the number <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span>, the number of a friend who has bought the artifact (<span class="tex-span">1 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ <i>k</i></span>), and the name of the purchased basic artifact. Let's assume that the backpacks of the heroes are infinitely large and any artifact bought later can fit in there.</p><p>It is guaranteed that after the <span class="tex-span"><i>i</i></span>-th purchase no more than one opportunity to collect the composite artifact appears. If such an opportunity arose, the hero must take advantage of it.</p></div><div class="output-specification"><div class="section-title">Output</div><p>The output file should consist of <span class="tex-span"><i>k</i></span> blocks. The first line should contain number <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> — the number of different artifacts the <span class="tex-span"><i>i</i></span>-th ally has. Then the block should contain <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> lines with the names of these artifacts and the number of these artifacts. At that the lines should be printed in accordance with the lexicographical order of the names of the artifacts. In each block all the artifacts must be different, and all the numbers except the <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> should be positive.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2 3 2 5<br />desolator<br />refresher<br />perseverance<br />vanguard: desolator 1, refresher 1<br />maelstorm: perseverance 2<br />1 desolator<br />2 perseverance<br />1 refresher<br />2 desolator<br />2 perseverance<br /></pre></div><div class="output"><div class="title">Output</div><pre>1<br />vanguard 1<br />2<br />desolator 1<br />maelstorm 1<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=C]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); 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["Implementation problems, programming technics, simulation"]
["implementation", "*2000"]
https://codeforces.com/blog/entry/1571
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<a href="/blog/entry/120644">Codeforces Round 899 (Div. 2)</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/Misa-Misa" title="Expert Misa-Misa" class="rated-user user-blue">Misa-Misa</a> &rarr; <a href="/blog/entry/121157">Someone please help me understand this.</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/shivam565" title="Specialist shivam565" class="rated-user user-cyan">shivam565</a> &rarr; <a href="/blog/entry/108348">Total number of subarrays with sum atmost k</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> </ul> </div> <div class="bottom-links"> <table style="width:100%;"> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:right;"> <a href="/recent-actions">Detailed &rarr;</a> </td> </tr> </tbody> </table> </div> </div> </div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li><a href="/profile/map">map</a></li> <li class="current selectedLava"><a href="/blog/map">Blog</a></li> <li><a href="/teams/with/map">Teams</a></li> <li><a href="/submissions/map">Submissions</a></li> <li><a href="/groups/with/map">Groups</a></li> <li><a href="/contests/with/map">Contests</a></li> <li><a href="/contests/writer/map">Problemsetting</a></li> </ul> </div> <div style="margin-top:0;"> <div> <h3><a href="/blog/map" style="text-decoration:none;color:black !important;">map's blog</a></h3> </div> <div style="margin-top:2em;"> <div class="has-topic-id topic" topicId="1571"> <div class="title"> <a href="/blog/entry/1571"> Analysis Codeforces Beta Round #63 (Div. 2) </a> </div> <div class="info" style="position:relative;"> By&nbsp;<a href="/profile/map" title="International Master map" class="rated-user user-orange">map</a>, <span class="format-humantime" title="Mar/22/2011 21:02">13 years ago</span>, translation, <img style="position: relative;top: 5px;" src="//codeforces.org/s/81027/images/flags/24/gb.png" alt="In English" title="In English"/> <span style="position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;"> <div style="margin-top:0.25em;"> </div> </span> </div> <div class="content"> <div class="ttypography"><div><div><div><p></p><p></p><p><span lang="EN-US" style="">Problem A.</span></p> <p><span lang="EN-US" style="">In this task all you had to do was to make sure that the sum of all </span>Σ<span lang="EN-US" style="">x<sub>i</sub> is 0, the sum of all </span>Σ<span lang="EN-US" style="">y<span style="font-size: 13.0px;"><sub>i</sub></span> is 0 and that the sum of all </span>Σ<span lang="EN-US" style="">z<sub>i</sub> - 0 . </span><br /> <span lang="X-NONE" style="">We have not written that condition evidently in order that participants will have a chance to break a solution.</span><span lang="EN-US" style=""></span></p> <p><span lang="EN-US" style=""> </span></p><p><span lang="EN-US" style=""></span>Problem B.</p><p></p><p>In this problem, in fact, you should find a winner at every section. For each section, you must do a full search of all competitors to find a competitor with a minimum section time, which ran that section. Asymptotic of the solution is O(nm).</p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">Problem C.</span></p> <p><span lang="EN-US" style="">In this task, you had to update the collection of artifacts, which belong to Kostya’s friends, after each purchase . You had to set<span style="">  </span>a matrix c[i][j] - number of the j-th basic artifact that is required in order to collect the i-th component artifact. Further, one can make a matrix of composite artifacts, where a[i][j] is number of the j-th basic artifact of the i-th friend and a similar matrix b of composite artifacts, and<span style="">  </span>check whether i-th friend has any a composite artifact of O (MN) after each<span style="">  </span>i-th friend’s<span style="">  </span>purchase. Check whether one component of the artifact assembles for O (N): while checking whether the i-th friend is able to collect the j-th artifact you have to check, if there is such u, that c[j [u]&gt; a[i][u], if so, the j-th artefact will not be collected, if not, then you have to increase the b[i][j] and update the values in a[i]). </span></p> <p><span lang="EN-US" style="">So.the asymptotics of the processing of all purchases will be O (NQM). Then, we need<span style="">  </span>to make a list of artifacts for each person, keeping their quantity(a total of O (KN + KM), and sort it (a total of O (QlogQ)).</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">Problem D.</span></p> <p><span lang="EN-US" style="">This game is over, because except for a finite number (2) of reflections about the line y = x,the coordinates are changed to non-negative integer (and at least one coordinate is changed to a positive number).</span></p> <p><span lang="EN-US" style="">Algorithm for solving this problem<span style="">  </span>is DFS / BFS (states) where the state is a pair of coordinates, and two logical variables, which denote if the 1 (2) player had reflected a point about the line y = x.</span></p> <p><span lang="EN-US" style="">Total number of states is obtained by S &lt;= 4D^2 (pairs of coordinates) * 4 (Boolean variables).</span></p> <p><span lang="EN-US" style="">Processing of one state takes O (N) actions (do not forget to try to reflect the point about the line y = x, if the player had not made it earlier in the game). Thereby, we have the overall asymptotic O (ND^2), which works on C + + in less than 200ms.</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">Problem E</span></p> <p><span lang="EN-US" style="">To solve this problem you have to do a &quot;move&quot; subsegment and know :</span></p> <p><span lang="EN-US" style=""><span style=""> </span>1. The set B of numbers, meeting once, with the function of extracting the maximum for O (logN) </span></p> <p><span lang="EN-US" style="">2.The set of numbers appearing on this subsegments with keeping the number of times,that this number is found on this subsegments, with function of verifying how many times the number in this subsegments for O (logN).</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">While moving a segment from (a[i] .. a[i + k - 1]) for 1 item left (a[I + 1] .. a[I + k]) you have to:</span></p> <p><span lang="EN-US" style="">1) Check whether a[i] with a[I + k]. If yes, then there is no need to modify the set, otherwise proceed to item 2 and 3.</span></p> <p><span lang="EN-US" style="">2) Check how many times we have a[i] in the set A: if 2, then add a[i] to B, if 1, then remove it from<span style="">  </span>A and B. Do not forget to reduce the corresponding number of occurrences of a[i] in the current segment 1.</span></p> <p><span lang="EN-US" style="">3) Check, how many times we have a[I + k] in the set A: if 0, then add a[i] in the B and A, if 1, then remove it from B. Do not forget to increase the corresponding number of occurrences of a[i] the current interval to 1.</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">After that, if the set is not empty, we should take peak from it.</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">So the asymptotics of this process will be O(NlogN).</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">As such data structures<span style="">  </span>set / map(for those who use C + +) and the Cartesian tree are suitable.</span></p><p></p></div></div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/69" class="notice" style="text-decoration: none;">Codeforces Beta Round 63 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-3346-1571").click(function() { var that = this; 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line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/map"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/map"> map </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Mar/22/2011 21:02">13 years ago</span> </li> <li> <a href="/blog/entry/1571#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1571#comments"> 29 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1581"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (20)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="29594" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/P___" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/P___" title="Expert P___" class="rated-user user-blue">P___</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:40">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29594" href="?#comment-29594" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29594" class="CommentVoteFrame" data-commentRating="4" data-commentUserId="333" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+4</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29594"> <div class="moveup"> <div class="ttypography">You don't have to check reflections at all in task D. If player is in loosing position he can reflect coordinates, but the opponent (who had winnig strategy, so didn't use the reflection) also reflects.</div> </div> </div> <div class="reply info"> <a class="comment-29594 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29594 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29594"> <li> <div class="comment"> <table class="comment-table" commentId="29608" commentParentId="29594"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/rizwanhudda" style="position: relative;"> <img src='https://userpic.codeforces.org/616/avatar/255f41799f0df297.jpg'/> </a> <div><a href="/profile/rizwanhudda" title="Expert rizwanhudda" class="rated-user user-blue">rizwanhudda</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:43">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29608" href="?#comment-29608" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29594" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29608" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="616" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29608"> <div class="moveup"> <div class="ttypography">Can you please explain this?</div> </div> </div> <div class="reply info"> <a class="comment-29608 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29608 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29608"> <li> <div class="comment"> <table class="comment-table" commentId="29613" commentParentId="29608"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/riadwaw" style="position: relative;"> <img src='https://userpic.codeforces.org/8452/avatar/7b374574b05a50df.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/riadwaw" title="International Master riadwaw" class="rated-user user-orange">riadwaw</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:47">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29613" href="?#comment-29613" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29608" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29613" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="8452" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29613"> <div class="moveup"> <div class="ttypography">Lets see on game without reflects. Somebody have win strategy.<div><br /></div><div>So, in this game he should use it only after opp's reflection ad win</div></div> </div> </div> <div class="reply info"> <a class="comment-29613 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29613 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29613"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="29616" commentParentId="29608"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/P___" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/P___" title="Expert P___" class="rated-user user-blue">P___</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:50">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29616" href="?#comment-29616" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29608" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="29616" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="29616" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="333" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29616"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">Suppose that we can't make reflections, so for each reachable position you can determine whether player who starts at this position has a winning strategy (no matter what his opponent does) or he must lose no matter what he does. Suppose that the player starts in losing position, so the only rescue for him is to reflect coordinates and then his opponent starts at losing position (if a position is losing/winning, then reflected position has the same state). But since his opponent has a winning strategy without using reflections, you know that he didn't need to use reflection and can use this reflection now to make his opponent start in losing position again.</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-29616 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29616 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29616"> <li> <div class="comment"> <table class="comment-table" commentId="29637" commentParentId="29616"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/rizwanhudda" style="position: relative;"> <img src='https://userpic.codeforces.org/616/avatar/255f41799f0df297.jpg'/> </a> <div><a href="/profile/rizwanhudda" title="Expert rizwanhudda" class="rated-user user-blue">rizwanhudda</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 22:08">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29637" href="?#comment-29637" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29616" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29637" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="616" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29637"> <div class="moveup"> <div class="ttypography">Great explanation..:)</div> </div> </div> <div class="reply info"> <a class="comment-29637 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29637 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29637"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29598" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cauchyk" style="position: relative;"> <img src='https://userpic.codeforces.org/6307/avatar/1be12bd76cca6bd4.jpg'/> </a> <div><a href="/profile/cauchyk" title="Expert cauchyk" class="rated-user user-blue">cauchyk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:41">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29598" href="?#comment-29598" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="29598" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="29598" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6307" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29598"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"></div></div> </div> </div> <div class="reply info"> <a class="comment-29598 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29598 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29598"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29602" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/map" style="position: relative;"> <img src='https://userpic.codeforces.org/8362/avatar/5def203e6aa044bf.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/map" title="International Master map" class="rated-user user-orange">map</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:42">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29602" href="?#comment-29602" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29602" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="8362" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29602"> <div class="moveup"> <div class="ttypography">Yes, of course. You are absolutely right.</div> </div> </div> <div class="reply info"> <a class="comment-29602 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29602 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29602"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29614" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Anurag" style="position: relative;"> <img src='https://userpic.codeforces.org/1040/avatar/83f11106d57a9eef.jpg'/> </a> <div><a href="/profile/Anurag" title="Newbie Anurag" class="rated-user user-gray">Anurag</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:48">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29614" href="?#comment-29614" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29614" class="CommentVoteFrame" data-commentRating="5" data-commentUserId="1040" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+5</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29614"> <div class="moveup"> <div class="ttypography">For problem E , if my solution was O(n<sup>2</sup>) then it would have led to TLE?</div> </div> </div> <div class="reply info"> <a class="comment-29614 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29614 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29614"> <li> <div class="comment"> <table class="comment-table" commentId="29620" commentParentId="29614"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/logic_max" style="position: relative;"> <img src='https://userpic.codeforces.org/6829/avatar/abbf50e9dcdf31d9.jpg'/> </a> <div><a href="/profile/logic_max" title="Expert logic_max" class="rated-user user-blue">logic_max</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:53">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29620" href="?#comment-29620" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29614" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29620" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29620"> <div class="moveup"> <div class="ttypography">Yes.</div> </div> </div> <div class="reply info"> <a class="comment-29620 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29620 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29620"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="29703" commentParentId="29614"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Shafaet" style="position: relative;"> <img src='https://userpic.codeforces.org/5137/avatar/bcd103c3d3c35548.jpg'/> </a> <div><a href="/profile/Shafaet" title="Expert Shafaet" class="rated-user user-blue">Shafaet</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/23/2011 15:06">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29703" href="?#comment-29703" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29614" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29703" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5137" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29703"> <div class="moveup"> <div class="ttypography">n=10^5,so n^2 will certainly lead to TLE. <br />Here is my approach:<br /><br />Process first K numbers at once. Store frequencies of each number in hash table and maintain a set which contain values which occurred only once. then process rest of the numbers while taking input. reduce frequency of i-K th number, modify the set according to frequency. <br /><br />Suppose input is:<br />6 3<br />1<br />1<br />2<br />6<br />6<br />First i will process first 3 numbers. so the set will be {2} and map will be freq[1]=2,freq[2]=1. <br />When i get 4th number 6,i will reduce freq of 1st number. freq[1] will become 1 from 2. as it has become 1,the set will be {1,2,6}(as i got 6 for the first time). <br /><br />Then i get 5th number 6,i will reduce freq of 2nd number. freq[1] is now 0. as it went 0 from 1, i need to remove it from set too. so the set becomes{2}(i will remove 6 too as i got it 2 times now).<br /><br />Every time print the largest number from set. If the set is empty print &quot;nothing&quot;. i've used c++ stl &lt;set&gt;.</div> </div> </div> <div class="reply info"> <a class="comment-29703 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29703 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29703"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29632" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cauchyk" style="position: relative;"> <img src='https://userpic.codeforces.org/6307/avatar/1be12bd76cca6bd4.jpg'/> </a> <div><a href="/profile/cauchyk" title="Expert cauchyk" class="rated-user user-blue">cauchyk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 22:02">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29632" href="?#comment-29632" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29632" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6307" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29632"> <div class="moveup"> <div class="ttypography"><div style="text-align: left;"><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 13.0px;">please check my submission for problem C id: 350527 it says answer mismatch in line 2 but it does not...</span></div></div> </div> </div> <div class="reply info"> <a class="comment-29632 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29632 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29632"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29642" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/VladBelous" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/VladBelous" title="Expert VladBelous" class="rated-user user-blue">VladBelous</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 22:14">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29642" href="?#comment-29642" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29642" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3894" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29642"> <div class="moveup"> <div class="ttypography"><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">About D:</span><div><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">&quot;Thereby, we have the overall asymptotic O (ND^2), which works on C + + in less than 600ms&quot;</span><div><font face="verdana, arial, sans-serif"><span style="font-size: 12.0px;line-height: 20.0px;"><br /></span></font></div></span></div><div><font face="verdana, arial, sans-serif"><span style="font-size: 12.0px;line-height: 20.0px;">My solution used the same complexity, but ran in 80ms. Reason (I think) is that once I find a move to a losing position, I declare current position as winning and return (i.e. no need to look at other moves).</span></font></div><div><font face="verdana, arial, sans-serif"><span style="font-size: 12.0px;line-height: 20.0px;">This is trivial optimization, but I think an important one, because some Java solutions with </span></font><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">O(ND^2) failed due to TLE. (600ms in C++ does not leave a good margin)</span></div><div><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><br /></span></div></div> </div> </div> <div class="reply info"> <a class="comment-29642 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29642 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29642"> <li> <div class="comment"> <table class="comment-table" commentId="29644" commentParentId="29642"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/map" style="position: relative;"> <img src='https://userpic.codeforces.org/8362/avatar/5def203e6aa044bf.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/map" title="International Master map" class="rated-user user-orange">map</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 22:18">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29644" href="?#comment-29644" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29642" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29644" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="8362" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29644"> <div class="moveup"> <div class="ttypography">200ms. T<span style="font-family: arial , sans-serif;font-size: 13.0px;white-space: nowrap;">yping error. We have same correct JAVA solution.</span></div> </div> </div> <div class="reply info"> <a class="comment-29644 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29644 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29644"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29738" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cornflow" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/cornflow" title="Expert cornflow" class="rated-user user-blue">cornflow</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/23/2011 20:09">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29738" href="?#comment-29738" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="29738" revisionCount="3" revision="3"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">3</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="29738" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14075" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29738"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><p>When I changed &quot;double&quot; to &quot;int&quot; in task E, I've got AC (with double - WA). But I can't find any words in problem statement about representation of numbers in answer. Also I can't find nothing in problem statement to determine if numbers are integers or not...</p></div> </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-29738 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29738 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29738"> <li> <div class="comment"> <table class="comment-table" commentId="29834" commentParentId="29738"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/timmy" style="position: relative;"> <img src='https://userpic.codeforces.org/2446/avatar/d9bd36d3627fc50e.jpg'/> </a> <div><a href="/profile/timmy" title="Expert timmy" class="rated-user user-blue">timmy</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/25/2011 15:27">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29834" href="?#comment-29834" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29738" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29834" class="CommentVoteFrame" class="negative-comment-vote" data-commentRating="-11" data-commentUserId="2446" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">-11</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29834"> <div class="moveup"> <div class="ttypography"><p>ATTENTION! THIS CONTEST SHOULD BE UNRATED!</p><p>Maybe now you will read my message carefully :) I think that Corny is right. His solution works just after replacing &quot;double&quot; to &quot;int&quot;.</p></div> </div> </div> <div class="reply info"> <a class="comment-29834 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29834 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29834"> <li> <div class="comment"> <table class="comment-table" commentId="29903" commentParentId="29834"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cornflow" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/cornflow" title="Expert cornflow" class="rated-user user-blue">cornflow</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/26/2011 11:01">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29903" href="?#comment-29903" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29834" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29903" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14075" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29903"> <div class="moveup"> <div class="ttypography">I've found problem. It with presentation, but it's my fault. When answer is 994790178 I write 9.9479e+008. I should be more careful next time.</div> </div> </div> <div class="reply info"> <a class="comment-29903 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29903 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29903"> <li> <div class="comment"> <table class="comment-table" commentId="29907" commentParentId="29903"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/timmy" style="position: relative;"> <img src='https://userpic.codeforces.org/2446/avatar/d9bd36d3627fc50e.jpg'/> </a> <div><a href="/profile/timmy" title="Expert timmy" class="rated-user user-blue">timmy</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/26/2011 12:19">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29907" href="?#comment-29907" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29903" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29907" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2446" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29907"> <div class="moveup"> <div class="ttypography"><p>Really? Ok, try to output floating-point numbers with 1e-10 precision.</p><p>I think result would be the same :) </p></div> </div> </div> <div class="reply info"> <a class="comment-29907 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29907 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29907"> <li> <div class="comment"> <table class="comment-table" commentId="29946" commentParentId="29907"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cornflow" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/cornflow" title="Expert cornflow" class="rated-user user-blue">cornflow</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/26/2011 18:38">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29946" href="?#comment-29946" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29907" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29946" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14075" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29946"> <div class="moveup"> <div class="ttypography">I've tried to output correct floating-point numbers. It got WA. So maybe statement should be more precise.</div> </div> </div> <div class="reply info"> <a class="comment-29946 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29946 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29946"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29748" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mostafa_fahim" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/mostafa_fahim" title="Expert mostafa_fahim" class="rated-user user-blue">mostafa_fahim</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/23/2011 21:57">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29748" href="?#comment-29748" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29748" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5382" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29748"> <div class="moveup"> <div class="ttypography">About Task C <div>for this input </div><div><span style="font-family: verdana , arial , sans-serif;font-size: 11.0px;"><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">1 1 2 2 a b: a 2 c: a 1 1 a 1 a  </pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">I am printing </pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><span style="font-family: verdana , arial , sans-serif;white-space: normal;"><pre class="output" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">1 </pre></span>b 1</pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">while the answer is</pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><span style="font-family: verdana , arial , sans-serif;white-space: normal;"><pre class="answer" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">1 </pre></span>c 2</pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">I can't see why my output is wrong (I think both outputs are correct in this case) <br /></pre></span></div></div> </div> </div> <div class="reply info"> <a class="comment-29748 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29748 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29748"> <li> <div class="comment"> <table class="comment-table" commentId="29774" commentParentId="29748"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/adavydow" style="position: relative;"> <img src='https://userpic.codeforces.org/2385/avatar/11fa80222a24e45c.jpg'/> </a> <div><a href="/profile/adavydow" title="Master adavydow" class="rated-user user-orange">adavydow</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/23/2011 22:55">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29774" href="?#comment-29774" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29748" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29774" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="2385" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29774"> <div class="moveup"> <div class="ttypography">&quot;It is guaranteed that after the <span class="tex-span"><i>i</i></span>-th purchase no more than one opportunity to collect the composite artifact appears. If such an opportunity arose, the hero must take advantage of it.&quot;<br />So your solution is wrong. After buyin first 'a' artifact player has oportunity to build artifact 'c' but in your solution he didn't take advantage of it, he waited for the second 'a' to compose 'b'</div> </div> </div> <div class="reply info"> <a class="comment-29774 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29774 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29774"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1581" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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69D
69
D
en
D. Dot
<div class="problem-statement"><div class="header"><div class="title">D. Dot</div><div class="time-limit"><div class="property-title">time limit per test</div>3 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Anton and Dasha like to play different games during breaks on checkered paper. By the 11th grade they managed to play all the games of this type and asked Vova the programmer to come up with a new game. Vova suggested to them to play a game under the code name "dot" with the following rules: </p><ul><li> On the checkered paper a coordinate system is drawn. A dot is initially put in the position <span class="tex-span">(<i>x</i>, <i>y</i>)</span>. </li><li> A move is shifting a dot to one of the pre-selected vectors. Also each player can once per game symmetrically reflect a dot relatively to the line <span class="tex-span"><i>y</i> = <i>x</i></span>. </li><li> Anton and Dasha take turns. Anton goes first. </li><li> The player after whose move the distance from the dot to the coordinates' origin exceeds <span class="tex-span"><i>d</i></span>, loses. </li></ul><p>Help them to determine the winner.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of the input file contains 4 integers <span class="tex-span"><i>x</i></span>, <span class="tex-span"><i>y</i></span>, <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>d</i></span> (<span class="tex-span"> - 200 ≤ <i>x</i>, <i>y</i> ≤ 200, 1 ≤ <i>d</i> ≤ 200, 1 ≤ <i>n</i> ≤ 20</span>) — the initial coordinates of the dot, the distance <span class="tex-span"><i>d</i></span> and the number of vectors. It is guaranteed that the initial dot is at the distance less than <span class="tex-span"><i>d</i></span> from the origin of the coordinates. The following <span class="tex-span"><i>n</i></span> lines each contain two non-negative numbers <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">0 ≤ <i>x</i><sub class="lower-index"><i>i</i></sub>, <i>y</i><sub class="lower-index"><i>i</i></sub> ≤ 200</span>) — the coordinates of the i-th vector. It is guaranteed that all the vectors are nonzero and different.</p></div><div class="output-specification"><div class="section-title">Output</div><p>You should print "<span class="tex-font-style-tt">Anton</span>", if the winner is Anton in case of both players play the game optimally, and "<span class="tex-font-style-tt">Dasha</span>" otherwise.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>0 0 2 3<br/>1 1<br/>1 2<br/></pre></div><div class="output"><div class="title">Output</div><pre>Anton</pre></div><div class="input"><div class="title">Input</div><pre>0 0 2 4<br/>1 1<br/>1 2<br/></pre></div><div class="output"><div class="title">Output</div><pre>Dasha</pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first test, Anton goes to the vector (1;2), and Dasha loses. In the second test Dasha with her first move shifts the dot so that its coordinates are (2;3), and Anton loses, as he has the only possible move — to reflect relatively to the line <span class="tex-span"><i>y</i> = <i>x</i></span>. Dasha will respond to it with the same move and return the dot in position (2;3).</p></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/69">Codeforces Beta Round 63 (Div. 2)</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="D" data-uuid="ps_d9032b2ab93eed36d9a09c19ec32703249aaa440"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">D. Dot</div><div class="time-limit"><div class="property-title">time limit per test</div>3 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Anton and Dasha like to play different games during breaks on checkered paper. By the 11th grade they managed to play all the games of this type and asked Vova the programmer to come up with a new game. Vova suggested to them to play a game under the code name &quot;dot&quot; with the following rules: </p><ul><li> On the checkered paper a coordinate system is drawn. A dot is initially put in the position <span class="tex-span">(<i>x</i>, <i>y</i>)</span>. </li><li> A move is shifting a dot to one of the pre-selected vectors. Also each player can once per game symmetrically reflect a dot relatively to the line <span class="tex-span"><i>y</i> = <i>x</i></span>. </li><li> Anton and Dasha take turns. Anton goes first. </li><li> The player after whose move the distance from the dot to the coordinates' origin exceeds <span class="tex-span"><i>d</i></span>, loses. </li></ul><p>Help them to determine the winner.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of the input file contains 4 integers <span class="tex-span"><i>x</i></span>, <span class="tex-span"><i>y</i></span>, <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>d</i></span> (<span class="tex-span"> - 200 ≤ <i>x</i>, <i>y</i> ≤ 200, 1 ≤ <i>d</i> ≤ 200, 1 ≤ <i>n</i> ≤ 20</span>) — the initial coordinates of the dot, the distance <span class="tex-span"><i>d</i></span> and the number of vectors. It is guaranteed that the initial dot is at the distance less than <span class="tex-span"><i>d</i></span> from the origin of the coordinates. The following <span class="tex-span"><i>n</i></span> lines each contain two non-negative numbers <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">0 ≤ <i>x</i><sub class="lower-index"><i>i</i></sub>, <i>y</i><sub class="lower-index"><i>i</i></sub> ≤ 200</span>) — the coordinates of the i-th vector. It is guaranteed that all the vectors are nonzero and different.</p></div><div class="output-specification"><div class="section-title">Output</div><p>You should print &quot;<span class="tex-font-style-tt">Anton</span>&quot;, if the winner is Anton in case of both players play the game optimally, and &quot;<span class="tex-font-style-tt">Dasha</span>&quot; otherwise.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>0 0 2 3<br />1 1<br />1 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>Anton</pre></div><div class="input"><div class="title">Input</div><pre>0 0 2 4<br />1 1<br />1 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>Dasha</pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first test, Anton goes to the vector (1;2), and Dasha loses. In the second test Dasha with her first move shifts the dot so that its coordinates are (2;3), and Anton loses, as he has the only possible move — to reflect relatively to the line <span class="tex-span"><i>y</i> = <i>x</i></span>. 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["Dynamic programming", "Games, Sprague\u2013Grundy theorem"]
["dp", "games", "*1900"]
https://codeforces.com/blog/entry/1571
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<a href="/blog/entry/120644">Codeforces Round 899 (Div. 2)</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/Misa-Misa" title="Expert Misa-Misa" class="rated-user user-blue">Misa-Misa</a> &rarr; <a href="/blog/entry/121157">Someone please help me understand this.</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/shivam565" title="Specialist shivam565" class="rated-user user-cyan">shivam565</a> &rarr; <a href="/blog/entry/108348">Total number of subarrays with sum atmost k</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> </ul> </div> <div class="bottom-links"> <table style="width:100%;"> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:right;"> <a href="/recent-actions">Detailed &rarr;</a> </td> </tr> </tbody> </table> </div> </div> </div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li><a href="/profile/map">map</a></li> <li class="current selectedLava"><a href="/blog/map">Blog</a></li> <li><a href="/teams/with/map">Teams</a></li> <li><a href="/submissions/map">Submissions</a></li> <li><a href="/groups/with/map">Groups</a></li> <li><a href="/contests/with/map">Contests</a></li> <li><a href="/contests/writer/map">Problemsetting</a></li> </ul> </div> <div style="margin-top:0;"> <div> <h3><a href="/blog/map" style="text-decoration:none;color:black !important;">map's blog</a></h3> </div> <div style="margin-top:2em;"> <div class="has-topic-id topic" topicId="1571"> <div class="title"> <a href="/blog/entry/1571"> Analysis Codeforces Beta Round #63 (Div. 2) </a> </div> <div class="info" style="position:relative;"> By&nbsp;<a href="/profile/map" title="International Master map" class="rated-user user-orange">map</a>, <span class="format-humantime" title="Mar/22/2011 21:02">13 years ago</span>, translation, <img style="position: relative;top: 5px;" src="//codeforces.org/s/81027/images/flags/24/gb.png" alt="In English" title="In English"/> <span style="position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;"> <div style="margin-top:0.25em;"> </div> </span> </div> <div class="content"> <div class="ttypography"><div><div><div><p></p><p></p><p><span lang="EN-US" style="">Problem A.</span></p> <p><span lang="EN-US" style="">In this task all you had to do was to make sure that the sum of all </span>Σ<span lang="EN-US" style="">x<sub>i</sub> is 0, the sum of all </span>Σ<span lang="EN-US" style="">y<span style="font-size: 13.0px;"><sub>i</sub></span> is 0 and that the sum of all </span>Σ<span lang="EN-US" style="">z<sub>i</sub> - 0 . </span><br /> <span lang="X-NONE" style="">We have not written that condition evidently in order that participants will have a chance to break a solution.</span><span lang="EN-US" style=""></span></p> <p><span lang="EN-US" style=""> </span></p><p><span lang="EN-US" style=""></span>Problem B.</p><p></p><p>In this problem, in fact, you should find a winner at every section. For each section, you must do a full search of all competitors to find a competitor with a minimum section time, which ran that section. Asymptotic of the solution is O(nm).</p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">Problem C.</span></p> <p><span lang="EN-US" style="">In this task, you had to update the collection of artifacts, which belong to Kostya’s friends, after each purchase . You had to set<span style="">  </span>a matrix c[i][j] - number of the j-th basic artifact that is required in order to collect the i-th component artifact. Further, one can make a matrix of composite artifacts, where a[i][j] is number of the j-th basic artifact of the i-th friend and a similar matrix b of composite artifacts, and<span style="">  </span>check whether i-th friend has any a composite artifact of O (MN) after each<span style="">  </span>i-th friend’s<span style="">  </span>purchase. Check whether one component of the artifact assembles for O (N): while checking whether the i-th friend is able to collect the j-th artifact you have to check, if there is such u, that c[j [u]&gt; a[i][u], if so, the j-th artefact will not be collected, if not, then you have to increase the b[i][j] and update the values in a[i]). </span></p> <p><span lang="EN-US" style="">So.the asymptotics of the processing of all purchases will be O (NQM). Then, we need<span style="">  </span>to make a list of artifacts for each person, keeping their quantity(a total of O (KN + KM), and sort it (a total of O (QlogQ)).</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">Problem D.</span></p> <p><span lang="EN-US" style="">This game is over, because except for a finite number (2) of reflections about the line y = x,the coordinates are changed to non-negative integer (and at least one coordinate is changed to a positive number).</span></p> <p><span lang="EN-US" style="">Algorithm for solving this problem<span style="">  </span>is DFS / BFS (states) where the state is a pair of coordinates, and two logical variables, which denote if the 1 (2) player had reflected a point about the line y = x.</span></p> <p><span lang="EN-US" style="">Total number of states is obtained by S &lt;= 4D^2 (pairs of coordinates) * 4 (Boolean variables).</span></p> <p><span lang="EN-US" style="">Processing of one state takes O (N) actions (do not forget to try to reflect the point about the line y = x, if the player had not made it earlier in the game). Thereby, we have the overall asymptotic O (ND^2), which works on C + + in less than 200ms.</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">Problem E</span></p> <p><span lang="EN-US" style="">To solve this problem you have to do a &quot;move&quot; subsegment and know :</span></p> <p><span lang="EN-US" style=""><span style=""> </span>1. The set B of numbers, meeting once, with the function of extracting the maximum for O (logN) </span></p> <p><span lang="EN-US" style="">2.The set of numbers appearing on this subsegments with keeping the number of times,that this number is found on this subsegments, with function of verifying how many times the number in this subsegments for O (logN).</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">While moving a segment from (a[i] .. a[i + k - 1]) for 1 item left (a[I + 1] .. a[I + k]) you have to:</span></p> <p><span lang="EN-US" style="">1) Check whether a[i] with a[I + k]. If yes, then there is no need to modify the set, otherwise proceed to item 2 and 3.</span></p> <p><span lang="EN-US" style="">2) Check how many times we have a[i] in the set A: if 2, then add a[i] to B, if 1, then remove it from<span style="">  </span>A and B. Do not forget to reduce the corresponding number of occurrences of a[i] in the current segment 1.</span></p> <p><span lang="EN-US" style="">3) Check, how many times we have a[I + k] in the set A: if 0, then add a[i] in the B and A, if 1, then remove it from B. Do not forget to increase the corresponding number of occurrences of a[i] the current interval to 1.</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">After that, if the set is not empty, we should take peak from it.</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">So the asymptotics of this process will be O(NlogN).</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">As such data structures<span style="">  </span>set / map(for those who use C + +) and the Cartesian tree are suitable.</span></p><p></p></div></div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/69" class="notice" style="text-decoration: none;">Codeforces Beta Round 63 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-3346-1571").click(function() { var that = this; 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line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/map"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/map"> map </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Mar/22/2011 21:02">13 years ago</span> </li> <li> <a href="/blog/entry/1571#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1571#comments"> 29 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1581"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (20)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="29594" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/P___" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/P___" title="Expert P___" class="rated-user user-blue">P___</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:40">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29594" href="?#comment-29594" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29594" class="CommentVoteFrame" data-commentRating="4" data-commentUserId="333" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+4</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29594"> <div class="moveup"> <div class="ttypography">You don't have to check reflections at all in task D. If player is in loosing position he can reflect coordinates, but the opponent (who had winnig strategy, so didn't use the reflection) also reflects.</div> </div> </div> <div class="reply info"> <a class="comment-29594 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29594 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29594"> <li> <div class="comment"> <table class="comment-table" commentId="29608" commentParentId="29594"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/rizwanhudda" style="position: relative;"> <img src='https://userpic.codeforces.org/616/avatar/255f41799f0df297.jpg'/> </a> <div><a href="/profile/rizwanhudda" title="Expert rizwanhudda" class="rated-user user-blue">rizwanhudda</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:43">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29608" href="?#comment-29608" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29594" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29608" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="616" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29608"> <div class="moveup"> <div class="ttypography">Can you please explain this?</div> </div> </div> <div class="reply info"> <a class="comment-29608 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29608 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29608"> <li> <div class="comment"> <table class="comment-table" commentId="29613" commentParentId="29608"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/riadwaw" style="position: relative;"> <img src='https://userpic.codeforces.org/8452/avatar/7b374574b05a50df.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/riadwaw" title="International Master riadwaw" class="rated-user user-orange">riadwaw</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:47">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29613" href="?#comment-29613" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29608" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29613" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="8452" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29613"> <div class="moveup"> <div class="ttypography">Lets see on game without reflects. Somebody have win strategy.<div><br /></div><div>So, in this game he should use it only after opp's reflection ad win</div></div> </div> </div> <div class="reply info"> <a class="comment-29613 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29613 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29613"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="29616" commentParentId="29608"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/P___" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/P___" title="Expert P___" class="rated-user user-blue">P___</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:50">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29616" href="?#comment-29616" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29608" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="29616" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="29616" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="333" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29616"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">Suppose that we can't make reflections, so for each reachable position you can determine whether player who starts at this position has a winning strategy (no matter what his opponent does) or he must lose no matter what he does. Suppose that the player starts in losing position, so the only rescue for him is to reflect coordinates and then his opponent starts at losing position (if a position is losing/winning, then reflected position has the same state). But since his opponent has a winning strategy without using reflections, you know that he didn't need to use reflection and can use this reflection now to make his opponent start in losing position again.</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-29616 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29616 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29616"> <li> <div class="comment"> <table class="comment-table" commentId="29637" commentParentId="29616"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/rizwanhudda" style="position: relative;"> <img src='https://userpic.codeforces.org/616/avatar/255f41799f0df297.jpg'/> </a> <div><a href="/profile/rizwanhudda" title="Expert rizwanhudda" class="rated-user user-blue">rizwanhudda</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 22:08">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29637" href="?#comment-29637" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29616" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29637" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="616" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29637"> <div class="moveup"> <div class="ttypography">Great explanation..:)</div> </div> </div> <div class="reply info"> <a class="comment-29637 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29637 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29637"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29598" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cauchyk" style="position: relative;"> <img src='https://userpic.codeforces.org/6307/avatar/1be12bd76cca6bd4.jpg'/> </a> <div><a href="/profile/cauchyk" title="Expert cauchyk" class="rated-user user-blue">cauchyk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:41">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29598" href="?#comment-29598" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="29598" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="29598" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6307" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29598"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"></div></div> </div> </div> <div class="reply info"> <a class="comment-29598 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29598 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29598"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29602" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/map" style="position: relative;"> <img src='https://userpic.codeforces.org/8362/avatar/5def203e6aa044bf.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/map" title="International Master map" class="rated-user user-orange">map</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:42">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29602" href="?#comment-29602" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29602" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="8362" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29602"> <div class="moveup"> <div class="ttypography">Yes, of course. You are absolutely right.</div> </div> </div> <div class="reply info"> <a class="comment-29602 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29602 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29602"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29614" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Anurag" style="position: relative;"> <img src='https://userpic.codeforces.org/1040/avatar/83f11106d57a9eef.jpg'/> </a> <div><a href="/profile/Anurag" title="Newbie Anurag" class="rated-user user-gray">Anurag</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:48">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29614" href="?#comment-29614" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29614" class="CommentVoteFrame" data-commentRating="5" data-commentUserId="1040" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+5</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29614"> <div class="moveup"> <div class="ttypography">For problem E , if my solution was O(n<sup>2</sup>) then it would have led to TLE?</div> </div> </div> <div class="reply info"> <a class="comment-29614 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29614 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29614"> <li> <div class="comment"> <table class="comment-table" commentId="29620" commentParentId="29614"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/logic_max" style="position: relative;"> <img src='https://userpic.codeforces.org/6829/avatar/abbf50e9dcdf31d9.jpg'/> </a> <div><a href="/profile/logic_max" title="Expert logic_max" class="rated-user user-blue">logic_max</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:53">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29620" href="?#comment-29620" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29614" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29620" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29620"> <div class="moveup"> <div class="ttypography">Yes.</div> </div> </div> <div class="reply info"> <a class="comment-29620 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29620 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29620"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="29703" commentParentId="29614"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Shafaet" style="position: relative;"> <img src='https://userpic.codeforces.org/5137/avatar/bcd103c3d3c35548.jpg'/> </a> <div><a href="/profile/Shafaet" title="Expert Shafaet" class="rated-user user-blue">Shafaet</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/23/2011 15:06">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29703" href="?#comment-29703" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29614" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29703" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5137" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29703"> <div class="moveup"> <div class="ttypography">n=10^5,so n^2 will certainly lead to TLE. <br />Here is my approach:<br /><br />Process first K numbers at once. Store frequencies of each number in hash table and maintain a set which contain values which occurred only once. then process rest of the numbers while taking input. reduce frequency of i-K th number, modify the set according to frequency. <br /><br />Suppose input is:<br />6 3<br />1<br />1<br />2<br />6<br />6<br />First i will process first 3 numbers. so the set will be {2} and map will be freq[1]=2,freq[2]=1. <br />When i get 4th number 6,i will reduce freq of 1st number. freq[1] will become 1 from 2. as it has become 1,the set will be {1,2,6}(as i got 6 for the first time). <br /><br />Then i get 5th number 6,i will reduce freq of 2nd number. freq[1] is now 0. as it went 0 from 1, i need to remove it from set too. so the set becomes{2}(i will remove 6 too as i got it 2 times now).<br /><br />Every time print the largest number from set. If the set is empty print &quot;nothing&quot;. i've used c++ stl &lt;set&gt;.</div> </div> </div> <div class="reply info"> <a class="comment-29703 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29703 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29703"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29632" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cauchyk" style="position: relative;"> <img src='https://userpic.codeforces.org/6307/avatar/1be12bd76cca6bd4.jpg'/> </a> <div><a href="/profile/cauchyk" title="Expert cauchyk" class="rated-user user-blue">cauchyk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 22:02">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29632" href="?#comment-29632" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29632" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6307" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29632"> <div class="moveup"> <div class="ttypography"><div style="text-align: left;"><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 13.0px;">please check my submission for problem C id: 350527 it says answer mismatch in line 2 but it does not...</span></div></div> </div> </div> <div class="reply info"> <a class="comment-29632 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29632 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29632"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29642" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/VladBelous" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/VladBelous" title="Expert VladBelous" class="rated-user user-blue">VladBelous</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 22:14">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29642" href="?#comment-29642" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29642" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3894" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29642"> <div class="moveup"> <div class="ttypography"><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">About D:</span><div><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">&quot;Thereby, we have the overall asymptotic O (ND^2), which works on C + + in less than 600ms&quot;</span><div><font face="verdana, arial, sans-serif"><span style="font-size: 12.0px;line-height: 20.0px;"><br /></span></font></div></span></div><div><font face="verdana, arial, sans-serif"><span style="font-size: 12.0px;line-height: 20.0px;">My solution used the same complexity, but ran in 80ms. Reason (I think) is that once I find a move to a losing position, I declare current position as winning and return (i.e. no need to look at other moves).</span></font></div><div><font face="verdana, arial, sans-serif"><span style="font-size: 12.0px;line-height: 20.0px;">This is trivial optimization, but I think an important one, because some Java solutions with </span></font><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">O(ND^2) failed due to TLE. (600ms in C++ does not leave a good margin)</span></div><div><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><br /></span></div></div> </div> </div> <div class="reply info"> <a class="comment-29642 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29642 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29642"> <li> <div class="comment"> <table class="comment-table" commentId="29644" commentParentId="29642"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/map" style="position: relative;"> <img src='https://userpic.codeforces.org/8362/avatar/5def203e6aa044bf.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/map" title="International Master map" class="rated-user user-orange">map</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 22:18">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29644" href="?#comment-29644" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29642" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29644" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="8362" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29644"> <div class="moveup"> <div class="ttypography">200ms. T<span style="font-family: arial , sans-serif;font-size: 13.0px;white-space: nowrap;">yping error. We have same correct JAVA solution.</span></div> </div> </div> <div class="reply info"> <a class="comment-29644 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29644 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29644"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29738" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cornflow" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/cornflow" title="Expert cornflow" class="rated-user user-blue">cornflow</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/23/2011 20:09">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29738" href="?#comment-29738" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="29738" revisionCount="3" revision="3"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">3</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="29738" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14075" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29738"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><p>When I changed &quot;double&quot; to &quot;int&quot; in task E, I've got AC (with double - WA). But I can't find any words in problem statement about representation of numbers in answer. Also I can't find nothing in problem statement to determine if numbers are integers or not...</p></div> </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-29738 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29738 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29738"> <li> <div class="comment"> <table class="comment-table" commentId="29834" commentParentId="29738"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/timmy" style="position: relative;"> <img src='https://userpic.codeforces.org/2446/avatar/d9bd36d3627fc50e.jpg'/> </a> <div><a href="/profile/timmy" title="Expert timmy" class="rated-user user-blue">timmy</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/25/2011 15:27">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29834" href="?#comment-29834" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29738" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29834" class="CommentVoteFrame" class="negative-comment-vote" data-commentRating="-11" data-commentUserId="2446" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">-11</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29834"> <div class="moveup"> <div class="ttypography"><p>ATTENTION! THIS CONTEST SHOULD BE UNRATED!</p><p>Maybe now you will read my message carefully :) I think that Corny is right. His solution works just after replacing &quot;double&quot; to &quot;int&quot;.</p></div> </div> </div> <div class="reply info"> <a class="comment-29834 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29834 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29834"> <li> <div class="comment"> <table class="comment-table" commentId="29903" commentParentId="29834"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cornflow" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/cornflow" title="Expert cornflow" class="rated-user user-blue">cornflow</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/26/2011 11:01">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29903" href="?#comment-29903" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29834" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29903" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14075" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29903"> <div class="moveup"> <div class="ttypography">I've found problem. It with presentation, but it's my fault. When answer is 994790178 I write 9.9479e+008. I should be more careful next time.</div> </div> </div> <div class="reply info"> <a class="comment-29903 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29903 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29903"> <li> <div class="comment"> <table class="comment-table" commentId="29907" commentParentId="29903"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/timmy" style="position: relative;"> <img src='https://userpic.codeforces.org/2446/avatar/d9bd36d3627fc50e.jpg'/> </a> <div><a href="/profile/timmy" title="Expert timmy" class="rated-user user-blue">timmy</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/26/2011 12:19">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29907" href="?#comment-29907" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29903" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29907" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2446" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29907"> <div class="moveup"> <div class="ttypography"><p>Really? Ok, try to output floating-point numbers with 1e-10 precision.</p><p>I think result would be the same :) </p></div> </div> </div> <div class="reply info"> <a class="comment-29907 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29907 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29907"> <li> <div class="comment"> <table class="comment-table" commentId="29946" commentParentId="29907"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cornflow" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/cornflow" title="Expert cornflow" class="rated-user user-blue">cornflow</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/26/2011 18:38">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29946" href="?#comment-29946" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29907" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29946" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14075" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29946"> <div class="moveup"> <div class="ttypography">I've tried to output correct floating-point numbers. It got WA. So maybe statement should be more precise.</div> </div> </div> <div class="reply info"> <a class="comment-29946 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29946 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29946"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29748" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mostafa_fahim" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/mostafa_fahim" title="Expert mostafa_fahim" class="rated-user user-blue">mostafa_fahim</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/23/2011 21:57">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29748" href="?#comment-29748" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29748" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5382" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29748"> <div class="moveup"> <div class="ttypography">About Task C <div>for this input </div><div><span style="font-family: verdana , arial , sans-serif;font-size: 11.0px;"><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">1 1 2 2 a b: a 2 c: a 1 1 a 1 a  </pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">I am printing </pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><span style="font-family: verdana , arial , sans-serif;white-space: normal;"><pre class="output" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">1 </pre></span>b 1</pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">while the answer is</pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><span style="font-family: verdana , arial , sans-serif;white-space: normal;"><pre class="answer" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">1 </pre></span>c 2</pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">I can't see why my output is wrong (I think both outputs are correct in this case) <br /></pre></span></div></div> </div> </div> <div class="reply info"> <a class="comment-29748 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29748 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29748"> <li> <div class="comment"> <table class="comment-table" commentId="29774" commentParentId="29748"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/adavydow" style="position: relative;"> <img src='https://userpic.codeforces.org/2385/avatar/11fa80222a24e45c.jpg'/> </a> <div><a href="/profile/adavydow" title="Master adavydow" class="rated-user user-orange">adavydow</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/23/2011 22:55">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29774" href="?#comment-29774" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29748" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29774" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="2385" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29774"> <div class="moveup"> <div class="ttypography">&quot;It is guaranteed that after the <span class="tex-span"><i>i</i></span>-th purchase no more than one opportunity to collect the composite artifact appears. If such an opportunity arose, the hero must take advantage of it.&quot;<br />So your solution is wrong. After buyin first 'a' artifact player has oportunity to build artifact 'c' but in your solution he didn't take advantage of it, he waited for the second 'a' to compose 'b'</div> </div> </div> <div class="reply info"> <a class="comment-29774 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29774 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29774"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1581" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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69E
69
E
en
E. Subsegments
<div class="problem-statement"><div class="header"><div class="title">E. Subsegments</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Programmer Sasha has recently begun to study data structures. His coach Stas told him to solve the problem of finding a minimum on the segment of the array in <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png" style="max-width: 100.0%;max-height: 100.0%;"/>, which Sasha coped with. For Sasha not to think that he had learned all, Stas gave him a new task. For each segment of the fixed length Sasha must find the maximum element of those that occur on the given segment exactly once. Help Sasha solve this problem. </p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two positive integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup>, 1 ≤ <i>k</i> ≤ <i>n</i></span>) — the number of array elements and the length of the segment. </p><p>Then follow <span class="tex-span"><i>n</i></span> lines: the <span class="tex-span"><i>i</i></span>-th one contains a single number <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span"> - 10<sup class="upper-index">9</sup> ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">9</sup></span>). </p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span"><i>n</i>–<i>k</i> + 1</span> numbers, one per line: on the <span class="tex-span"><i>i</i></span>-th line print of the maximum number of those numbers from the subarray <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i> + 1</sub></span> … <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i> + <i>k</i> - 1</sub></span> that occur in this subarray exactly 1 time. If there are no such numbers in this subarray, print "<span class="tex-font-style-tt">Nothing</span>".</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>5 3<br/>1<br/>2<br/>2<br/>3<br/>3<br/></pre></div><div class="output"><div class="title">Output</div><pre>1<br/>3<br/>2<br/></pre></div><div class="input"><div class="title">Input</div><pre>6 4<br/>3<br/>3<br/>3<br/>4<br/>4<br/>2<br/></pre></div><div class="output"><div class="title">Output</div><pre>4<br/>Nothing<br/>3<br/></pre></div></div></div></div>
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If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. Never use someone else's code, read the tutorials or communicate with other person during a virtual contest. </div> <div style="text-align:center;margin:1em;"> <form action="/contest/69/virtual" method="get"> <input type="submit" name="submit" value="Start virtual contest" style="padding:0 0.5em;"> </form> </div> </div> <script> $(function () { $(".ContestVirtualFrame .sidebar-caption-icon").click(function() { $(this).toggleClass("la-angle-down la-angle-right"); const $target = $(this).parent().next(); $target.toggle(); const dataPageUrl = $target.attr("data-page-url"); const collapsed = $(this).hasClass("la-angle-right"); const params = { action: "setCollapsed", sidebarFrameSimpleClassName: "ContestVirtualFrame", collapsed }; $.each($target[0].attributes, function(i, a) { const name = a.name; if (name.startsWith("data-extra-key-")) { const key = a.value; const keyIndex = parseInt(name.substring("data-extra-key-".length)); const value = $target.attr("data-extra-value-" + keyIndex); params[key] = value; 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="E" data-uuid="ps_b861120309efa776ca5926e1237f9d7609b00e23"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">E. Subsegments</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Programmer Sasha has recently begun to study data structures. His coach Stas told him to solve the problem of finding a minimum on the segment of the array in <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png" style="max-width: 100.0%;max-height: 100.0%;" />, which Sasha coped with. For Sasha not to think that he had learned all, Stas gave him a new task. For each segment of the fixed length Sasha must find the maximum element of those that occur on the given segment exactly once. Help Sasha solve this problem. </p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two positive integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup>, 1 ≤ <i>k</i> ≤ <i>n</i></span>) — the number of array elements and the length of the segment. </p><p>Then follow <span class="tex-span"><i>n</i></span> lines: the <span class="tex-span"><i>i</i></span>-th one contains a single number <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span"> - 10<sup class="upper-index">9</sup> ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">9</sup></span>). </p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span"><i>n</i>–<i>k</i> + 1</span> numbers, one per line: on the <span class="tex-span"><i>i</i></span>-th line print of the maximum number of those numbers from the subarray <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i> + 1</sub></span> … <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i> + <i>k</i> - 1</sub></span> that occur in this subarray exactly 1 time. 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["Heaps, binary search trees, segment trees, hash tables, etc", "Implementation problems, programming technics, simulation"]
["data structures", "implementation", "*1800"]
https://codeforces.com/blog/entry/1571
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For each section, you must do a full search of all competitors to find a competitor with a minimum section time, which ran that section. Asymptotic of the solution is O(nm).</p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">Problem C.</span></p> <p><span lang="EN-US" style="">In this task, you had to update the collection of artifacts, which belong to Kostya’s friends, after each purchase . You had to set<span style="">  </span>a matrix c[i][j] - number of the j-th basic artifact that is required in order to collect the i-th component artifact. Further, one can make a matrix of composite artifacts, where a[i][j] is number of the j-th basic artifact of the i-th friend and a similar matrix b of composite artifacts, and<span style="">  </span>check whether i-th friend has any a composite artifact of O (MN) after each<span style="">  </span>i-th friend’s<span style="">  </span>purchase. Check whether one component of the artifact assembles for O (N): while checking whether the i-th friend is able to collect the j-th artifact you have to check, if there is such u, that c[j [u]&gt; a[i][u], if so, the j-th artefact will not be collected, if not, then you have to increase the b[i][j] and update the values in a[i]). </span></p> <p><span lang="EN-US" style="">So.the asymptotics of the processing of all purchases will be O (NQM). Then, we need<span style="">  </span>to make a list of artifacts for each person, keeping their quantity(a total of O (KN + KM), and sort it (a total of O (QlogQ)).</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">Problem D.</span></p> <p><span lang="EN-US" style="">This game is over, because except for a finite number (2) of reflections about the line y = x,the coordinates are changed to non-negative integer (and at least one coordinate is changed to a positive number).</span></p> <p><span lang="EN-US" style="">Algorithm for solving this problem<span style="">  </span>is DFS / BFS (states) where the state is a pair of coordinates, and two logical variables, which denote if the 1 (2) player had reflected a point about the line y = x.</span></p> <p><span lang="EN-US" style="">Total number of states is obtained by S &lt;= 4D^2 (pairs of coordinates) * 4 (Boolean variables).</span></p> <p><span lang="EN-US" style="">Processing of one state takes O (N) actions (do not forget to try to reflect the point about the line y = x, if the player had not made it earlier in the game). Thereby, we have the overall asymptotic O (ND^2), which works on C + + in less than 200ms.</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">Problem E</span></p> <p><span lang="EN-US" style="">To solve this problem you have to do a &quot;move&quot; subsegment and know :</span></p> <p><span lang="EN-US" style=""><span style=""> </span>1. The set B of numbers, meeting once, with the function of extracting the maximum for O (logN) </span></p> <p><span lang="EN-US" style="">2.The set of numbers appearing on this subsegments with keeping the number of times,that this number is found on this subsegments, with function of verifying how many times the number in this subsegments for O (logN).</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">While moving a segment from (a[i] .. a[i + k - 1]) for 1 item left (a[I + 1] .. a[I + k]) you have to:</span></p> <p><span lang="EN-US" style="">1) Check whether a[i] with a[I + k]. If yes, then there is no need to modify the set, otherwise proceed to item 2 and 3.</span></p> <p><span lang="EN-US" style="">2) Check how many times we have a[i] in the set A: if 2, then add a[i] to B, if 1, then remove it from<span style="">  </span>A and B. Do not forget to reduce the corresponding number of occurrences of a[i] in the current segment 1.</span></p> <p><span lang="EN-US" style="">3) Check, how many times we have a[I + k] in the set A: if 0, then add a[i] in the B and A, if 1, then remove it from B. Do not forget to increase the corresponding number of occurrences of a[i] the current interval to 1.</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">After that, if the set is not empty, we should take peak from it.</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">So the asymptotics of this process will be O(NlogN).</span></p> <p><span lang="EN-US" style=""> </span></p> <p><span lang="EN-US" style="">As such data structures<span style="">  </span>set / map(for those who use C + +) and the Cartesian tree are suitable.</span></p><p></p></div></div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/69" class="notice" style="text-decoration: none;">Codeforces Beta Round 63 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-3346-1571").click(function() { var that = this; 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line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/map"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/map"> map </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Mar/22/2011 21:02">13 years ago</span> </li> <li> <a href="/blog/entry/1571#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1571#comments"> 29 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1581"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (20)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="29594" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/P___" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/P___" title="Expert P___" class="rated-user user-blue">P___</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:40">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29594" href="?#comment-29594" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29594" class="CommentVoteFrame" data-commentRating="4" data-commentUserId="333" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+4</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29594"> <div class="moveup"> <div class="ttypography">You don't have to check reflections at all in task D. If player is in loosing position he can reflect coordinates, but the opponent (who had winnig strategy, so didn't use the reflection) also reflects.</div> </div> </div> <div class="reply info"> <a class="comment-29594 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29594 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29594"> <li> <div class="comment"> <table class="comment-table" commentId="29608" commentParentId="29594"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/rizwanhudda" style="position: relative;"> <img src='https://userpic.codeforces.org/616/avatar/255f41799f0df297.jpg'/> </a> <div><a href="/profile/rizwanhudda" title="Expert rizwanhudda" class="rated-user user-blue">rizwanhudda</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:43">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29608" href="?#comment-29608" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29594" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29608" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="616" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29608"> <div class="moveup"> <div class="ttypography">Can you please explain this?</div> </div> </div> <div class="reply info"> <a class="comment-29608 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29608 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29608"> <li> <div class="comment"> <table class="comment-table" commentId="29613" commentParentId="29608"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/riadwaw" style="position: relative;"> <img src='https://userpic.codeforces.org/8452/avatar/7b374574b05a50df.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/riadwaw" title="International Master riadwaw" class="rated-user user-orange">riadwaw</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:47">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29613" href="?#comment-29613" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29608" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29613" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="8452" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29613"> <div class="moveup"> <div class="ttypography">Lets see on game without reflects. Somebody have win strategy.<div><br /></div><div>So, in this game he should use it only after opp's reflection ad win</div></div> </div> </div> <div class="reply info"> <a class="comment-29613 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29613 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29613"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="29616" commentParentId="29608"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/P___" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/P___" title="Expert P___" class="rated-user user-blue">P___</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:50">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29616" href="?#comment-29616" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29608" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="29616" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="29616" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="333" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29616"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">Suppose that we can't make reflections, so for each reachable position you can determine whether player who starts at this position has a winning strategy (no matter what his opponent does) or he must lose no matter what he does. Suppose that the player starts in losing position, so the only rescue for him is to reflect coordinates and then his opponent starts at losing position (if a position is losing/winning, then reflected position has the same state). But since his opponent has a winning strategy without using reflections, you know that he didn't need to use reflection and can use this reflection now to make his opponent start in losing position again.</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-29616 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29616 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29616"> <li> <div class="comment"> <table class="comment-table" commentId="29637" commentParentId="29616"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/rizwanhudda" style="position: relative;"> <img src='https://userpic.codeforces.org/616/avatar/255f41799f0df297.jpg'/> </a> <div><a href="/profile/rizwanhudda" title="Expert rizwanhudda" class="rated-user user-blue">rizwanhudda</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 22:08">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29637" href="?#comment-29637" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29616" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29637" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="616" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29637"> <div class="moveup"> <div class="ttypography">Great explanation..:)</div> </div> </div> <div class="reply info"> <a class="comment-29637 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29637 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29637"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29598" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cauchyk" style="position: relative;"> <img src='https://userpic.codeforces.org/6307/avatar/1be12bd76cca6bd4.jpg'/> </a> <div><a href="/profile/cauchyk" title="Expert cauchyk" class="rated-user user-blue">cauchyk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:41">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29598" href="?#comment-29598" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="29598" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="29598" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6307" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29598"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"></div></div> </div> </div> <div class="reply info"> <a class="comment-29598 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29598 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29598"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29602" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/map" style="position: relative;"> <img src='https://userpic.codeforces.org/8362/avatar/5def203e6aa044bf.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/map" title="International Master map" class="rated-user user-orange">map</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:42">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29602" href="?#comment-29602" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29602" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="8362" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29602"> <div class="moveup"> <div class="ttypography">Yes, of course. You are absolutely right.</div> </div> </div> <div class="reply info"> <a class="comment-29602 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29602 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29602"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29614" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Anurag" style="position: relative;"> <img src='https://userpic.codeforces.org/1040/avatar/83f11106d57a9eef.jpg'/> </a> <div><a href="/profile/Anurag" title="Newbie Anurag" class="rated-user user-gray">Anurag</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:48">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29614" href="?#comment-29614" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29614" class="CommentVoteFrame" data-commentRating="5" data-commentUserId="1040" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+5</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29614"> <div class="moveup"> <div class="ttypography">For problem E , if my solution was O(n<sup>2</sup>) then it would have led to TLE?</div> </div> </div> <div class="reply info"> <a class="comment-29614 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29614 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29614"> <li> <div class="comment"> <table class="comment-table" commentId="29620" commentParentId="29614"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/logic_max" style="position: relative;"> <img src='https://userpic.codeforces.org/6829/avatar/abbf50e9dcdf31d9.jpg'/> </a> <div><a href="/profile/logic_max" title="Expert logic_max" class="rated-user user-blue">logic_max</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 21:53">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29620" href="?#comment-29620" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29614" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29620" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29620"> <div class="moveup"> <div class="ttypography">Yes.</div> </div> </div> <div class="reply info"> <a class="comment-29620 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29620 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29620"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="29703" commentParentId="29614"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Shafaet" style="position: relative;"> <img src='https://userpic.codeforces.org/5137/avatar/bcd103c3d3c35548.jpg'/> </a> <div><a href="/profile/Shafaet" title="Expert Shafaet" class="rated-user user-blue">Shafaet</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/23/2011 15:06">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29703" href="?#comment-29703" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29614" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29703" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5137" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29703"> <div class="moveup"> <div class="ttypography">n=10^5,so n^2 will certainly lead to TLE. <br />Here is my approach:<br /><br />Process first K numbers at once. Store frequencies of each number in hash table and maintain a set which contain values which occurred only once. then process rest of the numbers while taking input. reduce frequency of i-K th number, modify the set according to frequency. <br /><br />Suppose input is:<br />6 3<br />1<br />1<br />2<br />6<br />6<br />First i will process first 3 numbers. so the set will be {2} and map will be freq[1]=2,freq[2]=1. <br />When i get 4th number 6,i will reduce freq of 1st number. freq[1] will become 1 from 2. as it has become 1,the set will be {1,2,6}(as i got 6 for the first time). <br /><br />Then i get 5th number 6,i will reduce freq of 2nd number. freq[1] is now 0. as it went 0 from 1, i need to remove it from set too. so the set becomes{2}(i will remove 6 too as i got it 2 times now).<br /><br />Every time print the largest number from set. If the set is empty print &quot;nothing&quot;. i've used c++ stl &lt;set&gt;.</div> </div> </div> <div class="reply info"> <a class="comment-29703 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29703 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29703"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29632" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cauchyk" style="position: relative;"> <img src='https://userpic.codeforces.org/6307/avatar/1be12bd76cca6bd4.jpg'/> </a> <div><a href="/profile/cauchyk" title="Expert cauchyk" class="rated-user user-blue">cauchyk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 22:02">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29632" href="?#comment-29632" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29632" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6307" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29632"> <div class="moveup"> <div class="ttypography"><div style="text-align: left;"><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 13.0px;">please check my submission for problem C id: 350527 it says answer mismatch in line 2 but it does not...</span></div></div> </div> </div> <div class="reply info"> <a class="comment-29632 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29632 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29632"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29642" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/VladBelous" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/VladBelous" title="Expert VladBelous" class="rated-user user-blue">VladBelous</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 22:14">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29642" href="?#comment-29642" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29642" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3894" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29642"> <div class="moveup"> <div class="ttypography"><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">About D:</span><div><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">&quot;Thereby, we have the overall asymptotic O (ND^2), which works on C + + in less than 600ms&quot;</span><div><font face="verdana, arial, sans-serif"><span style="font-size: 12.0px;line-height: 20.0px;"><br /></span></font></div></span></div><div><font face="verdana, arial, sans-serif"><span style="font-size: 12.0px;line-height: 20.0px;">My solution used the same complexity, but ran in 80ms. Reason (I think) is that once I find a move to a losing position, I declare current position as winning and return (i.e. no need to look at other moves).</span></font></div><div><font face="verdana, arial, sans-serif"><span style="font-size: 12.0px;line-height: 20.0px;">This is trivial optimization, but I think an important one, because some Java solutions with </span></font><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">O(ND^2) failed due to TLE. (600ms in C++ does not leave a good margin)</span></div><div><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><br /></span></div></div> </div> </div> <div class="reply info"> <a class="comment-29642 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29642 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29642"> <li> <div class="comment"> <table class="comment-table" commentId="29644" commentParentId="29642"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/map" style="position: relative;"> <img src='https://userpic.codeforces.org/8362/avatar/5def203e6aa044bf.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/map" title="International Master map" class="rated-user user-orange">map</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/22/2011 22:18">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29644" href="?#comment-29644" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29642" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29644" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="8362" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29644"> <div class="moveup"> <div class="ttypography">200ms. T<span style="font-family: arial , sans-serif;font-size: 13.0px;white-space: nowrap;">yping error. We have same correct JAVA solution.</span></div> </div> </div> <div class="reply info"> <a class="comment-29644 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29644 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29644"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29738" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cornflow" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/cornflow" title="Expert cornflow" class="rated-user user-blue">cornflow</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/23/2011 20:09">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29738" href="?#comment-29738" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="29738" revisionCount="3" revision="3"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">3</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="29738" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14075" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29738"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><p>When I changed &quot;double&quot; to &quot;int&quot; in task E, I've got AC (with double - WA). But I can't find any words in problem statement about representation of numbers in answer. Also I can't find nothing in problem statement to determine if numbers are integers or not...</p></div> </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-29738 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29738 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29738"> <li> <div class="comment"> <table class="comment-table" commentId="29834" commentParentId="29738"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/timmy" style="position: relative;"> <img src='https://userpic.codeforces.org/2446/avatar/d9bd36d3627fc50e.jpg'/> </a> <div><a href="/profile/timmy" title="Expert timmy" class="rated-user user-blue">timmy</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/25/2011 15:27">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29834" href="?#comment-29834" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29738" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29834" class="CommentVoteFrame" class="negative-comment-vote" data-commentRating="-11" data-commentUserId="2446" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">-11</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29834"> <div class="moveup"> <div class="ttypography"><p>ATTENTION! THIS CONTEST SHOULD BE UNRATED!</p><p>Maybe now you will read my message carefully :) I think that Corny is right. His solution works just after replacing &quot;double&quot; to &quot;int&quot;.</p></div> </div> </div> <div class="reply info"> <a class="comment-29834 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29834 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29834"> <li> <div class="comment"> <table class="comment-table" commentId="29903" commentParentId="29834"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cornflow" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/cornflow" title="Expert cornflow" class="rated-user user-blue">cornflow</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/26/2011 11:01">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29903" href="?#comment-29903" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29834" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29903" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14075" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29903"> <div class="moveup"> <div class="ttypography">I've found problem. It with presentation, but it's my fault. When answer is 994790178 I write 9.9479e+008. I should be more careful next time.</div> </div> </div> <div class="reply info"> <a class="comment-29903 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29903 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29903"> <li> <div class="comment"> <table class="comment-table" commentId="29907" commentParentId="29903"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/timmy" style="position: relative;"> <img src='https://userpic.codeforces.org/2446/avatar/d9bd36d3627fc50e.jpg'/> </a> <div><a href="/profile/timmy" title="Expert timmy" class="rated-user user-blue">timmy</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/26/2011 12:19">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29907" href="?#comment-29907" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29903" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29907" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2446" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29907"> <div class="moveup"> <div class="ttypography"><p>Really? Ok, try to output floating-point numbers with 1e-10 precision.</p><p>I think result would be the same :) </p></div> </div> </div> <div class="reply info"> <a class="comment-29907 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29907 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29907"> <li> <div class="comment"> <table class="comment-table" commentId="29946" commentParentId="29907"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/cornflow" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/cornflow" title="Expert cornflow" class="rated-user user-blue">cornflow</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/26/2011 18:38">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29946" href="?#comment-29946" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29907" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29946" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14075" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29946"> <div class="moveup"> <div class="ttypography">I've tried to output correct floating-point numbers. It got WA. So maybe statement should be more precise.</div> </div> </div> <div class="reply info"> <a class="comment-29946 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29946 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29946"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="29748" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mostafa_fahim" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/mostafa_fahim" title="Expert mostafa_fahim" class="rated-user user-blue">mostafa_fahim</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/23/2011 21:57">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29748" href="?#comment-29748" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29748" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5382" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29748"> <div class="moveup"> <div class="ttypography">About Task C <div>for this input </div><div><span style="font-family: verdana , arial , sans-serif;font-size: 11.0px;"><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">1 1 2 2 a b: a 2 c: a 1 1 a 1 a  </pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">I am printing </pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><span style="font-family: verdana , arial , sans-serif;white-space: normal;"><pre class="output" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">1 </pre></span>b 1</pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">while the answer is</pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><span style="font-family: verdana , arial , sans-serif;white-space: normal;"><pre class="answer" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">1 </pre></span>c 2</pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);"><br /></pre><pre class="input" style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;font-size: 11.0px;border-top-width: 1.0px;border-right-width: 1.0px;border-bottom-width: 1.0px;border-left-width: 1.0px;border-right-style: solid;border-bottom-style: solid;border-left-style: solid;border-top-color: rgb(170,170,170);border-right-color: rgb(170,170,170);border-bottom-color: rgb(170,170,170);border-left-color: rgb(170,170,170);background-color: rgb(238,238,238);">I can't see why my output is wrong (I think both outputs are correct in this case) <br /></pre></span></div></div> </div> </div> <div class="reply info"> <a class="comment-29748 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29748 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29748"> <li> <div class="comment"> <table class="comment-table" commentId="29774" commentParentId="29748"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/adavydow" style="position: relative;"> <img src='https://userpic.codeforces.org/2385/avatar/11fa80222a24e45c.jpg'/> </a> <div><a href="/profile/adavydow" title="Master adavydow" class="rated-user user-orange">adavydow</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/23/2011 22:55">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-29774" href="?#comment-29774" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-29748" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="29774" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="2385" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-29774"> <div class="moveup"> <div class="ttypography">&quot;It is guaranteed that after the <span class="tex-span"><i>i</i></span>-th purchase no more than one opportunity to collect the composite artifact appears. If such an opportunity arose, the hero must take advantage of it.&quot;<br />So your solution is wrong. After buyin first 'a' artifact player has oportunity to build artifact 'c' but in your solution he didn't take advantage of it, he waited for the second 'a' to compose 'b'</div> </div> </div> <div class="reply info"> <a class="comment-29774 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-29774 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-29774"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1581" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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70A
70
A
en
A. Cookies
<div class="problem-statement"><div class="header"><div class="title">A. Cookies</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Fangy collects cookies. Once he decided to take a box and put cookies into it in some way. If we take a square <span class="tex-span"><i>k</i> × <i>k</i></span> in size, divided into blocks <span class="tex-span">1 × 1</span> in size and paint there the main diagonal together with cells, which lie above it, then the painted area will be equal to the area occupied by one cookie <span class="tex-span"><i>k</i></span> in size. Fangy also has a box with a square base <span class="tex-span">2<sup class="upper-index"><i>n</i></sup> × 2<sup class="upper-index"><i>n</i></sup></span>, divided into blocks <span class="tex-span">1 × 1</span> in size. In a box the cookies should not overlap, and they should not be turned over or rotated. See cookies of sizes <span class="tex-span">2</span> and <span class="tex-span">4</span> respectively on the figure: </p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/e8dd202a2adae78f835e32a5a7e412e81fe560aa.png" style="max-width: 100.0%;max-height: 100.0%;"/> </center> <p>To stack the cookies the little walrus uses the following algorithm. He takes out of the repository the largest cookie which can fit in some place in the box and puts it there. Everything could be perfect but alas, in the repository the little walrus has infinitely many cookies of size <span class="tex-span">2</span> and larger, and there are no cookies of size <span class="tex-span">1</span>, therefore, empty cells will remain in the box. Fangy wants to know how many empty cells will be left in the end.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains a single integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">0 ≤ <i>n</i> ≤ 1000</span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print the single number, equal to the number of empty cells in the box. The answer should be printed modulo <span class="tex-span">10<sup class="upper-index">6</sup> + 3</span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br/></pre></div><div class="output"><div class="title">Output</div><pre>9</pre></div></div></div><div class="note"><div class="section-title">Note</div><p>If the box possesses the base of <span class="tex-span">2<sup class="upper-index">3</sup> × 2<sup class="upper-index">3</sup></span> (as in the example), then the cookies will be put there in the following manner: </p><center><img class="tex-graphics" src="https://espresso.codeforces.com/56a5f9a583d6799457fb7b8720da1cacc4f34111.png" style="max-width: 100.0%;max-height: 100.0%;"/></center></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="A" data-uuid="ps_55fe0dc8bbdbf6dc44fff57694ee3a4978a4ed5f"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">A. Cookies</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Fangy collects cookies. Once he decided to take a box and put cookies into it in some way. If we take a square <span class="tex-span"><i>k</i> × <i>k</i></span> in size, divided into blocks <span class="tex-span">1 × 1</span> in size and paint there the main diagonal together with cells, which lie above it, then the painted area will be equal to the area occupied by one cookie <span class="tex-span"><i>k</i></span> in size. Fangy also has a box with a square base <span class="tex-span">2<sup class="upper-index"><i>n</i></sup> × 2<sup class="upper-index"><i>n</i></sup></span>, divided into blocks <span class="tex-span">1 × 1</span> in size. In a box the cookies should not overlap, and they should not be turned over or rotated. See cookies of sizes <span class="tex-span">2</span> and <span class="tex-span">4</span> respectively on the figure: </p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/e8dd202a2adae78f835e32a5a7e412e81fe560aa.png" style="max-width: 100.0%;max-height: 100.0%;" /> </center> <p>To stack the cookies the little walrus uses the following algorithm. He takes out of the repository the largest cookie which can fit in some place in the box and puts it there. Everything could be perfect but alas, in the repository the little walrus has infinitely many cookies of size <span class="tex-span">2</span> and larger, and there are no cookies of size <span class="tex-span">1</span>, therefore, empty cells will remain in the box. Fangy wants to know how many empty cells will be left in the end.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains a single integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">0 ≤ <i>n</i> ≤ 1000</span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print the single number, equal to the number of empty cells in the box. The answer should be printed modulo <span class="tex-span">10<sup class="upper-index">6</sup> + 3</span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br /></pre></div><div class="output"><div class="title">Output</div><pre>9</pre></div></div></div><div class="note"><div class="section-title">Note</div><p>If the box possesses the base of <span class="tex-span">2<sup class="upper-index">3</sup> × 2<sup class="upper-index">3</sup></span> (as in the example), then the cookies will be put there in the following manner: </p><center><img class="tex-graphics" src="https://espresso.codeforces.com/56a5f9a583d6799457fb7b8720da1cacc4f34111.png" style="max-width: 100.0%;max-height: 100.0%;" /></center></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=A]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); 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["Mathematics including integration, differential equations, etc"]
["math", "*1300"]
https://codeforces.com/blog/entry/1598
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After performing the same actions with the three half-filled squares we will get nine half-filled squares of size <span class="tex-span">2<sup class="upper-index"><i>n</i> - 2</sup> × 2<sup class="upper-index"><i>n</i> - 2</sup></span> and so on. It's easy to get the formula <span class="tex-span"><i>f</i>(<i>n</i>) = 3 * <i>f</i>(<i>n</i> - 1)</span>, <span class="tex-span"><i>f</i>(0) = <i>f</i>(1) = 1</span>. <span class="tex-span">3<sup class="upper-index"><i>n</i> - 1</sup></span> (for <span class="tex-span"><i>n</i> &gt; 0</span>) and <span class="tex-span">1</span> (for <span class="tex-span"><i>n</i> = 0</span>).<br /><p><strong> </strong><strong>Problem </strong><strong>B.</strong><strong><br /></strong></p><p>It's obviously, that sentences should be added into the SMS greedily. Really, if we put the sentence into the new message, when it's possible to add into previous, the number of messages may be increased. The only thing you should pay attention is correct processing whitespaces between the sentences.</p><p><strong> </strong><strong>Problem </strong><strong>C.</strong></p><p>Will be added soon.</p><p>Let's learn how to solve more easy problem: it's need to count a number of lucky tickets with <span class="tex-span">1 ≤ <i>a</i> ≤ <i>x</i></span> and <span class="tex-span">1 ≤ <i>b</i> ≤ <i>y</i></span>. Rewrite sentence <span class="tex-span"><i>a</i> * <i>b</i> = <i>rev</i>(<i>a</i>) * <i>rev</i>(<i>b</i>)</span> as <span class="tex-span"><i>a</i> / <i>rev</i>(<i>a</i>) = <i>rev</i>(<i>b</i>) / <i>b</i></span>. Brute all <span class="tex-span"><i>a</i></span> and count a number of irreducible fractions <span class="tex-span"><i>a</i> / <i>rev</i>(<i>a</i>)</span> using, for example, map from STL. Now for every <span class="tex-span"><i>b</i></span> you should count the number of fractions <span class="tex-span"><i>a</i> / <i>rev</i>(<i>a</i>)</span> equal to <span class="tex-span"><i>rev</i>(<i>b</i>) / <i>b</i></span> and add to answer.<br /><br />Come back to our problem. <br /><br />If the number of lucky tickets with <span class="tex-span">1 ≤ <i>a</i> ≤ <i>max</i><sub class="lower-index"><i>x</i></sub></span> and <span class="tex-span">1 ≤ <i>b</i> ≤ <i>max</i><sub class="lower-index"><i>y</i></sub></span> less than <span class="tex-span"><i>w</i></span>, it should be printed <span class="tex-span"> - 1</span>. If the solution exist, let's use the method of two pointers. <br /><br />We need to keep up the quantity of lucky tickets with <span class="tex-span">1 ≤ <i>a</i> ≤ <i>x</i></span> and <span class="tex-span">1 ≤ <i>b</i> ≤ <i>y</i></span> for some state <span class="tex-span">(<i>x</i>, <i>y</i>)</span> an change it to (x,y+1), (x+1,y), (x,y-1), (x-1,y). That's why we create two structures of type map (named m1 and m2). Let's learn how to change state from (x,y) to (x,y+1), (x+1,y), (x,y-1), (x-1,y). If we want to increase  (decrase) the value of <span class="tex-span"><i>x</i></span>, we should add (subtract) m2[x/rev(x)] to (from) the number of lucky tickets and increase (decrease) m1[x/rev(x)] by one. In the case of changing <span class="tex-span"><i>y</i></span> you should do the similar actions.<br /><br />Let's set the state <span class="tex-span">(<i>x</i>, <i>y</i>)</span>, where <span class="tex-span"><i>x</i> = <i>max</i><sub class="lower-index"><i>x</i></sub></span>, <span class="tex-span"><i>y</i> = 1</span> and count the quantity of lucky tickets for it. We will be increase <span class="tex-span"><i>y</i></span>, while the number of lucky tickets is less than <span class="tex-span"><i>w</i></span>. Obviously, that it will be the least <span class="tex-span"><i>y</i></span> for <span class="tex-span"><i>x</i></span>, such as it will be enough lucky tickets in the range. Relax the answer. You had to decrease <span class="tex-span"><i>x</i></span> by one and do the same actions while <span class="tex-span"><i>x</i></span> is greater than one.</p><p>The anser have the least value of <span class="tex-span"><i>x</i> * <i>y</i></span> because we relaxed it with the optimal state for <u>every</u> <span class="tex-span"><i>x</i></span>.<br /><br />So, the <span class="tex-span"><i>x</i></span> was equael to every value between <span class="tex-span">1</span> and <span class="tex-span"><i>max</i><sub class="lower-index"><i>x</i></sub></span> not more than once. The similar is correct for <span class="tex-span"><i>y</i></span> because it was only increasing. The time need for change the value in map is O(log(map_size)), that's why the algorithm lave an asymptotic form as <span class="tex-span"><i>O</i>(<i>max</i><sub class="lower-index"><i>x</i></sub> * <i>log</i>(<i>max</i><sub class="lower-index"><i>y</i></sub>) + <i>max</i><sub class="lower-index"><i>y</i></sub> * <i>log</i>(<i>max</i><sub class="lower-index"><i>x</i></sub>))</span>.</p><p><strong> </strong><strong>Problem </strong><strong>D.</strong><strong><br /></strong></p><p>Notice, that any point from the triangle based on first three points will be into the area bounded with the convex hull in the future. Let choose one of these points ad set it as the origin. All points of convex hull will keep in structure like map in C++, where the key is the angle of vector from the origin to a point. No two points from the hull will have the same angle.</p><p>How to answer the second-type queries? For the point from the query (<span class="tex-span"><i>A</i></span>) let's find the closest point clockwise (<span class="tex-span"><i>B</i></span>) and the closest point anticlockwise (<span class="tex-span"><i>C</i></span>). If the vectors <span class="tex-span"><i>AB</i></span> and <span class="tex-span"><i>AC</i></span> make up a clockwise rotation, then point A doesn't lay into the convex or on it's bounds. </p><p>How to answer the first-type queries? If the point from the query (<span class="tex-span"><i>C</i></span>) lays into the convex hull, then do nothing else let's find two closest points clockwise relative to point <span class="tex-span"><i>C</i></span> (the closest will be named <span class="tex-span"><i>A</i></span>, tho other will be named <span class="tex-span"><i>B</i></span>). If rotation from the vector <span class="tex-span"><i>AB</i></span> to the vector <span class="tex-span"><i>AC</i></span> is a counterclockwise rotation then processing points laying clockwise relative to point <span class="tex-span"><i>C</i></span> in ended, else you have to delete point <span class="tex-span"><i>A</i></span> from the structure and repeat the same actions. The similar actions you should apply to points anticlockwise relative to point <span class="tex-span"><i>C</i></span>.<br /><br />All points will be added and deleted in the structure not more than once. These operations need <span class="tex-span"><i>O</i>(<i>log</i>(<i>h</i>))</span> time, where <span class="tex-span"><i>h</i></span> is a number of point in convex hull. Total  asymptotic form is <span class="tex-span"><i>O</i>(<i>q</i> * <i>log</i>(<i>h</i>))</span>.</p><p><strong> </strong><strong>Problem </strong><strong>E.</strong></p><p>Notice next facts. If we have the fixed state of some regional centers then for every city will be assigned the nearest regional center. The regional center of some city will be assigned for all cities between this city and it's regional center. It means that tree should be divided into some subtrees. Also define <span class="tex-span"><i>d</i>[0] = 0</span>.<br /><br />Let's solve the problem using &quot;crossed&quot; Dynamic Programming.<br /><br />First function of DP. D1(T, g, x, s) will be responsible for forming the subtree with the regional center g. T is somme subtree of tree from the input defined with edge <span class="tex-span"><i>uv</i></span>. regional center g must be situated in T. Let's consider that <span class="tex-span"><i>g</i></span> is assigned to <span class="tex-span"><i>v</i></span>. The aim will be considered in choosing edges which will bound our subtree. Picture:<br /></p><p><img src="/predownloaded/54/0f/540fe8f5eb82d70bf170ded0318f02c50d79bed4.jpg" style="max-width: 100.0%;max-height: 100.0%;" /></p><p>Green and red edges connect cities which g was assigned. Purple edge bounds the set of such cities. Notice, that vertexes laying on the red pass cannot be bounding, because g is assigned to v. <br /><br />Let <span class="tex-span"><i>xs</i></span> edge be bounding, then for subtree <span class="tex-span"><i>T</i>'</span> (vertexes of it's subtree are into the circle) call the secnod funtion of DP <span class="tex-span"><i>D</i>2(<i>T</i>')</span>.<br /></p><p>The second function of DP will brute every point of subtree <span class="tex-span"><i>T</i>'</span> as a regional center and call D1.<br /></p><p>D1 have <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">3</sup>)</span> states, because the number of subtrees <span class="tex-span"><i>T</i></span> is <span class="tex-span"><i>O</i>(<i>n</i>)</span>, number of options to choose g is the same and pair (x;s) makes up an edge, number of edges is 2*n-2. The second function of DP has <span class="tex-span"><i>O</i>(<i>v</i>)</span> states and transition need <span class="tex-span"><i>O</i>(<i>v</i>)</span> iterations. Thats why solution need <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">3</sup>)</span> memory and have asymptotic form <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">3</sup>)</span>.</p></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/70" class="notice" style="text-decoration: none;">Codeforces Beta Round 64</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-531-1598").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "531", blogEntryId: "1598", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); 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top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30158" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30158" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="11753" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30158"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">thank's for your very good Analaysis. ;)</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30158 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30158 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30158"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30458" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 13:28">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30458" href="?#comment-30458" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30458" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30458"> <div class="moveup"> <div class="ttypography">Hi,<br /><br />Sorry, I dont really understand the analysis and have a few questions. Hope that you can help me out. Thanks!<br /><br />Problem D:<br /><br />May I know why the first three points of the input will definitely be in the convex hull? Is such an input impossible?<br /><br />1 1 0<br />1 0 0<br />1 0 1<br />1 -1 2<br />1 2 -1<br />1 -1 -1<br /><br />In such an input, the convex hull will be (-1,2) (-1,-1) (2,-1).<br /><br />Also, for the queries B and C, how do you find the nearest point anti-clockwise and clockwise? Which line of reference do you take to determine whether a point is clockwise or anti-clockwise? And may I know how do you find the nearest point efficiently?<br /><br />Problem E:<br /><br />I am not too sure about the DP state definition :(. <br /><br />I think that what you are saying that first, you root the tree. Then, suppose the edge uv is bounding. Then you are going to get a subtree T, which is bounded by the edge uv. In this subtree, you choose g as the regional centre. Then you try each edge and try to set it as a bounding edge for the next subtree. Suppose you have chosen the edge xs. Then you recursively work on this new subtree. You call DP 2 to bruteforce which vertex should be regional centre be located at. Then you call DP 1 again. So say you call the next subtree T' and the node you are building regional centre p. Then you will call DP1 (T', p, x, s). <br /><br />Is this what you are saying? Please correct me if I am wrong. <br /><br />Also, may I know how do you represent a subtree in your DP state? And it seems to me that given any tree, there are a lot more than N different subtrees (for example, given a line graph I think there are about N^2 different subtrees. There are about N^2 different sets of endpoints you can choose from, and each set defines a unique subtree). Am I missing something here?<br /><br />Sorry, I am new to this kind of DP, so my questions might sound a bit obvious XD. Thanks a lot!</div> </div> </div> <div class="reply info"> <a class="comment-30458 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30458 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30458"> <li> <div class="comment"> <table class="comment-table" commentId="30471" commentParentId="30458"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Connector" style="position: relative;"> <img src='https://userpic.codeforces.org/1490/avatar/a8c455a6747f4912.jpg'/> </a> <div><a href="/profile/Connector" title="Candidate Master Connector" class="rated-user user-violet">Connector</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 14:37">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30471" href="?#comment-30471" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30458" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30471" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30471" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="1490" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30471"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><p>Sorry, posted message in the wrong place: <a href="https://codeforces.com/blog/entry/1598#comment-30470">http://codeforces.com/blog/entry/1598#comment-30470</a></p></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30471 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30471 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30471"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30470" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Connector" style="position: relative;"> <img src='https://userpic.codeforces.org/1490/avatar/a8c455a6747f4912.jpg'/> </a> <div><a href="/profile/Connector" title="Candidate Master Connector" class="rated-user user-violet">Connector</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 14:32">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30470" href="?#comment-30470" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30470" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="1490" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30470"> <div class="moveup"> <div class="ttypography"><p>D.</p><p><strong>UPD:</strong> any point from the triangle based on first three points will be<u> into the area bounded with the convex hull</u> in the future.</p><p>To find the nearest point efficiently use binary search tree (if you write in C++ you can use map class).</p><p>E. </p><p>Yes, you understood what I mean. You should recursively bruteforce xs edge. T is represented in next way: edge uv divides tree into two subtrees, T is one of these subtrees containing vertex v.</p><p><br /></p></div> </div> </div> <div class="reply info"> <a class="comment-30470 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30470 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30470"> <li> <div class="comment"> <table class="comment-table" commentId="30495" commentParentId="30470"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 19:02">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30495" href="?#comment-30495" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30470" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30495" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30495"> <div class="moveup"> <div class="ttypography">Hi,<br /><br />Thanks for your reply! I think I understand how to do problem D now.<br /><br />But I am still not too sure about problem E. I dont quite understand the function DP 2. What does it store? Does DP 2[x] store the min cost if you build a regional centre at x? But won't the answer be different if your subtree is different? What is the recursion for DP 2 like?<br /><br />Thanks in advance again!</div> </div> </div> <div class="reply info"> <a class="comment-30495 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30495 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30495"> <li> <div class="comment"> <table class="comment-table" commentId="30497" commentParentId="30495"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Connector" style="position: relative;"> <img src='https://userpic.codeforces.org/1490/avatar/a8c455a6747f4912.jpg'/> </a> <div><a href="/profile/Connector" title="Candidate Master Connector" class="rated-user user-violet">Connector</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 19:26">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30497" href="?#comment-30497" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30495" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30497" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1490" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30497"> <div class="moveup"> <div class="ttypography">D2[T'] store the minimum cost of the maintaining the subtree T'. Let's T' be represented with the edge uv using the way described in previous post. Bruteforce all the vertexes in the sebtree T'. Let the vertex g will be fixed, let's say that it is some regional center assigned to v. Call the D1(T',g,g,0 (the first neighbour)) and relax the answer for the D2[T'] with the returned value.</div> </div> </div> <div class="reply info"> <a class="comment-30497 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30497 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30497"> <li> <div class="comment"> <table class="comment-table" commentId="30557" commentParentId="30497"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 14:06">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30557" href="?#comment-30557" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30497" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30557" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30557" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30557"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">Hi,<br /><br />I have finally understood how this works. Thanks! =D<br /><br />Is it possible for you to look at this problem and give me your thoughts? It does sound very similar. Thanks in advance! <a href="//codeforces.com/blog/entry/1621">http://codeforces.com/blog/entry/1621</a></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30557 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30557 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30557"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1608" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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70B
70
B
en
B. Text Messaging
<div class="problem-statement"><div class="header"><div class="title">B. Text Messaging</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Fangy the little walrus, as all the modern walruses, loves to communicate via text messaging. One day he faced the following problem: When he sends large texts, they are split into parts each containing <span class="tex-span"><i>n</i></span> characters (which is the size of one text message). Thus, whole sentences and words get split!</p><p>Fangy did not like it, so he faced the task of breaking the text into minimal messages on his own so that no sentence were broken into pieces when it is sent and the number of text messages to be sent would be minimal. If two consecutive sentences are in different messages, the space between them can be ignored (Fangy does not write this space).</p><p>The little walrus's text looks in the following manner: </p><pre class="verbatim">TEXT ::= SENTENCE | SENTENCE SPACE TEXT<br/>SENTENCE ::= WORD SPACE SENTENCE | WORD END<br/>END ::= {'.', '?', '!'}<br/>WORD ::= LETTER | LETTER WORD<br/>LETTER ::= {'a'..'z', 'A'..'Z'}<br/>SPACE ::= ' '<br/></pre><p>SPACE stands for the symbol of a space.</p><p>So, how many messages did Fangy send?</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains an integer <span class="tex-span"><i>n</i></span>, which is the size of one message (<span class="tex-span">2 ≤ <i>n</i> ≤ 255</span>). The second line contains the text. The length of the text does not exceed <span class="tex-span">10<sup class="upper-index">4</sup></span> characters. It is guaranteed that the text satisfies the above described format. Specifically, this implies that the text is not empty.</p></div><div class="output-specification"><div class="section-title">Output</div><p>On the first and only line print the number of text messages Fangy will need. If it is impossible to split the text, print "<span class="tex-font-style-tt">Impossible</span>" without the quotes.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>25<br/>Hello. I am a little walrus.<br/></pre></div><div class="output"><div class="title">Output</div><pre>2<br/></pre></div><div class="input"><div class="title">Input</div><pre>2<br/>How are you?<br/></pre></div><div class="output"><div class="title">Output</div><pre>Impossible<br/></pre></div><div class="input"><div class="title">Input</div><pre>19<br/>Hello! Do you like fish? Why?<br/></pre></div><div class="output"><div class="title">Output</div><pre>3<br/></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>Let's take a look at the third sample. The text will be split into three messages: "<span class="tex-font-style-tt">Hello!</span>", "<span class="tex-font-style-tt">Do you like fish?</span>" and "<span class="tex-font-style-tt">Why?</span>".</p></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="B" data-uuid="ps_5ecdc0306721f9596030c9d39339c3afee2916f1"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">B. Text Messaging</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Fangy the little walrus, as all the modern walruses, loves to communicate via text messaging. One day he faced the following problem: When he sends large texts, they are split into parts each containing <span class="tex-span"><i>n</i></span> characters (which is the size of one text message). Thus, whole sentences and words get split!</p><p>Fangy did not like it, so he faced the task of breaking the text into minimal messages on his own so that no sentence were broken into pieces when it is sent and the number of text messages to be sent would be minimal. If two consecutive sentences are in different messages, the space between them can be ignored (Fangy does not write this space).</p><p>The little walrus's text looks in the following manner: </p><pre class="verbatim">TEXT ::= SENTENCE | SENTENCE SPACE TEXT<br />SENTENCE ::= WORD SPACE SENTENCE | WORD END<br />END ::= {'.', '?', '!'}<br />WORD ::= LETTER | LETTER WORD<br />LETTER ::= {'a'..'z', 'A'..'Z'}<br />SPACE ::= ' '<br /></pre><p>SPACE stands for the symbol of a space.</p><p>So, how many messages did Fangy send?</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains an integer <span class="tex-span"><i>n</i></span>, which is the size of one message (<span class="tex-span">2 ≤ <i>n</i> ≤ 255</span>). The second line contains the text. The length of the text does not exceed <span class="tex-span">10<sup class="upper-index">4</sup></span> characters. It is guaranteed that the text satisfies the above described format. Specifically, this implies that the text is not empty.</p></div><div class="output-specification"><div class="section-title">Output</div><p>On the first and only line print the number of text messages Fangy will need. If it is impossible to split the text, print &quot;<span class="tex-font-style-tt">Impossible</span>&quot; without the quotes.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>25<br />Hello. I am a little walrus.<br /></pre></div><div class="output"><div class="title">Output</div><pre>2<br /></pre></div><div class="input"><div class="title">Input</div><pre>2<br />How are you?<br /></pre></div><div class="output"><div class="title">Output</div><pre>Impossible<br /></pre></div><div class="input"><div class="title">Input</div><pre>19<br />Hello! Do you like fish? Why?<br /></pre></div><div class="output"><div class="title">Output</div><pre>3<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>Let's take a look at the third sample. 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["Parsing expression grammar", "Greedy algorithms", "Prefix- and Z-functions, suffix structures, Knuth\u2013Morris\u2013Pratt algorithm, etc"]
["expression parsing", "greedy", "strings", "*1600"]
https://codeforces.com/blog/entry/1598
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After performing the same actions with the three half-filled squares we will get nine half-filled squares of size <span class="tex-span">2<sup class="upper-index"><i>n</i> - 2</sup> × 2<sup class="upper-index"><i>n</i> - 2</sup></span> and so on. It's easy to get the formula <span class="tex-span"><i>f</i>(<i>n</i>) = 3 * <i>f</i>(<i>n</i> - 1)</span>, <span class="tex-span"><i>f</i>(0) = <i>f</i>(1) = 1</span>. <span class="tex-span">3<sup class="upper-index"><i>n</i> - 1</sup></span> (for <span class="tex-span"><i>n</i> &gt; 0</span>) and <span class="tex-span">1</span> (for <span class="tex-span"><i>n</i> = 0</span>).<br /><p><strong> </strong><strong>Problem </strong><strong>B.</strong><strong><br /></strong></p><p>It's obviously, that sentences should be added into the SMS greedily. Really, if we put the sentence into the new message, when it's possible to add into previous, the number of messages may be increased. The only thing you should pay attention is correct processing whitespaces between the sentences.</p><p><strong> </strong><strong>Problem </strong><strong>C.</strong></p><p>Will be added soon.</p><p>Let's learn how to solve more easy problem: it's need to count a number of lucky tickets with <span class="tex-span">1 ≤ <i>a</i> ≤ <i>x</i></span> and <span class="tex-span">1 ≤ <i>b</i> ≤ <i>y</i></span>. Rewrite sentence <span class="tex-span"><i>a</i> * <i>b</i> = <i>rev</i>(<i>a</i>) * <i>rev</i>(<i>b</i>)</span> as <span class="tex-span"><i>a</i> / <i>rev</i>(<i>a</i>) = <i>rev</i>(<i>b</i>) / <i>b</i></span>. Brute all <span class="tex-span"><i>a</i></span> and count a number of irreducible fractions <span class="tex-span"><i>a</i> / <i>rev</i>(<i>a</i>)</span> using, for example, map from STL. Now for every <span class="tex-span"><i>b</i></span> you should count the number of fractions <span class="tex-span"><i>a</i> / <i>rev</i>(<i>a</i>)</span> equal to <span class="tex-span"><i>rev</i>(<i>b</i>) / <i>b</i></span> and add to answer.<br /><br />Come back to our problem. <br /><br />If the number of lucky tickets with <span class="tex-span">1 ≤ <i>a</i> ≤ <i>max</i><sub class="lower-index"><i>x</i></sub></span> and <span class="tex-span">1 ≤ <i>b</i> ≤ <i>max</i><sub class="lower-index"><i>y</i></sub></span> less than <span class="tex-span"><i>w</i></span>, it should be printed <span class="tex-span"> - 1</span>. If the solution exist, let's use the method of two pointers. <br /><br />We need to keep up the quantity of lucky tickets with <span class="tex-span">1 ≤ <i>a</i> ≤ <i>x</i></span> and <span class="tex-span">1 ≤ <i>b</i> ≤ <i>y</i></span> for some state <span class="tex-span">(<i>x</i>, <i>y</i>)</span> an change it to (x,y+1), (x+1,y), (x,y-1), (x-1,y). That's why we create two structures of type map (named m1 and m2). Let's learn how to change state from (x,y) to (x,y+1), (x+1,y), (x,y-1), (x-1,y). If we want to increase  (decrase) the value of <span class="tex-span"><i>x</i></span>, we should add (subtract) m2[x/rev(x)] to (from) the number of lucky tickets and increase (decrease) m1[x/rev(x)] by one. In the case of changing <span class="tex-span"><i>y</i></span> you should do the similar actions.<br /><br />Let's set the state <span class="tex-span">(<i>x</i>, <i>y</i>)</span>, where <span class="tex-span"><i>x</i> = <i>max</i><sub class="lower-index"><i>x</i></sub></span>, <span class="tex-span"><i>y</i> = 1</span> and count the quantity of lucky tickets for it. We will be increase <span class="tex-span"><i>y</i></span>, while the number of lucky tickets is less than <span class="tex-span"><i>w</i></span>. Obviously, that it will be the least <span class="tex-span"><i>y</i></span> for <span class="tex-span"><i>x</i></span>, such as it will be enough lucky tickets in the range. Relax the answer. You had to decrease <span class="tex-span"><i>x</i></span> by one and do the same actions while <span class="tex-span"><i>x</i></span> is greater than one.</p><p>The anser have the least value of <span class="tex-span"><i>x</i> * <i>y</i></span> because we relaxed it with the optimal state for <u>every</u> <span class="tex-span"><i>x</i></span>.<br /><br />So, the <span class="tex-span"><i>x</i></span> was equael to every value between <span class="tex-span">1</span> and <span class="tex-span"><i>max</i><sub class="lower-index"><i>x</i></sub></span> not more than once. The similar is correct for <span class="tex-span"><i>y</i></span> because it was only increasing. The time need for change the value in map is O(log(map_size)), that's why the algorithm lave an asymptotic form as <span class="tex-span"><i>O</i>(<i>max</i><sub class="lower-index"><i>x</i></sub> * <i>log</i>(<i>max</i><sub class="lower-index"><i>y</i></sub>) + <i>max</i><sub class="lower-index"><i>y</i></sub> * <i>log</i>(<i>max</i><sub class="lower-index"><i>x</i></sub>))</span>.</p><p><strong> </strong><strong>Problem </strong><strong>D.</strong><strong><br /></strong></p><p>Notice, that any point from the triangle based on first three points will be into the area bounded with the convex hull in the future. Let choose one of these points ad set it as the origin. All points of convex hull will keep in structure like map in C++, where the key is the angle of vector from the origin to a point. No two points from the hull will have the same angle.</p><p>How to answer the second-type queries? For the point from the query (<span class="tex-span"><i>A</i></span>) let's find the closest point clockwise (<span class="tex-span"><i>B</i></span>) and the closest point anticlockwise (<span class="tex-span"><i>C</i></span>). If the vectors <span class="tex-span"><i>AB</i></span> and <span class="tex-span"><i>AC</i></span> make up a clockwise rotation, then point A doesn't lay into the convex or on it's bounds. </p><p>How to answer the first-type queries? If the point from the query (<span class="tex-span"><i>C</i></span>) lays into the convex hull, then do nothing else let's find two closest points clockwise relative to point <span class="tex-span"><i>C</i></span> (the closest will be named <span class="tex-span"><i>A</i></span>, tho other will be named <span class="tex-span"><i>B</i></span>). If rotation from the vector <span class="tex-span"><i>AB</i></span> to the vector <span class="tex-span"><i>AC</i></span> is a counterclockwise rotation then processing points laying clockwise relative to point <span class="tex-span"><i>C</i></span> in ended, else you have to delete point <span class="tex-span"><i>A</i></span> from the structure and repeat the same actions. The similar actions you should apply to points anticlockwise relative to point <span class="tex-span"><i>C</i></span>.<br /><br />All points will be added and deleted in the structure not more than once. These operations need <span class="tex-span"><i>O</i>(<i>log</i>(<i>h</i>))</span> time, where <span class="tex-span"><i>h</i></span> is a number of point in convex hull. Total  asymptotic form is <span class="tex-span"><i>O</i>(<i>q</i> * <i>log</i>(<i>h</i>))</span>.</p><p><strong> </strong><strong>Problem </strong><strong>E.</strong></p><p>Notice next facts. If we have the fixed state of some regional centers then for every city will be assigned the nearest regional center. The regional center of some city will be assigned for all cities between this city and it's regional center. It means that tree should be divided into some subtrees. Also define <span class="tex-span"><i>d</i>[0] = 0</span>.<br /><br />Let's solve the problem using &quot;crossed&quot; Dynamic Programming.<br /><br />First function of DP. D1(T, g, x, s) will be responsible for forming the subtree with the regional center g. T is somme subtree of tree from the input defined with edge <span class="tex-span"><i>uv</i></span>. regional center g must be situated in T. Let's consider that <span class="tex-span"><i>g</i></span> is assigned to <span class="tex-span"><i>v</i></span>. The aim will be considered in choosing edges which will bound our subtree. Picture:<br /></p><p><img src="/predownloaded/54/0f/540fe8f5eb82d70bf170ded0318f02c50d79bed4.jpg" style="max-width: 100.0%;max-height: 100.0%;" /></p><p>Green and red edges connect cities which g was assigned. Purple edge bounds the set of such cities. Notice, that vertexes laying on the red pass cannot be bounding, because g is assigned to v. <br /><br />Let <span class="tex-span"><i>xs</i></span> edge be bounding, then for subtree <span class="tex-span"><i>T</i>'</span> (vertexes of it's subtree are into the circle) call the secnod funtion of DP <span class="tex-span"><i>D</i>2(<i>T</i>')</span>.<br /></p><p>The second function of DP will brute every point of subtree <span class="tex-span"><i>T</i>'</span> as a regional center and call D1.<br /></p><p>D1 have <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">3</sup>)</span> states, because the number of subtrees <span class="tex-span"><i>T</i></span> is <span class="tex-span"><i>O</i>(<i>n</i>)</span>, number of options to choose g is the same and pair (x;s) makes up an edge, number of edges is 2*n-2. The second function of DP has <span class="tex-span"><i>O</i>(<i>v</i>)</span> states and transition need <span class="tex-span"><i>O</i>(<i>v</i>)</span> iterations. Thats why solution need <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">3</sup>)</span> memory and have asymptotic form <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">3</sup>)</span>.</p></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/70" class="notice" style="text-decoration: none;">Codeforces Beta Round 64</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-531-1598").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "531", blogEntryId: "1598", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); 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top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30158" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30158" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="11753" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30158"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">thank's for your very good Analaysis. ;)</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30158 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30158 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30158"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30458" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 13:28">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30458" href="?#comment-30458" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30458" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30458"> <div class="moveup"> <div class="ttypography">Hi,<br /><br />Sorry, I dont really understand the analysis and have a few questions. Hope that you can help me out. Thanks!<br /><br />Problem D:<br /><br />May I know why the first three points of the input will definitely be in the convex hull? Is such an input impossible?<br /><br />1 1 0<br />1 0 0<br />1 0 1<br />1 -1 2<br />1 2 -1<br />1 -1 -1<br /><br />In such an input, the convex hull will be (-1,2) (-1,-1) (2,-1).<br /><br />Also, for the queries B and C, how do you find the nearest point anti-clockwise and clockwise? Which line of reference do you take to determine whether a point is clockwise or anti-clockwise? And may I know how do you find the nearest point efficiently?<br /><br />Problem E:<br /><br />I am not too sure about the DP state definition :(. <br /><br />I think that what you are saying that first, you root the tree. Then, suppose the edge uv is bounding. Then you are going to get a subtree T, which is bounded by the edge uv. In this subtree, you choose g as the regional centre. Then you try each edge and try to set it as a bounding edge for the next subtree. Suppose you have chosen the edge xs. Then you recursively work on this new subtree. You call DP 2 to bruteforce which vertex should be regional centre be located at. Then you call DP 1 again. So say you call the next subtree T' and the node you are building regional centre p. Then you will call DP1 (T', p, x, s). <br /><br />Is this what you are saying? Please correct me if I am wrong. <br /><br />Also, may I know how do you represent a subtree in your DP state? And it seems to me that given any tree, there are a lot more than N different subtrees (for example, given a line graph I think there are about N^2 different subtrees. There are about N^2 different sets of endpoints you can choose from, and each set defines a unique subtree). Am I missing something here?<br /><br />Sorry, I am new to this kind of DP, so my questions might sound a bit obvious XD. Thanks a lot!</div> </div> </div> <div class="reply info"> <a class="comment-30458 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30458 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30458"> <li> <div class="comment"> <table class="comment-table" commentId="30471" commentParentId="30458"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Connector" style="position: relative;"> <img src='https://userpic.codeforces.org/1490/avatar/a8c455a6747f4912.jpg'/> </a> <div><a href="/profile/Connector" title="Candidate Master Connector" class="rated-user user-violet">Connector</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 14:37">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30471" href="?#comment-30471" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30458" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30471" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30471" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="1490" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30471"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><p>Sorry, posted message in the wrong place: <a href="https://codeforces.com/blog/entry/1598#comment-30470">http://codeforces.com/blog/entry/1598#comment-30470</a></p></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30471 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30471 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30471"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30470" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Connector" style="position: relative;"> <img src='https://userpic.codeforces.org/1490/avatar/a8c455a6747f4912.jpg'/> </a> <div><a href="/profile/Connector" title="Candidate Master Connector" class="rated-user user-violet">Connector</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 14:32">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30470" href="?#comment-30470" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30470" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="1490" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30470"> <div class="moveup"> <div class="ttypography"><p>D.</p><p><strong>UPD:</strong> any point from the triangle based on first three points will be<u> into the area bounded with the convex hull</u> in the future.</p><p>To find the nearest point efficiently use binary search tree (if you write in C++ you can use map class).</p><p>E. </p><p>Yes, you understood what I mean. You should recursively bruteforce xs edge. T is represented in next way: edge uv divides tree into two subtrees, T is one of these subtrees containing vertex v.</p><p><br /></p></div> </div> </div> <div class="reply info"> <a class="comment-30470 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30470 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30470"> <li> <div class="comment"> <table class="comment-table" commentId="30495" commentParentId="30470"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 19:02">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30495" href="?#comment-30495" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30470" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30495" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30495"> <div class="moveup"> <div class="ttypography">Hi,<br /><br />Thanks for your reply! I think I understand how to do problem D now.<br /><br />But I am still not too sure about problem E. I dont quite understand the function DP 2. What does it store? Does DP 2[x] store the min cost if you build a regional centre at x? But won't the answer be different if your subtree is different? What is the recursion for DP 2 like?<br /><br />Thanks in advance again!</div> </div> </div> <div class="reply info"> <a class="comment-30495 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30495 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30495"> <li> <div class="comment"> <table class="comment-table" commentId="30497" commentParentId="30495"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Connector" style="position: relative;"> <img src='https://userpic.codeforces.org/1490/avatar/a8c455a6747f4912.jpg'/> </a> <div><a href="/profile/Connector" title="Candidate Master Connector" class="rated-user user-violet">Connector</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 19:26">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30497" href="?#comment-30497" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30495" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30497" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1490" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30497"> <div class="moveup"> <div class="ttypography">D2[T'] store the minimum cost of the maintaining the subtree T'. Let's T' be represented with the edge uv using the way described in previous post. Bruteforce all the vertexes in the sebtree T'. Let the vertex g will be fixed, let's say that it is some regional center assigned to v. Call the D1(T',g,g,0 (the first neighbour)) and relax the answer for the D2[T'] with the returned value.</div> </div> </div> <div class="reply info"> <a class="comment-30497 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30497 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30497"> <li> <div class="comment"> <table class="comment-table" commentId="30557" commentParentId="30497"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 14:06">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30557" href="?#comment-30557" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30497" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30557" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30557" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30557"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">Hi,<br /><br />I have finally understood how this works. Thanks! =D<br /><br />Is it possible for you to look at this problem and give me your thoughts? It does sound very similar. Thanks in advance! <a href="//codeforces.com/blog/entry/1621">http://codeforces.com/blog/entry/1621</a></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30557 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30557 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30557"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1608" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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70C
70
C
en
C. Lucky Tickets
<div class="problem-statement"><div class="header"><div class="title">C. Lucky Tickets</div><div class="time-limit"><div class="property-title">time limit per test</div>1.5 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>In Walrusland public transport tickets are characterized by two integers: by the number of the series and by the number of the ticket in the series. Let the series number be represented by <span class="tex-span"><i>a</i></span> and the ticket number — by <span class="tex-span"><i>b</i></span>, then a ticket is described by the ordered pair of numbers <span class="tex-span">(<i>a</i>, <i>b</i>)</span>. </p><p>The walruses believe that a ticket is lucky if <span class="tex-span"><i>a</i> * <i>b</i> = <i>rev</i>(<i>a</i>) * <i>rev</i>(<i>b</i>)</span>. The function <span class="tex-span"><i>rev</i>(<i>x</i>)</span> reverses a number written in the decimal system, at that the leading zeroes disappear. For example, <span class="tex-span"><i>rev</i>(12343) = 34321</span>, <span class="tex-span"><i>rev</i>(1200) = 21</span>.</p><p>The Public Transport Management Committee wants to release <span class="tex-span"><i>x</i></span> series, each containing <span class="tex-span"><i>y</i></span> tickets, so that <span class="tex-font-style-bf">at</span> <span class="tex-font-style-bf">least</span> <span class="tex-span"><i>w</i></span> lucky tickets were released and the total number of released tickets (<span class="tex-span"><i>x</i> * <i>y</i></span>) were minimum. The series are numbered from <span class="tex-span">1</span> to <span class="tex-span"><i>x</i></span> inclusive. The tickets in each series are numbered from <span class="tex-span">1</span> to <span class="tex-span"><i>y</i></span> inclusive. The Transport Committee cannot release more than <span class="tex-span"><i>max</i><sub class="lower-index"><i>x</i></sub></span> series and more than <span class="tex-span"><i>max</i><sub class="lower-index"><i>y</i></sub></span> tickets in one series.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains three integers <span class="tex-span"><i>max</i><sub class="lower-index"><i>x</i></sub></span>, <span class="tex-span"><i>max</i><sub class="lower-index"><i>y</i></sub></span>, <span class="tex-span"><i>w</i></span> (<span class="tex-span">1 ≤ <i>max</i><sub class="lower-index"><i>x</i></sub>, <i>max</i><sub class="lower-index"><i>y</i></sub> ≤ 10<sup class="upper-index">5</sup></span>, <span class="tex-span">1 ≤ <i>w</i> ≤ 10<sup class="upper-index">7</sup></span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print on a single line two space-separated numbers, the <span class="tex-span"><i>x</i></span> and the <span class="tex-span"><i>y</i></span>. If there are several possible variants, print any of them. If such <span class="tex-span"><i>x</i></span> and <span class="tex-span"><i>y</i></span> do not exist, print a single number <span class="tex-span"> - 1</span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2 2 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>1 1</pre></div><div class="input"><div class="title">Input</div><pre>132 10 35<br/></pre></div><div class="output"><div class="title">Output</div><pre>7 5</pre></div><div class="input"><div class="title">Input</div><pre>5 18 1000<br/></pre></div><div class="output"><div class="title">Output</div><pre>-1<br/></pre></div><div class="input"><div class="title">Input</div><pre>48 132 235<br/></pre></div><div class="output"><div class="title">Output</div><pre>22 111</pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="C" data-uuid="ps_ea0d732fd86c797b9a8875eeb4594b80970cdd5c"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. Lucky Tickets</div><div class="time-limit"><div class="property-title">time limit per test</div>1.5 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>In Walrusland public transport tickets are characterized by two integers: by the number of the series and by the number of the ticket in the series. Let the series number be represented by <span class="tex-span"><i>a</i></span> and the ticket number — by <span class="tex-span"><i>b</i></span>, then a ticket is described by the ordered pair of numbers <span class="tex-span">(<i>a</i>, <i>b</i>)</span>. </p><p>The walruses believe that a ticket is lucky if <span class="tex-span"><i>a</i> * <i>b</i> = <i>rev</i>(<i>a</i>) * <i>rev</i>(<i>b</i>)</span>. The function <span class="tex-span"><i>rev</i>(<i>x</i>)</span> reverses a number written in the decimal system, at that the leading zeroes disappear. For example, <span class="tex-span"><i>rev</i>(12343) = 34321</span>, <span class="tex-span"><i>rev</i>(1200) = 21</span>.</p><p>The Public Transport Management Committee wants to release <span class="tex-span"><i>x</i></span> series, each containing <span class="tex-span"><i>y</i></span> tickets, so that <span class="tex-font-style-bf">at</span> <span class="tex-font-style-bf">least</span> <span class="tex-span"><i>w</i></span> lucky tickets were released and the total number of released tickets (<span class="tex-span"><i>x</i> * <i>y</i></span>) were minimum. The series are numbered from <span class="tex-span">1</span> to <span class="tex-span"><i>x</i></span> inclusive. The tickets in each series are numbered from <span class="tex-span">1</span> to <span class="tex-span"><i>y</i></span> inclusive. The Transport Committee cannot release more than <span class="tex-span"><i>max</i><sub class="lower-index"><i>x</i></sub></span> series and more than <span class="tex-span"><i>max</i><sub class="lower-index"><i>y</i></sub></span> tickets in one series.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains three integers <span class="tex-span"><i>max</i><sub class="lower-index"><i>x</i></sub></span>, <span class="tex-span"><i>max</i><sub class="lower-index"><i>y</i></sub></span>, <span class="tex-span"><i>w</i></span> (<span class="tex-span">1 ≤ <i>max</i><sub class="lower-index"><i>x</i></sub>, <i>max</i><sub class="lower-index"><i>y</i></sub> ≤ 10<sup class="upper-index">5</sup></span>, <span class="tex-span">1 ≤ <i>w</i> ≤ 10<sup class="upper-index">7</sup></span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print on a single line two space-separated numbers, the <span class="tex-span"><i>x</i></span> and the <span class="tex-span"><i>y</i></span>. If there are several possible variants, print any of them. If such <span class="tex-span"><i>x</i></span> and <span class="tex-span"><i>y</i></span> do not exist, print a single number <span class="tex-span"> - 1</span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2 2 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>1 1</pre></div><div class="input"><div class="title">Input</div><pre>132 10 35<br /></pre></div><div class="output"><div class="title">Output</div><pre>7 5</pre></div><div class="input"><div class="title">Input</div><pre>5 18 1000<br /></pre></div><div class="output"><div class="title">Output</div><pre>-1<br /></pre></div><div class="input"><div class="title">Input</div><pre>48 132 235<br /></pre></div><div class="output"><div class="title">Output</div><pre>22 111</pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=C]"); 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["Binary search", "Heaps, binary search trees, segment trees, hash tables, etc", "Sortings, orderings", "Two pointers"]
["binary search", "data structures", "sortings", "two pointers", "*2200"]
https://codeforces.com/blog/entry/1598
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After performing the same actions with the three half-filled squares we will get nine half-filled squares of size <span class="tex-span">2<sup class="upper-index"><i>n</i> - 2</sup> × 2<sup class="upper-index"><i>n</i> - 2</sup></span> and so on. It's easy to get the formula <span class="tex-span"><i>f</i>(<i>n</i>) = 3 * <i>f</i>(<i>n</i> - 1)</span>, <span class="tex-span"><i>f</i>(0) = <i>f</i>(1) = 1</span>. <span class="tex-span">3<sup class="upper-index"><i>n</i> - 1</sup></span> (for <span class="tex-span"><i>n</i> &gt; 0</span>) and <span class="tex-span">1</span> (for <span class="tex-span"><i>n</i> = 0</span>).<br /><p><strong> </strong><strong>Problem </strong><strong>B.</strong><strong><br /></strong></p><p>It's obviously, that sentences should be added into the SMS greedily. Really, if we put the sentence into the new message, when it's possible to add into previous, the number of messages may be increased. The only thing you should pay attention is correct processing whitespaces between the sentences.</p><p><strong> </strong><strong>Problem </strong><strong>C.</strong></p><p>Will be added soon.</p><p>Let's learn how to solve more easy problem: it's need to count a number of lucky tickets with <span class="tex-span">1 ≤ <i>a</i> ≤ <i>x</i></span> and <span class="tex-span">1 ≤ <i>b</i> ≤ <i>y</i></span>. Rewrite sentence <span class="tex-span"><i>a</i> * <i>b</i> = <i>rev</i>(<i>a</i>) * <i>rev</i>(<i>b</i>)</span> as <span class="tex-span"><i>a</i> / <i>rev</i>(<i>a</i>) = <i>rev</i>(<i>b</i>) / <i>b</i></span>. Brute all <span class="tex-span"><i>a</i></span> and count a number of irreducible fractions <span class="tex-span"><i>a</i> / <i>rev</i>(<i>a</i>)</span> using, for example, map from STL. Now for every <span class="tex-span"><i>b</i></span> you should count the number of fractions <span class="tex-span"><i>a</i> / <i>rev</i>(<i>a</i>)</span> equal to <span class="tex-span"><i>rev</i>(<i>b</i>) / <i>b</i></span> and add to answer.<br /><br />Come back to our problem. <br /><br />If the number of lucky tickets with <span class="tex-span">1 ≤ <i>a</i> ≤ <i>max</i><sub class="lower-index"><i>x</i></sub></span> and <span class="tex-span">1 ≤ <i>b</i> ≤ <i>max</i><sub class="lower-index"><i>y</i></sub></span> less than <span class="tex-span"><i>w</i></span>, it should be printed <span class="tex-span"> - 1</span>. If the solution exist, let's use the method of two pointers. <br /><br />We need to keep up the quantity of lucky tickets with <span class="tex-span">1 ≤ <i>a</i> ≤ <i>x</i></span> and <span class="tex-span">1 ≤ <i>b</i> ≤ <i>y</i></span> for some state <span class="tex-span">(<i>x</i>, <i>y</i>)</span> an change it to (x,y+1), (x+1,y), (x,y-1), (x-1,y). That's why we create two structures of type map (named m1 and m2). Let's learn how to change state from (x,y) to (x,y+1), (x+1,y), (x,y-1), (x-1,y). If we want to increase  (decrase) the value of <span class="tex-span"><i>x</i></span>, we should add (subtract) m2[x/rev(x)] to (from) the number of lucky tickets and increase (decrease) m1[x/rev(x)] by one. In the case of changing <span class="tex-span"><i>y</i></span> you should do the similar actions.<br /><br />Let's set the state <span class="tex-span">(<i>x</i>, <i>y</i>)</span>, where <span class="tex-span"><i>x</i> = <i>max</i><sub class="lower-index"><i>x</i></sub></span>, <span class="tex-span"><i>y</i> = 1</span> and count the quantity of lucky tickets for it. We will be increase <span class="tex-span"><i>y</i></span>, while the number of lucky tickets is less than <span class="tex-span"><i>w</i></span>. Obviously, that it will be the least <span class="tex-span"><i>y</i></span> for <span class="tex-span"><i>x</i></span>, such as it will be enough lucky tickets in the range. Relax the answer. You had to decrease <span class="tex-span"><i>x</i></span> by one and do the same actions while <span class="tex-span"><i>x</i></span> is greater than one.</p><p>The anser have the least value of <span class="tex-span"><i>x</i> * <i>y</i></span> because we relaxed it with the optimal state for <u>every</u> <span class="tex-span"><i>x</i></span>.<br /><br />So, the <span class="tex-span"><i>x</i></span> was equael to every value between <span class="tex-span">1</span> and <span class="tex-span"><i>max</i><sub class="lower-index"><i>x</i></sub></span> not more than once. The similar is correct for <span class="tex-span"><i>y</i></span> because it was only increasing. The time need for change the value in map is O(log(map_size)), that's why the algorithm lave an asymptotic form as <span class="tex-span"><i>O</i>(<i>max</i><sub class="lower-index"><i>x</i></sub> * <i>log</i>(<i>max</i><sub class="lower-index"><i>y</i></sub>) + <i>max</i><sub class="lower-index"><i>y</i></sub> * <i>log</i>(<i>max</i><sub class="lower-index"><i>x</i></sub>))</span>.</p><p><strong> </strong><strong>Problem </strong><strong>D.</strong><strong><br /></strong></p><p>Notice, that any point from the triangle based on first three points will be into the area bounded with the convex hull in the future. Let choose one of these points ad set it as the origin. All points of convex hull will keep in structure like map in C++, where the key is the angle of vector from the origin to a point. No two points from the hull will have the same angle.</p><p>How to answer the second-type queries? For the point from the query (<span class="tex-span"><i>A</i></span>) let's find the closest point clockwise (<span class="tex-span"><i>B</i></span>) and the closest point anticlockwise (<span class="tex-span"><i>C</i></span>). If the vectors <span class="tex-span"><i>AB</i></span> and <span class="tex-span"><i>AC</i></span> make up a clockwise rotation, then point A doesn't lay into the convex or on it's bounds. </p><p>How to answer the first-type queries? If the point from the query (<span class="tex-span"><i>C</i></span>) lays into the convex hull, then do nothing else let's find two closest points clockwise relative to point <span class="tex-span"><i>C</i></span> (the closest will be named <span class="tex-span"><i>A</i></span>, tho other will be named <span class="tex-span"><i>B</i></span>). If rotation from the vector <span class="tex-span"><i>AB</i></span> to the vector <span class="tex-span"><i>AC</i></span> is a counterclockwise rotation then processing points laying clockwise relative to point <span class="tex-span"><i>C</i></span> in ended, else you have to delete point <span class="tex-span"><i>A</i></span> from the structure and repeat the same actions. The similar actions you should apply to points anticlockwise relative to point <span class="tex-span"><i>C</i></span>.<br /><br />All points will be added and deleted in the structure not more than once. These operations need <span class="tex-span"><i>O</i>(<i>log</i>(<i>h</i>))</span> time, where <span class="tex-span"><i>h</i></span> is a number of point in convex hull. Total  asymptotic form is <span class="tex-span"><i>O</i>(<i>q</i> * <i>log</i>(<i>h</i>))</span>.</p><p><strong> </strong><strong>Problem </strong><strong>E.</strong></p><p>Notice next facts. If we have the fixed state of some regional centers then for every city will be assigned the nearest regional center. The regional center of some city will be assigned for all cities between this city and it's regional center. It means that tree should be divided into some subtrees. Also define <span class="tex-span"><i>d</i>[0] = 0</span>.<br /><br />Let's solve the problem using &quot;crossed&quot; Dynamic Programming.<br /><br />First function of DP. D1(T, g, x, s) will be responsible for forming the subtree with the regional center g. T is somme subtree of tree from the input defined with edge <span class="tex-span"><i>uv</i></span>. regional center g must be situated in T. Let's consider that <span class="tex-span"><i>g</i></span> is assigned to <span class="tex-span"><i>v</i></span>. The aim will be considered in choosing edges which will bound our subtree. Picture:<br /></p><p><img src="/predownloaded/54/0f/540fe8f5eb82d70bf170ded0318f02c50d79bed4.jpg" style="max-width: 100.0%;max-height: 100.0%;" /></p><p>Green and red edges connect cities which g was assigned. Purple edge bounds the set of such cities. Notice, that vertexes laying on the red pass cannot be bounding, because g is assigned to v. <br /><br />Let <span class="tex-span"><i>xs</i></span> edge be bounding, then for subtree <span class="tex-span"><i>T</i>'</span> (vertexes of it's subtree are into the circle) call the secnod funtion of DP <span class="tex-span"><i>D</i>2(<i>T</i>')</span>.<br /></p><p>The second function of DP will brute every point of subtree <span class="tex-span"><i>T</i>'</span> as a regional center and call D1.<br /></p><p>D1 have <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">3</sup>)</span> states, because the number of subtrees <span class="tex-span"><i>T</i></span> is <span class="tex-span"><i>O</i>(<i>n</i>)</span>, number of options to choose g is the same and pair (x;s) makes up an edge, number of edges is 2*n-2. The second function of DP has <span class="tex-span"><i>O</i>(<i>v</i>)</span> states and transition need <span class="tex-span"><i>O</i>(<i>v</i>)</span> iterations. Thats why solution need <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">3</sup>)</span> memory and have asymptotic form <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">3</sup>)</span>.</p></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/70" class="notice" style="text-decoration: none;">Codeforces Beta Round 64</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-531-1598").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "531", blogEntryId: "1598", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); 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top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30158" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30158" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="11753" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30158"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">thank's for your very good Analaysis. ;)</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30158 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30158 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30158"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30458" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 13:28">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30458" href="?#comment-30458" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30458" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30458"> <div class="moveup"> <div class="ttypography">Hi,<br /><br />Sorry, I dont really understand the analysis and have a few questions. Hope that you can help me out. Thanks!<br /><br />Problem D:<br /><br />May I know why the first three points of the input will definitely be in the convex hull? Is such an input impossible?<br /><br />1 1 0<br />1 0 0<br />1 0 1<br />1 -1 2<br />1 2 -1<br />1 -1 -1<br /><br />In such an input, the convex hull will be (-1,2) (-1,-1) (2,-1).<br /><br />Also, for the queries B and C, how do you find the nearest point anti-clockwise and clockwise? Which line of reference do you take to determine whether a point is clockwise or anti-clockwise? And may I know how do you find the nearest point efficiently?<br /><br />Problem E:<br /><br />I am not too sure about the DP state definition :(. <br /><br />I think that what you are saying that first, you root the tree. Then, suppose the edge uv is bounding. Then you are going to get a subtree T, which is bounded by the edge uv. In this subtree, you choose g as the regional centre. Then you try each edge and try to set it as a bounding edge for the next subtree. Suppose you have chosen the edge xs. Then you recursively work on this new subtree. You call DP 2 to bruteforce which vertex should be regional centre be located at. Then you call DP 1 again. So say you call the next subtree T' and the node you are building regional centre p. Then you will call DP1 (T', p, x, s). <br /><br />Is this what you are saying? Please correct me if I am wrong. <br /><br />Also, may I know how do you represent a subtree in your DP state? And it seems to me that given any tree, there are a lot more than N different subtrees (for example, given a line graph I think there are about N^2 different subtrees. There are about N^2 different sets of endpoints you can choose from, and each set defines a unique subtree). Am I missing something here?<br /><br />Sorry, I am new to this kind of DP, so my questions might sound a bit obvious XD. Thanks a lot!</div> </div> </div> <div class="reply info"> <a class="comment-30458 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30458 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30458"> <li> <div class="comment"> <table class="comment-table" commentId="30471" commentParentId="30458"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Connector" style="position: relative;"> <img src='https://userpic.codeforces.org/1490/avatar/a8c455a6747f4912.jpg'/> </a> <div><a href="/profile/Connector" title="Candidate Master Connector" class="rated-user user-violet">Connector</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 14:37">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30471" href="?#comment-30471" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30458" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30471" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30471" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="1490" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30471"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><p>Sorry, posted message in the wrong place: <a href="https://codeforces.com/blog/entry/1598#comment-30470">http://codeforces.com/blog/entry/1598#comment-30470</a></p></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30471 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30471 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30471"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30470" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Connector" style="position: relative;"> <img src='https://userpic.codeforces.org/1490/avatar/a8c455a6747f4912.jpg'/> </a> <div><a href="/profile/Connector" title="Candidate Master Connector" class="rated-user user-violet">Connector</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 14:32">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30470" href="?#comment-30470" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30470" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="1490" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30470"> <div class="moveup"> <div class="ttypography"><p>D.</p><p><strong>UPD:</strong> any point from the triangle based on first three points will be<u> into the area bounded with the convex hull</u> in the future.</p><p>To find the nearest point efficiently use binary search tree (if you write in C++ you can use map class).</p><p>E. </p><p>Yes, you understood what I mean. You should recursively bruteforce xs edge. T is represented in next way: edge uv divides tree into two subtrees, T is one of these subtrees containing vertex v.</p><p><br /></p></div> </div> </div> <div class="reply info"> <a class="comment-30470 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30470 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30470"> <li> <div class="comment"> <table class="comment-table" commentId="30495" commentParentId="30470"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 19:02">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30495" href="?#comment-30495" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30470" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30495" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30495"> <div class="moveup"> <div class="ttypography">Hi,<br /><br />Thanks for your reply! I think I understand how to do problem D now.<br /><br />But I am still not too sure about problem E. I dont quite understand the function DP 2. What does it store? Does DP 2[x] store the min cost if you build a regional centre at x? But won't the answer be different if your subtree is different? What is the recursion for DP 2 like?<br /><br />Thanks in advance again!</div> </div> </div> <div class="reply info"> <a class="comment-30495 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30495 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30495"> <li> <div class="comment"> <table class="comment-table" commentId="30497" commentParentId="30495"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Connector" style="position: relative;"> <img src='https://userpic.codeforces.org/1490/avatar/a8c455a6747f4912.jpg'/> </a> <div><a href="/profile/Connector" title="Candidate Master Connector" class="rated-user user-violet">Connector</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 19:26">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30497" href="?#comment-30497" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30495" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30497" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1490" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30497"> <div class="moveup"> <div class="ttypography">D2[T'] store the minimum cost of the maintaining the subtree T'. Let's T' be represented with the edge uv using the way described in previous post. Bruteforce all the vertexes in the sebtree T'. Let the vertex g will be fixed, let's say that it is some regional center assigned to v. Call the D1(T',g,g,0 (the first neighbour)) and relax the answer for the D2[T'] with the returned value.</div> </div> </div> <div class="reply info"> <a class="comment-30497 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30497 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30497"> <li> <div class="comment"> <table class="comment-table" commentId="30557" commentParentId="30497"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 14:06">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30557" href="?#comment-30557" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30497" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30557" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30557" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30557"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">Hi,<br /><br />I have finally understood how this works. Thanks! =D<br /><br />Is it possible for you to look at this problem and give me your thoughts? It does sound very similar. Thanks in advance! <a href="//codeforces.com/blog/entry/1621">http://codeforces.com/blog/entry/1621</a></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30557 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30557 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30557"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1608" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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70D
70
D
en
D. Professor's task
<div class="problem-statement"><div class="header"><div class="title">D. Professor's task</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Once a walrus professor Plato asked his programming students to perform the following practical task. </p><p>The students had to implement such a data structure that would support a convex hull on some set of points <span class="tex-span"><i>S</i></span>. The input to the program had <span class="tex-span"><i>q</i></span> queries of two types: </p><p>1. Add a point with coordinates <span class="tex-span">(<i>x</i>, <i>y</i>)</span> into the set <span class="tex-span"><i>S</i></span>. Note that in this case the convex hull of <span class="tex-span"><i>S</i></span> could have changed, and could have remained the same. </p><p>2. Say whether a point with coordinates <span class="tex-span">(<i>x</i>, <i>y</i>)</span> belongs to an area limited by the convex hull, including the border. </p><p>All the students coped with the task. What about you?</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains an integer <span class="tex-span"><i>q</i></span> (<span class="tex-span">4 ≤ <i>q</i> ≤ 10<sup class="upper-index">5</sup></span>). </p><p>Then follow <span class="tex-span"><i>q</i></span> lines in the following way: "<span class="tex-span"><i>t</i></span> <span class="tex-span"><i>x</i></span> <span class="tex-span"><i>y</i></span>", where <span class="tex-span"><i>t</i></span> is the query type (1 or 2), and <span class="tex-span">(<i>x</i>, <i>y</i>)</span> are the coordinates of the point (<span class="tex-span"> - 10<sup class="upper-index">6</sup> ≤ <i>x</i>, <i>y</i> ≤ 10<sup class="upper-index">6</sup></span>, <span class="tex-span"><i>x</i></span> and <span class="tex-span"><i>y</i></span> are integers). </p><p>There is at least one query of type 2.</p><p>It is guaranteed that the three queries of the first type follow first and the points given in the queries form a non-degenerative triangle. Also all the points added in <span class="tex-span"><i>S</i></span> are distinct.</p></div><div class="output-specification"><div class="section-title">Output</div><p>For each query of the second type print one string containing "<span class="tex-font-style-tt">YES</span>", if the point lies inside the convex hull or on its border. Otherwise, print "<span class="tex-font-style-tt">NO</span>".</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>8<br/>1 0 0<br/>1 2 0<br/>1 2 2<br/>2 1 0<br/>1 0 2<br/>2 1 1<br/>2 2 1<br/>2 20 -1<br/></pre></div><div class="output"><div class="title">Output</div><pre>YES<br/>YES<br/>YES<br/>NO<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="D" data-uuid="ps_d983f1482dd9a9f7513caef4a013144c2e377177"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">D. Professor's task</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Once a walrus professor Plato asked his programming students to perform the following practical task. </p><p>The students had to implement such a data structure that would support a convex hull on some set of points <span class="tex-span"><i>S</i></span>. The input to the program had <span class="tex-span"><i>q</i></span> queries of two types: </p><p>1. Add a point with coordinates <span class="tex-span">(<i>x</i>, <i>y</i>)</span> into the set <span class="tex-span"><i>S</i></span>. Note that in this case the convex hull of <span class="tex-span"><i>S</i></span> could have changed, and could have remained the same. </p><p>2. Say whether a point with coordinates <span class="tex-span">(<i>x</i>, <i>y</i>)</span> belongs to an area limited by the convex hull, including the border. </p><p>All the students coped with the task. What about you?</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains an integer <span class="tex-span"><i>q</i></span> (<span class="tex-span">4 ≤ <i>q</i> ≤ 10<sup class="upper-index">5</sup></span>). </p><p>Then follow <span class="tex-span"><i>q</i></span> lines in the following way: &quot;<span class="tex-span"><i>t</i></span> <span class="tex-span"><i>x</i></span> <span class="tex-span"><i>y</i></span>&quot;, where <span class="tex-span"><i>t</i></span> is the query type (1 or 2), and <span class="tex-span">(<i>x</i>, <i>y</i>)</span> are the coordinates of the point (<span class="tex-span"> - 10<sup class="upper-index">6</sup> ≤ <i>x</i>, <i>y</i> ≤ 10<sup class="upper-index">6</sup></span>, <span class="tex-span"><i>x</i></span> and <span class="tex-span"><i>y</i></span> are integers). </p><p>There is at least one query of type 2.</p><p>It is guaranteed that the three queries of the first type follow first and the points given in the queries form a non-degenerative triangle. Also all the points added in <span class="tex-span"><i>S</i></span> are distinct.</p></div><div class="output-specification"><div class="section-title">Output</div><p>For each query of the second type print one string containing &quot;<span class="tex-font-style-tt">YES</span>&quot;, if the point lies inside the convex hull or on its border. Otherwise, print &quot;<span class="tex-font-style-tt">NO</span>&quot;.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>8<br />1 0 0<br />1 2 0<br />1 2 2<br />2 1 0<br />1 0 2<br />2 1 1<br />2 2 1<br />2 20 -1<br /></pre></div><div class="output"><div class="title">Output</div><pre>YES<br />YES<br />YES<br />NO<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=D]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); if (previousStatementText) { if (previousStatementText !== statementText) { $problem.find(".diff-notifier").show(); $problem.find(".diff-notifier-close").click(function() { Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60); $problem.find(".diff-notifier").hide(); 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["Heaps, binary search trees, segment trees, hash tables, etc", "Geometry, computational geometry"]
["data structures", "geometry", "*2700"]
https://codeforces.com/blog/entry/1598
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After performing the same actions with the three half-filled squares we will get nine half-filled squares of size <span class="tex-span">2<sup class="upper-index"><i>n</i> - 2</sup> × 2<sup class="upper-index"><i>n</i> - 2</sup></span> and so on. It's easy to get the formula <span class="tex-span"><i>f</i>(<i>n</i>) = 3 * <i>f</i>(<i>n</i> - 1)</span>, <span class="tex-span"><i>f</i>(0) = <i>f</i>(1) = 1</span>. <span class="tex-span">3<sup class="upper-index"><i>n</i> - 1</sup></span> (for <span class="tex-span"><i>n</i> &gt; 0</span>) and <span class="tex-span">1</span> (for <span class="tex-span"><i>n</i> = 0</span>).<br /><p><strong> </strong><strong>Problem </strong><strong>B.</strong><strong><br /></strong></p><p>It's obviously, that sentences should be added into the SMS greedily. Really, if we put the sentence into the new message, when it's possible to add into previous, the number of messages may be increased. The only thing you should pay attention is correct processing whitespaces between the sentences.</p><p><strong> </strong><strong>Problem </strong><strong>C.</strong></p><p>Will be added soon.</p><p>Let's learn how to solve more easy problem: it's need to count a number of lucky tickets with <span class="tex-span">1 ≤ <i>a</i> ≤ <i>x</i></span> and <span class="tex-span">1 ≤ <i>b</i> ≤ <i>y</i></span>. Rewrite sentence <span class="tex-span"><i>a</i> * <i>b</i> = <i>rev</i>(<i>a</i>) * <i>rev</i>(<i>b</i>)</span> as <span class="tex-span"><i>a</i> / <i>rev</i>(<i>a</i>) = <i>rev</i>(<i>b</i>) / <i>b</i></span>. Brute all <span class="tex-span"><i>a</i></span> and count a number of irreducible fractions <span class="tex-span"><i>a</i> / <i>rev</i>(<i>a</i>)</span> using, for example, map from STL. Now for every <span class="tex-span"><i>b</i></span> you should count the number of fractions <span class="tex-span"><i>a</i> / <i>rev</i>(<i>a</i>)</span> equal to <span class="tex-span"><i>rev</i>(<i>b</i>) / <i>b</i></span> and add to answer.<br /><br />Come back to our problem. <br /><br />If the number of lucky tickets with <span class="tex-span">1 ≤ <i>a</i> ≤ <i>max</i><sub class="lower-index"><i>x</i></sub></span> and <span class="tex-span">1 ≤ <i>b</i> ≤ <i>max</i><sub class="lower-index"><i>y</i></sub></span> less than <span class="tex-span"><i>w</i></span>, it should be printed <span class="tex-span"> - 1</span>. If the solution exist, let's use the method of two pointers. <br /><br />We need to keep up the quantity of lucky tickets with <span class="tex-span">1 ≤ <i>a</i> ≤ <i>x</i></span> and <span class="tex-span">1 ≤ <i>b</i> ≤ <i>y</i></span> for some state <span class="tex-span">(<i>x</i>, <i>y</i>)</span> an change it to (x,y+1), (x+1,y), (x,y-1), (x-1,y). That's why we create two structures of type map (named m1 and m2). Let's learn how to change state from (x,y) to (x,y+1), (x+1,y), (x,y-1), (x-1,y). If we want to increase  (decrase) the value of <span class="tex-span"><i>x</i></span>, we should add (subtract) m2[x/rev(x)] to (from) the number of lucky tickets and increase (decrease) m1[x/rev(x)] by one. In the case of changing <span class="tex-span"><i>y</i></span> you should do the similar actions.<br /><br />Let's set the state <span class="tex-span">(<i>x</i>, <i>y</i>)</span>, where <span class="tex-span"><i>x</i> = <i>max</i><sub class="lower-index"><i>x</i></sub></span>, <span class="tex-span"><i>y</i> = 1</span> and count the quantity of lucky tickets for it. We will be increase <span class="tex-span"><i>y</i></span>, while the number of lucky tickets is less than <span class="tex-span"><i>w</i></span>. Obviously, that it will be the least <span class="tex-span"><i>y</i></span> for <span class="tex-span"><i>x</i></span>, such as it will be enough lucky tickets in the range. Relax the answer. You had to decrease <span class="tex-span"><i>x</i></span> by one and do the same actions while <span class="tex-span"><i>x</i></span> is greater than one.</p><p>The anser have the least value of <span class="tex-span"><i>x</i> * <i>y</i></span> because we relaxed it with the optimal state for <u>every</u> <span class="tex-span"><i>x</i></span>.<br /><br />So, the <span class="tex-span"><i>x</i></span> was equael to every value between <span class="tex-span">1</span> and <span class="tex-span"><i>max</i><sub class="lower-index"><i>x</i></sub></span> not more than once. The similar is correct for <span class="tex-span"><i>y</i></span> because it was only increasing. The time need for change the value in map is O(log(map_size)), that's why the algorithm lave an asymptotic form as <span class="tex-span"><i>O</i>(<i>max</i><sub class="lower-index"><i>x</i></sub> * <i>log</i>(<i>max</i><sub class="lower-index"><i>y</i></sub>) + <i>max</i><sub class="lower-index"><i>y</i></sub> * <i>log</i>(<i>max</i><sub class="lower-index"><i>x</i></sub>))</span>.</p><p><strong> </strong><strong>Problem </strong><strong>D.</strong><strong><br /></strong></p><p>Notice, that any point from the triangle based on first three points will be into the area bounded with the convex hull in the future. Let choose one of these points ad set it as the origin. All points of convex hull will keep in structure like map in C++, where the key is the angle of vector from the origin to a point. No two points from the hull will have the same angle.</p><p>How to answer the second-type queries? For the point from the query (<span class="tex-span"><i>A</i></span>) let's find the closest point clockwise (<span class="tex-span"><i>B</i></span>) and the closest point anticlockwise (<span class="tex-span"><i>C</i></span>). If the vectors <span class="tex-span"><i>AB</i></span> and <span class="tex-span"><i>AC</i></span> make up a clockwise rotation, then point A doesn't lay into the convex or on it's bounds. </p><p>How to answer the first-type queries? If the point from the query (<span class="tex-span"><i>C</i></span>) lays into the convex hull, then do nothing else let's find two closest points clockwise relative to point <span class="tex-span"><i>C</i></span> (the closest will be named <span class="tex-span"><i>A</i></span>, tho other will be named <span class="tex-span"><i>B</i></span>). If rotation from the vector <span class="tex-span"><i>AB</i></span> to the vector <span class="tex-span"><i>AC</i></span> is a counterclockwise rotation then processing points laying clockwise relative to point <span class="tex-span"><i>C</i></span> in ended, else you have to delete point <span class="tex-span"><i>A</i></span> from the structure and repeat the same actions. The similar actions you should apply to points anticlockwise relative to point <span class="tex-span"><i>C</i></span>.<br /><br />All points will be added and deleted in the structure not more than once. These operations need <span class="tex-span"><i>O</i>(<i>log</i>(<i>h</i>))</span> time, where <span class="tex-span"><i>h</i></span> is a number of point in convex hull. Total  asymptotic form is <span class="tex-span"><i>O</i>(<i>q</i> * <i>log</i>(<i>h</i>))</span>.</p><p><strong> </strong><strong>Problem </strong><strong>E.</strong></p><p>Notice next facts. If we have the fixed state of some regional centers then for every city will be assigned the nearest regional center. The regional center of some city will be assigned for all cities between this city and it's regional center. It means that tree should be divided into some subtrees. Also define <span class="tex-span"><i>d</i>[0] = 0</span>.<br /><br />Let's solve the problem using &quot;crossed&quot; Dynamic Programming.<br /><br />First function of DP. D1(T, g, x, s) will be responsible for forming the subtree with the regional center g. T is somme subtree of tree from the input defined with edge <span class="tex-span"><i>uv</i></span>. regional center g must be situated in T. Let's consider that <span class="tex-span"><i>g</i></span> is assigned to <span class="tex-span"><i>v</i></span>. The aim will be considered in choosing edges which will bound our subtree. Picture:<br /></p><p><img src="/predownloaded/54/0f/540fe8f5eb82d70bf170ded0318f02c50d79bed4.jpg" style="max-width: 100.0%;max-height: 100.0%;" /></p><p>Green and red edges connect cities which g was assigned. Purple edge bounds the set of such cities. Notice, that vertexes laying on the red pass cannot be bounding, because g is assigned to v. <br /><br />Let <span class="tex-span"><i>xs</i></span> edge be bounding, then for subtree <span class="tex-span"><i>T</i>'</span> (vertexes of it's subtree are into the circle) call the secnod funtion of DP <span class="tex-span"><i>D</i>2(<i>T</i>')</span>.<br /></p><p>The second function of DP will brute every point of subtree <span class="tex-span"><i>T</i>'</span> as a regional center and call D1.<br /></p><p>D1 have <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">3</sup>)</span> states, because the number of subtrees <span class="tex-span"><i>T</i></span> is <span class="tex-span"><i>O</i>(<i>n</i>)</span>, number of options to choose g is the same and pair (x;s) makes up an edge, number of edges is 2*n-2. The second function of DP has <span class="tex-span"><i>O</i>(<i>v</i>)</span> states and transition need <span class="tex-span"><i>O</i>(<i>v</i>)</span> iterations. Thats why solution need <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">3</sup>)</span> memory and have asymptotic form <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">3</sup>)</span>.</p></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/70" class="notice" style="text-decoration: none;">Codeforces Beta Round 64</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-531-1598").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "531", blogEntryId: "1598", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); 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top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30158" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30158" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="11753" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30158"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">thank's for your very good Analaysis. ;)</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30158 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30158 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30158"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30458" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 13:28">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30458" href="?#comment-30458" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30458" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30458"> <div class="moveup"> <div class="ttypography">Hi,<br /><br />Sorry, I dont really understand the analysis and have a few questions. Hope that you can help me out. Thanks!<br /><br />Problem D:<br /><br />May I know why the first three points of the input will definitely be in the convex hull? Is such an input impossible?<br /><br />1 1 0<br />1 0 0<br />1 0 1<br />1 -1 2<br />1 2 -1<br />1 -1 -1<br /><br />In such an input, the convex hull will be (-1,2) (-1,-1) (2,-1).<br /><br />Also, for the queries B and C, how do you find the nearest point anti-clockwise and clockwise? Which line of reference do you take to determine whether a point is clockwise or anti-clockwise? And may I know how do you find the nearest point efficiently?<br /><br />Problem E:<br /><br />I am not too sure about the DP state definition :(. <br /><br />I think that what you are saying that first, you root the tree. Then, suppose the edge uv is bounding. Then you are going to get a subtree T, which is bounded by the edge uv. In this subtree, you choose g as the regional centre. Then you try each edge and try to set it as a bounding edge for the next subtree. Suppose you have chosen the edge xs. Then you recursively work on this new subtree. You call DP 2 to bruteforce which vertex should be regional centre be located at. Then you call DP 1 again. So say you call the next subtree T' and the node you are building regional centre p. Then you will call DP1 (T', p, x, s). <br /><br />Is this what you are saying? Please correct me if I am wrong. <br /><br />Also, may I know how do you represent a subtree in your DP state? And it seems to me that given any tree, there are a lot more than N different subtrees (for example, given a line graph I think there are about N^2 different subtrees. There are about N^2 different sets of endpoints you can choose from, and each set defines a unique subtree). Am I missing something here?<br /><br />Sorry, I am new to this kind of DP, so my questions might sound a bit obvious XD. Thanks a lot!</div> </div> </div> <div class="reply info"> <a class="comment-30458 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30458 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30458"> <li> <div class="comment"> <table class="comment-table" commentId="30471" commentParentId="30458"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Connector" style="position: relative;"> <img src='https://userpic.codeforces.org/1490/avatar/a8c455a6747f4912.jpg'/> </a> <div><a href="/profile/Connector" title="Candidate Master Connector" class="rated-user user-violet">Connector</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 14:37">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30471" href="?#comment-30471" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30458" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30471" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30471" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="1490" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30471"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><p>Sorry, posted message in the wrong place: <a href="https://codeforces.com/blog/entry/1598#comment-30470">http://codeforces.com/blog/entry/1598#comment-30470</a></p></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30471 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30471 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30471"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30470" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Connector" style="position: relative;"> <img src='https://userpic.codeforces.org/1490/avatar/a8c455a6747f4912.jpg'/> </a> <div><a href="/profile/Connector" title="Candidate Master Connector" class="rated-user user-violet">Connector</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 14:32">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30470" href="?#comment-30470" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30470" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="1490" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30470"> <div class="moveup"> <div class="ttypography"><p>D.</p><p><strong>UPD:</strong> any point from the triangle based on first three points will be<u> into the area bounded with the convex hull</u> in the future.</p><p>To find the nearest point efficiently use binary search tree (if you write in C++ you can use map class).</p><p>E. </p><p>Yes, you understood what I mean. You should recursively bruteforce xs edge. T is represented in next way: edge uv divides tree into two subtrees, T is one of these subtrees containing vertex v.</p><p><br /></p></div> </div> </div> <div class="reply info"> <a class="comment-30470 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30470 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30470"> <li> <div class="comment"> <table class="comment-table" commentId="30495" commentParentId="30470"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 19:02">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30495" href="?#comment-30495" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30470" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30495" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30495"> <div class="moveup"> <div class="ttypography">Hi,<br /><br />Thanks for your reply! I think I understand how to do problem D now.<br /><br />But I am still not too sure about problem E. I dont quite understand the function DP 2. What does it store? Does DP 2[x] store the min cost if you build a regional centre at x? But won't the answer be different if your subtree is different? What is the recursion for DP 2 like?<br /><br />Thanks in advance again!</div> </div> </div> <div class="reply info"> <a class="comment-30495 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30495 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30495"> <li> <div class="comment"> <table class="comment-table" commentId="30497" commentParentId="30495"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Connector" style="position: relative;"> <img src='https://userpic.codeforces.org/1490/avatar/a8c455a6747f4912.jpg'/> </a> <div><a href="/profile/Connector" title="Candidate Master Connector" class="rated-user user-violet">Connector</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 19:26">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30497" href="?#comment-30497" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30495" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30497" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1490" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30497"> <div class="moveup"> <div class="ttypography">D2[T'] store the minimum cost of the maintaining the subtree T'. Let's T' be represented with the edge uv using the way described in previous post. Bruteforce all the vertexes in the sebtree T'. Let the vertex g will be fixed, let's say that it is some regional center assigned to v. Call the D1(T',g,g,0 (the first neighbour)) and relax the answer for the D2[T'] with the returned value.</div> </div> </div> <div class="reply info"> <a class="comment-30497 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30497 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30497"> <li> <div class="comment"> <table class="comment-table" commentId="30557" commentParentId="30497"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 14:06">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30557" href="?#comment-30557" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30497" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30557" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30557" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30557"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">Hi,<br /><br />I have finally understood how this works. Thanks! =D<br /><br />Is it possible for you to look at this problem and give me your thoughts? It does sound very similar. Thanks in advance! <a href="//codeforces.com/blog/entry/1621">http://codeforces.com/blog/entry/1621</a></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30557 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30557 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30557"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1608" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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70E
70
E
en
E. Information Reform
<div class="problem-statement"><div class="header"><div class="title">E. Information Reform</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Thought it is already the XXI century, the Mass Media isn't very popular in Walrusland. The cities get news from messengers who can only travel along roads. The network of roads in Walrusland is built so that it is possible to get to any city from any other one in exactly one way, and the roads' lengths are equal.</p><p>The North Pole governor decided to carry out an information reform. Several cities were decided to be chosen and made regional centers. Maintaining a region center takes <span class="tex-span"><i>k</i></span> fishlars (which is a local currency) per year. It is assumed that a regional center always has information on the latest news.</p><p>For every city which is not a regional center, it was decided to appoint a regional center which will be responsible for keeping this city informed. In that case the maintenance costs will be equal to <span class="tex-span"><i>d</i><sub class="lower-index"><i>len</i></sub></span> fishlars per year, where <span class="tex-span"><i>len</i></span> is the distance from a city to the corresponding regional center, measured in the number of roads along which one needs to go.</p><p>Your task is to minimize the costs to carry out the reform.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two given numbers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 180, 1 ≤ <i>k</i> ≤ 10<sup class="upper-index">5</sup></span>).</p><p>The second line contains <span class="tex-span"><i>n</i> - 1</span> integers <span class="tex-span"><i>d</i><sub class="lower-index"><i>i</i></sub></span>, numbered starting with 1 (<span class="tex-span"><i>d</i><sub class="lower-index"><i>i</i></sub> ≤ <i>d</i><sub class="lower-index"><i>i</i> + 1</sub>, 0 ≤ <i>d</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">5</sup></span>).</p><p>Next <span class="tex-span"><i>n</i> - 1</span> lines contain the pairs of cities connected by a road.</p></div><div class="output-specification"><div class="section-title">Output</div><p>On the first line print the minimum number of fishlars needed for a year's maintenance. On the second line print <span class="tex-span"><i>n</i></span> numbers, where the <span class="tex-span"><i>i</i></span>-th number will represent the number of the regional center, appointed to the <span class="tex-span"><i>i</i></span>-th city. If the <span class="tex-span"><i>i</i></span>-th city is a regional center itself, then you should print number <span class="tex-span"><i>i</i></span>.</p><p>If there are several solutions to that problem, print any of them.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>8 10<br/>2 5 9 11 15 19 20<br/>1 4<br/>1 3<br/>1 7<br/>4 6<br/>2 8<br/>2 3<br/>3 5<br/></pre></div><div class="output"><div class="title">Output</div><pre>38<br/>3 3 3 4 3 4 3 3 </pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="E" data-uuid="ps_0abe82e3f81ba34af89c253a3b83fee9608b5841"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">E. Information Reform</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Thought it is already the XXI century, the Mass Media isn't very popular in Walrusland. The cities get news from messengers who can only travel along roads. The network of roads in Walrusland is built so that it is possible to get to any city from any other one in exactly one way, and the roads' lengths are equal.</p><p>The North Pole governor decided to carry out an information reform. Several cities were decided to be chosen and made regional centers. Maintaining a region center takes <span class="tex-span"><i>k</i></span> fishlars (which is a local currency) per year. It is assumed that a regional center always has information on the latest news.</p><p>For every city which is not a regional center, it was decided to appoint a regional center which will be responsible for keeping this city informed. In that case the maintenance costs will be equal to <span class="tex-span"><i>d</i><sub class="lower-index"><i>len</i></sub></span> fishlars per year, where <span class="tex-span"><i>len</i></span> is the distance from a city to the corresponding regional center, measured in the number of roads along which one needs to go.</p><p>Your task is to minimize the costs to carry out the reform.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two given numbers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 180, 1 ≤ <i>k</i> ≤ 10<sup class="upper-index">5</sup></span>).</p><p>The second line contains <span class="tex-span"><i>n</i> - 1</span> integers <span class="tex-span"><i>d</i><sub class="lower-index"><i>i</i></sub></span>, numbered starting with 1 (<span class="tex-span"><i>d</i><sub class="lower-index"><i>i</i></sub> ≤ <i>d</i><sub class="lower-index"><i>i</i> + 1</sub>, 0 ≤ <i>d</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">5</sup></span>).</p><p>Next <span class="tex-span"><i>n</i> - 1</span> lines contain the pairs of cities connected by a road.</p></div><div class="output-specification"><div class="section-title">Output</div><p>On the first line print the minimum number of fishlars needed for a year's maintenance. On the second line print <span class="tex-span"><i>n</i></span> numbers, where the <span class="tex-span"><i>i</i></span>-th number will represent the number of the regional center, appointed to the <span class="tex-span"><i>i</i></span>-th city. If the <span class="tex-span"><i>i</i></span>-th city is a regional center itself, then you should print number <span class="tex-span"><i>i</i></span>.</p><p>If there are several solutions to that problem, print any of them.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>8 10<br />2 5 9 11 15 19 20<br />1 4<br />1 3<br />1 7<br />4 6<br />2 8<br />2 3<br />3 5<br /></pre></div><div class="output"><div class="title">Output</div><pre>38<br />3 3 3 4 3 4 3 3 </pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=E]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); if (previousStatementText) { if (previousStatementText !== statementText) { $problem.find(".diff-notifier").show(); 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["Dynamic programming", "Implementation problems, programming technics, simulation", "Trees"]
["dp", "implementation", "trees", "*2700"]
https://codeforces.com/blog/entry/1598
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After performing the same actions with the three half-filled squares we will get nine half-filled squares of size <span class="tex-span">2<sup class="upper-index"><i>n</i> - 2</sup> × 2<sup class="upper-index"><i>n</i> - 2</sup></span> and so on. It's easy to get the formula <span class="tex-span"><i>f</i>(<i>n</i>) = 3 * <i>f</i>(<i>n</i> - 1)</span>, <span class="tex-span"><i>f</i>(0) = <i>f</i>(1) = 1</span>. <span class="tex-span">3<sup class="upper-index"><i>n</i> - 1</sup></span> (for <span class="tex-span"><i>n</i> &gt; 0</span>) and <span class="tex-span">1</span> (for <span class="tex-span"><i>n</i> = 0</span>).<br /><p><strong> </strong><strong>Problem </strong><strong>B.</strong><strong><br /></strong></p><p>It's obviously, that sentences should be added into the SMS greedily. Really, if we put the sentence into the new message, when it's possible to add into previous, the number of messages may be increased. The only thing you should pay attention is correct processing whitespaces between the sentences.</p><p><strong> </strong><strong>Problem </strong><strong>C.</strong></p><p>Will be added soon.</p><p>Let's learn how to solve more easy problem: it's need to count a number of lucky tickets with <span class="tex-span">1 ≤ <i>a</i> ≤ <i>x</i></span> and <span class="tex-span">1 ≤ <i>b</i> ≤ <i>y</i></span>. Rewrite sentence <span class="tex-span"><i>a</i> * <i>b</i> = <i>rev</i>(<i>a</i>) * <i>rev</i>(<i>b</i>)</span> as <span class="tex-span"><i>a</i> / <i>rev</i>(<i>a</i>) = <i>rev</i>(<i>b</i>) / <i>b</i></span>. Brute all <span class="tex-span"><i>a</i></span> and count a number of irreducible fractions <span class="tex-span"><i>a</i> / <i>rev</i>(<i>a</i>)</span> using, for example, map from STL. Now for every <span class="tex-span"><i>b</i></span> you should count the number of fractions <span class="tex-span"><i>a</i> / <i>rev</i>(<i>a</i>)</span> equal to <span class="tex-span"><i>rev</i>(<i>b</i>) / <i>b</i></span> and add to answer.<br /><br />Come back to our problem. <br /><br />If the number of lucky tickets with <span class="tex-span">1 ≤ <i>a</i> ≤ <i>max</i><sub class="lower-index"><i>x</i></sub></span> and <span class="tex-span">1 ≤ <i>b</i> ≤ <i>max</i><sub class="lower-index"><i>y</i></sub></span> less than <span class="tex-span"><i>w</i></span>, it should be printed <span class="tex-span"> - 1</span>. If the solution exist, let's use the method of two pointers. <br /><br />We need to keep up the quantity of lucky tickets with <span class="tex-span">1 ≤ <i>a</i> ≤ <i>x</i></span> and <span class="tex-span">1 ≤ <i>b</i> ≤ <i>y</i></span> for some state <span class="tex-span">(<i>x</i>, <i>y</i>)</span> an change it to (x,y+1), (x+1,y), (x,y-1), (x-1,y). That's why we create two structures of type map (named m1 and m2). Let's learn how to change state from (x,y) to (x,y+1), (x+1,y), (x,y-1), (x-1,y). If we want to increase  (decrase) the value of <span class="tex-span"><i>x</i></span>, we should add (subtract) m2[x/rev(x)] to (from) the number of lucky tickets and increase (decrease) m1[x/rev(x)] by one. In the case of changing <span class="tex-span"><i>y</i></span> you should do the similar actions.<br /><br />Let's set the state <span class="tex-span">(<i>x</i>, <i>y</i>)</span>, where <span class="tex-span"><i>x</i> = <i>max</i><sub class="lower-index"><i>x</i></sub></span>, <span class="tex-span"><i>y</i> = 1</span> and count the quantity of lucky tickets for it. We will be increase <span class="tex-span"><i>y</i></span>, while the number of lucky tickets is less than <span class="tex-span"><i>w</i></span>. Obviously, that it will be the least <span class="tex-span"><i>y</i></span> for <span class="tex-span"><i>x</i></span>, such as it will be enough lucky tickets in the range. Relax the answer. You had to decrease <span class="tex-span"><i>x</i></span> by one and do the same actions while <span class="tex-span"><i>x</i></span> is greater than one.</p><p>The anser have the least value of <span class="tex-span"><i>x</i> * <i>y</i></span> because we relaxed it with the optimal state for <u>every</u> <span class="tex-span"><i>x</i></span>.<br /><br />So, the <span class="tex-span"><i>x</i></span> was equael to every value between <span class="tex-span">1</span> and <span class="tex-span"><i>max</i><sub class="lower-index"><i>x</i></sub></span> not more than once. The similar is correct for <span class="tex-span"><i>y</i></span> because it was only increasing. The time need for change the value in map is O(log(map_size)), that's why the algorithm lave an asymptotic form as <span class="tex-span"><i>O</i>(<i>max</i><sub class="lower-index"><i>x</i></sub> * <i>log</i>(<i>max</i><sub class="lower-index"><i>y</i></sub>) + <i>max</i><sub class="lower-index"><i>y</i></sub> * <i>log</i>(<i>max</i><sub class="lower-index"><i>x</i></sub>))</span>.</p><p><strong> </strong><strong>Problem </strong><strong>D.</strong><strong><br /></strong></p><p>Notice, that any point from the triangle based on first three points will be into the area bounded with the convex hull in the future. Let choose one of these points ad set it as the origin. All points of convex hull will keep in structure like map in C++, where the key is the angle of vector from the origin to a point. No two points from the hull will have the same angle.</p><p>How to answer the second-type queries? For the point from the query (<span class="tex-span"><i>A</i></span>) let's find the closest point clockwise (<span class="tex-span"><i>B</i></span>) and the closest point anticlockwise (<span class="tex-span"><i>C</i></span>). If the vectors <span class="tex-span"><i>AB</i></span> and <span class="tex-span"><i>AC</i></span> make up a clockwise rotation, then point A doesn't lay into the convex or on it's bounds. </p><p>How to answer the first-type queries? If the point from the query (<span class="tex-span"><i>C</i></span>) lays into the convex hull, then do nothing else let's find two closest points clockwise relative to point <span class="tex-span"><i>C</i></span> (the closest will be named <span class="tex-span"><i>A</i></span>, tho other will be named <span class="tex-span"><i>B</i></span>). If rotation from the vector <span class="tex-span"><i>AB</i></span> to the vector <span class="tex-span"><i>AC</i></span> is a counterclockwise rotation then processing points laying clockwise relative to point <span class="tex-span"><i>C</i></span> in ended, else you have to delete point <span class="tex-span"><i>A</i></span> from the structure and repeat the same actions. The similar actions you should apply to points anticlockwise relative to point <span class="tex-span"><i>C</i></span>.<br /><br />All points will be added and deleted in the structure not more than once. These operations need <span class="tex-span"><i>O</i>(<i>log</i>(<i>h</i>))</span> time, where <span class="tex-span"><i>h</i></span> is a number of point in convex hull. Total  asymptotic form is <span class="tex-span"><i>O</i>(<i>q</i> * <i>log</i>(<i>h</i>))</span>.</p><p><strong> </strong><strong>Problem </strong><strong>E.</strong></p><p>Notice next facts. If we have the fixed state of some regional centers then for every city will be assigned the nearest regional center. The regional center of some city will be assigned for all cities between this city and it's regional center. It means that tree should be divided into some subtrees. Also define <span class="tex-span"><i>d</i>[0] = 0</span>.<br /><br />Let's solve the problem using &quot;crossed&quot; Dynamic Programming.<br /><br />First function of DP. D1(T, g, x, s) will be responsible for forming the subtree with the regional center g. T is somme subtree of tree from the input defined with edge <span class="tex-span"><i>uv</i></span>. regional center g must be situated in T. Let's consider that <span class="tex-span"><i>g</i></span> is assigned to <span class="tex-span"><i>v</i></span>. The aim will be considered in choosing edges which will bound our subtree. Picture:<br /></p><p><img src="/predownloaded/54/0f/540fe8f5eb82d70bf170ded0318f02c50d79bed4.jpg" style="max-width: 100.0%;max-height: 100.0%;" /></p><p>Green and red edges connect cities which g was assigned. Purple edge bounds the set of such cities. Notice, that vertexes laying on the red pass cannot be bounding, because g is assigned to v. <br /><br />Let <span class="tex-span"><i>xs</i></span> edge be bounding, then for subtree <span class="tex-span"><i>T</i>'</span> (vertexes of it's subtree are into the circle) call the secnod funtion of DP <span class="tex-span"><i>D</i>2(<i>T</i>')</span>.<br /></p><p>The second function of DP will brute every point of subtree <span class="tex-span"><i>T</i>'</span> as a regional center and call D1.<br /></p><p>D1 have <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">3</sup>)</span> states, because the number of subtrees <span class="tex-span"><i>T</i></span> is <span class="tex-span"><i>O</i>(<i>n</i>)</span>, number of options to choose g is the same and pair (x;s) makes up an edge, number of edges is 2*n-2. The second function of DP has <span class="tex-span"><i>O</i>(<i>v</i>)</span> states and transition need <span class="tex-span"><i>O</i>(<i>v</i>)</span> iterations. Thats why solution need <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">3</sup>)</span> memory and have asymptotic form <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">3</sup>)</span>.</p></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/70" class="notice" style="text-decoration: none;">Codeforces Beta Round 64</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-531-1598").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "531", blogEntryId: "1598", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); 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top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30158" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30158" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="11753" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30158"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">thank's for your very good Analaysis. ;)</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30158 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30158 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30158"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30458" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 13:28">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30458" href="?#comment-30458" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30458" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30458"> <div class="moveup"> <div class="ttypography">Hi,<br /><br />Sorry, I dont really understand the analysis and have a few questions. Hope that you can help me out. Thanks!<br /><br />Problem D:<br /><br />May I know why the first three points of the input will definitely be in the convex hull? Is such an input impossible?<br /><br />1 1 0<br />1 0 0<br />1 0 1<br />1 -1 2<br />1 2 -1<br />1 -1 -1<br /><br />In such an input, the convex hull will be (-1,2) (-1,-1) (2,-1).<br /><br />Also, for the queries B and C, how do you find the nearest point anti-clockwise and clockwise? Which line of reference do you take to determine whether a point is clockwise or anti-clockwise? And may I know how do you find the nearest point efficiently?<br /><br />Problem E:<br /><br />I am not too sure about the DP state definition :(. <br /><br />I think that what you are saying that first, you root the tree. Then, suppose the edge uv is bounding. Then you are going to get a subtree T, which is bounded by the edge uv. In this subtree, you choose g as the regional centre. Then you try each edge and try to set it as a bounding edge for the next subtree. Suppose you have chosen the edge xs. Then you recursively work on this new subtree. You call DP 2 to bruteforce which vertex should be regional centre be located at. Then you call DP 1 again. So say you call the next subtree T' and the node you are building regional centre p. Then you will call DP1 (T', p, x, s). <br /><br />Is this what you are saying? Please correct me if I am wrong. <br /><br />Also, may I know how do you represent a subtree in your DP state? And it seems to me that given any tree, there are a lot more than N different subtrees (for example, given a line graph I think there are about N^2 different subtrees. There are about N^2 different sets of endpoints you can choose from, and each set defines a unique subtree). Am I missing something here?<br /><br />Sorry, I am new to this kind of DP, so my questions might sound a bit obvious XD. Thanks a lot!</div> </div> </div> <div class="reply info"> <a class="comment-30458 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30458 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30458"> <li> <div class="comment"> <table class="comment-table" commentId="30471" commentParentId="30458"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Connector" style="position: relative;"> <img src='https://userpic.codeforces.org/1490/avatar/a8c455a6747f4912.jpg'/> </a> <div><a href="/profile/Connector" title="Candidate Master Connector" class="rated-user user-violet">Connector</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 14:37">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30471" href="?#comment-30471" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30458" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30471" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30471" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="1490" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30471"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><p>Sorry, posted message in the wrong place: <a href="https://codeforces.com/blog/entry/1598#comment-30470">http://codeforces.com/blog/entry/1598#comment-30470</a></p></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30471 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30471 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30471"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30470" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Connector" style="position: relative;"> <img src='https://userpic.codeforces.org/1490/avatar/a8c455a6747f4912.jpg'/> </a> <div><a href="/profile/Connector" title="Candidate Master Connector" class="rated-user user-violet">Connector</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 14:32">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30470" href="?#comment-30470" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30470" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="1490" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30470"> <div class="moveup"> <div class="ttypography"><p>D.</p><p><strong>UPD:</strong> any point from the triangle based on first three points will be<u> into the area bounded with the convex hull</u> in the future.</p><p>To find the nearest point efficiently use binary search tree (if you write in C++ you can use map class).</p><p>E. </p><p>Yes, you understood what I mean. You should recursively bruteforce xs edge. T is represented in next way: edge uv divides tree into two subtrees, T is one of these subtrees containing vertex v.</p><p><br /></p></div> </div> </div> <div class="reply info"> <a class="comment-30470 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30470 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30470"> <li> <div class="comment"> <table class="comment-table" commentId="30495" commentParentId="30470"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 19:02">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30495" href="?#comment-30495" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30470" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30495" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30495"> <div class="moveup"> <div class="ttypography">Hi,<br /><br />Thanks for your reply! I think I understand how to do problem D now.<br /><br />But I am still not too sure about problem E. I dont quite understand the function DP 2. What does it store? Does DP 2[x] store the min cost if you build a regional centre at x? But won't the answer be different if your subtree is different? What is the recursion for DP 2 like?<br /><br />Thanks in advance again!</div> </div> </div> <div class="reply info"> <a class="comment-30495 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30495 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30495"> <li> <div class="comment"> <table class="comment-table" commentId="30497" commentParentId="30495"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Connector" style="position: relative;"> <img src='https://userpic.codeforces.org/1490/avatar/a8c455a6747f4912.jpg'/> </a> <div><a href="/profile/Connector" title="Candidate Master Connector" class="rated-user user-violet">Connector</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/28/2011 19:26">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30497" href="?#comment-30497" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30495" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30497" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1490" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30497"> <div class="moveup"> <div class="ttypography">D2[T'] store the minimum cost of the maintaining the subtree T'. Let's T' be represented with the edge uv using the way described in previous post. Bruteforce all the vertexes in the sebtree T'. Let the vertex g will be fixed, let's say that it is some regional center assigned to v. Call the D1(T',g,g,0 (the first neighbour)) and relax the answer for the D2[T'] with the returned value.</div> </div> </div> <div class="reply info"> <a class="comment-30497 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30497 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30497"> <li> <div class="comment"> <table class="comment-table" commentId="30557" commentParentId="30497"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 14:06">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30557" href="?#comment-30557" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30497" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30557" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30557" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30557"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">Hi,<br /><br />I have finally understood how this works. Thanks! =D<br /><br />Is it possible for you to look at this problem and give me your thoughts? It does sound very similar. Thanks in advance! <a href="//codeforces.com/blog/entry/1621">http://codeforces.com/blog/entry/1621</a></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30557 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30557 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30557"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1608" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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71A
71
A
en
A. Way Too Long Words
<div class="problem-statement"><div class="header"><div class="title">A. Way Too Long Words</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Sometimes some words like "<span class="tex-font-style-tt">localization</span>" or "<span class="tex-font-style-tt">internationalization</span>" are so long that writing them many times in one text is quite tiresome.</p><p>Let's consider a word <span class="tex-font-style-it">too long</span>, if its length is <span class="tex-font-style-bf">strictly more</span> than <span class="tex-span">10</span> characters. All too long words should be replaced with a special abbreviation.</p><p>This abbreviation is made like this: we write down the first and the last letter of a word and between them we write the number of letters between the first and the last letters. That number is in decimal system and doesn't contain any leading zeroes.</p><p>Thus, "<span class="tex-font-style-tt">localization</span>" will be spelt as "<span class="tex-font-style-tt">l10n</span>", and "<span class="tex-font-style-tt">internationalization</span>» will be spelt as "<span class="tex-font-style-tt">i18n</span>".</p><p>You are suggested to automatize the process of changing the words with abbreviations. At that all too long words should be replaced by the abbreviation and the words that are not too long should not undergo any changes.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains an integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 100</span>). Each of the following <span class="tex-span"><i>n</i></span> lines contains one word. All the words consist of lowercase Latin letters and possess the lengths of from <span class="tex-span">1</span> to <span class="tex-span">100</span> characters.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span"><i>n</i></span> lines. The <span class="tex-span"><i>i</i></span>-th line should contain the result of replacing of the <span class="tex-span"><i>i</i></span>-th word from the input data.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>4<br/>word<br/>localization<br/>internationalization<br/>pneumonoultramicroscopicsilicovolcanoconiosis<br/></pre></div><div class="output"><div class="title">Output</div><pre>word<br/>l10n<br/>i18n<br/>p43s<br/></pre></div></div></div></div>
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If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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} </style> <div class="roundbox sidebox sidebar-menu borderTopRound " style=""> <div class="caption titled">&rarr; Contest materials <div class="top-links"> </div> </div> <ul> <li> <span> <a href="/blog/entry/1623" title="Codeforces Beta Round #65 (Div. 2)" target="_blank">Announcement</a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="248:249" resourceName="Announcement" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1624" title="Разбор задач Codeforces Beta Round #65 (Div. 2)" target="_blank">Tutorial</a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="250:251" resourceName="Tutorial" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> </ul> </div></div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li class="current selectedLava"><a href="/contest/71">Problems</a></li> <li><a href="/contest/71/submit">Submit Code</a></li> <li><a href="/contest/71/my">My Submissions</a></li> <li><a href="/contest/71/status">Status</a></li> <li><a href="/contest/71/hacks">Hacks</a></li> <li><a href="/contest/71/room/1">Room</a></li> <li><a href="/contest/71/standings">Standings</a></li> <li><a href="/contest/71/customtest">Custom Invocation</a></li> </ul> </div> <style> #facebox .content:has(.diff-popup) { width: 90vw; 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="A" data-uuid="ps_3f177467e5e6ce4ac4b1a790ee1882e6e3d5ba16"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">A. Way Too Long Words</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Sometimes some words like &quot;<span class="tex-font-style-tt">localization</span>&quot; or &quot;<span class="tex-font-style-tt">internationalization</span>&quot; are so long that writing them many times in one text is quite tiresome.</p><p>Let's consider a word <span class="tex-font-style-it">too long</span>, if its length is <span class="tex-font-style-bf">strictly more</span> than <span class="tex-span">10</span> characters. All too long words should be replaced with a special abbreviation.</p><p>This abbreviation is made like this: we write down the first and the last letter of a word and between them we write the number of letters between the first and the last letters. That number is in decimal system and doesn't contain any leading zeroes.</p><p>Thus, &quot;<span class="tex-font-style-tt">localization</span>&quot; will be spelt as &quot;<span class="tex-font-style-tt">l10n</span>&quot;, and &quot;<span class="tex-font-style-tt">internationalization</span>» will be spelt as &quot;<span class="tex-font-style-tt">i18n</span>&quot;.</p><p>You are suggested to automatize the process of changing the words with abbreviations. At that all too long words should be replaced by the abbreviation and the words that are not too long should not undergo any changes.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains an integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 100</span>). Each of the following <span class="tex-span"><i>n</i></span> lines contains one word. All the words consist of lowercase Latin letters and possess the lengths of from <span class="tex-span">1</span> to <span class="tex-span">100</span> characters.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span"><i>n</i></span> lines. 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["Prefix- and Z-functions, suffix structures, Knuth\u2013Morris\u2013Pratt algorithm, etc"]
["strings", "*800"]
https://codeforces.com/blog/entry/1624
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Let read all words. For each of them compute its length <span class="tex-span"><i>L</i></span>, its the first and the last letter. If <span class="tex-span"><i>L</i> &gt; 10</span>, output word without any changes, otherwise output the first letter, next <span class="tex-span"><i>L</i> - 2</span> and finally the last letter.<br /> <br /><b>B.</b> At first, compute <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/b30b1e63221e427063b3814647939d0afe0d9e2a.png" style="max-width: 100.0%;max-height: 100.0%;" />. It equals <span class="tex-span">⌊ <i>mnk</i> / 100⌋</span>, where <span class="tex-span">⌊ <i>x</i>⌋</span> is rounding down. Next we fill first <span class="tex-span">⌊ <i>z</i> / <i>k</i>⌋</span> squares with a saturation <span class="tex-span"><i>k</i></span>. <span class="tex-span">(⌊ <i>z</i> / <i>k</i>⌋ + 1)</span>-th square (if it exists) we fill in a saturation <span class="tex-span"><i>z</i> - ⌊ <i>z</i> / <i>k</i>⌋ <i>k</i></span>. All other squares we leave with a saturation <span class="tex-span">0</span>.<br /><br /><b>C.</b> Define an <i>good</i> polygon as a regular polygon which has a knight in a good mood in every of its vertex. Side of polygon we will measure in arcs which is obtained by dividing border of round table with knights.<br /><br />Freeze the length of the side. Let this length equals <span class="tex-span"><i>k</i></span>. Observe that the regular polygon with such length of side exists only if <span class="tex-span"><i>k</i></span> divides <span class="tex-span"><i>n</i></span>. We have exactly <span class="tex-span"><i>k</i></span> of such polygons. Every of them has exactly <span class="tex-span"><i>n</i> / <i>k</i></span> vertices. Check every of the polygons for goodness by review all of its vertices. <br /><br />If sum of vertices with knight in a good mood equals to <span class="tex-span"><i>n</i> / <i>k</i></span>, this polygon is good. Checking of all polygons with some frozen length of side works in an <span class="tex-span"><i>O</i>(<i>n</i>)</span>.<br /><br />Now observe that <span class="tex-span"><i>n</i></span> has <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5a41da22acdba46e7c8eeeaddbc58625f49cbfe5.png" style="max-width: 100.0%;max-height: 100.0%;" /> of divisors. Really, all divisors (may be except only one) we can divide into pairs (for <span class="tex-span"><i>i</i></span> corresponds <span class="tex-span"><i>n</i> / <i>i</i></span>, for <span class="tex-span"><i>i</i> = <i>n</i> / <i>i</i></span> there is no pair). One of divisors in every pair less than <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/712f9a224d6c7824add37b6cd766c21f73a40d59.png" style="max-width: 100.0%;max-height: 100.0%;" />. It means thah number of pairs no more than <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/712f9a224d6c7824add37b6cd766c21f73a40d59.png" style="max-width: 100.0%;max-height: 100.0%;" /> and number of divisors no more than <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/6b8f80d5708602c9727bc53c820fc6ad559209a0.png" style="max-width: 100.0%;max-height: 100.0%;" />.<br /><br />It gives solution - iterate over all divisors of <span class="tex-span"><i>n</i></span> and for every of them check existence of good polygon with length side equals this divisor. Solution has an <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/0c18a224e805d960478a53ca7ac5ae33eaed6dd7.png" style="max-width: 100.0%;max-height: 100.0%;" /> time.<br /><br />In reality for big <span class="tex-span"><i>n</i></span> is has <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7acd26c81b1f055b12a3b1e53f7a9814fd517a81.png" style="max-width: 100.0%;max-height: 100.0%;" /> divisors. So solution actually has <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">4 / 3</sup>)</span>-complexity. For all numbers less than <span class="tex-span">10<sup class="upper-index">5</sup></span> maximal number of divisors is 128.<br /><br />UPD. There was found an <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png" style="max-width: 100.0%;max-height: 100.0%;" /> solution by some participants. This solution uses following idea. If we have a good polygon with <span class="tex-span"><i>xy</i></span> vertices, we also have a good polygon with <span class="tex-span"><i>x</i></span> vertices. So we can check only prime divisors of <span class="tex-span"><i>n</i></span> (except 2 - here we must check 4).<br /><br /><b>D.</b> This problem can be divided into some subproblems.<br /> Author's solution means following ones:<br /><br />1. Check validness of square <span class="tex-span">3 × 3</span>. Square is valid if all cards in it has equal suit or different rank. You may not check equal suit because equal suits imply different ranks.<br /><br />2. Find 2 valid noninetsect squares <span class="tex-span">3 × 3</span> or return thah there are no ones. You can check all pairs of squares for inetsection. If some pair has no intersections check them with solution of subproblem 1.<br /><br />3. Build set of cards which can be replaced with jokers. Generate full deck without jokers and drop from it all cards which in rectangle <span class="tex-span"><i>n</i> × <i>m</i></span> are present.<br /><br />4. Find number of jokers and its positions in rectangle.<br /><br />5. Main subproblem. At first, solve subproblems 3 and 4. Now replace jokers in rectangle with cards from deck from subproblem 3 by all possible ways. For every replace solve subproblem 2. Arter all of variants of replacement just output answer.<br /><br />There are <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">2</sup><i>m</i><sup class="upper-index">2</sup>)</span> solution with small constant.<br /><br /><b>E.</b> At first, you can use some search engine for find periodic table in some printable form. Next use copy-paste (one or several times) and format it by deleting all excess. It is mechanical work for no more than 5 minutes. Also some parser may be written. Note than author's solution does not mean write 100 symbols by hand from a picture. Next build some functions which transform symbols into numbers and vice versa.<br /><br />So, we have some set of numbers. We need summarize some from them and get some another set of numbers. We will use dymanic programming over subsets.<br /><br />Compute the first dp dp1[mask]-&gt;sum. For each subset calculate sum of numbers of all atoms in this subset. It can be done in <span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>n</i></sup><i>n</i>)</span>.<br /><br />Now compute the second dp dp2[mask]-&gt;length. The &quot;length&quot; is a length of some prefix of result sequence of atoms which can be obtained by subset mask. If length -1, it means that it is impossible to get any prefix from this subset.<br /><br />The second dp we can calculate in <span class="tex-span"><i>O</i>(3<sup class="upper-index"><i>n</i></sup>)</span>. Iterate over all masks and if dp2[mask]!=-1, iterate all its subsets of remained atoms (invert mask and get all its submasks). If some subset has sum of numbers which equals number of (dp2[маска]+1)-th atom from result set, recalculate dp2[mask XOR submask]=dp2[mask]+1.<br /><br />At end, if dp2[<span class="tex-span">2<sup class="upper-index"><i>n</i></sup> - 1</span>]=k, there are solution.<br /><br />There are <span class="tex-span"><i>O</i>(3<sup class="upper-index"><i>n</i></sup> + 2<sup class="upper-index"><i>n</i></sup><i>n</i>)</span> solution.<br /><br />In this problem some brutforce solutions are passed because it is difficult to pick up some counterexample.<br /><br />UPD. <a class="rated-user user-orange" href="../../../profile/SkorKNURE" title="Майор SkorKNURE">SkorKNURE</a> found a solution in <span class="tex-span"><span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>n</i></sup><i>n</i>)</span></span>. This solution is some <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">modification</span></span> of the author's solution.<br /><br /><span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">Instead of</span></span> dp2 calculate dp dp2'[mask]-&gt;(i,j), where i is a length of prefix which mask covers and j is part of number of (i+1)-th atom which mask covers.<br /><br />Iterate over all masks. For each mask iterate over all its 0-bits<span class="tex-span"></span> (they are atoms which cover nothing from the finish set). We try to cover with this 0-bit a <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">remainder of</span></span> number of the (i+1)-th atom from the finish set. Let atomic number of an atom for current 0-bit is p and this atom is q-th in the start set. If we cover with this atom only part of the remainder of number of the (i+1)-th atom, dp2'[mask XOR (1&lt;&lt;q)]=(i,j+p). If we cover with this atom the remainder fully (and exactly this remainder, no more!), dp2'[mask XOR (1&lt;&lt;q)]=(i+1,0).<br /><br />Now dp1 is useless. If at end dp2'[<span class="tex-span"><span class="tex-span">2<sup class="upper-index"><i>n</i></sup> - 1</span></span>]=(k,0), solution exists (it is easy to <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">restore it</span></span>), otherwise there is no solution.<span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод"></span></span><span class="tex-span"></span></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/71" class="notice" style="text-decoration: none;">Codeforces Beta Round 65 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-440-1624").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "440", blogEntryId: "1624", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces" class="tag notice" style="text-decoration: none;">codeforces</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=editorial" class="tag notice" style="text-decoration: none;">editorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1624"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+47</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1624"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/Ripatti"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/Ripatti"> Ripatti </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Mar/29/2011 21:20">13 years ago</span> </li> <li> <a href="/blog/entry/1624#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1624#comments"> 39 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1634"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (25)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="30627" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/sicasli" style="position: relative;"> <img src='https://userpic.codeforces.org/10281/avatar/8aa5e308717a2754.jpg'/> </a> <div><a href="/profile/sicasli" title="Expert sicasli" class="rated-user user-blue">sicasli</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 21:51">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30627" href="?#comment-30627" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30627" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="10281" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30627"> <div class="moveup"> <div class="ttypography">system testing took very long time.. and on the middle of contest, server down once.. what happened here?</div> </div> </div> <div class="reply info"> <a class="comment-30627 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30627 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30627"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30631" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/WXYZ" style="position: relative;"> <img src='https://userpic.codeforces.org/16492/avatar/caece4fb867dc8fb.jpg'/> </a> <div><a href="/profile/WXYZ" title="Master WXYZ" class="rated-user user-orange">WXYZ</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 21:58">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30631" href="?#comment-30631" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30631" class="CommentVoteFrame" data-commentRating="4" data-commentUserId="16492" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+4</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30631"> <div class="moveup"> <div class="ttypography">bd</div> </div> </div> <div class="reply info"> <a class="comment-30631 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30631 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30631"> <li> <div class="comment"> <table class="comment-table" commentId="30633" commentParentId="30631"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/pva701" style="position: relative;"> <img src='https://userpic.codeforces.org/3957/avatar/e47deec1b5b8677f.jpg'/> </a> <div><a href="/profile/pva701" title="Expert pva701" class="rated-user user-blue">pva701</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 22:00">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30633" href="?#comment-30633" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30631" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30633" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="3957" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30633"> <div class="moveup"> <div class="ttypography">cool. I understand you. Its great!</div> </div> </div> <div class="reply info"> <a class="comment-30633 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30633 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30633"> <li> <div class="comment"> <table class="comment-table" commentId="30660" commentParentId="30633"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/_arjun" style="position: relative;"> <img src='https://userpic.codeforces.org/1553/avatar/1b0a6d8089c2ee88.jpg'/> </a> <div><a href="/profile/_arjun" title="Expert _arjun" class="rated-user user-blue">_arjun</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 22:37">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30660" href="?#comment-30660" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30633" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30660" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="1553" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30660"> <div class="moveup"> <div class="ttypography">I can't understand , tell me what is bd?</div> </div> </div> <div class="reply info"> <a class="comment-30660 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30660 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30660"> <li> <div class="comment"> <table class="comment-table" commentId="30711" commentParentId="30660"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/naagi" style="position: relative;"> <img src='https://userpic.codeforces.org/1436/avatar/b4261a7f23f18a7c.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/naagi" title="Expert naagi" class="rated-user user-blue">naagi</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 02:15">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30711" href="?#comment-30711" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30660" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30711" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="1436" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30711"> <div class="moveup"> <div class="ttypography">looks like &quot;thumbs up&quot;<br />(I feel proud of myself for this guess :))</div> </div> </div> <div class="reply info"> <a class="comment-30711 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30711 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30711"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="30714" commentParentId="30660"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/acmwe" style="position: relative;"> <img src='https://userpic.codeforces.org/15619/avatar/a74aaa0a09183ea8.jpg'/> </a> <div><a href="/profile/acmwe" title="Specialist acmwe" class="rated-user user-cyan">acmwe</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 06:21">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30714" href="?#comment-30714" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30660" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30714" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="15619" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30714"> <div class="moveup"> <div class="ttypography">It's ....Just like ORZ....</div> </div> </div> <div class="reply info"> <a class="comment-30714 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30714 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30714"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30638" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Lepetrandr" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Lepetrandr" title="Candidate Master Lepetrandr" class="rated-user user-violet">Lepetrandr</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 22:01">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30638" href="?#comment-30638" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30638" class="CommentVoteFrame" data-commentRating="7" data-commentUserId="1088" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+7</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30638"> <div class="moveup"> <div class="ttypography">In problem C we can consider only _prime_ divisors of n (at most 6 :), as number of vertices. But there is one tricky case that i've missed, unfortunately.</div> </div> </div> <div class="reply info"> <a class="comment-30638 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30638 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30638"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30686" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/sanchit_h" style="position: relative;"> <img src='https://userpic.codeforces.org/14424/avatar/ccd3178dffd08856.jpg'/> </a> <div><a href="/profile/sanchit_h" title="Expert sanchit_h" class="rated-user user-blue">sanchit_h</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 23:12">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30686" href="?#comment-30686" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30686" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14424" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30686"> <div class="moveup"> <div class="ttypography">In problem E, can you explain what is a mask and its submasks ?</div> </div> </div> <div class="reply info"> <a class="comment-30686 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30686 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30686"> <li> <div class="comment"> <table class="comment-table" commentId="30687" commentParentId="30686"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kilotaras" style="position: relative;"> <img src='https://userpic.codeforces.org/3934/avatar/1f5f8ec32edbfcfd.jpg'/> </a> <div><a href="/profile/kilotaras" title="Master kilotaras" class="rated-user user-orange">kilotaras</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 23:15">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30687" href="?#comment-30687" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30686" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30687" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30687" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3934" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30687"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div align="left"><a href="https://en.wikipedia.org/wiki/Mask_%28computing%29">http://en.wikipedia.org/wiki/Mask_%28computing%29</a><br /></div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30687 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30687 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30687"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="30688" commentParentId="30686"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Ripatti" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Ripatti" title="Master Ripatti" class="rated-user user-orange">Ripatti</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 23:15">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30688" href="?#comment-30688" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30686" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30688" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="472" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30688"> <div class="moveup"> <div class="ttypography">I will rewrite editorial more detail later.</div> </div> </div> <div class="reply info"> <a class="comment-30688 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30688 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30688"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30691" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/lunae" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/lunae" title="Candidate Master lunae" class="rated-user user-violet">lunae</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 23:29">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30691" href="?#comment-30691" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30691" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30691" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2939" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30691"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">edit: I'm sorry that I didn't notice Lepetrandr's post.<br /><br />For (C) it suffices to check polygons with a prime number of sides (except for 2, then check 4), that gives O(log n) divisors to check.<br /></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30691 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30691 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30691"> <li> <div class="comment"> <table class="comment-table" commentId="30851" commentParentId="30691"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kamranm" style="position: relative;"> <img src='https://userpic.codeforces.org/13373/avatar/bb36d6989328bef3.jpg'/> </a> <div><a href="/profile/kamranm" title="Expert kamranm" class="rated-user user-blue">kamranm</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 21:08">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30851" href="?#comment-30851" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30691" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30851" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13373" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30851"> <div class="moveup"> <div class="ttypography">Yes , because if the - polygon with length equal to n -  is regular , we can create another regular polygons which have the length of any prime divisors of n..but this number is not equal to log(n). This is equal to prime divisors of n.</div> </div> </div> <div class="reply info"> <a class="comment-30851 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30851 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30851"> <li> <div class="comment"> <table class="comment-table" commentId="30854" commentParentId="30851"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ostroumov" style="position: relative;"> <img src='https://userpic.codeforces.org/9567/avatar/daf141c3784f573c.jpg'/> </a> <div><a href="/profile/ostroumov" title="Expert ostroumov" class="rated-user user-blue">ostroumov</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 21:43">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30854" href="?#comment-30854" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30851" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30854" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="9567" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30854"> <div class="moveup"> <div class="ttypography">Number of prime divisors is about equal to ln (n) in case of big n.</div> </div> </div> <div class="reply info"> <a class="comment-30854 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30854 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30854"> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30812" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/wil93" style="position: relative;"> <img src='https://userpic.codeforces.org/14356/avatar/897f1996dfb7343b.jpg'/> </a> <div><a href="/profile/wil93" title="Expert wil93" class="rated-user user-blue">wil93</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 17:48">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30812" href="?#comment-30812" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30812" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="14356" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30812"> <div class="moveup"> <div class="ttypography">In the first problem explanation there's a type error:<div><br /></div><div><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">If</span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;"><i>L</i> &gt; 10</span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">, output word without any changes, otherwise output the first letter, next</span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;"><i>L</i> - 2</span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">and finally the last letter.</span></div><div><br /></div><div>Should be &quot;If L ≤ 10&quot;<br /></div></div> </div> </div> <div class="reply info"> <a class="comment-30812 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30812 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30812"> <li> <div class="comment"> <table class="comment-table" commentId="30868" commentParentId="30812"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/DimaPhil" style="position: relative;"> <img src='https://userpic.codeforces.org/7711/avatar/fb93b0fb945e93fe.jpg'/> </a> <div><a href="/profile/DimaPhil" title="Candidate Master DimaPhil" class="rated-user user-violet">DimaPhil</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 22:05">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30868" href="?#comment-30868" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30812" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30868" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="7711" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30868"> <div class="moveup"> <div class="ttypography">Where did you find it? The statement is correct.</div> </div> </div> <div class="reply info"> <a class="comment-30868 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30868 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30868"> <li> <div class="comment"> <table class="comment-table" commentId="30879" commentParentId="30868"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ostroumov" style="position: relative;"> <img src='https://userpic.codeforces.org/9567/avatar/daf141c3784f573c.jpg'/> </a> <div><a href="/profile/ostroumov" title="Expert ostroumov" class="rated-user user-blue">ostroumov</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 22:33">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30879" href="?#comment-30879" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30868" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30879" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="9567" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30879"> <div class="moveup"> <div class="ttypography"><a href="https://codeforces.com/blog/entry/1624?locale=en">Here</a></div> </div> </div> <div class="reply info"> <a class="comment-30879 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30879 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30879"> <li> <div class="comment"> <table class="comment-table" commentId="30884" commentParentId="30879"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/DimaPhil" style="position: relative;"> <img src='https://userpic.codeforces.org/7711/avatar/fb93b0fb945e93fe.jpg'/> </a> <div><a href="/profile/DimaPhil" title="Candidate Master DimaPhil" class="rated-user user-violet">DimaPhil</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 23:13">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30884" href="?#comment-30884" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30879" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30884" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="7711" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30884"> <div class="moveup"> <div class="ttypography">Oh, yes, i see.</div> </div> </div> <div class="reply info"> <a class="comment-30884 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30884 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30884"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30898" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/fura2" style="position: relative;"> <img src='https://userpic.codeforces.org/4118/avatar/98f7ddceb1dac755.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/fura2" title="Master fura2" class="rated-user user-orange">fura2</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/31/2011 09:54">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30898" href="?#comment-30898" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30898" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4118" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30898"> <div class="moveup"> <div class="ttypography">In author's solution of problem E,<br /> does dp1 calculation really need dynamic programming?<br /> I think, this part can be done by simple 2 loops.<br /> <div align="left"><br /></div> for(int mask=0;mask&lt;(1&lt;&lt;n);mask++){<br />   dp1[mask]=0;<br />   for(int i=0;i&lt;n;i++){<br />     if(mask&amp;(1&lt;&lt;i)) dp1[mask]+=(weight of i-th atom);<br />   }<br /> }<br /></div> </div> </div> <div class="reply info"> <a class="comment-30898 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30898 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30898"> <li> <div class="comment"> <table class="comment-table" commentId="30918" commentParentId="30898"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Ripatti" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Ripatti" title="Master Ripatti" class="rated-user user-orange">Ripatti</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/31/2011 13:36">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30918" href="?#comment-30918" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30898" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30918" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="472" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30918"> <div class="moveup"> <div class="ttypography">You are right. It can be calculated by your way. Also it is calculated in this way in the author's solution.</div> </div> </div> <div class="reply info"> <a class="comment-30918 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30918 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30918"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="31195" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/arpit_s" style="position: relative;"> <img src='https://userpic.codeforces.org/6116/avatar/34bf701a2e3bf99.jpg'/> </a> <div><a href="/profile/arpit_s" title="Pupil arpit_s" class="rated-user user-green">arpit_s</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/03/2011 11:04">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-31195" href="?#comment-31195" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="31195" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6116" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-31195"> <div class="moveup"> <div class="ttypography">can you please explain O(nlog(n)) solution for question C ?</div> </div> </div> <div class="reply info"> <a class="comment-31195 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-31195 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-31195"> <li> <div class="comment"> <table class="comment-table" commentId="31215" commentParentId="31195"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mR.ilchi" style="position: relative;"> <img src='https://userpic.codeforces.org/11753/avatar/b0675918b77546aa.jpg'/> </a> <div><a href="/profile/mR.ilchi" title="International Grandmaster mR.ilchi" class="rated-user user-red">mR.ilchi</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/03/2011 20:07">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-31215" href="?#comment-31215" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-31195" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="31215" revisionCount="3" revision="3"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">3</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="31215" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="11753" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-31215"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer">assume n= p<sub>1</sub><sup>q</sup><sup>1</sup> * p<sub>2</sub><sup>q2 </sup>* ... * p<sub>m</sub><sup>qm</sup>, where all the p<sub>i </sub>is prime.<div>then for each i, (1&lt;=i&lt;=m), check if exist good polygyn with exactly p<sub>i </sub>vertex. if at least one of this question has positive answer then output &quot;YES&quot;, otherwise output &quot;NO&quot;. because if we have a good polygyn with <b>A*B</b> vertex, then we have a good polygyn with <b>A</b> vertex.</div><div>sorry for my poor english!</div><div><br /></div></div> </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-31215 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-31215 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-31215"> <li> <div class="comment"> <table class="comment-table" commentId="31276" commentParentId="31215"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/arpit_s" style="position: relative;"> <img src='https://userpic.codeforces.org/6116/avatar/34bf701a2e3bf99.jpg'/> </a> <div><a href="/profile/arpit_s" title="Pupil arpit_s" class="rated-user user-green">arpit_s</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/04/2011 13:16">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-31276" href="?#comment-31276" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-31215" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="31276" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6116" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-31276"> <div class="moveup"> <div class="ttypography">sorry, couldn't understand, can you explain with one example ?</div> </div> </div> <div class="reply info"> <a class="comment-31276 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-31276 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-31276"> <li> <div class="comment"> <table class="comment-table" commentId="31290" commentParentId="31276"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mR.ilchi" style="position: relative;"> <img src='https://userpic.codeforces.org/11753/avatar/b0675918b77546aa.jpg'/> </a> <div><a href="/profile/mR.ilchi" title="International Grandmaster mR.ilchi" class="rated-user user-red">mR.ilchi</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/04/2011 15:32">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-31290" href="?#comment-31290" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-31276" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="31290" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="31290" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="11753" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-31290"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">assume this good polygyn with <b>A*B</b> vertex:<div>S<sub>1</sub>, S<sub>2</sub>, ... , S<sub>A*B</sub></div><div>now we have subpolygyn which have only <b>A </b>vertex, like this:</div><div>S<sub>1*B</sub>, S<sub>2*B</sub>, ... , S<sub>A*B.</sub></div><div>now it's obviously that if the circle  has a good polygyn then it has a polygyn with prime vertex. it's algo is O(nlgn) because for each i, p<sub>i</sub> &gt;=2</div><div>so m&lt;=lgn, and check function is O(n). therefore main algo is O(nlgn). </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-31290 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-31290 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-31290"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="50340" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/dalex" style="position: relative;"> <img src='https://userpic.codeforces.org/4200/avatar/fe9bfc44be854399.jpg'/> </a> <div><a href="/profile/dalex" title="Master dalex" class="rated-user user-orange">dalex</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Aug/04/2011 22:51">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-50340" href="?#comment-50340" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="50340" revisionCount="3" revision="3"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">3</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="50340" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4200" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-50340"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><p> </p><div class="from-renderer">Some help for Java users with problem E: <a href="http://pastebin.com/ZsDc3P1E">http://pastebin.com/ZsDc3P1E</a><br /><br />(Yes, I'm a necroposter)<br /></div> </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-50340 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-50340 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-50340"> <li> <div class="comment"> <table class="comment-table" commentId="651690" commentParentId="50340"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/the_hyp0cr1t3" style="position: relative;"> <img src='https://userpic.codeforces.org/1236992/avatar/92bd73b5049b4093.jpg'/> </a> <div><a href="/profile/the_hyp0cr1t3" title="Candidate Master the_hyp0cr1t3" class="rated-user user-violet">the_hyp0cr1t3</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/27/2020 22:53">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-651690" href="?#comment-651690" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-50340" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="651690" class="CommentVoteFrame" data-commentRating="-8" data-commentUserId="1236992" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">-8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-651690"> <div class="moveup"> <div class="ttypography"><p>Me too apparently</p></div> </div> </div> <div class="reply info"> <a class="comment-651690 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-651690 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-651690"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1634" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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71B
71
B
en
B. Progress Bar
<div class="problem-statement"><div class="header"><div class="title">B. Progress Bar</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>A progress bar is an element of graphical interface that displays the progress of a process for this very moment before it is completed. Let's take a look at the following form of such a bar.</p><p>A bar is represented as <span class="tex-span"><i>n</i></span> squares, located in line. To add clarity, let's number them with positive integers from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span> from the left to the right. Each square has saturation (<span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> for the <span class="tex-span"><i>i</i></span>-th square), which is measured by an integer from <span class="tex-span">0</span> to <span class="tex-span"><i>k</i></span>. When the bar for some <span class="tex-span"><i>i</i></span> (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>n</i></span>) is displayed, squares <span class="tex-span">1, 2, ... , <i>i</i> - 1</span> has the saturation <span class="tex-span"><i>k</i></span>, squares <span class="tex-span"><i>i</i> + 1, <i>i</i> + 2, ... , <i>n</i></span> has the saturation <span class="tex-span">0</span>, and the saturation of the square <span class="tex-span"><i>i</i></span> can have any value from <span class="tex-span">0</span> to <span class="tex-span"><i>k</i></span>.</p><p>So some first squares of the progress bar always have the saturation <span class="tex-span"><i>k</i></span>. Some last squares always have the saturation <span class="tex-span">0</span>. And there is no more than one square that has the saturation different from <span class="tex-span">0</span> and <span class="tex-span"><i>k</i></span>.</p><p>The degree of the process's completion is measured in percents. Let the process be <span class="tex-span"><i>t</i></span>% completed. Then the following inequation is fulfilled: </p><center class="tex-equation"><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/b409a1d17f3e5356e7e72566ff1b99fd47ec1b59.png" style="max-width: 100.0%;max-height: 100.0%;"/></center><p>An example of such a bar can be seen on the picture.</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/c5c3951d407b9d376bf210a8c1a4010bfedcaf36.png" style="max-width: 100.0%;max-height: 100.0%;"/> </center><p>For the given <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>k</i></span>, <span class="tex-span"><i>t</i></span> determine the measures of saturation for all the squares <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> of the progress bar.</p></div><div class="input-specification"><div class="section-title">Input</div><p>We are given 3 space-separated integers <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>k</i></span>, <span class="tex-span"><i>t</i></span> (<span class="tex-span">1 ≤ <i>n</i>, <i>k</i> ≤ 100</span>, <span class="tex-span">0 ≤ <i>t</i> ≤ 100</span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span"><i>n</i></span> numbers. The <span class="tex-span"><i>i</i></span>-th of them should be equal to <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>10 10 54<br/></pre></div><div class="output"><div class="title">Output</div><pre>10 10 10 10 10 4 0 0 0 0 </pre></div><div class="input"><div class="title">Input</div><pre>11 13 37<br/></pre></div><div class="output"><div class="title">Output</div><pre>13 13 13 13 0 0 0 0 0 0 0 </pre></div></div></div></div>
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Just register for practice and you will be able to submit solutions. </div> <div style="text-align:center;margin:1em;"> <form action="" method="post"><input type='hidden' name='csrf_token' value='218636ebf2ca2478e6c0f9cbb26334a1'/> <input type="hidden" name="action" value="registerForPractice"/> <input type="submit" name="submit" value="Register for practice" style="padding:0 0.5em;"> </form> </div> </div> </div> <div class="roundbox sidebox ContestVirtualFrame borderTopRound " style=""> <div class="caption titled">&rarr; Virtual participation <i class="sidebar-caption-icon las la-angle-down"></i> <div class="top-links"> </div> </div> <div style=" " data-page-url="/data/sidebarFrames" > <div style="margin:1em;font-size:0.8em;"> Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests. If you've seen these problems, a virtual contest is not for you - solve these problems in the archive. If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. Never use someone else's code, read the tutorials or communicate with other person during a virtual contest. </div> <div style="text-align:center;margin:1em;"> <form action="/contest/71/virtual" method="get"> <input type="submit" name="submit" value="Start virtual contest" style="padding:0 0.5em;"> </form> </div> </div> <script> $(function () { $(".ContestVirtualFrame .sidebar-caption-icon").click(function() { $(this).toggleClass("la-angle-down la-angle-right"); const $target = $(this).parent().next(); $target.toggle(); const dataPageUrl = $target.attr("data-page-url"); const collapsed = $(this).hasClass("la-angle-right"); const params = { action: "setCollapsed", sidebarFrameSimpleClassName: "ContestVirtualFrame", collapsed }; $.each($target[0].attributes, function(i, a) { const name = a.name; if (name.startsWith("data-extra-key-")) { const key = a.value; const keyIndex = parseInt(name.substring("data-extra-key-".length)); const value = $target.attr("data-extra-value-" + keyIndex); params[key] = value; 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="B" data-uuid="ps_9204b92ef34c0a497f55ebaaa7f9aeabe356a569"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">B. Progress Bar</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>A progress bar is an element of graphical interface that displays the progress of a process for this very moment before it is completed. Let's take a look at the following form of such a bar.</p><p>A bar is represented as <span class="tex-span"><i>n</i></span> squares, located in line. To add clarity, let's number them with positive integers from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span> from the left to the right. Each square has saturation (<span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> for the <span class="tex-span"><i>i</i></span>-th square), which is measured by an integer from <span class="tex-span">0</span> to <span class="tex-span"><i>k</i></span>. When the bar for some <span class="tex-span"><i>i</i></span> (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>n</i></span>) is displayed, squares <span class="tex-span">1, 2, ... , <i>i</i> - 1</span> has the saturation <span class="tex-span"><i>k</i></span>, squares <span class="tex-span"><i>i</i> + 1, <i>i</i> + 2, ... , <i>n</i></span> has the saturation <span class="tex-span">0</span>, and the saturation of the square <span class="tex-span"><i>i</i></span> can have any value from <span class="tex-span">0</span> to <span class="tex-span"><i>k</i></span>.</p><p>So some first squares of the progress bar always have the saturation <span class="tex-span"><i>k</i></span>. Some last squares always have the saturation <span class="tex-span">0</span>. And there is no more than one square that has the saturation different from <span class="tex-span">0</span> and <span class="tex-span"><i>k</i></span>.</p><p>The degree of the process's completion is measured in percents. Let the process be <span class="tex-span"><i>t</i></span>% completed. Then the following inequation is fulfilled: </p><center class="tex-equation"><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/b409a1d17f3e5356e7e72566ff1b99fd47ec1b59.png" style="max-width: 100.0%;max-height: 100.0%;" /></center><p>An example of such a bar can be seen on the picture.</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/c5c3951d407b9d376bf210a8c1a4010bfedcaf36.png" style="max-width: 100.0%;max-height: 100.0%;" /> </center><p>For the given <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>k</i></span>, <span class="tex-span"><i>t</i></span> determine the measures of saturation for all the squares <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> of the progress bar.</p></div><div class="input-specification"><div class="section-title">Input</div><p>We are given 3 space-separated integers <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>k</i></span>, <span class="tex-span"><i>t</i></span> (<span class="tex-span">1 ≤ <i>n</i>, <i>k</i> ≤ 100</span>, <span class="tex-span">0 ≤ <i>t</i> ≤ 100</span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span"><i>n</i></span> numbers. 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["Implementation problems, programming technics, simulation", "Mathematics including integration, differential equations, etc"]
["implementation", "math", "*1300"]
https://codeforces.com/blog/entry/1624
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Let read all words. For each of them compute its length <span class="tex-span"><i>L</i></span>, its the first and the last letter. If <span class="tex-span"><i>L</i> &gt; 10</span>, output word without any changes, otherwise output the first letter, next <span class="tex-span"><i>L</i> - 2</span> and finally the last letter.<br /> <br /><b>B.</b> At first, compute <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/b30b1e63221e427063b3814647939d0afe0d9e2a.png" style="max-width: 100.0%;max-height: 100.0%;" />. It equals <span class="tex-span">⌊ <i>mnk</i> / 100⌋</span>, where <span class="tex-span">⌊ <i>x</i>⌋</span> is rounding down. Next we fill first <span class="tex-span">⌊ <i>z</i> / <i>k</i>⌋</span> squares with a saturation <span class="tex-span"><i>k</i></span>. <span class="tex-span">(⌊ <i>z</i> / <i>k</i>⌋ + 1)</span>-th square (if it exists) we fill in a saturation <span class="tex-span"><i>z</i> - ⌊ <i>z</i> / <i>k</i>⌋ <i>k</i></span>. All other squares we leave with a saturation <span class="tex-span">0</span>.<br /><br /><b>C.</b> Define an <i>good</i> polygon as a regular polygon which has a knight in a good mood in every of its vertex. Side of polygon we will measure in arcs which is obtained by dividing border of round table with knights.<br /><br />Freeze the length of the side. Let this length equals <span class="tex-span"><i>k</i></span>. Observe that the regular polygon with such length of side exists only if <span class="tex-span"><i>k</i></span> divides <span class="tex-span"><i>n</i></span>. We have exactly <span class="tex-span"><i>k</i></span> of such polygons. Every of them has exactly <span class="tex-span"><i>n</i> / <i>k</i></span> vertices. Check every of the polygons for goodness by review all of its vertices. <br /><br />If sum of vertices with knight in a good mood equals to <span class="tex-span"><i>n</i> / <i>k</i></span>, this polygon is good. Checking of all polygons with some frozen length of side works in an <span class="tex-span"><i>O</i>(<i>n</i>)</span>.<br /><br />Now observe that <span class="tex-span"><i>n</i></span> has <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5a41da22acdba46e7c8eeeaddbc58625f49cbfe5.png" style="max-width: 100.0%;max-height: 100.0%;" /> of divisors. Really, all divisors (may be except only one) we can divide into pairs (for <span class="tex-span"><i>i</i></span> corresponds <span class="tex-span"><i>n</i> / <i>i</i></span>, for <span class="tex-span"><i>i</i> = <i>n</i> / <i>i</i></span> there is no pair). One of divisors in every pair less than <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/712f9a224d6c7824add37b6cd766c21f73a40d59.png" style="max-width: 100.0%;max-height: 100.0%;" />. It means thah number of pairs no more than <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/712f9a224d6c7824add37b6cd766c21f73a40d59.png" style="max-width: 100.0%;max-height: 100.0%;" /> and number of divisors no more than <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/6b8f80d5708602c9727bc53c820fc6ad559209a0.png" style="max-width: 100.0%;max-height: 100.0%;" />.<br /><br />It gives solution - iterate over all divisors of <span class="tex-span"><i>n</i></span> and for every of them check existence of good polygon with length side equals this divisor. Solution has an <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/0c18a224e805d960478a53ca7ac5ae33eaed6dd7.png" style="max-width: 100.0%;max-height: 100.0%;" /> time.<br /><br />In reality for big <span class="tex-span"><i>n</i></span> is has <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7acd26c81b1f055b12a3b1e53f7a9814fd517a81.png" style="max-width: 100.0%;max-height: 100.0%;" /> divisors. So solution actually has <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">4 / 3</sup>)</span>-complexity. For all numbers less than <span class="tex-span">10<sup class="upper-index">5</sup></span> maximal number of divisors is 128.<br /><br />UPD. There was found an <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png" style="max-width: 100.0%;max-height: 100.0%;" /> solution by some participants. This solution uses following idea. If we have a good polygon with <span class="tex-span"><i>xy</i></span> vertices, we also have a good polygon with <span class="tex-span"><i>x</i></span> vertices. So we can check only prime divisors of <span class="tex-span"><i>n</i></span> (except 2 - here we must check 4).<br /><br /><b>D.</b> This problem can be divided into some subproblems.<br /> Author's solution means following ones:<br /><br />1. Check validness of square <span class="tex-span">3 × 3</span>. Square is valid if all cards in it has equal suit or different rank. You may not check equal suit because equal suits imply different ranks.<br /><br />2. Find 2 valid noninetsect squares <span class="tex-span">3 × 3</span> or return thah there are no ones. You can check all pairs of squares for inetsection. If some pair has no intersections check them with solution of subproblem 1.<br /><br />3. Build set of cards which can be replaced with jokers. Generate full deck without jokers and drop from it all cards which in rectangle <span class="tex-span"><i>n</i> × <i>m</i></span> are present.<br /><br />4. Find number of jokers and its positions in rectangle.<br /><br />5. Main subproblem. At first, solve subproblems 3 and 4. Now replace jokers in rectangle with cards from deck from subproblem 3 by all possible ways. For every replace solve subproblem 2. Arter all of variants of replacement just output answer.<br /><br />There are <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">2</sup><i>m</i><sup class="upper-index">2</sup>)</span> solution with small constant.<br /><br /><b>E.</b> At first, you can use some search engine for find periodic table in some printable form. Next use copy-paste (one or several times) and format it by deleting all excess. It is mechanical work for no more than 5 minutes. Also some parser may be written. Note than author's solution does not mean write 100 symbols by hand from a picture. Next build some functions which transform symbols into numbers and vice versa.<br /><br />So, we have some set of numbers. We need summarize some from them and get some another set of numbers. We will use dymanic programming over subsets.<br /><br />Compute the first dp dp1[mask]-&gt;sum. For each subset calculate sum of numbers of all atoms in this subset. It can be done in <span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>n</i></sup><i>n</i>)</span>.<br /><br />Now compute the second dp dp2[mask]-&gt;length. The &quot;length&quot; is a length of some prefix of result sequence of atoms which can be obtained by subset mask. If length -1, it means that it is impossible to get any prefix from this subset.<br /><br />The second dp we can calculate in <span class="tex-span"><i>O</i>(3<sup class="upper-index"><i>n</i></sup>)</span>. Iterate over all masks and if dp2[mask]!=-1, iterate all its subsets of remained atoms (invert mask and get all its submasks). If some subset has sum of numbers which equals number of (dp2[маска]+1)-th atom from result set, recalculate dp2[mask XOR submask]=dp2[mask]+1.<br /><br />At end, if dp2[<span class="tex-span">2<sup class="upper-index"><i>n</i></sup> - 1</span>]=k, there are solution.<br /><br />There are <span class="tex-span"><i>O</i>(3<sup class="upper-index"><i>n</i></sup> + 2<sup class="upper-index"><i>n</i></sup><i>n</i>)</span> solution.<br /><br />In this problem some brutforce solutions are passed because it is difficult to pick up some counterexample.<br /><br />UPD. <a class="rated-user user-orange" href="../../../profile/SkorKNURE" title="Майор SkorKNURE">SkorKNURE</a> found a solution in <span class="tex-span"><span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>n</i></sup><i>n</i>)</span></span>. This solution is some <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">modification</span></span> of the author's solution.<br /><br /><span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">Instead of</span></span> dp2 calculate dp dp2'[mask]-&gt;(i,j), where i is a length of prefix which mask covers and j is part of number of (i+1)-th atom which mask covers.<br /><br />Iterate over all masks. For each mask iterate over all its 0-bits<span class="tex-span"></span> (they are atoms which cover nothing from the finish set). We try to cover with this 0-bit a <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">remainder of</span></span> number of the (i+1)-th atom from the finish set. Let atomic number of an atom for current 0-bit is p and this atom is q-th in the start set. If we cover with this atom only part of the remainder of number of the (i+1)-th atom, dp2'[mask XOR (1&lt;&lt;q)]=(i,j+p). If we cover with this atom the remainder fully (and exactly this remainder, no more!), dp2'[mask XOR (1&lt;&lt;q)]=(i+1,0).<br /><br />Now dp1 is useless. If at end dp2'[<span class="tex-span"><span class="tex-span">2<sup class="upper-index"><i>n</i></sup> - 1</span></span>]=(k,0), solution exists (it is easy to <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">restore it</span></span>), otherwise there is no solution.<span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод"></span></span><span class="tex-span"></span></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/71" class="notice" style="text-decoration: none;">Codeforces Beta Round 65 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-440-1624").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "440", blogEntryId: "1624", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces" class="tag notice" style="text-decoration: none;">codeforces</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=editorial" class="tag notice" style="text-decoration: none;">editorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1624"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+47</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1624"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/Ripatti"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/Ripatti"> Ripatti </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Mar/29/2011 21:20">13 years ago</span> </li> <li> <a href="/blog/entry/1624#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1624#comments"> 39 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1634"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (25)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="30627" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/sicasli" style="position: relative;"> <img src='https://userpic.codeforces.org/10281/avatar/8aa5e308717a2754.jpg'/> </a> <div><a href="/profile/sicasli" title="Expert sicasli" class="rated-user user-blue">sicasli</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 21:51">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30627" href="?#comment-30627" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30627" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="10281" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30627"> <div class="moveup"> <div class="ttypography">system testing took very long time.. and on the middle of contest, server down once.. what happened here?</div> </div> </div> <div class="reply info"> <a class="comment-30627 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30627 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30627"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30631" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/WXYZ" style="position: relative;"> <img src='https://userpic.codeforces.org/16492/avatar/caece4fb867dc8fb.jpg'/> </a> <div><a href="/profile/WXYZ" title="Master WXYZ" class="rated-user user-orange">WXYZ</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 21:58">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30631" href="?#comment-30631" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30631" class="CommentVoteFrame" data-commentRating="4" data-commentUserId="16492" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+4</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30631"> <div class="moveup"> <div class="ttypography">bd</div> </div> </div> <div class="reply info"> <a class="comment-30631 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30631 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30631"> <li> <div class="comment"> <table class="comment-table" commentId="30633" commentParentId="30631"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/pva701" style="position: relative;"> <img src='https://userpic.codeforces.org/3957/avatar/e47deec1b5b8677f.jpg'/> </a> <div><a href="/profile/pva701" title="Expert pva701" class="rated-user user-blue">pva701</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 22:00">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30633" href="?#comment-30633" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30631" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30633" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="3957" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30633"> <div class="moveup"> <div class="ttypography">cool. I understand you. Its great!</div> </div> </div> <div class="reply info"> <a class="comment-30633 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30633 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30633"> <li> <div class="comment"> <table class="comment-table" commentId="30660" commentParentId="30633"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/_arjun" style="position: relative;"> <img src='https://userpic.codeforces.org/1553/avatar/1b0a6d8089c2ee88.jpg'/> </a> <div><a href="/profile/_arjun" title="Expert _arjun" class="rated-user user-blue">_arjun</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 22:37">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30660" href="?#comment-30660" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30633" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30660" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="1553" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30660"> <div class="moveup"> <div class="ttypography">I can't understand , tell me what is bd?</div> </div> </div> <div class="reply info"> <a class="comment-30660 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30660 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30660"> <li> <div class="comment"> <table class="comment-table" commentId="30711" commentParentId="30660"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/naagi" style="position: relative;"> <img src='https://userpic.codeforces.org/1436/avatar/b4261a7f23f18a7c.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/naagi" title="Expert naagi" class="rated-user user-blue">naagi</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 02:15">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30711" href="?#comment-30711" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30660" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30711" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="1436" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30711"> <div class="moveup"> <div class="ttypography">looks like &quot;thumbs up&quot;<br />(I feel proud of myself for this guess :))</div> </div> </div> <div class="reply info"> <a class="comment-30711 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30711 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30711"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="30714" commentParentId="30660"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/acmwe" style="position: relative;"> <img src='https://userpic.codeforces.org/15619/avatar/a74aaa0a09183ea8.jpg'/> </a> <div><a href="/profile/acmwe" title="Specialist acmwe" class="rated-user user-cyan">acmwe</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 06:21">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30714" href="?#comment-30714" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30660" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30714" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="15619" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30714"> <div class="moveup"> <div class="ttypography">It's ....Just like ORZ....</div> </div> </div> <div class="reply info"> <a class="comment-30714 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30714 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30714"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30638" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Lepetrandr" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Lepetrandr" title="Candidate Master Lepetrandr" class="rated-user user-violet">Lepetrandr</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 22:01">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30638" href="?#comment-30638" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30638" class="CommentVoteFrame" data-commentRating="7" data-commentUserId="1088" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+7</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30638"> <div class="moveup"> <div class="ttypography">In problem C we can consider only _prime_ divisors of n (at most 6 :), as number of vertices. But there is one tricky case that i've missed, unfortunately.</div> </div> </div> <div class="reply info"> <a class="comment-30638 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30638 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30638"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30686" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/sanchit_h" style="position: relative;"> <img src='https://userpic.codeforces.org/14424/avatar/ccd3178dffd08856.jpg'/> </a> <div><a href="/profile/sanchit_h" title="Expert sanchit_h" class="rated-user user-blue">sanchit_h</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 23:12">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30686" href="?#comment-30686" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30686" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14424" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30686"> <div class="moveup"> <div class="ttypography">In problem E, can you explain what is a mask and its submasks ?</div> </div> </div> <div class="reply info"> <a class="comment-30686 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30686 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30686"> <li> <div class="comment"> <table class="comment-table" commentId="30687" commentParentId="30686"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kilotaras" style="position: relative;"> <img src='https://userpic.codeforces.org/3934/avatar/1f5f8ec32edbfcfd.jpg'/> </a> <div><a href="/profile/kilotaras" title="Master kilotaras" class="rated-user user-orange">kilotaras</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 23:15">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30687" href="?#comment-30687" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30686" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30687" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30687" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3934" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30687"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div align="left"><a href="https://en.wikipedia.org/wiki/Mask_%28computing%29">http://en.wikipedia.org/wiki/Mask_%28computing%29</a><br /></div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30687 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30687 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30687"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="30688" commentParentId="30686"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Ripatti" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Ripatti" title="Master Ripatti" class="rated-user user-orange">Ripatti</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 23:15">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30688" href="?#comment-30688" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30686" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30688" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="472" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30688"> <div class="moveup"> <div class="ttypography">I will rewrite editorial more detail later.</div> </div> </div> <div class="reply info"> <a class="comment-30688 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30688 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30688"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30691" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/lunae" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/lunae" title="Candidate Master lunae" class="rated-user user-violet">lunae</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 23:29">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30691" href="?#comment-30691" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30691" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30691" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2939" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30691"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">edit: I'm sorry that I didn't notice Lepetrandr's post.<br /><br />For (C) it suffices to check polygons with a prime number of sides (except for 2, then check 4), that gives O(log n) divisors to check.<br /></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30691 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30691 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30691"> <li> <div class="comment"> <table class="comment-table" commentId="30851" commentParentId="30691"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kamranm" style="position: relative;"> <img src='https://userpic.codeforces.org/13373/avatar/bb36d6989328bef3.jpg'/> </a> <div><a href="/profile/kamranm" title="Expert kamranm" class="rated-user user-blue">kamranm</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 21:08">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30851" href="?#comment-30851" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30691" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30851" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13373" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30851"> <div class="moveup"> <div class="ttypography">Yes , because if the - polygon with length equal to n -  is regular , we can create another regular polygons which have the length of any prime divisors of n..but this number is not equal to log(n). This is equal to prime divisors of n.</div> </div> </div> <div class="reply info"> <a class="comment-30851 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30851 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30851"> <li> <div class="comment"> <table class="comment-table" commentId="30854" commentParentId="30851"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ostroumov" style="position: relative;"> <img src='https://userpic.codeforces.org/9567/avatar/daf141c3784f573c.jpg'/> </a> <div><a href="/profile/ostroumov" title="Expert ostroumov" class="rated-user user-blue">ostroumov</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 21:43">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30854" href="?#comment-30854" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30851" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30854" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="9567" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30854"> <div class="moveup"> <div class="ttypography">Number of prime divisors is about equal to ln (n) in case of big n.</div> </div> </div> <div class="reply info"> <a class="comment-30854 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30854 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30854"> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30812" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/wil93" style="position: relative;"> <img src='https://userpic.codeforces.org/14356/avatar/897f1996dfb7343b.jpg'/> </a> <div><a href="/profile/wil93" title="Expert wil93" class="rated-user user-blue">wil93</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 17:48">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30812" href="?#comment-30812" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30812" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="14356" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30812"> <div class="moveup"> <div class="ttypography">In the first problem explanation there's a type error:<div><br /></div><div><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">If</span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;"><i>L</i> &gt; 10</span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">, output word without any changes, otherwise output the first letter, next</span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;"><i>L</i> - 2</span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">and finally the last letter.</span></div><div><br /></div><div>Should be &quot;If L ≤ 10&quot;<br /></div></div> </div> </div> <div class="reply info"> <a class="comment-30812 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30812 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30812"> <li> <div class="comment"> <table class="comment-table" commentId="30868" commentParentId="30812"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/DimaPhil" style="position: relative;"> <img src='https://userpic.codeforces.org/7711/avatar/fb93b0fb945e93fe.jpg'/> </a> <div><a href="/profile/DimaPhil" title="Candidate Master DimaPhil" class="rated-user user-violet">DimaPhil</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 22:05">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30868" href="?#comment-30868" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30812" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30868" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="7711" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30868"> <div class="moveup"> <div class="ttypography">Where did you find it? The statement is correct.</div> </div> </div> <div class="reply info"> <a class="comment-30868 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30868 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30868"> <li> <div class="comment"> <table class="comment-table" commentId="30879" commentParentId="30868"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ostroumov" style="position: relative;"> <img src='https://userpic.codeforces.org/9567/avatar/daf141c3784f573c.jpg'/> </a> <div><a href="/profile/ostroumov" title="Expert ostroumov" class="rated-user user-blue">ostroumov</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 22:33">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30879" href="?#comment-30879" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30868" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30879" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="9567" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30879"> <div class="moveup"> <div class="ttypography"><a href="https://codeforces.com/blog/entry/1624?locale=en">Here</a></div> </div> </div> <div class="reply info"> <a class="comment-30879 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30879 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30879"> <li> <div class="comment"> <table class="comment-table" commentId="30884" commentParentId="30879"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/DimaPhil" style="position: relative;"> <img src='https://userpic.codeforces.org/7711/avatar/fb93b0fb945e93fe.jpg'/> </a> <div><a href="/profile/DimaPhil" title="Candidate Master DimaPhil" class="rated-user user-violet">DimaPhil</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 23:13">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30884" href="?#comment-30884" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30879" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30884" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="7711" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30884"> <div class="moveup"> <div class="ttypography">Oh, yes, i see.</div> </div> </div> <div class="reply info"> <a class="comment-30884 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30884 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30884"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30898" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/fura2" style="position: relative;"> <img src='https://userpic.codeforces.org/4118/avatar/98f7ddceb1dac755.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/fura2" title="Master fura2" class="rated-user user-orange">fura2</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/31/2011 09:54">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30898" href="?#comment-30898" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30898" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4118" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30898"> <div class="moveup"> <div class="ttypography">In author's solution of problem E,<br /> does dp1 calculation really need dynamic programming?<br /> I think, this part can be done by simple 2 loops.<br /> <div align="left"><br /></div> for(int mask=0;mask&lt;(1&lt;&lt;n);mask++){<br />   dp1[mask]=0;<br />   for(int i=0;i&lt;n;i++){<br />     if(mask&amp;(1&lt;&lt;i)) dp1[mask]+=(weight of i-th atom);<br />   }<br /> }<br /></div> </div> </div> <div class="reply info"> <a class="comment-30898 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30898 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30898"> <li> <div class="comment"> <table class="comment-table" commentId="30918" commentParentId="30898"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Ripatti" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Ripatti" title="Master Ripatti" class="rated-user user-orange">Ripatti</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/31/2011 13:36">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30918" href="?#comment-30918" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30898" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30918" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="472" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30918"> <div class="moveup"> <div class="ttypography">You are right. It can be calculated by your way. Also it is calculated in this way in the author's solution.</div> </div> </div> <div class="reply info"> <a class="comment-30918 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30918 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30918"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="31195" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/arpit_s" style="position: relative;"> <img src='https://userpic.codeforces.org/6116/avatar/34bf701a2e3bf99.jpg'/> </a> <div><a href="/profile/arpit_s" title="Pupil arpit_s" class="rated-user user-green">arpit_s</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/03/2011 11:04">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-31195" href="?#comment-31195" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="31195" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6116" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-31195"> <div class="moveup"> <div class="ttypography">can you please explain O(nlog(n)) solution for question C ?</div> </div> </div> <div class="reply info"> <a class="comment-31195 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-31195 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-31195"> <li> <div class="comment"> <table class="comment-table" commentId="31215" commentParentId="31195"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mR.ilchi" style="position: relative;"> <img src='https://userpic.codeforces.org/11753/avatar/b0675918b77546aa.jpg'/> </a> <div><a href="/profile/mR.ilchi" title="International Grandmaster mR.ilchi" class="rated-user user-red">mR.ilchi</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/03/2011 20:07">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-31215" href="?#comment-31215" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-31195" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="31215" revisionCount="3" revision="3"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">3</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="31215" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="11753" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-31215"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer">assume n= p<sub>1</sub><sup>q</sup><sup>1</sup> * p<sub>2</sub><sup>q2 </sup>* ... * p<sub>m</sub><sup>qm</sup>, where all the p<sub>i </sub>is prime.<div>then for each i, (1&lt;=i&lt;=m), check if exist good polygyn with exactly p<sub>i </sub>vertex. if at least one of this question has positive answer then output &quot;YES&quot;, otherwise output &quot;NO&quot;. because if we have a good polygyn with <b>A*B</b> vertex, then we have a good polygyn with <b>A</b> vertex.</div><div>sorry for my poor english!</div><div><br /></div></div> </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-31215 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-31215 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-31215"> <li> <div class="comment"> <table class="comment-table" commentId="31276" commentParentId="31215"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/arpit_s" style="position: relative;"> <img src='https://userpic.codeforces.org/6116/avatar/34bf701a2e3bf99.jpg'/> </a> <div><a href="/profile/arpit_s" title="Pupil arpit_s" class="rated-user user-green">arpit_s</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/04/2011 13:16">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-31276" href="?#comment-31276" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-31215" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="31276" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6116" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-31276"> <div class="moveup"> <div class="ttypography">sorry, couldn't understand, can you explain with one example ?</div> </div> </div> <div class="reply info"> <a class="comment-31276 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-31276 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-31276"> <li> <div class="comment"> <table class="comment-table" commentId="31290" commentParentId="31276"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mR.ilchi" style="position: relative;"> <img src='https://userpic.codeforces.org/11753/avatar/b0675918b77546aa.jpg'/> </a> <div><a href="/profile/mR.ilchi" title="International Grandmaster mR.ilchi" class="rated-user user-red">mR.ilchi</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/04/2011 15:32">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-31290" href="?#comment-31290" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-31276" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="31290" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="31290" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="11753" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-31290"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">assume this good polygyn with <b>A*B</b> vertex:<div>S<sub>1</sub>, S<sub>2</sub>, ... , S<sub>A*B</sub></div><div>now we have subpolygyn which have only <b>A </b>vertex, like this:</div><div>S<sub>1*B</sub>, S<sub>2*B</sub>, ... , S<sub>A*B.</sub></div><div>now it's obviously that if the circle  has a good polygyn then it has a polygyn with prime vertex. it's algo is O(nlgn) because for each i, p<sub>i</sub> &gt;=2</div><div>so m&lt;=lgn, and check function is O(n). therefore main algo is O(nlgn). </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-31290 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-31290 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-31290"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="50340" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/dalex" style="position: relative;"> <img src='https://userpic.codeforces.org/4200/avatar/fe9bfc44be854399.jpg'/> </a> <div><a href="/profile/dalex" title="Master dalex" class="rated-user user-orange">dalex</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Aug/04/2011 22:51">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-50340" href="?#comment-50340" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="50340" revisionCount="3" revision="3"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">3</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="50340" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4200" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-50340"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><p> </p><div class="from-renderer">Some help for Java users with problem E: <a href="http://pastebin.com/ZsDc3P1E">http://pastebin.com/ZsDc3P1E</a><br /><br />(Yes, I'm a necroposter)<br /></div> </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-50340 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-50340 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-50340"> <li> <div class="comment"> <table class="comment-table" commentId="651690" commentParentId="50340"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/the_hyp0cr1t3" style="position: relative;"> <img src='https://userpic.codeforces.org/1236992/avatar/92bd73b5049b4093.jpg'/> </a> <div><a href="/profile/the_hyp0cr1t3" title="Candidate Master the_hyp0cr1t3" class="rated-user user-violet">the_hyp0cr1t3</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/27/2020 22:53">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-651690" href="?#comment-651690" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-50340" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="651690" class="CommentVoteFrame" data-commentRating="-8" data-commentUserId="1236992" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">-8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-651690"> <div class="moveup"> <div class="ttypography"><p>Me too apparently</p></div> </div> </div> <div class="reply info"> <a class="comment-651690 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-651690 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-651690"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1634" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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71C
71
C
en
C. Round Table Knights
<div class="problem-statement"><div class="header"><div class="title">C. Round Table Knights</div><div class="time-limit"><div class="property-title">time limit per test</div>0.5 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>There are <span class="tex-span"><i>n</i></span> knights sitting at the Round Table at an equal distance from each other. Each of them is either in a good or in a bad mood.</p><p>Merlin, the wizard predicted to King Arthur that the next month will turn out to be particularly fortunate if the <span class="tex-font-style-it">regular</span> polygon can be found. On all vertices of the polygon knights in a good mood should be located. Otherwise, the next month will bring misfortunes.</p><p>A convex polygon is regular if all its sides have same length and all his angles are equal. In this problem we consider only regular polygons with at least 3 vertices, i. e. only nondegenerated.</p><p>On a picture below some examples of such polygons are present. Green points mean knights in a good mood. Red points mean ones in a bad mood.</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/74f876ccab06b18381319757d775aafd5756bf26.png" style="max-width: 100.0%;max-height: 100.0%;"/> </center><p>King Arthur knows the knights' moods. Help him find out if the next month will be fortunate or not.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains number <span class="tex-span"><i>n</i></span>, which is the number of knights at the round table (<span class="tex-span">3 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup></span>). The second line contains space-separated moods of all the <span class="tex-span"><i>n</i></span> knights in the order of passing them around the table. "1" means that the knight is in a good mood an "0" means that he is in a bad mood.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print "<span class="tex-font-style-tt">YES</span>" without the quotes if the following month will turn out to be lucky. Otherwise, print "<span class="tex-font-style-tt">NO</span>".</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br/>1 1 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>YES</pre></div><div class="input"><div class="title">Input</div><pre>6<br/>1 0 1 1 1 0<br/></pre></div><div class="output"><div class="title">Output</div><pre>YES</pre></div><div class="input"><div class="title">Input</div><pre>6<br/>1 0 0 1 0 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>NO</pre></div></div></div></div>
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Just register for practice and you will be able to submit solutions. </div> <div style="text-align:center;margin:1em;"> <form action="" method="post"><input type='hidden' name='csrf_token' value='9f4cf3890b3d563ccd392b38aea4f93c'/> <input type="hidden" name="action" value="registerForPractice"/> <input type="submit" name="submit" value="Register for practice" style="padding:0 0.5em;"> </form> </div> </div> </div> <div class="roundbox sidebox ContestVirtualFrame borderTopRound " style=""> <div class="caption titled">&rarr; Virtual participation <i class="sidebar-caption-icon las la-angle-down"></i> <div class="top-links"> </div> </div> <div style=" " data-page-url="/data/sidebarFrames" > <div style="margin:1em;font-size:0.8em;"> Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests. If you've seen these problems, a virtual contest is not for you - solve these problems in the archive. If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. Never use someone else's code, read the tutorials or communicate with other person during a virtual contest. </div> <div style="text-align:center;margin:1em;"> <form action="/contest/71/virtual" method="get"> <input type="submit" name="submit" value="Start virtual contest" style="padding:0 0.5em;"> </form> </div> </div> <script> $(function () { $(".ContestVirtualFrame .sidebar-caption-icon").click(function() { $(this).toggleClass("la-angle-down la-angle-right"); const $target = $(this).parent().next(); $target.toggle(); const dataPageUrl = $target.attr("data-page-url"); const collapsed = $(this).hasClass("la-angle-right"); const params = { action: "setCollapsed", sidebarFrameSimpleClassName: "ContestVirtualFrame", collapsed }; $.each($target[0].attributes, function(i, a) { const name = a.name; if (name.startsWith("data-extra-key-")) { const key = a.value; const keyIndex = parseInt(name.substring("data-extra-key-".length)); const value = $target.attr("data-extra-value-" + keyIndex); params[key] = value; 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="C" data-uuid="ps_790e21efc7cf4a941b6e44caa9a631a4103d2c94"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. Round Table Knights</div><div class="time-limit"><div class="property-title">time limit per test</div>0.5 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>There are <span class="tex-span"><i>n</i></span> knights sitting at the Round Table at an equal distance from each other. Each of them is either in a good or in a bad mood.</p><p>Merlin, the wizard predicted to King Arthur that the next month will turn out to be particularly fortunate if the <span class="tex-font-style-it">regular</span> polygon can be found. On all vertices of the polygon knights in a good mood should be located. Otherwise, the next month will bring misfortunes.</p><p>A convex polygon is regular if all its sides have same length and all his angles are equal. In this problem we consider only regular polygons with at least 3 vertices, i. e. only nondegenerated.</p><p>On a picture below some examples of such polygons are present. Green points mean knights in a good mood. Red points mean ones in a bad mood.</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/74f876ccab06b18381319757d775aafd5756bf26.png" style="max-width: 100.0%;max-height: 100.0%;" /> </center><p>King Arthur knows the knights' moods. Help him find out if the next month will be fortunate or not.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains number <span class="tex-span"><i>n</i></span>, which is the number of knights at the round table (<span class="tex-span">3 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup></span>). The second line contains space-separated moods of all the <span class="tex-span"><i>n</i></span> knights in the order of passing them around the table. &quot;1&quot; means that the knight is in a good mood an &quot;0&quot; means that he is in a bad mood.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print &quot;<span class="tex-font-style-tt">YES</span>&quot; without the quotes if the following month will turn out to be lucky. 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["Dynamic programming", "Mathematics including integration, differential equations, etc", "Number theory: Euler function, GCD, divisibility, etc"]
["dp", "math", "number theory", "*1600"]
https://codeforces.com/blog/entry/1624
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Let read all words. For each of them compute its length <span class="tex-span"><i>L</i></span>, its the first and the last letter. If <span class="tex-span"><i>L</i> &gt; 10</span>, output word without any changes, otherwise output the first letter, next <span class="tex-span"><i>L</i> - 2</span> and finally the last letter.<br /> <br /><b>B.</b> At first, compute <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/b30b1e63221e427063b3814647939d0afe0d9e2a.png" style="max-width: 100.0%;max-height: 100.0%;" />. It equals <span class="tex-span">⌊ <i>mnk</i> / 100⌋</span>, where <span class="tex-span">⌊ <i>x</i>⌋</span> is rounding down. Next we fill first <span class="tex-span">⌊ <i>z</i> / <i>k</i>⌋</span> squares with a saturation <span class="tex-span"><i>k</i></span>. <span class="tex-span">(⌊ <i>z</i> / <i>k</i>⌋ + 1)</span>-th square (if it exists) we fill in a saturation <span class="tex-span"><i>z</i> - ⌊ <i>z</i> / <i>k</i>⌋ <i>k</i></span>. All other squares we leave with a saturation <span class="tex-span">0</span>.<br /><br /><b>C.</b> Define an <i>good</i> polygon as a regular polygon which has a knight in a good mood in every of its vertex. Side of polygon we will measure in arcs which is obtained by dividing border of round table with knights.<br /><br />Freeze the length of the side. Let this length equals <span class="tex-span"><i>k</i></span>. Observe that the regular polygon with such length of side exists only if <span class="tex-span"><i>k</i></span> divides <span class="tex-span"><i>n</i></span>. We have exactly <span class="tex-span"><i>k</i></span> of such polygons. Every of them has exactly <span class="tex-span"><i>n</i> / <i>k</i></span> vertices. Check every of the polygons for goodness by review all of its vertices. <br /><br />If sum of vertices with knight in a good mood equals to <span class="tex-span"><i>n</i> / <i>k</i></span>, this polygon is good. Checking of all polygons with some frozen length of side works in an <span class="tex-span"><i>O</i>(<i>n</i>)</span>.<br /><br />Now observe that <span class="tex-span"><i>n</i></span> has <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5a41da22acdba46e7c8eeeaddbc58625f49cbfe5.png" style="max-width: 100.0%;max-height: 100.0%;" /> of divisors. Really, all divisors (may be except only one) we can divide into pairs (for <span class="tex-span"><i>i</i></span> corresponds <span class="tex-span"><i>n</i> / <i>i</i></span>, for <span class="tex-span"><i>i</i> = <i>n</i> / <i>i</i></span> there is no pair). One of divisors in every pair less than <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/712f9a224d6c7824add37b6cd766c21f73a40d59.png" style="max-width: 100.0%;max-height: 100.0%;" />. It means thah number of pairs no more than <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/712f9a224d6c7824add37b6cd766c21f73a40d59.png" style="max-width: 100.0%;max-height: 100.0%;" /> and number of divisors no more than <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/6b8f80d5708602c9727bc53c820fc6ad559209a0.png" style="max-width: 100.0%;max-height: 100.0%;" />.<br /><br />It gives solution - iterate over all divisors of <span class="tex-span"><i>n</i></span> and for every of them check existence of good polygon with length side equals this divisor. Solution has an <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/0c18a224e805d960478a53ca7ac5ae33eaed6dd7.png" style="max-width: 100.0%;max-height: 100.0%;" /> time.<br /><br />In reality for big <span class="tex-span"><i>n</i></span> is has <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7acd26c81b1f055b12a3b1e53f7a9814fd517a81.png" style="max-width: 100.0%;max-height: 100.0%;" /> divisors. So solution actually has <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">4 / 3</sup>)</span>-complexity. For all numbers less than <span class="tex-span">10<sup class="upper-index">5</sup></span> maximal number of divisors is 128.<br /><br />UPD. There was found an <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png" style="max-width: 100.0%;max-height: 100.0%;" /> solution by some participants. This solution uses following idea. If we have a good polygon with <span class="tex-span"><i>xy</i></span> vertices, we also have a good polygon with <span class="tex-span"><i>x</i></span> vertices. So we can check only prime divisors of <span class="tex-span"><i>n</i></span> (except 2 - here we must check 4).<br /><br /><b>D.</b> This problem can be divided into some subproblems.<br /> Author's solution means following ones:<br /><br />1. Check validness of square <span class="tex-span">3 × 3</span>. Square is valid if all cards in it has equal suit or different rank. You may not check equal suit because equal suits imply different ranks.<br /><br />2. Find 2 valid noninetsect squares <span class="tex-span">3 × 3</span> or return thah there are no ones. You can check all pairs of squares for inetsection. If some pair has no intersections check them with solution of subproblem 1.<br /><br />3. Build set of cards which can be replaced with jokers. Generate full deck without jokers and drop from it all cards which in rectangle <span class="tex-span"><i>n</i> × <i>m</i></span> are present.<br /><br />4. Find number of jokers and its positions in rectangle.<br /><br />5. Main subproblem. At first, solve subproblems 3 and 4. Now replace jokers in rectangle with cards from deck from subproblem 3 by all possible ways. For every replace solve subproblem 2. Arter all of variants of replacement just output answer.<br /><br />There are <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">2</sup><i>m</i><sup class="upper-index">2</sup>)</span> solution with small constant.<br /><br /><b>E.</b> At first, you can use some search engine for find periodic table in some printable form. Next use copy-paste (one or several times) and format it by deleting all excess. It is mechanical work for no more than 5 minutes. Also some parser may be written. Note than author's solution does not mean write 100 symbols by hand from a picture. Next build some functions which transform symbols into numbers and vice versa.<br /><br />So, we have some set of numbers. We need summarize some from them and get some another set of numbers. We will use dymanic programming over subsets.<br /><br />Compute the first dp dp1[mask]-&gt;sum. For each subset calculate sum of numbers of all atoms in this subset. It can be done in <span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>n</i></sup><i>n</i>)</span>.<br /><br />Now compute the second dp dp2[mask]-&gt;length. The &quot;length&quot; is a length of some prefix of result sequence of atoms which can be obtained by subset mask. If length -1, it means that it is impossible to get any prefix from this subset.<br /><br />The second dp we can calculate in <span class="tex-span"><i>O</i>(3<sup class="upper-index"><i>n</i></sup>)</span>. Iterate over all masks and if dp2[mask]!=-1, iterate all its subsets of remained atoms (invert mask and get all its submasks). If some subset has sum of numbers which equals number of (dp2[маска]+1)-th atom from result set, recalculate dp2[mask XOR submask]=dp2[mask]+1.<br /><br />At end, if dp2[<span class="tex-span">2<sup class="upper-index"><i>n</i></sup> - 1</span>]=k, there are solution.<br /><br />There are <span class="tex-span"><i>O</i>(3<sup class="upper-index"><i>n</i></sup> + 2<sup class="upper-index"><i>n</i></sup><i>n</i>)</span> solution.<br /><br />In this problem some brutforce solutions are passed because it is difficult to pick up some counterexample.<br /><br />UPD. <a class="rated-user user-orange" href="../../../profile/SkorKNURE" title="Майор SkorKNURE">SkorKNURE</a> found a solution in <span class="tex-span"><span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>n</i></sup><i>n</i>)</span></span>. This solution is some <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">modification</span></span> of the author's solution.<br /><br /><span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">Instead of</span></span> dp2 calculate dp dp2'[mask]-&gt;(i,j), where i is a length of prefix which mask covers and j is part of number of (i+1)-th atom which mask covers.<br /><br />Iterate over all masks. For each mask iterate over all its 0-bits<span class="tex-span"></span> (they are atoms which cover nothing from the finish set). We try to cover with this 0-bit a <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">remainder of</span></span> number of the (i+1)-th atom from the finish set. Let atomic number of an atom for current 0-bit is p and this atom is q-th in the start set. If we cover with this atom only part of the remainder of number of the (i+1)-th atom, dp2'[mask XOR (1&lt;&lt;q)]=(i,j+p). If we cover with this atom the remainder fully (and exactly this remainder, no more!), dp2'[mask XOR (1&lt;&lt;q)]=(i+1,0).<br /><br />Now dp1 is useless. If at end dp2'[<span class="tex-span"><span class="tex-span">2<sup class="upper-index"><i>n</i></sup> - 1</span></span>]=(k,0), solution exists (it is easy to <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">restore it</span></span>), otherwise there is no solution.<span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод"></span></span><span class="tex-span"></span></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/71" class="notice" style="text-decoration: none;">Codeforces Beta Round 65 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-440-1624").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "440", blogEntryId: "1624", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces" class="tag notice" style="text-decoration: none;">codeforces</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=editorial" class="tag notice" style="text-decoration: none;">editorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1624"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+47</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1624"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/Ripatti"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/Ripatti"> Ripatti </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Mar/29/2011 21:20">13 years ago</span> </li> <li> <a href="/blog/entry/1624#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1624#comments"> 39 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1634"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (25)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="30627" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/sicasli" style="position: relative;"> <img src='https://userpic.codeforces.org/10281/avatar/8aa5e308717a2754.jpg'/> </a> <div><a href="/profile/sicasli" title="Expert sicasli" class="rated-user user-blue">sicasli</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 21:51">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30627" href="?#comment-30627" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30627" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="10281" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30627"> <div class="moveup"> <div class="ttypography">system testing took very long time.. and on the middle of contest, server down once.. what happened here?</div> </div> </div> <div class="reply info"> <a class="comment-30627 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30627 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30627"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30631" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/WXYZ" style="position: relative;"> <img src='https://userpic.codeforces.org/16492/avatar/caece4fb867dc8fb.jpg'/> </a> <div><a href="/profile/WXYZ" title="Master WXYZ" class="rated-user user-orange">WXYZ</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 21:58">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30631" href="?#comment-30631" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30631" class="CommentVoteFrame" data-commentRating="4" data-commentUserId="16492" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+4</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30631"> <div class="moveup"> <div class="ttypography">bd</div> </div> </div> <div class="reply info"> <a class="comment-30631 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30631 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30631"> <li> <div class="comment"> <table class="comment-table" commentId="30633" commentParentId="30631"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/pva701" style="position: relative;"> <img src='https://userpic.codeforces.org/3957/avatar/e47deec1b5b8677f.jpg'/> </a> <div><a href="/profile/pva701" title="Expert pva701" class="rated-user user-blue">pva701</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 22:00">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30633" href="?#comment-30633" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30631" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30633" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="3957" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30633"> <div class="moveup"> <div class="ttypography">cool. I understand you. Its great!</div> </div> </div> <div class="reply info"> <a class="comment-30633 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30633 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30633"> <li> <div class="comment"> <table class="comment-table" commentId="30660" commentParentId="30633"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/_arjun" style="position: relative;"> <img src='https://userpic.codeforces.org/1553/avatar/1b0a6d8089c2ee88.jpg'/> </a> <div><a href="/profile/_arjun" title="Expert _arjun" class="rated-user user-blue">_arjun</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 22:37">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30660" href="?#comment-30660" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30633" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30660" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="1553" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30660"> <div class="moveup"> <div class="ttypography">I can't understand , tell me what is bd?</div> </div> </div> <div class="reply info"> <a class="comment-30660 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30660 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30660"> <li> <div class="comment"> <table class="comment-table" commentId="30711" commentParentId="30660"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/naagi" style="position: relative;"> <img src='https://userpic.codeforces.org/1436/avatar/b4261a7f23f18a7c.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/naagi" title="Expert naagi" class="rated-user user-blue">naagi</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 02:15">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30711" href="?#comment-30711" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30660" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30711" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="1436" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30711"> <div class="moveup"> <div class="ttypography">looks like &quot;thumbs up&quot;<br />(I feel proud of myself for this guess :))</div> </div> </div> <div class="reply info"> <a class="comment-30711 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30711 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30711"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="30714" commentParentId="30660"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/acmwe" style="position: relative;"> <img src='https://userpic.codeforces.org/15619/avatar/a74aaa0a09183ea8.jpg'/> </a> <div><a href="/profile/acmwe" title="Specialist acmwe" class="rated-user user-cyan">acmwe</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 06:21">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30714" href="?#comment-30714" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30660" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30714" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="15619" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30714"> <div class="moveup"> <div class="ttypography">It's ....Just like ORZ....</div> </div> </div> <div class="reply info"> <a class="comment-30714 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30714 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30714"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30638" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Lepetrandr" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Lepetrandr" title="Candidate Master Lepetrandr" class="rated-user user-violet">Lepetrandr</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 22:01">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30638" href="?#comment-30638" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30638" class="CommentVoteFrame" data-commentRating="7" data-commentUserId="1088" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+7</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30638"> <div class="moveup"> <div class="ttypography">In problem C we can consider only _prime_ divisors of n (at most 6 :), as number of vertices. But there is one tricky case that i've missed, unfortunately.</div> </div> </div> <div class="reply info"> <a class="comment-30638 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30638 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30638"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30686" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/sanchit_h" style="position: relative;"> <img src='https://userpic.codeforces.org/14424/avatar/ccd3178dffd08856.jpg'/> </a> <div><a href="/profile/sanchit_h" title="Expert sanchit_h" class="rated-user user-blue">sanchit_h</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 23:12">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30686" href="?#comment-30686" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30686" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14424" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30686"> <div class="moveup"> <div class="ttypography">In problem E, can you explain what is a mask and its submasks ?</div> </div> </div> <div class="reply info"> <a class="comment-30686 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30686 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30686"> <li> <div class="comment"> <table class="comment-table" commentId="30687" commentParentId="30686"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kilotaras" style="position: relative;"> <img src='https://userpic.codeforces.org/3934/avatar/1f5f8ec32edbfcfd.jpg'/> </a> <div><a href="/profile/kilotaras" title="Master kilotaras" class="rated-user user-orange">kilotaras</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 23:15">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30687" href="?#comment-30687" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30686" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30687" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30687" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3934" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30687"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div align="left"><a href="https://en.wikipedia.org/wiki/Mask_%28computing%29">http://en.wikipedia.org/wiki/Mask_%28computing%29</a><br /></div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30687 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30687 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30687"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="30688" commentParentId="30686"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Ripatti" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Ripatti" title="Master Ripatti" class="rated-user user-orange">Ripatti</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 23:15">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30688" href="?#comment-30688" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30686" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30688" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="472" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30688"> <div class="moveup"> <div class="ttypography">I will rewrite editorial more detail later.</div> </div> </div> <div class="reply info"> <a class="comment-30688 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30688 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30688"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30691" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/lunae" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/lunae" title="Candidate Master lunae" class="rated-user user-violet">lunae</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 23:29">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30691" href="?#comment-30691" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30691" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30691" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2939" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30691"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">edit: I'm sorry that I didn't notice Lepetrandr's post.<br /><br />For (C) it suffices to check polygons with a prime number of sides (except for 2, then check 4), that gives O(log n) divisors to check.<br /></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30691 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30691 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30691"> <li> <div class="comment"> <table class="comment-table" commentId="30851" commentParentId="30691"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kamranm" style="position: relative;"> <img src='https://userpic.codeforces.org/13373/avatar/bb36d6989328bef3.jpg'/> </a> <div><a href="/profile/kamranm" title="Expert kamranm" class="rated-user user-blue">kamranm</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 21:08">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30851" href="?#comment-30851" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30691" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30851" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13373" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30851"> <div class="moveup"> <div class="ttypography">Yes , because if the - polygon with length equal to n -  is regular , we can create another regular polygons which have the length of any prime divisors of n..but this number is not equal to log(n). This is equal to prime divisors of n.</div> </div> </div> <div class="reply info"> <a class="comment-30851 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30851 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30851"> <li> <div class="comment"> <table class="comment-table" commentId="30854" commentParentId="30851"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ostroumov" style="position: relative;"> <img src='https://userpic.codeforces.org/9567/avatar/daf141c3784f573c.jpg'/> </a> <div><a href="/profile/ostroumov" title="Expert ostroumov" class="rated-user user-blue">ostroumov</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 21:43">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30854" href="?#comment-30854" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30851" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30854" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="9567" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30854"> <div class="moveup"> <div class="ttypography">Number of prime divisors is about equal to ln (n) in case of big n.</div> </div> </div> <div class="reply info"> <a class="comment-30854 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30854 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30854"> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30812" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/wil93" style="position: relative;"> <img src='https://userpic.codeforces.org/14356/avatar/897f1996dfb7343b.jpg'/> </a> <div><a href="/profile/wil93" title="Expert wil93" class="rated-user user-blue">wil93</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 17:48">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30812" href="?#comment-30812" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30812" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="14356" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30812"> <div class="moveup"> <div class="ttypography">In the first problem explanation there's a type error:<div><br /></div><div><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">If</span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;"><i>L</i> &gt; 10</span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">, output word without any changes, otherwise output the first letter, next</span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;"><i>L</i> - 2</span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">and finally the last letter.</span></div><div><br /></div><div>Should be &quot;If L ≤ 10&quot;<br /></div></div> </div> </div> <div class="reply info"> <a class="comment-30812 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30812 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30812"> <li> <div class="comment"> <table class="comment-table" commentId="30868" commentParentId="30812"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/DimaPhil" style="position: relative;"> <img src='https://userpic.codeforces.org/7711/avatar/fb93b0fb945e93fe.jpg'/> </a> <div><a href="/profile/DimaPhil" title="Candidate Master DimaPhil" class="rated-user user-violet">DimaPhil</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 22:05">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30868" href="?#comment-30868" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30812" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30868" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="7711" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30868"> <div class="moveup"> <div class="ttypography">Where did you find it? The statement is correct.</div> </div> </div> <div class="reply info"> <a class="comment-30868 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30868 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30868"> <li> <div class="comment"> <table class="comment-table" commentId="30879" commentParentId="30868"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ostroumov" style="position: relative;"> <img src='https://userpic.codeforces.org/9567/avatar/daf141c3784f573c.jpg'/> </a> <div><a href="/profile/ostroumov" title="Expert ostroumov" class="rated-user user-blue">ostroumov</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 22:33">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30879" href="?#comment-30879" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30868" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30879" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="9567" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30879"> <div class="moveup"> <div class="ttypography"><a href="https://codeforces.com/blog/entry/1624?locale=en">Here</a></div> </div> </div> <div class="reply info"> <a class="comment-30879 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30879 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30879"> <li> <div class="comment"> <table class="comment-table" commentId="30884" commentParentId="30879"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/DimaPhil" style="position: relative;"> <img src='https://userpic.codeforces.org/7711/avatar/fb93b0fb945e93fe.jpg'/> </a> <div><a href="/profile/DimaPhil" title="Candidate Master DimaPhil" class="rated-user user-violet">DimaPhil</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 23:13">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30884" href="?#comment-30884" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30879" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30884" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="7711" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30884"> <div class="moveup"> <div class="ttypography">Oh, yes, i see.</div> </div> </div> <div class="reply info"> <a class="comment-30884 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30884 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30884"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30898" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/fura2" style="position: relative;"> <img src='https://userpic.codeforces.org/4118/avatar/98f7ddceb1dac755.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/fura2" title="Master fura2" class="rated-user user-orange">fura2</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/31/2011 09:54">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30898" href="?#comment-30898" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30898" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4118" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30898"> <div class="moveup"> <div class="ttypography">In author's solution of problem E,<br /> does dp1 calculation really need dynamic programming?<br /> I think, this part can be done by simple 2 loops.<br /> <div align="left"><br /></div> for(int mask=0;mask&lt;(1&lt;&lt;n);mask++){<br />   dp1[mask]=0;<br />   for(int i=0;i&lt;n;i++){<br />     if(mask&amp;(1&lt;&lt;i)) dp1[mask]+=(weight of i-th atom);<br />   }<br /> }<br /></div> </div> </div> <div class="reply info"> <a class="comment-30898 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30898 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30898"> <li> <div class="comment"> <table class="comment-table" commentId="30918" commentParentId="30898"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Ripatti" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Ripatti" title="Master Ripatti" class="rated-user user-orange">Ripatti</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/31/2011 13:36">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30918" href="?#comment-30918" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30898" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30918" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="472" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30918"> <div class="moveup"> <div class="ttypography">You are right. It can be calculated by your way. Also it is calculated in this way in the author's solution.</div> </div> </div> <div class="reply info"> <a class="comment-30918 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30918 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30918"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="31195" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/arpit_s" style="position: relative;"> <img src='https://userpic.codeforces.org/6116/avatar/34bf701a2e3bf99.jpg'/> </a> <div><a href="/profile/arpit_s" title="Pupil arpit_s" class="rated-user user-green">arpit_s</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/03/2011 11:04">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-31195" href="?#comment-31195" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="31195" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6116" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-31195"> <div class="moveup"> <div class="ttypography">can you please explain O(nlog(n)) solution for question C ?</div> </div> </div> <div class="reply info"> <a class="comment-31195 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-31195 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-31195"> <li> <div class="comment"> <table class="comment-table" commentId="31215" commentParentId="31195"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mR.ilchi" style="position: relative;"> <img src='https://userpic.codeforces.org/11753/avatar/b0675918b77546aa.jpg'/> </a> <div><a href="/profile/mR.ilchi" title="International Grandmaster mR.ilchi" class="rated-user user-red">mR.ilchi</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/03/2011 20:07">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-31215" href="?#comment-31215" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-31195" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="31215" revisionCount="3" revision="3"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">3</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="31215" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="11753" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-31215"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer">assume n= p<sub>1</sub><sup>q</sup><sup>1</sup> * p<sub>2</sub><sup>q2 </sup>* ... * p<sub>m</sub><sup>qm</sup>, where all the p<sub>i </sub>is prime.<div>then for each i, (1&lt;=i&lt;=m), check if exist good polygyn with exactly p<sub>i </sub>vertex. if at least one of this question has positive answer then output &quot;YES&quot;, otherwise output &quot;NO&quot;. because if we have a good polygyn with <b>A*B</b> vertex, then we have a good polygyn with <b>A</b> vertex.</div><div>sorry for my poor english!</div><div><br /></div></div> </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-31215 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-31215 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-31215"> <li> <div class="comment"> <table class="comment-table" commentId="31276" commentParentId="31215"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/arpit_s" style="position: relative;"> <img src='https://userpic.codeforces.org/6116/avatar/34bf701a2e3bf99.jpg'/> </a> <div><a href="/profile/arpit_s" title="Pupil arpit_s" class="rated-user user-green">arpit_s</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/04/2011 13:16">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-31276" href="?#comment-31276" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-31215" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="31276" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6116" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-31276"> <div class="moveup"> <div class="ttypography">sorry, couldn't understand, can you explain with one example ?</div> </div> </div> <div class="reply info"> <a class="comment-31276 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-31276 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-31276"> <li> <div class="comment"> <table class="comment-table" commentId="31290" commentParentId="31276"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mR.ilchi" style="position: relative;"> <img src='https://userpic.codeforces.org/11753/avatar/b0675918b77546aa.jpg'/> </a> <div><a href="/profile/mR.ilchi" title="International Grandmaster mR.ilchi" class="rated-user user-red">mR.ilchi</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/04/2011 15:32">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-31290" href="?#comment-31290" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-31276" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="31290" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="31290" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="11753" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-31290"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">assume this good polygyn with <b>A*B</b> vertex:<div>S<sub>1</sub>, S<sub>2</sub>, ... , S<sub>A*B</sub></div><div>now we have subpolygyn which have only <b>A </b>vertex, like this:</div><div>S<sub>1*B</sub>, S<sub>2*B</sub>, ... , S<sub>A*B.</sub></div><div>now it's obviously that if the circle  has a good polygyn then it has a polygyn with prime vertex. it's algo is O(nlgn) because for each i, p<sub>i</sub> &gt;=2</div><div>so m&lt;=lgn, and check function is O(n). therefore main algo is O(nlgn). </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-31290 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-31290 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-31290"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="50340" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/dalex" style="position: relative;"> <img src='https://userpic.codeforces.org/4200/avatar/fe9bfc44be854399.jpg'/> </a> <div><a href="/profile/dalex" title="Master dalex" class="rated-user user-orange">dalex</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Aug/04/2011 22:51">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-50340" href="?#comment-50340" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="50340" revisionCount="3" revision="3"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">3</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="50340" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4200" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-50340"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><p> </p><div class="from-renderer">Some help for Java users with problem E: <a href="http://pastebin.com/ZsDc3P1E">http://pastebin.com/ZsDc3P1E</a><br /><br />(Yes, I'm a necroposter)<br /></div> </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-50340 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-50340 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-50340"> <li> <div class="comment"> <table class="comment-table" commentId="651690" commentParentId="50340"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/the_hyp0cr1t3" style="position: relative;"> <img src='https://userpic.codeforces.org/1236992/avatar/92bd73b5049b4093.jpg'/> </a> <div><a href="/profile/the_hyp0cr1t3" title="Candidate Master the_hyp0cr1t3" class="rated-user user-violet">the_hyp0cr1t3</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/27/2020 22:53">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-651690" href="?#comment-651690" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-50340" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="651690" class="CommentVoteFrame" data-commentRating="-8" data-commentUserId="1236992" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">-8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-651690"> <div class="moveup"> <div class="ttypography"><p>Me too apparently</p></div> </div> </div> <div class="reply info"> <a class="comment-651690 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-651690 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-651690"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1634" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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71D
71
D
en
D. Solitaire
<div class="problem-statement"><div class="header"><div class="title">D. Solitaire</div><div class="time-limit"><div class="property-title">time limit per test</div>1.5 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Vasya has a pack of <span class="tex-span">54</span> cards (<span class="tex-span">52</span> standard cards and <span class="tex-span">2</span> distinct jokers). That is all he has at the moment. Not to die from boredom, Vasya plays Solitaire with them.</p><p>Vasya lays out <span class="tex-span"><i>nm</i></span> cards as a rectangle <span class="tex-span"><i>n</i> × <i>m</i></span>. If there are jokers among them, then Vasya should change them with some of the rest of <span class="tex-span">54 - <i>nm</i></span> cards (which are not layed out) so that there were no jokers left. Vasya can pick the cards to replace the jokers arbitrarily. Remember, that each card presents in pack exactly once (i. e. <span class="tex-font-style-bf">in a single copy</span>). Vasya tries to perform the replacements so that the solitaire was <span class="tex-font-style-it">solved</span>.</p><p>Vasya thinks that the solitaire is solved if after the jokers are replaced, there exist two non-overlapping squares <span class="tex-span">3 × 3</span>, inside each of which all the cards either have the same suit, or pairwise different ranks.</p><p>Determine by the initial position whether the solitaire can be solved or not. If it can be solved, show the way in which it is possible.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>m</i></span> (<span class="tex-span">3 ≤ <i>n</i>, <i>m</i> ≤ 17</span>, <span class="tex-span"><i>n</i> × <i>m</i> ≤ 52</span>). Next <span class="tex-span"><i>n</i></span> lines contain <span class="tex-span"><i>m</i></span> words each. Each word consists of two letters. The jokers are defined as "<span class="tex-font-style-tt">J1</span>" and "<span class="tex-font-style-tt">J2</span>" correspondingly. For the rest of the cards, the first letter stands for the rank and the second one — for the suit. The possible ranks are: "<span class="tex-font-style-tt">2</span>", "<span class="tex-font-style-tt">3</span>", "<span class="tex-font-style-tt">4</span>", "<span class="tex-font-style-tt">5</span>", "<span class="tex-font-style-tt">6</span>", "<span class="tex-font-style-tt">7</span>", "<span class="tex-font-style-tt">8</span>", "<span class="tex-font-style-tt">9</span>", "<span class="tex-font-style-tt">T</span>", "<span class="tex-font-style-tt">J</span>", "<span class="tex-font-style-tt">Q</span>", "<span class="tex-font-style-tt">K</span>" and "<span class="tex-font-style-tt">A</span>". The possible suits are: "<span class="tex-font-style-tt">C</span>", "<span class="tex-font-style-tt">D</span>", "<span class="tex-font-style-tt">H</span>" and "<span class="tex-font-style-tt">S</span>". All the cards are different.</p></div><div class="output-specification"><div class="section-title">Output</div><p>If the Solitaire can be solved, print on the first line "<span class="tex-font-style-tt">Solution exists.</span>" without the quotes. On the second line print in what way the jokers can be replaced. Three variants are possible:</p><ul> <li> "<span class="tex-font-style-tt">There are no jokers.</span>", if there are no jokers in the input data.</li><li> "<span class="tex-font-style-tt">Replace J<span class="tex-span"><i>x</i></span> with <span class="tex-span"><i>y</i></span>.</span>", if there is one joker. <span class="tex-span"><i>x</i></span> is its number, and <span class="tex-span"><i>y</i></span> is the card it should be replaced with.</li><li> "<span class="tex-font-style-tt">Replace J1 with <span class="tex-span"><i>x</i></span> and J2 with <span class="tex-span"><i>y</i></span>.</span>", if both jokers are present in the input data. <span class="tex-span"><i>x</i></span> and <span class="tex-span"><i>y</i></span> here represent distinct cards with which one should replace the first and the second jokers correspondingly.</li></ul><p>On the third line print the coordinates of the upper left corner of the first square <span class="tex-span">3 × 3</span> in the format "<span class="tex-font-style-tt">Put the first square to (<span class="tex-span"><i>r</i></span>, <span class="tex-span"><i>c</i></span>).</span>", where <span class="tex-span"><i>r</i></span> and <span class="tex-span"><i>c</i></span> are the row and the column correspondingly. In the same manner print on the fourth line the coordinates of the second square <span class="tex-span">3 × 3</span> in the format "<span class="tex-font-style-tt">Put the second square to (<span class="tex-span"><i>r</i></span>, <span class="tex-span"><i>c</i></span>).</span>".</p><p>If there are several solutions to that problem, print any of them.</p><p>If there are no solutions, print of the single line "<span class="tex-font-style-tt">No solution.</span>" without the quotes.</p><p>See the samples to understand the output format better.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>4 6<br/>2S 3S 4S 7S 8S AS<br/>5H 6H 7H 5S TC AC<br/>8H 9H TH 7C 8C 9C<br/>2D 2C 3C 4C 5C 6C<br/></pre></div><div class="output"><div class="title">Output</div><pre>No solution.</pre></div><div class="input"><div class="title">Input</div><pre>4 6<br/>2S 3S 4S 7S 8S AS<br/>5H 6H 7H J1 TC AC<br/>8H 9H TH 7C 8C 9C<br/>2D 2C 3C 4C 5C 6C<br/></pre></div><div class="output"><div class="title">Output</div><pre>Solution exists.<br/>Replace J1 with 2H.<br/>Put the first square to (1, 1).<br/>Put the second square to (2, 4).<br/></pre></div><div class="input"><div class="title">Input</div><pre>4 6<br/>2S 3S 4S 7S 8S AS<br/>5H 6H 7H QC TC AC<br/>8H 9H TH 7C 8C 9C<br/>2D 2C 3C 4C 5C 6C<br/></pre></div><div class="output"><div class="title">Output</div><pre>Solution exists.<br/>There are no jokers.<br/>Put the first square to (1, 1).<br/>Put the second square to (2, 4).<br/></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>The pretests cover all the possible output formats.</p></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="D" data-uuid="ps_943e44daebc1c18edd3f1b3b6691585974c62f14"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">D. Solitaire</div><div class="time-limit"><div class="property-title">time limit per test</div>1.5 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Vasya has a pack of <span class="tex-span">54</span> cards (<span class="tex-span">52</span> standard cards and <span class="tex-span">2</span> distinct jokers). That is all he has at the moment. Not to die from boredom, Vasya plays Solitaire with them.</p><p>Vasya lays out <span class="tex-span"><i>nm</i></span> cards as a rectangle <span class="tex-span"><i>n</i> × <i>m</i></span>. If there are jokers among them, then Vasya should change them with some of the rest of <span class="tex-span">54 - <i>nm</i></span> cards (which are not layed out) so that there were no jokers left. Vasya can pick the cards to replace the jokers arbitrarily. Remember, that each card presents in pack exactly once (i. e. <span class="tex-font-style-bf">in a single copy</span>). Vasya tries to perform the replacements so that the solitaire was <span class="tex-font-style-it">solved</span>.</p><p>Vasya thinks that the solitaire is solved if after the jokers are replaced, there exist two non-overlapping squares <span class="tex-span">3 × 3</span>, inside each of which all the cards either have the same suit, or pairwise different ranks.</p><p>Determine by the initial position whether the solitaire can be solved or not. If it can be solved, show the way in which it is possible.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>m</i></span> (<span class="tex-span">3 ≤ <i>n</i>, <i>m</i> ≤ 17</span>, <span class="tex-span"><i>n</i> × <i>m</i> ≤ 52</span>). Next <span class="tex-span"><i>n</i></span> lines contain <span class="tex-span"><i>m</i></span> words each. Each word consists of two letters. The jokers are defined as &quot;<span class="tex-font-style-tt">J1</span>&quot; and &quot;<span class="tex-font-style-tt">J2</span>&quot; correspondingly. For the rest of the cards, the first letter stands for the rank and the second one — for the suit. The possible ranks are: &quot;<span class="tex-font-style-tt">2</span>&quot;, &quot;<span class="tex-font-style-tt">3</span>&quot;, &quot;<span class="tex-font-style-tt">4</span>&quot;, &quot;<span class="tex-font-style-tt">5</span>&quot;, &quot;<span class="tex-font-style-tt">6</span>&quot;, &quot;<span class="tex-font-style-tt">7</span>&quot;, &quot;<span class="tex-font-style-tt">8</span>&quot;, &quot;<span class="tex-font-style-tt">9</span>&quot;, &quot;<span class="tex-font-style-tt">T</span>&quot;, &quot;<span class="tex-font-style-tt">J</span>&quot;, &quot;<span class="tex-font-style-tt">Q</span>&quot;, &quot;<span class="tex-font-style-tt">K</span>&quot; and &quot;<span class="tex-font-style-tt">A</span>&quot;. The possible suits are: &quot;<span class="tex-font-style-tt">C</span>&quot;, &quot;<span class="tex-font-style-tt">D</span>&quot;, &quot;<span class="tex-font-style-tt">H</span>&quot; and &quot;<span class="tex-font-style-tt">S</span>&quot;. All the cards are different.</p></div><div class="output-specification"><div class="section-title">Output</div><p>If the Solitaire can be solved, print on the first line &quot;<span class="tex-font-style-tt">Solution exists.</span>&quot; without the quotes. On the second line print in what way the jokers can be replaced. Three variants are possible:</p><ul> <li> &quot;<span class="tex-font-style-tt">There are no jokers.</span>&quot;, if there are no jokers in the input data.</li><li> &quot;<span class="tex-font-style-tt">Replace J<span class="tex-span"><i>x</i></span> with <span class="tex-span"><i>y</i></span>.</span>&quot;, if there is one joker. <span class="tex-span"><i>x</i></span> is its number, and <span class="tex-span"><i>y</i></span> is the card it should be replaced with.</li><li> &quot;<span class="tex-font-style-tt">Replace J1 with <span class="tex-span"><i>x</i></span> and J2 with <span class="tex-span"><i>y</i></span>.</span>&quot;, if both jokers are present in the input data. <span class="tex-span"><i>x</i></span> and <span class="tex-span"><i>y</i></span> here represent distinct cards with which one should replace the first and the second jokers correspondingly.</li></ul><p>On the third line print the coordinates of the upper left corner of the first square <span class="tex-span">3 × 3</span> in the format &quot;<span class="tex-font-style-tt">Put the first square to (<span class="tex-span"><i>r</i></span>, <span class="tex-span"><i>c</i></span>).</span>&quot;, where <span class="tex-span"><i>r</i></span> and <span class="tex-span"><i>c</i></span> are the row and the column correspondingly. In the same manner print on the fourth line the coordinates of the second square <span class="tex-span">3 × 3</span> in the format &quot;<span class="tex-font-style-tt">Put the second square to (<span class="tex-span"><i>r</i></span>, <span class="tex-span"><i>c</i></span>).</span>&quot;.</p><p>If there are several solutions to that problem, print any of them.</p><p>If there are no solutions, print of the single line &quot;<span class="tex-font-style-tt">No solution.</span>&quot; without the quotes.</p><p>See the samples to understand the output format better.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>4 6<br />2S 3S 4S 7S 8S AS<br />5H 6H 7H 5S TC AC<br />8H 9H TH 7C 8C 9C<br />2D 2C 3C 4C 5C 6C<br /></pre></div><div class="output"><div class="title">Output</div><pre>No solution.</pre></div><div class="input"><div class="title">Input</div><pre>4 6<br />2S 3S 4S 7S 8S AS<br />5H 6H 7H J1 TC AC<br />8H 9H TH 7C 8C 9C<br />2D 2C 3C 4C 5C 6C<br /></pre></div><div class="output"><div class="title">Output</div><pre>Solution exists.<br />Replace J1 with 2H.<br />Put the first square to (1, 1).<br />Put the second square to (2, 4).<br /></pre></div><div class="input"><div class="title">Input</div><pre>4 6<br />2S 3S 4S 7S 8S AS<br />5H 6H 7H QC TC AC<br />8H 9H TH 7C 8C 9C<br />2D 2C 3C 4C 5C 6C<br /></pre></div><div class="output"><div class="title">Output</div><pre>Solution exists.<br />There are no jokers.<br />Put the first square to (1, 1).<br />Put the second square to (2, 4).<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>The pretests cover all the possible output formats.</p></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=D]"); 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["Brute force", "Implementation problems, programming technics, simulation"]
["brute force", "implementation", "*2200"]
https://codeforces.com/blog/entry/1624
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<a href="/blog/entry/120644">Codeforces Round 899 (Div. 2)</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/Misa-Misa" title="Expert Misa-Misa" class="rated-user user-blue">Misa-Misa</a> &rarr; <a href="/blog/entry/121157">Someone please help me understand this.</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/shivam565" title="Specialist shivam565" class="rated-user user-cyan">shivam565</a> &rarr; <a href="/blog/entry/108348">Total number of subarrays with sum atmost k</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> </ul> </div> <div class="bottom-links"> <table style="width:100%;"> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:right;"> <a href="/recent-actions">Detailed &rarr;</a> </td> </tr> </tbody> </table> </div> </div> </div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li><a href="/profile/Ripatti">Ripatti</a></li> <li class="current selectedLava"><a href="/blog/Ripatti">Blog</a></li> <li><a href="/teams/with/Ripatti">Teams</a></li> <li><a href="/submissions/Ripatti">Submissions</a></li> <li><a href="/groups/with/Ripatti">Groups</a></li> <li><a href="/contests/with/Ripatti">Contests</a></li> <li><a href="/contests/writer/Ripatti">Problemsetting</a></li> </ul> </div> <div style="margin-top:0;"> <div> <h3><a href="/blog/Ripatti" style="text-decoration:none;color:black !important;">Ripatti's blog</a></h3> </div> <div style="margin-top:2em;"> <div class="has-topic-id topic" topicId="1624"> <div class="title"> <a href="/blog/entry/1624"> Solutions for Codeforces Beta Round #65 (Div. 2) </a> </div> <div class="info" style="position:relative;"> By&nbsp;<a href="/profile/Ripatti" title="Master Ripatti" class="rated-user user-orange">Ripatti</a>, <span class="format-humantime" title="Mar/29/2011 21:20">13 years ago</span>, translation, <img style="position: relative;top: 5px;" src="//codeforces.org/s/81027/images/flags/24/gb.png" alt="In English" title="In English"/> <span style="position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;"> <div style="margin-top:0.25em;"> </div> </span> </div> <div class="content"> <div class="ttypography"><b>A.</b> In this problem you can just do what is written in the statement. Let read all words. For each of them compute its length <span class="tex-span"><i>L</i></span>, its the first and the last letter. If <span class="tex-span"><i>L</i> &gt; 10</span>, output word without any changes, otherwise output the first letter, next <span class="tex-span"><i>L</i> - 2</span> and finally the last letter.<br /> <br /><b>B.</b> At first, compute <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/b30b1e63221e427063b3814647939d0afe0d9e2a.png" style="max-width: 100.0%;max-height: 100.0%;" />. It equals <span class="tex-span">⌊ <i>mnk</i> / 100⌋</span>, where <span class="tex-span">⌊ <i>x</i>⌋</span> is rounding down. Next we fill first <span class="tex-span">⌊ <i>z</i> / <i>k</i>⌋</span> squares with a saturation <span class="tex-span"><i>k</i></span>. <span class="tex-span">(⌊ <i>z</i> / <i>k</i>⌋ + 1)</span>-th square (if it exists) we fill in a saturation <span class="tex-span"><i>z</i> - ⌊ <i>z</i> / <i>k</i>⌋ <i>k</i></span>. All other squares we leave with a saturation <span class="tex-span">0</span>.<br /><br /><b>C.</b> Define an <i>good</i> polygon as a regular polygon which has a knight in a good mood in every of its vertex. Side of polygon we will measure in arcs which is obtained by dividing border of round table with knights.<br /><br />Freeze the length of the side. Let this length equals <span class="tex-span"><i>k</i></span>. Observe that the regular polygon with such length of side exists only if <span class="tex-span"><i>k</i></span> divides <span class="tex-span"><i>n</i></span>. We have exactly <span class="tex-span"><i>k</i></span> of such polygons. Every of them has exactly <span class="tex-span"><i>n</i> / <i>k</i></span> vertices. Check every of the polygons for goodness by review all of its vertices. <br /><br />If sum of vertices with knight in a good mood equals to <span class="tex-span"><i>n</i> / <i>k</i></span>, this polygon is good. Checking of all polygons with some frozen length of side works in an <span class="tex-span"><i>O</i>(<i>n</i>)</span>.<br /><br />Now observe that <span class="tex-span"><i>n</i></span> has <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5a41da22acdba46e7c8eeeaddbc58625f49cbfe5.png" style="max-width: 100.0%;max-height: 100.0%;" /> of divisors. Really, all divisors (may be except only one) we can divide into pairs (for <span class="tex-span"><i>i</i></span> corresponds <span class="tex-span"><i>n</i> / <i>i</i></span>, for <span class="tex-span"><i>i</i> = <i>n</i> / <i>i</i></span> there is no pair). One of divisors in every pair less than <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/712f9a224d6c7824add37b6cd766c21f73a40d59.png" style="max-width: 100.0%;max-height: 100.0%;" />. It means thah number of pairs no more than <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/712f9a224d6c7824add37b6cd766c21f73a40d59.png" style="max-width: 100.0%;max-height: 100.0%;" /> and number of divisors no more than <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/6b8f80d5708602c9727bc53c820fc6ad559209a0.png" style="max-width: 100.0%;max-height: 100.0%;" />.<br /><br />It gives solution - iterate over all divisors of <span class="tex-span"><i>n</i></span> and for every of them check existence of good polygon with length side equals this divisor. Solution has an <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/0c18a224e805d960478a53ca7ac5ae33eaed6dd7.png" style="max-width: 100.0%;max-height: 100.0%;" /> time.<br /><br />In reality for big <span class="tex-span"><i>n</i></span> is has <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7acd26c81b1f055b12a3b1e53f7a9814fd517a81.png" style="max-width: 100.0%;max-height: 100.0%;" /> divisors. So solution actually has <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">4 / 3</sup>)</span>-complexity. For all numbers less than <span class="tex-span">10<sup class="upper-index">5</sup></span> maximal number of divisors is 128.<br /><br />UPD. There was found an <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png" style="max-width: 100.0%;max-height: 100.0%;" /> solution by some participants. This solution uses following idea. If we have a good polygon with <span class="tex-span"><i>xy</i></span> vertices, we also have a good polygon with <span class="tex-span"><i>x</i></span> vertices. So we can check only prime divisors of <span class="tex-span"><i>n</i></span> (except 2 - here we must check 4).<br /><br /><b>D.</b> This problem can be divided into some subproblems.<br /> Author's solution means following ones:<br /><br />1. Check validness of square <span class="tex-span">3 × 3</span>. Square is valid if all cards in it has equal suit or different rank. You may not check equal suit because equal suits imply different ranks.<br /><br />2. Find 2 valid noninetsect squares <span class="tex-span">3 × 3</span> or return thah there are no ones. You can check all pairs of squares for inetsection. If some pair has no intersections check them with solution of subproblem 1.<br /><br />3. Build set of cards which can be replaced with jokers. Generate full deck without jokers and drop from it all cards which in rectangle <span class="tex-span"><i>n</i> × <i>m</i></span> are present.<br /><br />4. Find number of jokers and its positions in rectangle.<br /><br />5. Main subproblem. At first, solve subproblems 3 and 4. Now replace jokers in rectangle with cards from deck from subproblem 3 by all possible ways. For every replace solve subproblem 2. Arter all of variants of replacement just output answer.<br /><br />There are <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">2</sup><i>m</i><sup class="upper-index">2</sup>)</span> solution with small constant.<br /><br /><b>E.</b> At first, you can use some search engine for find periodic table in some printable form. Next use copy-paste (one or several times) and format it by deleting all excess. It is mechanical work for no more than 5 minutes. Also some parser may be written. Note than author's solution does not mean write 100 symbols by hand from a picture. Next build some functions which transform symbols into numbers and vice versa.<br /><br />So, we have some set of numbers. We need summarize some from them and get some another set of numbers. We will use dymanic programming over subsets.<br /><br />Compute the first dp dp1[mask]-&gt;sum. For each subset calculate sum of numbers of all atoms in this subset. It can be done in <span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>n</i></sup><i>n</i>)</span>.<br /><br />Now compute the second dp dp2[mask]-&gt;length. The &quot;length&quot; is a length of some prefix of result sequence of atoms which can be obtained by subset mask. If length -1, it means that it is impossible to get any prefix from this subset.<br /><br />The second dp we can calculate in <span class="tex-span"><i>O</i>(3<sup class="upper-index"><i>n</i></sup>)</span>. Iterate over all masks and if dp2[mask]!=-1, iterate all its subsets of remained atoms (invert mask and get all its submasks). If some subset has sum of numbers which equals number of (dp2[маска]+1)-th atom from result set, recalculate dp2[mask XOR submask]=dp2[mask]+1.<br /><br />At end, if dp2[<span class="tex-span">2<sup class="upper-index"><i>n</i></sup> - 1</span>]=k, there are solution.<br /><br />There are <span class="tex-span"><i>O</i>(3<sup class="upper-index"><i>n</i></sup> + 2<sup class="upper-index"><i>n</i></sup><i>n</i>)</span> solution.<br /><br />In this problem some brutforce solutions are passed because it is difficult to pick up some counterexample.<br /><br />UPD. <a class="rated-user user-orange" href="../../../profile/SkorKNURE" title="Майор SkorKNURE">SkorKNURE</a> found a solution in <span class="tex-span"><span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>n</i></sup><i>n</i>)</span></span>. This solution is some <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">modification</span></span> of the author's solution.<br /><br /><span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">Instead of</span></span> dp2 calculate dp dp2'[mask]-&gt;(i,j), where i is a length of prefix which mask covers and j is part of number of (i+1)-th atom which mask covers.<br /><br />Iterate over all masks. For each mask iterate over all its 0-bits<span class="tex-span"></span> (they are atoms which cover nothing from the finish set). We try to cover with this 0-bit a <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">remainder of</span></span> number of the (i+1)-th atom from the finish set. Let atomic number of an atom for current 0-bit is p and this atom is q-th in the start set. If we cover with this atom only part of the remainder of number of the (i+1)-th atom, dp2'[mask XOR (1&lt;&lt;q)]=(i,j+p). If we cover with this atom the remainder fully (and exactly this remainder, no more!), dp2'[mask XOR (1&lt;&lt;q)]=(i+1,0).<br /><br />Now dp1 is useless. If at end dp2'[<span class="tex-span"><span class="tex-span">2<sup class="upper-index"><i>n</i></sup> - 1</span></span>]=(k,0), solution exists (it is easy to <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">restore it</span></span>), otherwise there is no solution.<span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод"></span></span><span class="tex-span"></span></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/71" class="notice" style="text-decoration: none;">Codeforces Beta Round 65 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-440-1624").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "440", blogEntryId: "1624", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces" class="tag notice" style="text-decoration: none;">codeforces</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=editorial" class="tag notice" style="text-decoration: none;">editorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1624"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+47</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1624"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; 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margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1634"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (25)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="30627" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/sicasli" style="position: relative;"> <img src='https://userpic.codeforces.org/10281/avatar/8aa5e308717a2754.jpg'/> </a> <div><a href="/profile/sicasli" title="Expert sicasli" class="rated-user user-blue">sicasli</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 21:51">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30627" href="?#comment-30627" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30627" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="10281" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30627"> <div class="moveup"> <div class="ttypography">system testing took very long time.. and on the middle of contest, server down once.. what happened here?</div> </div> </div> <div class="reply info"> <a class="comment-30627 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30627 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30627"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30631" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/WXYZ" style="position: relative;"> <img src='https://userpic.codeforces.org/16492/avatar/caece4fb867dc8fb.jpg'/> </a> <div><a href="/profile/WXYZ" title="Master WXYZ" class="rated-user user-orange">WXYZ</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 21:58">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30631" href="?#comment-30631" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30631" class="CommentVoteFrame" data-commentRating="4" data-commentUserId="16492" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+4</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30631"> <div class="moveup"> <div class="ttypography">bd</div> </div> </div> <div class="reply info"> <a class="comment-30631 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30631 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30631"> <li> <div class="comment"> <table class="comment-table" commentId="30633" commentParentId="30631"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/pva701" style="position: relative;"> <img src='https://userpic.codeforces.org/3957/avatar/e47deec1b5b8677f.jpg'/> </a> <div><a href="/profile/pva701" title="Expert pva701" class="rated-user user-blue">pva701</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 22:00">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30633" href="?#comment-30633" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30631" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30633" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="3957" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30633"> <div class="moveup"> <div class="ttypography">cool. I understand you. Its great!</div> </div> </div> <div class="reply info"> <a class="comment-30633 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30633 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30633"> <li> <div class="comment"> <table class="comment-table" commentId="30660" commentParentId="30633"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/_arjun" style="position: relative;"> <img src='https://userpic.codeforces.org/1553/avatar/1b0a6d8089c2ee88.jpg'/> </a> <div><a href="/profile/_arjun" title="Expert _arjun" class="rated-user user-blue">_arjun</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 22:37">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30660" href="?#comment-30660" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30633" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30660" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="1553" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30660"> <div class="moveup"> <div class="ttypography">I can't understand , tell me what is bd?</div> </div> </div> <div class="reply info"> <a class="comment-30660 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30660 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30660"> <li> <div class="comment"> <table class="comment-table" commentId="30711" commentParentId="30660"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/naagi" style="position: relative;"> <img src='https://userpic.codeforces.org/1436/avatar/b4261a7f23f18a7c.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/naagi" title="Expert naagi" class="rated-user user-blue">naagi</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 02:15">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30711" href="?#comment-30711" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30660" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30711" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="1436" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30711"> <div class="moveup"> <div class="ttypography">looks like &quot;thumbs up&quot;<br />(I feel proud of myself for this guess :))</div> </div> </div> <div class="reply info"> <a class="comment-30711 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30711 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30711"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="30714" commentParentId="30660"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/acmwe" style="position: relative;"> <img src='https://userpic.codeforces.org/15619/avatar/a74aaa0a09183ea8.jpg'/> </a> <div><a href="/profile/acmwe" title="Specialist acmwe" class="rated-user user-cyan">acmwe</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 06:21">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30714" href="?#comment-30714" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30660" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30714" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="15619" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30714"> <div class="moveup"> <div class="ttypography">It's ....Just like ORZ....</div> </div> </div> <div class="reply info"> <a class="comment-30714 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30714 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30714"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30638" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Lepetrandr" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Lepetrandr" title="Candidate Master Lepetrandr" class="rated-user user-violet">Lepetrandr</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 22:01">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30638" href="?#comment-30638" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30638" class="CommentVoteFrame" data-commentRating="7" data-commentUserId="1088" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+7</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30638"> <div class="moveup"> <div class="ttypography">In problem C we can consider only _prime_ divisors of n (at most 6 :), as number of vertices. But there is one tricky case that i've missed, unfortunately.</div> </div> </div> <div class="reply info"> <a class="comment-30638 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30638 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30638"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30686" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/sanchit_h" style="position: relative;"> <img src='https://userpic.codeforces.org/14424/avatar/ccd3178dffd08856.jpg'/> </a> <div><a href="/profile/sanchit_h" title="Expert sanchit_h" class="rated-user user-blue">sanchit_h</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 23:12">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30686" href="?#comment-30686" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30686" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14424" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30686"> <div class="moveup"> <div class="ttypography">In problem E, can you explain what is a mask and its submasks ?</div> </div> </div> <div class="reply info"> <a class="comment-30686 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30686 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30686"> <li> <div class="comment"> <table class="comment-table" commentId="30687" commentParentId="30686"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kilotaras" style="position: relative;"> <img src='https://userpic.codeforces.org/3934/avatar/1f5f8ec32edbfcfd.jpg'/> </a> <div><a href="/profile/kilotaras" title="Master kilotaras" class="rated-user user-orange">kilotaras</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 23:15">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30687" href="?#comment-30687" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30686" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30687" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30687" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3934" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30687"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div align="left"><a href="https://en.wikipedia.org/wiki/Mask_%28computing%29">http://en.wikipedia.org/wiki/Mask_%28computing%29</a><br /></div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30687 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30687 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30687"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="30688" commentParentId="30686"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Ripatti" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Ripatti" title="Master Ripatti" class="rated-user user-orange">Ripatti</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 23:15">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30688" href="?#comment-30688" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30686" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30688" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="472" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30688"> <div class="moveup"> <div class="ttypography">I will rewrite editorial more detail later.</div> </div> </div> <div class="reply info"> <a class="comment-30688 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30688 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30688"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30691" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/lunae" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/lunae" title="Candidate Master lunae" class="rated-user user-violet">lunae</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 23:29">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30691" href="?#comment-30691" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30691" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30691" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2939" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30691"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">edit: I'm sorry that I didn't notice Lepetrandr's post.<br /><br />For (C) it suffices to check polygons with a prime number of sides (except for 2, then check 4), that gives O(log n) divisors to check.<br /></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30691 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30691 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30691"> <li> <div class="comment"> <table class="comment-table" commentId="30851" commentParentId="30691"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kamranm" style="position: relative;"> <img src='https://userpic.codeforces.org/13373/avatar/bb36d6989328bef3.jpg'/> </a> <div><a href="/profile/kamranm" title="Expert kamranm" class="rated-user user-blue">kamranm</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 21:08">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30851" href="?#comment-30851" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30691" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30851" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13373" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30851"> <div class="moveup"> <div class="ttypography">Yes , because if the - polygon with length equal to n -  is regular , we can create another regular polygons which have the length of any prime divisors of n..but this number is not equal to log(n). This is equal to prime divisors of n.</div> </div> </div> <div class="reply info"> <a class="comment-30851 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30851 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30851"> <li> <div class="comment"> <table class="comment-table" commentId="30854" commentParentId="30851"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ostroumov" style="position: relative;"> <img src='https://userpic.codeforces.org/9567/avatar/daf141c3784f573c.jpg'/> </a> <div><a href="/profile/ostroumov" title="Expert ostroumov" class="rated-user user-blue">ostroumov</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 21:43">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30854" href="?#comment-30854" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30851" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30854" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="9567" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30854"> <div class="moveup"> <div class="ttypography">Number of prime divisors is about equal to ln (n) in case of big n.</div> </div> </div> <div class="reply info"> <a class="comment-30854 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30854 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30854"> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30812" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/wil93" style="position: relative;"> <img src='https://userpic.codeforces.org/14356/avatar/897f1996dfb7343b.jpg'/> </a> <div><a href="/profile/wil93" title="Expert wil93" class="rated-user user-blue">wil93</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 17:48">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30812" href="?#comment-30812" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30812" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="14356" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30812"> <div class="moveup"> <div class="ttypography">In the first problem explanation there's a type error:<div><br /></div><div><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">If</span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;"><i>L</i> &gt; 10</span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">, output word without any changes, otherwise output the first letter, next</span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;"><i>L</i> - 2</span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">and finally the last letter.</span></div><div><br /></div><div>Should be &quot;If L ≤ 10&quot;<br /></div></div> </div> </div> <div class="reply info"> <a class="comment-30812 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30812 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30812"> <li> <div class="comment"> <table class="comment-table" commentId="30868" commentParentId="30812"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/DimaPhil" style="position: relative;"> <img src='https://userpic.codeforces.org/7711/avatar/fb93b0fb945e93fe.jpg'/> </a> <div><a href="/profile/DimaPhil" title="Candidate Master DimaPhil" class="rated-user user-violet">DimaPhil</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 22:05">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30868" href="?#comment-30868" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30812" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30868" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="7711" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30868"> <div class="moveup"> <div class="ttypography">Where did you find it? The statement is correct.</div> </div> </div> <div class="reply info"> <a class="comment-30868 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30868 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30868"> <li> <div class="comment"> <table class="comment-table" commentId="30879" commentParentId="30868"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ostroumov" style="position: relative;"> <img src='https://userpic.codeforces.org/9567/avatar/daf141c3784f573c.jpg'/> </a> <div><a href="/profile/ostroumov" title="Expert ostroumov" class="rated-user user-blue">ostroumov</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 22:33">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30879" href="?#comment-30879" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30868" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30879" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="9567" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30879"> <div class="moveup"> <div class="ttypography"><a href="https://codeforces.com/blog/entry/1624?locale=en">Here</a></div> </div> </div> <div class="reply info"> <a class="comment-30879 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30879 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30879"> <li> <div class="comment"> <table class="comment-table" commentId="30884" commentParentId="30879"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/DimaPhil" style="position: relative;"> <img src='https://userpic.codeforces.org/7711/avatar/fb93b0fb945e93fe.jpg'/> </a> <div><a href="/profile/DimaPhil" title="Candidate Master DimaPhil" class="rated-user user-violet">DimaPhil</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 23:13">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30884" href="?#comment-30884" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30879" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30884" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="7711" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30884"> <div class="moveup"> <div class="ttypography">Oh, yes, i see.</div> </div> </div> <div class="reply info"> <a class="comment-30884 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30884 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30884"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30898" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/fura2" style="position: relative;"> <img src='https://userpic.codeforces.org/4118/avatar/98f7ddceb1dac755.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/fura2" title="Master fura2" class="rated-user user-orange">fura2</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/31/2011 09:54">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30898" href="?#comment-30898" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30898" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4118" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30898"> <div class="moveup"> <div class="ttypography">In author's solution of problem E,<br /> does dp1 calculation really need dynamic programming?<br /> I think, this part can be done by simple 2 loops.<br /> <div align="left"><br /></div> for(int mask=0;mask&lt;(1&lt;&lt;n);mask++){<br />   dp1[mask]=0;<br />   for(int i=0;i&lt;n;i++){<br />     if(mask&amp;(1&lt;&lt;i)) dp1[mask]+=(weight of i-th atom);<br />   }<br /> }<br /></div> </div> </div> <div class="reply info"> <a class="comment-30898 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30898 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30898"> <li> <div class="comment"> <table class="comment-table" commentId="30918" commentParentId="30898"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Ripatti" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Ripatti" title="Master Ripatti" class="rated-user user-orange">Ripatti</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/31/2011 13:36">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30918" href="?#comment-30918" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30898" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30918" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="472" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30918"> <div class="moveup"> <div class="ttypography">You are right. It can be calculated by your way. Also it is calculated in this way in the author's solution.</div> </div> </div> <div class="reply info"> <a class="comment-30918 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30918 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30918"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="31195" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/arpit_s" style="position: relative;"> <img src='https://userpic.codeforces.org/6116/avatar/34bf701a2e3bf99.jpg'/> </a> <div><a href="/profile/arpit_s" title="Pupil arpit_s" class="rated-user user-green">arpit_s</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/03/2011 11:04">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-31195" href="?#comment-31195" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="31195" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6116" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-31195"> <div class="moveup"> <div class="ttypography">can you please explain O(nlog(n)) solution for question C ?</div> </div> </div> <div class="reply info"> <a class="comment-31195 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-31195 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-31195"> <li> <div class="comment"> <table class="comment-table" commentId="31215" commentParentId="31195"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mR.ilchi" style="position: relative;"> <img src='https://userpic.codeforces.org/11753/avatar/b0675918b77546aa.jpg'/> </a> <div><a href="/profile/mR.ilchi" title="International Grandmaster mR.ilchi" class="rated-user user-red">mR.ilchi</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/03/2011 20:07">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-31215" href="?#comment-31215" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-31195" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="31215" revisionCount="3" revision="3"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">3</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="31215" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="11753" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-31215"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer">assume n= p<sub>1</sub><sup>q</sup><sup>1</sup> * p<sub>2</sub><sup>q2 </sup>* ... * p<sub>m</sub><sup>qm</sup>, where all the p<sub>i </sub>is prime.<div>then for each i, (1&lt;=i&lt;=m), check if exist good polygyn with exactly p<sub>i </sub>vertex. if at least one of this question has positive answer then output &quot;YES&quot;, otherwise output &quot;NO&quot;. because if we have a good polygyn with <b>A*B</b> vertex, then we have a good polygyn with <b>A</b> vertex.</div><div>sorry for my poor english!</div><div><br /></div></div> </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-31215 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-31215 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-31215"> <li> <div class="comment"> <table class="comment-table" commentId="31276" commentParentId="31215"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/arpit_s" style="position: relative;"> <img src='https://userpic.codeforces.org/6116/avatar/34bf701a2e3bf99.jpg'/> </a> <div><a href="/profile/arpit_s" title="Pupil arpit_s" class="rated-user user-green">arpit_s</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/04/2011 13:16">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-31276" href="?#comment-31276" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-31215" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="31276" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6116" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-31276"> <div class="moveup"> <div class="ttypography">sorry, couldn't understand, can you explain with one example ?</div> </div> </div> <div class="reply info"> <a class="comment-31276 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-31276 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-31276"> <li> <div class="comment"> <table class="comment-table" commentId="31290" commentParentId="31276"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mR.ilchi" style="position: relative;"> <img src='https://userpic.codeforces.org/11753/avatar/b0675918b77546aa.jpg'/> </a> <div><a href="/profile/mR.ilchi" title="International Grandmaster mR.ilchi" class="rated-user user-red">mR.ilchi</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/04/2011 15:32">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-31290" href="?#comment-31290" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-31276" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="31290" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="31290" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="11753" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-31290"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">assume this good polygyn with <b>A*B</b> vertex:<div>S<sub>1</sub>, S<sub>2</sub>, ... , S<sub>A*B</sub></div><div>now we have subpolygyn which have only <b>A </b>vertex, like this:</div><div>S<sub>1*B</sub>, S<sub>2*B</sub>, ... , S<sub>A*B.</sub></div><div>now it's obviously that if the circle  has a good polygyn then it has a polygyn with prime vertex. it's algo is O(nlgn) because for each i, p<sub>i</sub> &gt;=2</div><div>so m&lt;=lgn, and check function is O(n). therefore main algo is O(nlgn). </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-31290 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-31290 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-31290"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="50340" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/dalex" style="position: relative;"> <img src='https://userpic.codeforces.org/4200/avatar/fe9bfc44be854399.jpg'/> </a> <div><a href="/profile/dalex" title="Master dalex" class="rated-user user-orange">dalex</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Aug/04/2011 22:51">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-50340" href="?#comment-50340" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="50340" revisionCount="3" revision="3"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">3</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="50340" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4200" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-50340"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><p> </p><div class="from-renderer">Some help for Java users with problem E: <a href="http://pastebin.com/ZsDc3P1E">http://pastebin.com/ZsDc3P1E</a><br /><br />(Yes, I'm a necroposter)<br /></div> </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-50340 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-50340 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-50340"> <li> <div class="comment"> <table class="comment-table" commentId="651690" commentParentId="50340"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/the_hyp0cr1t3" style="position: relative;"> <img src='https://userpic.codeforces.org/1236992/avatar/92bd73b5049b4093.jpg'/> </a> <div><a href="/profile/the_hyp0cr1t3" title="Candidate Master the_hyp0cr1t3" class="rated-user user-violet">the_hyp0cr1t3</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/27/2020 22:53">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-651690" href="?#comment-651690" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-50340" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="651690" class="CommentVoteFrame" data-commentRating="-8" data-commentUserId="1236992" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">-8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-651690"> <div class="moveup"> <div class="ttypography"><p>Me too apparently</p></div> </div> </div> <div class="reply info"> <a class="comment-651690 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-651690 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-651690"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1634" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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71E
71
E
en
E. Nuclear Fusion
<div class="problem-statement"><div class="header"><div class="title">E. Nuclear Fusion</div><div class="time-limit"><div class="property-title">time limit per test</div>1.5 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>There is the following puzzle popular among nuclear physicists.</p><p>A reactor contains a set of <span class="tex-span"><i>n</i></span> atoms of some chemical elements. We shall understand the phrase "atomic number" as the number of this atom's element in the periodic table of the chemical elements.</p><p>You are allowed to take any two different atoms and fuse a new one from them. That results in a new atom, whose number is equal to the sum of the numbers of original atoms. The fusion operation can be performed several times.</p><p>The aim is getting a new pregiven set of <span class="tex-span"><i>k</i></span> atoms.</p><p>The puzzle's difficulty is that it is only allowed to fuse two atoms into one, it is not allowed to split an atom into several atoms. You are suggested to try to solve the puzzle.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>k</i> ≤ <i>n</i> ≤ 17</span>). The second line contains space-separated symbols of elements of <span class="tex-span"><i>n</i></span> atoms, which are available from the start. The third line contains space-separated symbols of elements of <span class="tex-span"><i>k</i></span> atoms which need to be the result of the fusion. The symbols of the elements coincide with the symbols from the periodic table of the chemical elements. The atomic numbers do not exceed <span class="tex-span">100</span> (elements possessing larger numbers are highly unstable). Some atoms can have identical numbers (that is, there can be several atoms of the same element). The sum of numbers of initial atoms is equal to the sum of numbers of the atoms that need to be synthesized.</p></div><div class="output-specification"><div class="section-title">Output</div><p>If it is impossible to synthesize the required atoms, print "<span class="tex-font-style-tt">NO</span>" without the quotes. Otherwise, print on the first line «<span class="tex-font-style-tt">YES</span>», and on the next <span class="tex-span"><i>k</i></span> lines print the way of synthesizing each of <span class="tex-span"><i>k</i></span> atoms as equations. Each equation has the following form: "<span class="tex-span"><i>x</i><sub class="lower-index">1</sub></span><span class="tex-font-style-tt">+</span><span class="tex-span"><i>x</i><sub class="lower-index">2</sub></span><span class="tex-font-style-tt">+</span><span class="tex-span">...</span><span class="tex-font-style-tt">+</span><span class="tex-span"><i>x</i><sub class="lower-index"><i>t</i></sub></span><span class="tex-font-style-tt">-&gt;</span><span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span>", where <span class="tex-span"><i>x</i><sub class="lower-index"><i>j</i></sub></span> is the symbol of the element of some atom from the original set, and <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span> is the symbol of the element of some atom from the resulting set. Each atom from the input data should occur in the output data exactly one time. The order of summands in the equations, as well as the output order does not matter. If there are several solutions, print any of them. For a better understanding of the output format, see the samples.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>10 3<br/>Mn Co Li Mg C P F Zn Sc K<br/>Sn Pt Y<br/></pre></div><div class="output"><div class="title">Output</div><pre>YES<br/>Mn+C+K-&gt;Sn<br/>Co+Zn+Sc-&gt;Pt<br/>Li+Mg+P+F-&gt;Y<br/></pre></div><div class="input"><div class="title">Input</div><pre>2 1<br/>H H<br/>He<br/></pre></div><div class="output"><div class="title">Output</div><pre>YES<br/>H+H-&gt;He<br/></pre></div><div class="input"><div class="title">Input</div><pre>2 2<br/>Bk Fm<br/>Cf Es<br/></pre></div><div class="output"><div class="title">Output</div><pre>NO<br/></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>The reactions from the first example possess the following form (the atomic number is written below and to the left of the element):</p><p><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/6f2ce1bed492cbe40ff1bb4600fe53aebc680ace.png" style="max-width: 100.0%;max-height: 100.0%;"/></p><p><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/edbd66c81b30040884ff79761e8a0ff37dc1fa9d.png" style="max-width: 100.0%;max-height: 100.0%;"/></p><p><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/9f68585680e3f916d2ec79a9aac68b2ee880cba7.png" style="max-width: 100.0%;max-height: 100.0%;"/></p><p>To find a periodic table of the chemical elements, you may use your favorite search engine.</p><p>The pretest set contains each of the first <span class="tex-span">100</span> elements of the periodic table at least once. You can use that information to check for misprints.</p></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="E" data-uuid="ps_3bb44242e06f71845933b4c0712f43d134da46ca"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">E. Nuclear Fusion</div><div class="time-limit"><div class="property-title">time limit per test</div>1.5 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>There is the following puzzle popular among nuclear physicists.</p><p>A reactor contains a set of <span class="tex-span"><i>n</i></span> atoms of some chemical elements. We shall understand the phrase &quot;atomic number&quot; as the number of this atom's element in the periodic table of the chemical elements.</p><p>You are allowed to take any two different atoms and fuse a new one from them. That results in a new atom, whose number is equal to the sum of the numbers of original atoms. The fusion operation can be performed several times.</p><p>The aim is getting a new pregiven set of <span class="tex-span"><i>k</i></span> atoms.</p><p>The puzzle's difficulty is that it is only allowed to fuse two atoms into one, it is not allowed to split an atom into several atoms. You are suggested to try to solve the puzzle.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>k</i> ≤ <i>n</i> ≤ 17</span>). The second line contains space-separated symbols of elements of <span class="tex-span"><i>n</i></span> atoms, which are available from the start. The third line contains space-separated symbols of elements of <span class="tex-span"><i>k</i></span> atoms which need to be the result of the fusion. The symbols of the elements coincide with the symbols from the periodic table of the chemical elements. The atomic numbers do not exceed <span class="tex-span">100</span> (elements possessing larger numbers are highly unstable). Some atoms can have identical numbers (that is, there can be several atoms of the same element). The sum of numbers of initial atoms is equal to the sum of numbers of the atoms that need to be synthesized.</p></div><div class="output-specification"><div class="section-title">Output</div><p>If it is impossible to synthesize the required atoms, print &quot;<span class="tex-font-style-tt">NO</span>&quot; without the quotes. Otherwise, print on the first line «<span class="tex-font-style-tt">YES</span>», and on the next <span class="tex-span"><i>k</i></span> lines print the way of synthesizing each of <span class="tex-span"><i>k</i></span> atoms as equations. Each equation has the following form: &quot;<span class="tex-span"><i>x</i><sub class="lower-index">1</sub></span><span class="tex-font-style-tt">+</span><span class="tex-span"><i>x</i><sub class="lower-index">2</sub></span><span class="tex-font-style-tt">+</span><span class="tex-span">...</span><span class="tex-font-style-tt">+</span><span class="tex-span"><i>x</i><sub class="lower-index"><i>t</i></sub></span><span class="tex-font-style-tt">-&gt;</span><span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span>&quot;, where <span class="tex-span"><i>x</i><sub class="lower-index"><i>j</i></sub></span> is the symbol of the element of some atom from the original set, and <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span> is the symbol of the element of some atom from the resulting set. Each atom from the input data should occur in the output data exactly one time. The order of summands in the equations, as well as the output order does not matter. If there are several solutions, print any of them. For a better understanding of the output format, see the samples.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>10 3<br />Mn Co Li Mg C P F Zn Sc K<br />Sn Pt Y<br /></pre></div><div class="output"><div class="title">Output</div><pre>YES<br />Mn+C+K-&gt;Sn<br />Co+Zn+Sc-&gt;Pt<br />Li+Mg+P+F-&gt;Y<br /></pre></div><div class="input"><div class="title">Input</div><pre>2 1<br />H H<br />He<br /></pre></div><div class="output"><div class="title">Output</div><pre>YES<br />H+H-&gt;He<br /></pre></div><div class="input"><div class="title">Input</div><pre>2 2<br />Bk Fm<br />Cf Es<br /></pre></div><div class="output"><div class="title">Output</div><pre>NO<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>The reactions from the first example possess the following form (the atomic number is written below and to the left of the element):</p><p><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/6f2ce1bed492cbe40ff1bb4600fe53aebc680ace.png" style="max-width: 100.0%;max-height: 100.0%;" /></p><p><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/edbd66c81b30040884ff79761e8a0ff37dc1fa9d.png" style="max-width: 100.0%;max-height: 100.0%;" /></p><p><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/9f68585680e3f916d2ec79a9aac68b2ee880cba7.png" style="max-width: 100.0%;max-height: 100.0%;" /></p><p>To find a periodic table of the chemical elements, you may use your favorite search engine.</p><p>The pretest set contains each of the first <span class="tex-span">100</span> elements of the periodic table at least once. 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["Bitmasks", "Dynamic programming"]
["bitmasks", "dp", "*2200"]
https://codeforces.com/blog/entry/1624
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<a href="/blog/entry/120644">Codeforces Round 899 (Div. 2)</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/Misa-Misa" title="Expert Misa-Misa" class="rated-user user-blue">Misa-Misa</a> &rarr; <a href="/blog/entry/121157">Someone please help me understand this.</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/shivam565" title="Specialist shivam565" class="rated-user user-cyan">shivam565</a> &rarr; <a href="/blog/entry/108348">Total number of subarrays with sum atmost k</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> </ul> </div> <div class="bottom-links"> <table style="width:100%;"> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:right;"> <a href="/recent-actions">Detailed &rarr;</a> </td> </tr> </tbody> </table> </div> </div> </div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li><a href="/profile/Ripatti">Ripatti</a></li> <li class="current selectedLava"><a href="/blog/Ripatti">Blog</a></li> <li><a href="/teams/with/Ripatti">Teams</a></li> <li><a href="/submissions/Ripatti">Submissions</a></li> <li><a href="/groups/with/Ripatti">Groups</a></li> <li><a href="/contests/with/Ripatti">Contests</a></li> <li><a href="/contests/writer/Ripatti">Problemsetting</a></li> </ul> </div> <div style="margin-top:0;"> <div> <h3><a href="/blog/Ripatti" style="text-decoration:none;color:black !important;">Ripatti's blog</a></h3> </div> <div style="margin-top:2em;"> <div class="has-topic-id topic" topicId="1624"> <div class="title"> <a href="/blog/entry/1624"> Solutions for Codeforces Beta Round #65 (Div. 2) </a> </div> <div class="info" style="position:relative;"> By&nbsp;<a href="/profile/Ripatti" title="Master Ripatti" class="rated-user user-orange">Ripatti</a>, <span class="format-humantime" title="Mar/29/2011 21:20">13 years ago</span>, translation, <img style="position: relative;top: 5px;" src="//codeforces.org/s/81027/images/flags/24/gb.png" alt="In English" title="In English"/> <span style="position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;"> <div style="margin-top:0.25em;"> </div> </span> </div> <div class="content"> <div class="ttypography"><b>A.</b> In this problem you can just do what is written in the statement. Let read all words. For each of them compute its length <span class="tex-span"><i>L</i></span>, its the first and the last letter. If <span class="tex-span"><i>L</i> &gt; 10</span>, output word without any changes, otherwise output the first letter, next <span class="tex-span"><i>L</i> - 2</span> and finally the last letter.<br /> <br /><b>B.</b> At first, compute <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/b30b1e63221e427063b3814647939d0afe0d9e2a.png" style="max-width: 100.0%;max-height: 100.0%;" />. It equals <span class="tex-span">⌊ <i>mnk</i> / 100⌋</span>, where <span class="tex-span">⌊ <i>x</i>⌋</span> is rounding down. Next we fill first <span class="tex-span">⌊ <i>z</i> / <i>k</i>⌋</span> squares with a saturation <span class="tex-span"><i>k</i></span>. <span class="tex-span">(⌊ <i>z</i> / <i>k</i>⌋ + 1)</span>-th square (if it exists) we fill in a saturation <span class="tex-span"><i>z</i> - ⌊ <i>z</i> / <i>k</i>⌋ <i>k</i></span>. All other squares we leave with a saturation <span class="tex-span">0</span>.<br /><br /><b>C.</b> Define an <i>good</i> polygon as a regular polygon which has a knight in a good mood in every of its vertex. Side of polygon we will measure in arcs which is obtained by dividing border of round table with knights.<br /><br />Freeze the length of the side. Let this length equals <span class="tex-span"><i>k</i></span>. Observe that the regular polygon with such length of side exists only if <span class="tex-span"><i>k</i></span> divides <span class="tex-span"><i>n</i></span>. We have exactly <span class="tex-span"><i>k</i></span> of such polygons. Every of them has exactly <span class="tex-span"><i>n</i> / <i>k</i></span> vertices. Check every of the polygons for goodness by review all of its vertices. <br /><br />If sum of vertices with knight in a good mood equals to <span class="tex-span"><i>n</i> / <i>k</i></span>, this polygon is good. Checking of all polygons with some frozen length of side works in an <span class="tex-span"><i>O</i>(<i>n</i>)</span>.<br /><br />Now observe that <span class="tex-span"><i>n</i></span> has <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5a41da22acdba46e7c8eeeaddbc58625f49cbfe5.png" style="max-width: 100.0%;max-height: 100.0%;" /> of divisors. Really, all divisors (may be except only one) we can divide into pairs (for <span class="tex-span"><i>i</i></span> corresponds <span class="tex-span"><i>n</i> / <i>i</i></span>, for <span class="tex-span"><i>i</i> = <i>n</i> / <i>i</i></span> there is no pair). One of divisors in every pair less than <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/712f9a224d6c7824add37b6cd766c21f73a40d59.png" style="max-width: 100.0%;max-height: 100.0%;" />. It means thah number of pairs no more than <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/712f9a224d6c7824add37b6cd766c21f73a40d59.png" style="max-width: 100.0%;max-height: 100.0%;" /> and number of divisors no more than <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/6b8f80d5708602c9727bc53c820fc6ad559209a0.png" style="max-width: 100.0%;max-height: 100.0%;" />.<br /><br />It gives solution - iterate over all divisors of <span class="tex-span"><i>n</i></span> and for every of them check existence of good polygon with length side equals this divisor. Solution has an <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/0c18a224e805d960478a53ca7ac5ae33eaed6dd7.png" style="max-width: 100.0%;max-height: 100.0%;" /> time.<br /><br />In reality for big <span class="tex-span"><i>n</i></span> is has <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7acd26c81b1f055b12a3b1e53f7a9814fd517a81.png" style="max-width: 100.0%;max-height: 100.0%;" /> divisors. So solution actually has <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">4 / 3</sup>)</span>-complexity. For all numbers less than <span class="tex-span">10<sup class="upper-index">5</sup></span> maximal number of divisors is 128.<br /><br />UPD. There was found an <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png" style="max-width: 100.0%;max-height: 100.0%;" /> solution by some participants. This solution uses following idea. If we have a good polygon with <span class="tex-span"><i>xy</i></span> vertices, we also have a good polygon with <span class="tex-span"><i>x</i></span> vertices. So we can check only prime divisors of <span class="tex-span"><i>n</i></span> (except 2 - here we must check 4).<br /><br /><b>D.</b> This problem can be divided into some subproblems.<br /> Author's solution means following ones:<br /><br />1. Check validness of square <span class="tex-span">3 × 3</span>. Square is valid if all cards in it has equal suit or different rank. You may not check equal suit because equal suits imply different ranks.<br /><br />2. Find 2 valid noninetsect squares <span class="tex-span">3 × 3</span> or return thah there are no ones. You can check all pairs of squares for inetsection. If some pair has no intersections check them with solution of subproblem 1.<br /><br />3. Build set of cards which can be replaced with jokers. Generate full deck without jokers and drop from it all cards which in rectangle <span class="tex-span"><i>n</i> × <i>m</i></span> are present.<br /><br />4. Find number of jokers and its positions in rectangle.<br /><br />5. Main subproblem. At first, solve subproblems 3 and 4. Now replace jokers in rectangle with cards from deck from subproblem 3 by all possible ways. For every replace solve subproblem 2. Arter all of variants of replacement just output answer.<br /><br />There are <span class="tex-span"><i>O</i>(<i>n</i><sup class="upper-index">2</sup><i>m</i><sup class="upper-index">2</sup>)</span> solution with small constant.<br /><br /><b>E.</b> At first, you can use some search engine for find periodic table in some printable form. Next use copy-paste (one or several times) and format it by deleting all excess. It is mechanical work for no more than 5 minutes. Also some parser may be written. Note than author's solution does not mean write 100 symbols by hand from a picture. Next build some functions which transform symbols into numbers and vice versa.<br /><br />So, we have some set of numbers. We need summarize some from them and get some another set of numbers. We will use dymanic programming over subsets.<br /><br />Compute the first dp dp1[mask]-&gt;sum. For each subset calculate sum of numbers of all atoms in this subset. It can be done in <span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>n</i></sup><i>n</i>)</span>.<br /><br />Now compute the second dp dp2[mask]-&gt;length. The &quot;length&quot; is a length of some prefix of result sequence of atoms which can be obtained by subset mask. If length -1, it means that it is impossible to get any prefix from this subset.<br /><br />The second dp we can calculate in <span class="tex-span"><i>O</i>(3<sup class="upper-index"><i>n</i></sup>)</span>. Iterate over all masks and if dp2[mask]!=-1, iterate all its subsets of remained atoms (invert mask and get all its submasks). If some subset has sum of numbers which equals number of (dp2[маска]+1)-th atom from result set, recalculate dp2[mask XOR submask]=dp2[mask]+1.<br /><br />At end, if dp2[<span class="tex-span">2<sup class="upper-index"><i>n</i></sup> - 1</span>]=k, there are solution.<br /><br />There are <span class="tex-span"><i>O</i>(3<sup class="upper-index"><i>n</i></sup> + 2<sup class="upper-index"><i>n</i></sup><i>n</i>)</span> solution.<br /><br />In this problem some brutforce solutions are passed because it is difficult to pick up some counterexample.<br /><br />UPD. <a class="rated-user user-orange" href="../../../profile/SkorKNURE" title="Майор SkorKNURE">SkorKNURE</a> found a solution in <span class="tex-span"><span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>n</i></sup><i>n</i>)</span></span>. This solution is some <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">modification</span></span> of the author's solution.<br /><br /><span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">Instead of</span></span> dp2 calculate dp dp2'[mask]-&gt;(i,j), where i is a length of prefix which mask covers and j is part of number of (i+1)-th atom which mask covers.<br /><br />Iterate over all masks. For each mask iterate over all its 0-bits<span class="tex-span"></span> (they are atoms which cover nothing from the finish set). We try to cover with this 0-bit a <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">remainder of</span></span> number of the (i+1)-th atom from the finish set. Let atomic number of an atom for current 0-bit is p and this atom is q-th in the start set. If we cover with this atom only part of the remainder of number of the (i+1)-th atom, dp2'[mask XOR (1&lt;&lt;q)]=(i,j+p). If we cover with this atom the remainder fully (and exactly this remainder, no more!), dp2'[mask XOR (1&lt;&lt;q)]=(i+1,0).<br /><br />Now dp1 is useless. If at end dp2'[<span class="tex-span"><span class="tex-span">2<sup class="upper-index"><i>n</i></sup> - 1</span></span>]=(k,0), solution exists (it is easy to <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">restore it</span></span>), otherwise there is no solution.<span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод"></span></span><span class="tex-span"></span></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/71" class="notice" style="text-decoration: none;">Codeforces Beta Round 65 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-440-1624").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "440", blogEntryId: "1624", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces" class="tag notice" style="text-decoration: none;">codeforces</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=editorial" class="tag notice" style="text-decoration: none;">editorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1624"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+47</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1624"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; 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margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1634"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (25)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="30627" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/sicasli" style="position: relative;"> <img src='https://userpic.codeforces.org/10281/avatar/8aa5e308717a2754.jpg'/> </a> <div><a href="/profile/sicasli" title="Expert sicasli" class="rated-user user-blue">sicasli</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 21:51">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30627" href="?#comment-30627" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30627" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="10281" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30627"> <div class="moveup"> <div class="ttypography">system testing took very long time.. and on the middle of contest, server down once.. what happened here?</div> </div> </div> <div class="reply info"> <a class="comment-30627 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30627 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30627"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30631" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/WXYZ" style="position: relative;"> <img src='https://userpic.codeforces.org/16492/avatar/caece4fb867dc8fb.jpg'/> </a> <div><a href="/profile/WXYZ" title="Master WXYZ" class="rated-user user-orange">WXYZ</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 21:58">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30631" href="?#comment-30631" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30631" class="CommentVoteFrame" data-commentRating="4" data-commentUserId="16492" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+4</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30631"> <div class="moveup"> <div class="ttypography">bd</div> </div> </div> <div class="reply info"> <a class="comment-30631 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30631 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30631"> <li> <div class="comment"> <table class="comment-table" commentId="30633" commentParentId="30631"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/pva701" style="position: relative;"> <img src='https://userpic.codeforces.org/3957/avatar/e47deec1b5b8677f.jpg'/> </a> <div><a href="/profile/pva701" title="Expert pva701" class="rated-user user-blue">pva701</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 22:00">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30633" href="?#comment-30633" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30631" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30633" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="3957" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30633"> <div class="moveup"> <div class="ttypography">cool. I understand you. Its great!</div> </div> </div> <div class="reply info"> <a class="comment-30633 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30633 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30633"> <li> <div class="comment"> <table class="comment-table" commentId="30660" commentParentId="30633"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/_arjun" style="position: relative;"> <img src='https://userpic.codeforces.org/1553/avatar/1b0a6d8089c2ee88.jpg'/> </a> <div><a href="/profile/_arjun" title="Expert _arjun" class="rated-user user-blue">_arjun</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 22:37">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30660" href="?#comment-30660" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30633" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30660" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="1553" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30660"> <div class="moveup"> <div class="ttypography">I can't understand , tell me what is bd?</div> </div> </div> <div class="reply info"> <a class="comment-30660 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30660 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30660"> <li> <div class="comment"> <table class="comment-table" commentId="30711" commentParentId="30660"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/naagi" style="position: relative;"> <img src='https://userpic.codeforces.org/1436/avatar/b4261a7f23f18a7c.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/naagi" title="Expert naagi" class="rated-user user-blue">naagi</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 02:15">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30711" href="?#comment-30711" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30660" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30711" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="1436" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30711"> <div class="moveup"> <div class="ttypography">looks like &quot;thumbs up&quot;<br />(I feel proud of myself for this guess :))</div> </div> </div> <div class="reply info"> <a class="comment-30711 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30711 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30711"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="30714" commentParentId="30660"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/acmwe" style="position: relative;"> <img src='https://userpic.codeforces.org/15619/avatar/a74aaa0a09183ea8.jpg'/> </a> <div><a href="/profile/acmwe" title="Specialist acmwe" class="rated-user user-cyan">acmwe</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 06:21">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30714" href="?#comment-30714" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30660" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30714" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="15619" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30714"> <div class="moveup"> <div class="ttypography">It's ....Just like ORZ....</div> </div> </div> <div class="reply info"> <a class="comment-30714 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30714 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30714"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30638" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Lepetrandr" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Lepetrandr" title="Candidate Master Lepetrandr" class="rated-user user-violet">Lepetrandr</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 22:01">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30638" href="?#comment-30638" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30638" class="CommentVoteFrame" data-commentRating="7" data-commentUserId="1088" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+7</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30638"> <div class="moveup"> <div class="ttypography">In problem C we can consider only _prime_ divisors of n (at most 6 :), as number of vertices. But there is one tricky case that i've missed, unfortunately.</div> </div> </div> <div class="reply info"> <a class="comment-30638 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30638 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30638"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30686" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/sanchit_h" style="position: relative;"> <img src='https://userpic.codeforces.org/14424/avatar/ccd3178dffd08856.jpg'/> </a> <div><a href="/profile/sanchit_h" title="Expert sanchit_h" class="rated-user user-blue">sanchit_h</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 23:12">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30686" href="?#comment-30686" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30686" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14424" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30686"> <div class="moveup"> <div class="ttypography">In problem E, can you explain what is a mask and its submasks ?</div> </div> </div> <div class="reply info"> <a class="comment-30686 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30686 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30686"> <li> <div class="comment"> <table class="comment-table" commentId="30687" commentParentId="30686"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kilotaras" style="position: relative;"> <img src='https://userpic.codeforces.org/3934/avatar/1f5f8ec32edbfcfd.jpg'/> </a> <div><a href="/profile/kilotaras" title="Master kilotaras" class="rated-user user-orange">kilotaras</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 23:15">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30687" href="?#comment-30687" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30686" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30687" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30687" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3934" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30687"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div align="left"><a href="https://en.wikipedia.org/wiki/Mask_%28computing%29">http://en.wikipedia.org/wiki/Mask_%28computing%29</a><br /></div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30687 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30687 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30687"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="30688" commentParentId="30686"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Ripatti" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Ripatti" title="Master Ripatti" class="rated-user user-orange">Ripatti</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 23:15">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30688" href="?#comment-30688" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30686" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30688" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="472" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30688"> <div class="moveup"> <div class="ttypography">I will rewrite editorial more detail later.</div> </div> </div> <div class="reply info"> <a class="comment-30688 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30688 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30688"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30691" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/lunae" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/lunae" title="Candidate Master lunae" class="rated-user user-violet">lunae</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/29/2011 23:29">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30691" href="?#comment-30691" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="30691" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="30691" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2939" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30691"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">edit: I'm sorry that I didn't notice Lepetrandr's post.<br /><br />For (C) it suffices to check polygons with a prime number of sides (except for 2, then check 4), that gives O(log n) divisors to check.<br /></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-30691 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30691 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30691"> <li> <div class="comment"> <table class="comment-table" commentId="30851" commentParentId="30691"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/kamranm" style="position: relative;"> <img src='https://userpic.codeforces.org/13373/avatar/bb36d6989328bef3.jpg'/> </a> <div><a href="/profile/kamranm" title="Expert kamranm" class="rated-user user-blue">kamranm</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 21:08">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30851" href="?#comment-30851" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30691" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30851" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13373" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30851"> <div class="moveup"> <div class="ttypography">Yes , because if the - polygon with length equal to n -  is regular , we can create another regular polygons which have the length of any prime divisors of n..but this number is not equal to log(n). This is equal to prime divisors of n.</div> </div> </div> <div class="reply info"> <a class="comment-30851 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30851 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30851"> <li> <div class="comment"> <table class="comment-table" commentId="30854" commentParentId="30851"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ostroumov" style="position: relative;"> <img src='https://userpic.codeforces.org/9567/avatar/daf141c3784f573c.jpg'/> </a> <div><a href="/profile/ostroumov" title="Expert ostroumov" class="rated-user user-blue">ostroumov</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 21:43">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30854" href="?#comment-30854" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30851" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30854" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="9567" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30854"> <div class="moveup"> <div class="ttypography">Number of prime divisors is about equal to ln (n) in case of big n.</div> </div> </div> <div class="reply info"> <a class="comment-30854 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30854 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30854"> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30812" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/wil93" style="position: relative;"> <img src='https://userpic.codeforces.org/14356/avatar/897f1996dfb7343b.jpg'/> </a> <div><a href="/profile/wil93" title="Expert wil93" class="rated-user user-blue">wil93</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 17:48">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30812" href="?#comment-30812" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30812" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="14356" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30812"> <div class="moveup"> <div class="ttypography">In the first problem explanation there's a type error:<div><br /></div><div><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">If</span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;"><i>L</i> &gt; 10</span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">, output word without any changes, otherwise output the first letter, next</span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;"><i>L</i> - 2</span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">and finally the last letter.</span></div><div><br /></div><div>Should be &quot;If L ≤ 10&quot;<br /></div></div> </div> </div> <div class="reply info"> <a class="comment-30812 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30812 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30812"> <li> <div class="comment"> <table class="comment-table" commentId="30868" commentParentId="30812"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/DimaPhil" style="position: relative;"> <img src='https://userpic.codeforces.org/7711/avatar/fb93b0fb945e93fe.jpg'/> </a> <div><a href="/profile/DimaPhil" title="Candidate Master DimaPhil" class="rated-user user-violet">DimaPhil</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 22:05">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30868" href="?#comment-30868" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30812" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30868" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="7711" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30868"> <div class="moveup"> <div class="ttypography">Where did you find it? The statement is correct.</div> </div> </div> <div class="reply info"> <a class="comment-30868 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30868 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30868"> <li> <div class="comment"> <table class="comment-table" commentId="30879" commentParentId="30868"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ostroumov" style="position: relative;"> <img src='https://userpic.codeforces.org/9567/avatar/daf141c3784f573c.jpg'/> </a> <div><a href="/profile/ostroumov" title="Expert ostroumov" class="rated-user user-blue">ostroumov</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 22:33">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30879" href="?#comment-30879" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30868" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30879" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="9567" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30879"> <div class="moveup"> <div class="ttypography"><a href="https://codeforces.com/blog/entry/1624?locale=en">Here</a></div> </div> </div> <div class="reply info"> <a class="comment-30879 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30879 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30879"> <li> <div class="comment"> <table class="comment-table" commentId="30884" commentParentId="30879"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/DimaPhil" style="position: relative;"> <img src='https://userpic.codeforces.org/7711/avatar/fb93b0fb945e93fe.jpg'/> </a> <div><a href="/profile/DimaPhil" title="Candidate Master DimaPhil" class="rated-user user-violet">DimaPhil</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/30/2011 23:13">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30884" href="?#comment-30884" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30879" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30884" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="7711" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30884"> <div class="moveup"> <div class="ttypography">Oh, yes, i see.</div> </div> </div> <div class="reply info"> <a class="comment-30884 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30884 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30884"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="30898" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/fura2" style="position: relative;"> <img src='https://userpic.codeforces.org/4118/avatar/98f7ddceb1dac755.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/fura2" title="Master fura2" class="rated-user user-orange">fura2</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/31/2011 09:54">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30898" href="?#comment-30898" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30898" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4118" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30898"> <div class="moveup"> <div class="ttypography">In author's solution of problem E,<br /> does dp1 calculation really need dynamic programming?<br /> I think, this part can be done by simple 2 loops.<br /> <div align="left"><br /></div> for(int mask=0;mask&lt;(1&lt;&lt;n);mask++){<br />   dp1[mask]=0;<br />   for(int i=0;i&lt;n;i++){<br />     if(mask&amp;(1&lt;&lt;i)) dp1[mask]+=(weight of i-th atom);<br />   }<br /> }<br /></div> </div> </div> <div class="reply info"> <a class="comment-30898 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30898 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30898"> <li> <div class="comment"> <table class="comment-table" commentId="30918" commentParentId="30898"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Ripatti" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Ripatti" title="Master Ripatti" class="rated-user user-orange">Ripatti</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/31/2011 13:36">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-30918" href="?#comment-30918" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-30898" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="30918" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="472" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-30918"> <div class="moveup"> <div class="ttypography">You are right. It can be calculated by your way. Also it is calculated in this way in the author's solution.</div> </div> </div> <div class="reply info"> <a class="comment-30918 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-30918 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-30918"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="31195" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/arpit_s" style="position: relative;"> <img src='https://userpic.codeforces.org/6116/avatar/34bf701a2e3bf99.jpg'/> </a> <div><a href="/profile/arpit_s" title="Pupil arpit_s" class="rated-user user-green">arpit_s</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/03/2011 11:04">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-31195" href="?#comment-31195" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="31195" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6116" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-31195"> <div class="moveup"> <div class="ttypography">can you please explain O(nlog(n)) solution for question C ?</div> </div> </div> <div class="reply info"> <a class="comment-31195 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-31195 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-31195"> <li> <div class="comment"> <table class="comment-table" commentId="31215" commentParentId="31195"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mR.ilchi" style="position: relative;"> <img src='https://userpic.codeforces.org/11753/avatar/b0675918b77546aa.jpg'/> </a> <div><a href="/profile/mR.ilchi" title="International Grandmaster mR.ilchi" class="rated-user user-red">mR.ilchi</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/03/2011 20:07">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-31215" href="?#comment-31215" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-31195" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="31215" revisionCount="3" revision="3"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">3</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="31215" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="11753" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-31215"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer">assume n= p<sub>1</sub><sup>q</sup><sup>1</sup> * p<sub>2</sub><sup>q2 </sup>* ... * p<sub>m</sub><sup>qm</sup>, where all the p<sub>i </sub>is prime.<div>then for each i, (1&lt;=i&lt;=m), check if exist good polygyn with exactly p<sub>i </sub>vertex. if at least one of this question has positive answer then output &quot;YES&quot;, otherwise output &quot;NO&quot;. because if we have a good polygyn with <b>A*B</b> vertex, then we have a good polygyn with <b>A</b> vertex.</div><div>sorry for my poor english!</div><div><br /></div></div> </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-31215 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-31215 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-31215"> <li> <div class="comment"> <table class="comment-table" commentId="31276" commentParentId="31215"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/arpit_s" style="position: relative;"> <img src='https://userpic.codeforces.org/6116/avatar/34bf701a2e3bf99.jpg'/> </a> <div><a href="/profile/arpit_s" title="Pupil arpit_s" class="rated-user user-green">arpit_s</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/04/2011 13:16">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-31276" href="?#comment-31276" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-31215" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="31276" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6116" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-31276"> <div class="moveup"> <div class="ttypography">sorry, couldn't understand, can you explain with one example ?</div> </div> </div> <div class="reply info"> <a class="comment-31276 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-31276 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-31276"> <li> <div class="comment"> <table class="comment-table" commentId="31290" commentParentId="31276"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mR.ilchi" style="position: relative;"> <img src='https://userpic.codeforces.org/11753/avatar/b0675918b77546aa.jpg'/> </a> <div><a href="/profile/mR.ilchi" title="International Grandmaster mR.ilchi" class="rated-user user-red">mR.ilchi</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/04/2011 15:32">13 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-31290" href="?#comment-31290" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-31276" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="31290" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="31290" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="11753" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-31290"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">assume this good polygyn with <b>A*B</b> vertex:<div>S<sub>1</sub>, S<sub>2</sub>, ... , S<sub>A*B</sub></div><div>now we have subpolygyn which have only <b>A </b>vertex, like this:</div><div>S<sub>1*B</sub>, S<sub>2*B</sub>, ... , S<sub>A*B.</sub></div><div>now it's obviously that if the circle  has a good polygyn then it has a polygyn with prime vertex. it's algo is O(nlgn) because for each i, p<sub>i</sub> &gt;=2</div><div>so m&lt;=lgn, and check function is O(n). therefore main algo is O(nlgn). </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-31290 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-31290 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-31290"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="50340" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/dalex" style="position: relative;"> <img src='https://userpic.codeforces.org/4200/avatar/fe9bfc44be854399.jpg'/> </a> <div><a href="/profile/dalex" title="Master dalex" class="rated-user user-orange">dalex</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Aug/04/2011 22:51">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-50340" href="?#comment-50340" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="50340" revisionCount="3" revision="3"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">3</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="50340" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4200" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-50340"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><p> </p><div class="from-renderer">Some help for Java users with problem E: <a href="http://pastebin.com/ZsDc3P1E">http://pastebin.com/ZsDc3P1E</a><br /><br />(Yes, I'm a necroposter)<br /></div> </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-50340 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-50340 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-50340"> <li> <div class="comment"> <table class="comment-table" commentId="651690" commentParentId="50340"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/the_hyp0cr1t3" style="position: relative;"> <img src='https://userpic.codeforces.org/1236992/avatar/92bd73b5049b4093.jpg'/> </a> <div><a href="/profile/the_hyp0cr1t3" title="Candidate Master the_hyp0cr1t3" class="rated-user user-violet">the_hyp0cr1t3</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/27/2020 22:53">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-651690" href="?#comment-651690" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-50340" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="651690" class="CommentVoteFrame" data-commentRating="-8" data-commentUserId="1236992" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">-8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-651690"> <div class="moveup"> <div class="ttypography"><p>Me too apparently</p></div> </div> </div> <div class="reply info"> <a class="comment-651690 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-651690 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-651690"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1634" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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A. The Elder Trolls IV: Oblivon
<div class="problem-statement"><div class="header"><div class="title">A. The Elder Trolls IV: Oblivon</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Vasya plays The Elder Trolls IV: Oblivon. Oh, those creators of computer games! What they do not come up with! Absolutely unique monsters have been added to the The Elder Trolls IV: Oblivon. One of these monsters is Unkillable Slug. Why it is "Unkillable"? Firstly, because it can be killed with cutting weapon only, so lovers of two-handed amber hammers should find suitable knife themselves. Secondly, it is necessary to make so many cutting strokes to Unkillable Slug. Extremely many. Too many! </p><p>Vasya has already promoted his character to 80-th level and in order to gain level 81 he was asked to kill Unkillable Slug. The monster has a very interesting shape. It looks like a rectangular parallelepiped with size <span class="tex-span"><i>x</i> × <i>y</i> × <i>z</i></span>, consisting of undestructable cells <span class="tex-span">1 × 1 × 1</span>. At one stroke Vasya can cut the Slug along an imaginary grid, i.e. cut with a plane parallel to one of the parallelepiped side. Monster dies when amount of parts it is divided reaches some critical value.</p><p>All parts of monster do not fall after each cut, they remains exactly on its places. I. e. Vasya can cut several parts with one cut.</p><p>Vasya wants to know what the maximum number of pieces he can cut the Unkillable Slug into striking him at most <span class="tex-span"><i>k</i></span> times.</p><p>Vasya's character uses absolutely thin sword with infinite length.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of input contains four integer numbers <span class="tex-span"><i>x</i>, <i>y</i>, <i>z</i>, <i>k</i></span> (<span class="tex-span">1 ≤ <i>x</i>, <i>y</i>, <i>z</i> ≤ 10<sup class="upper-index">6</sup>, 0 ≤ <i>k</i> ≤ 10<sup class="upper-index">9</sup></span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Output the only number — the answer for the problem.</p><p>Please, do not use <span class="tex-font-style-tt">%lld</span> specificator to read or write 64-bit integers in C++. It is preffered to use <span class="tex-font-style-tt">cout</span> (also you may use <span class="tex-font-style-tt">%I64d</span>).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2 2 2 3<br/></pre></div><div class="output"><div class="title">Output</div><pre>8</pre></div><div class="input"><div class="title">Input</div><pre>2 2 2 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>2</pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first sample Vasya make 3 pairwise perpendicular cuts. He cuts monster on two parts with the first cut, then he divides each part on two with the second cut, and finally he divides each of the 4 parts on two.</p></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="A" data-uuid="ps_11e78e703c0b86d4c6ad48eff7d61959188e706a"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">A. The Elder Trolls IV: Oblivon</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Vasya plays The Elder Trolls IV: Oblivon. Oh, those creators of computer games! What they do not come up with! Absolutely unique monsters have been added to the The Elder Trolls IV: Oblivon. One of these monsters is Unkillable Slug. Why it is &quot;Unkillable&quot;? Firstly, because it can be killed with cutting weapon only, so lovers of two-handed amber hammers should find suitable knife themselves. Secondly, it is necessary to make so many cutting strokes to Unkillable Slug. Extremely many. Too many! </p><p>Vasya has already promoted his character to 80-th level and in order to gain level 81 he was asked to kill Unkillable Slug. The monster has a very interesting shape. It looks like a rectangular parallelepiped with size <span class="tex-span"><i>x</i> × <i>y</i> × <i>z</i></span>, consisting of undestructable cells <span class="tex-span">1 × 1 × 1</span>. At one stroke Vasya can cut the Slug along an imaginary grid, i.e. cut with a plane parallel to one of the parallelepiped side. Monster dies when amount of parts it is divided reaches some critical value.</p><p>All parts of monster do not fall after each cut, they remains exactly on its places. I. e. Vasya can cut several parts with one cut.</p><p>Vasya wants to know what the maximum number of pieces he can cut the Unkillable Slug into striking him at most <span class="tex-span"><i>k</i></span> times.</p><p>Vasya's character uses absolutely thin sword with infinite length.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of input contains four integer numbers <span class="tex-span"><i>x</i>, <i>y</i>, <i>z</i>, <i>k</i></span> (<span class="tex-span">1 ≤ <i>x</i>, <i>y</i>, <i>z</i> ≤ 10<sup class="upper-index">6</sup>, 0 ≤ <i>k</i> ≤ 10<sup class="upper-index">9</sup></span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Output the only number — the answer for the problem.</p><p>Please, do not use <span class="tex-font-style-tt">%lld</span> specificator to read or write 64-bit integers in C++. It is preffered to use <span class="tex-font-style-tt">cout</span> (also you may use <span class="tex-font-style-tt">%I64d</span>).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2 2 2 3<br /></pre></div><div class="output"><div class="title">Output</div><pre>8</pre></div><div class="input"><div class="title">Input</div><pre>2 2 2 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>2</pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first sample Vasya make 3 pairwise perpendicular cuts. He cuts monster on two parts with the first cut, then he divides each part on two with the second cut, and finally he divides each of the 4 parts on two.</p></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=A]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); if (previousStatementText) { if (previousStatementText !== statementText) { $problem.find(".diff-notifier").show(); $problem.find(".diff-notifier-close").click(function() { Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60); $problem.find(".diff-notifier").hide(); }); $problem.find("a.view-changes").click(function() { $.post("/data/diff", {action: "getDiff", a: previousStatementText, b: statementText}, function (result) { if (result["success"] === "true") { Codeforces.facebox(".diff-popup", "//codeforces.org/s/73366"); 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["Greedy algorithms", "Mathematics including integration, differential equations, etc"]
["greedy", "math", "*1600"]
https://codeforces.com/blog/entry/1700
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, serif;color: black;"><b>Problem A.</b></span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Let’s call the monster dimension sizes as <i>x<sub>1</sub>, x<sub>2</sub>, x<sub>3</sub></i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">1. <i>O(min(k, x<sub>1</sub> + x<sub>2</sub> + x<sub>3</sub>)) </i>solution</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">We can make at most <i>(x<sub>1</sub> – 1) + (x<sub>2</sub> – 1) + (x<sub>3</sub> – 1)</i> cuttings, so we may assume that <i>k &lt;= x<sub>1</sub> + x<sub>2</sub> + x<sub>3</sub> – 3</i>. For each of the three dimensions we will store an integer <i>a<sub>i</sub></i> – number of cuttings performed through the corresponding dimension. Let’s perform the following actions <i>k</i> times: consider all numbers <i>a<sub>i</sub> </i>which we may increase (<i>a<sub>i</sub> &lt;  x<sub>i</sub> - 1</i>) , call these dimensions “uncompleted”. Select the minimum number <i>a<sub>j</sub></i> among all uncompleted <i>a<sub>i</sub></i> and perform a cut through the corresponding dimension (<i>a<sub>j</sub></i> will be increased by 1 as the result). Now let’s consider the resulting set after <i>k</i> actions: <i>{a<sub>1</sub>, a<sub>2</sub>, a<sub>3</sub>}</i>. Using the described algorithm we grant that the maximum element of this set is as little as possible and the minimum element is as big as possible. Because the sum <i>a<sub>1</sub> + a<sub>2</sub> + a<sub>3</sub> = k</i> is fixed, we get the maximum product <i>(a<sub>1</sub> + 1) * (a<sub>2</sub> + 1) * (a<sub>3</sub> + 1)</i> which is the answer for the problem.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">2. <i>O(1) </i>solution</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Instead of simulation all the <i>k</i> actions we may quickly determine values of numbers <i>a<sub>i</sub></i> after using the algorithm described above.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Let <i>x</i> – the smallest value among <i>(x<sub>i </sub>– 1)</i>. When <i>x * 3 &gt;= k</i> on each of the algorithm iterations all three dimensions will be uncompleted. It means that during the first <i>(k / 3) * 3</i> steps each of numbers <i>a<sub>i</sub></i> will be increased by <i>(k / 3)</i>. Then 0, 1 or 2 numbers <i>a<sub>i</sub></i> will be increased by 1 subject to value of <i>k % 3</i>. So</span><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">, </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">we</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">have</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">found</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">values</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">a<sub>i</sub></span></i><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Otherwise (<i>x * 3 &lt; k</i>) during the first <i>x * 3</i> steps each of <i>a<sub>i</sub></i> will be increased by <i>x</i>. After that we will have at most two uncompleted dimensions which can be processed a similar way (we should choose the minimum value <i>x</i> among the remaining uncompleted dimensions).</span></p> <p><span lang="EN-US"> </span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"><b>Problem B.</b></span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">We may assume that we have exactly <i>n</i> awarded places but some of them give 0 points.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Let’s sort places by amount of points (<i>b<sub>i</sub></i>) and racers by amount of currently gained points (<i>a<sub>i</sub></i>). First let’s find the best place Vasya can reach. In the best case he will get <i>b<sub>0</sub></i> points (where <i>b<sub>0</sub></i> is the greatest number among <i>b<sub>i</sub></i>). So, let the total Vasya’s point is <i>v</i>. Now we should to distribute other prize points to racers so that the number of racers better than Vasya will be minimal. For doing that we are to give maximum number of prizes so that corresponding racers will have less than <i>v </i>points. Note that if we can give <i>k</i> prizes keeping this property, than we can give <i>k</i> “cheapest” prizes too. The following statement is also true: if we can get a prize with <i>t</i> points to racer <i>i</i> and to racer <i>j</i> , <i>a<sub>i</sub> &gt; a<sub>j</sub></i>, then it is better to give this prize to racer <i>i</i>. Formally: if there exists a way to give <i>k</i> prizes where this prize will get racer <i>j</i>, than there exists a way to give <i>k</i> prizes where this prize will get racer <i>i</i>. It can be proven the following way. Consider a way to give <i>k</i> prizes where racer <i>j</i> got prize with <i>t</i> points, racer <i>i</i> – <i>s</i> points or didn’t get prize at all. In the first case we can swap prizes for racers <i>i</i> and <i>j</i>: <i>a<sub>i</sub> &gt; a<sub>j</sub></i> and <i>a<sub>i</sub> + s &lt; v</i> (since racer <i>i</i> have got the prize), so <i>a<sub>j</sub> + s &lt; v</i>, and <i>a<sub>i</sub> + t &lt; v</i> i.e. this change is acceptable. In the second case we can just give the prize <i>t</i> to racer <i>i</i> instead of racer <i>j</i>. In the both cases we get a way to give <i>k</i> prizes where racer <i>i</i> receive prize<i> t</i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Now including this statement we may give prizes to racers using the following greedy algorithm. Let’s begin to give prizes starting from the cheapest one and check the racers starting from the best one (of course excluding Vasya and the best prize). For each prize <i>i</i> we will go through the racers until applicable racer (<i>j</i>) found: <i>b<sub>i</sub> + a<sub>j</sub> &lt; v</i>. If no such racers remain we are unable to give more prizes without violating the rule (racers should have less than <i>v</i> points). In this case we should stop the algorithm and the answer is <i>n – k </i>where <i>k</i> is the number of prizes we have given. If we have found such racer <i>j</i> we can give him prize <i>b<sub>i</sub></i> and go to the next prize. Complexity of this step is <i>O(n)</i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Similarly we can find the worst place for Vasya. For doing that we should give him the cheapest prize (note it may have positive points though). After that we should distribute the prizes iterating over prizes from the largest to cheapest and check racers from the worst to the best one trying to make sum of racer’s points more than <i>v</i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Total complexity of the described algorithm is <i>O(n * log(n))</i> because we have to sort prizes and racers.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"><b>Problem C.</b></span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">It is easy to see that if we put some symbol <i>c</i> at position <i>p</i> of the string <i>s</i> it will not affect symbols at positions (<i>p+2</i>) and greater. So</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">we</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">have a</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">standard</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">DP</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">problem</span><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">. </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">State of the dynamic is described by three parameters: <i>p</i> – the number of already processed symbols (or the index of currently processed symbol of the string), <i>c</i> – the previous symbol, <i>t</i> – the number of allowed symbol changes. To calculate the answer for a state we should choose the best value among all symbols for current position (when <i>t &gt; 0</i>) or just go to the index (<i>p + 1</i>) with current symbol <i>s[p]</i>. Thus we get the followings formulas:</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><i><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">d[n][*][*] = 0</span></i><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">d[p][c][t] = d[p + 1][s[p]][t] + bonus[c][s[p]] </span></i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">when<i> t = 0</i></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">d[p][c][t] = max(d[p + 1][c’][t – (c’ &lt;&gt; s[p])] + bonus[c][c’])</span></i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">where <i>n</i>  is the length of string <i>s</i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Computation complexity of the algorithm is <i>O(n * k * h^2)</i>, where <i>h</i> is the alphabet size (<i>h = 26</i> for current problem).<b></b></span></p></div><div /></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/73" class="notice" style="text-decoration: none;">Codeforces Beta Round 66</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-368-1700").click(function() { var that = this; 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line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/I_Remember_Olya_ashmelev"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/I_Remember_Olya_ashmelev"> I_Remember_Olya_ashmelev </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Apr/11/2011 05:48">12 years ago</span> </li> <li> <a href="/blog/entry/1700#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1700#comments"> 2 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; 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left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/time_14_07" style="position: relative;"> <img src='https://userpic.codeforces.org/1315340/avatar/caa9501b0e90f618.jpg'/> </a> <div><a href="/profile/time_14_07" title="Newbie time_14_07" class="rated-user user-gray">time_14_07</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/24/2020 15:40">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-628513" href="?#comment-628513" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="628513" class="CommentVoteFrame" data-commentRating="-8" data-commentUserId="1315340" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">-8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-628513"> <div class="moveup"> <div class="ttypography"><p>Please anyone explain problem C DP problem. It's states and recurrence relation.</p></div> </div> </div> <div class="reply info"> <a class="comment-628513 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-628513 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-628513"> <li> <div class="comment"> <table class="comment-table" commentId="781701" commentParentId="628513"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/arman.t" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/arman.t" title="Expert arman.t" class="rated-user user-blue">arman.t</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/18/2021 20:45">2 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-781701" href="?#comment-781701" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-628513" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="781701" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="208522" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-781701"> <div class="moveup"> <div class="ttypography"><p>You can take a look at solution <a href="/contest/73/submission/113434456" title="Submission 113434456 by arman.t">113434456</a>, I think it's a bit more intuitive than in the Editorial.</p></div> </div> </div> <div class="reply info"> <a class="comment-781701 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-781701 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-781701"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1710" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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73B
73
B
en
B. Need For Brake
<div class="problem-statement"><div class="header"><div class="title">B. Need For Brake</div><div class="time-limit"><div class="property-title">time limit per test</div>4 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Vasya plays the Need For Brake. He plays because he was presented with a new computer wheel for birthday! Now he is sure that he will win the first place in the championship in his favourite racing computer game! </p><p><span class="tex-span"><i>n</i></span> racers take part in the championship, which consists of a number of races. After each race racers are arranged from place first to <span class="tex-span"><i>n</i></span>-th (no two racers share the same place) and first <span class="tex-span"><i>m</i></span> places are awarded. Racer gains <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> points for <span class="tex-span"><i>i</i></span>-th awarded place, which are added to total points, obtained by him for previous races. It is known that current summary score of racer <span class="tex-span"><i>i</i></span> is <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> points. In the final standings of championship all the racers will be sorted in descending order of points. Racers with an equal amount of points are sorted by increasing of the name in lexicographical order.</p><p>Unfortunately, the championship has come to an end, and there is only one race left. Vasya decided to find out what the highest and lowest place he can take up as a result of the championship.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains number <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup></span>) — number of racers. Each of the next <span class="tex-span"><i>n</i></span> lines contains <span class="tex-span"><i>s</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> — nick of the racer (nonempty string, which consist of no more than 20 lowercase Latin letters) and the racer's points (<span class="tex-span">0 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">6</sup></span>). Racers are given in the arbitrary order.</p><p>The next line contains the number <span class="tex-span"><i>m</i></span> (<span class="tex-span">0 ≤ <i>m</i> ≤ <i>n</i></span>). Then <span class="tex-span"><i>m</i></span> nonnegative integer numbers <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> follow. <span class="tex-span"><i>i</i></span>-th number is equal to amount of points for the <span class="tex-span"><i>i</i></span>-th awarded place (<span class="tex-span">0 ≤ <i>b</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">6</sup></span>).</p><p>The last line contains Vasya's racer nick.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Output two numbers — the highest and the lowest place Vasya can take up as a result of the championship.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br/>teama 10<br/>teamb 20<br/>teamc 40<br/>2<br/>10 20<br/>teama<br/></pre></div><div class="output"><div class="title">Output</div><pre>2 3</pre></div><div class="input"><div class="title">Input</div><pre>2<br/>teama 10<br/>teamb 10<br/>2<br/>10 10<br/>teamb<br/></pre></div><div class="output"><div class="title">Output</div><pre>2 2</pre></div></div></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/73">Codeforces Beta Round 66</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? Just register for practice and you will be able to submit solutions. </div> <div style="text-align:center;margin:1em;"> <form action="" method="post"><input type='hidden' name='csrf_token' value='d5893aca716efb11803a061ada42425c'/> <input type="hidden" name="action" value="registerForPractice"/> <input type="submit" name="submit" value="Register for practice" style="padding:0 0.5em;"> </form> </div> </div> </div> <div class="roundbox sidebox ContestVirtualFrame borderTopRound " style=""> <div class="caption titled">&rarr; Virtual participation <i class="sidebar-caption-icon las la-angle-down"></i> <div class="top-links"> </div> </div> <div style=" " data-page-url="/data/sidebarFrames" > <div style="margin:1em;font-size:0.8em;"> Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests. If you've seen these problems, a virtual contest is not for you - solve these problems in the archive. If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="B" data-uuid="ps_0f0b3e9d56f45a8e39ccb9faf2e2266003d3a325"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">B. Need For Brake</div><div class="time-limit"><div class="property-title">time limit per test</div>4 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Vasya plays the Need For Brake. He plays because he was presented with a new computer wheel for birthday! Now he is sure that he will win the first place in the championship in his favourite racing computer game! </p><p><span class="tex-span"><i>n</i></span> racers take part in the championship, which consists of a number of races. After each race racers are arranged from place first to <span class="tex-span"><i>n</i></span>-th (no two racers share the same place) and first <span class="tex-span"><i>m</i></span> places are awarded. Racer gains <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> points for <span class="tex-span"><i>i</i></span>-th awarded place, which are added to total points, obtained by him for previous races. It is known that current summary score of racer <span class="tex-span"><i>i</i></span> is <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> points. In the final standings of championship all the racers will be sorted in descending order of points. Racers with an equal amount of points are sorted by increasing of the name in lexicographical order.</p><p>Unfortunately, the championship has come to an end, and there is only one race left. Vasya decided to find out what the highest and lowest place he can take up as a result of the championship.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains number <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup></span>) — number of racers. Each of the next <span class="tex-span"><i>n</i></span> lines contains <span class="tex-span"><i>s</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> — nick of the racer (nonempty string, which consist of no more than 20 lowercase Latin letters) and the racer's points (<span class="tex-span">0 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">6</sup></span>). Racers are given in the arbitrary order.</p><p>The next line contains the number <span class="tex-span"><i>m</i></span> (<span class="tex-span">0 ≤ <i>m</i> ≤ <i>n</i></span>). Then <span class="tex-span"><i>m</i></span> nonnegative integer numbers <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> follow. <span class="tex-span"><i>i</i></span>-th number is equal to amount of points for the <span class="tex-span"><i>i</i></span>-th awarded place (<span class="tex-span">0 ≤ <i>b</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">6</sup></span>).</p><p>The last line contains Vasya's racer nick.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Output two numbers — the highest and the lowest place Vasya can take up as a result of the championship.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br />teama 10<br />teamb 20<br />teamc 40<br />2<br />10 20<br />teama<br /></pre></div><div class="output"><div class="title">Output</div><pre>2 3</pre></div><div class="input"><div class="title">Input</div><pre>2<br />teama 10<br />teamb 10<br />2<br />10 10<br />teamb<br /></pre></div><div class="output"><div class="title">Output</div><pre>2 2</pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=B]"); 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["Binary search", "Greedy algorithms", "Sortings, orderings"]
["binary search", "greedy", "sortings", "*2000"]
https://codeforces.com/blog/entry/1700
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, serif;color: black;"><b>Problem A.</b></span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Let’s call the monster dimension sizes as <i>x<sub>1</sub>, x<sub>2</sub>, x<sub>3</sub></i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">1. <i>O(min(k, x<sub>1</sub> + x<sub>2</sub> + x<sub>3</sub>)) </i>solution</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">We can make at most <i>(x<sub>1</sub> – 1) + (x<sub>2</sub> – 1) + (x<sub>3</sub> – 1)</i> cuttings, so we may assume that <i>k &lt;= x<sub>1</sub> + x<sub>2</sub> + x<sub>3</sub> – 3</i>. For each of the three dimensions we will store an integer <i>a<sub>i</sub></i> – number of cuttings performed through the corresponding dimension. Let’s perform the following actions <i>k</i> times: consider all numbers <i>a<sub>i</sub> </i>which we may increase (<i>a<sub>i</sub> &lt;  x<sub>i</sub> - 1</i>) , call these dimensions “uncompleted”. Select the minimum number <i>a<sub>j</sub></i> among all uncompleted <i>a<sub>i</sub></i> and perform a cut through the corresponding dimension (<i>a<sub>j</sub></i> will be increased by 1 as the result). Now let’s consider the resulting set after <i>k</i> actions: <i>{a<sub>1</sub>, a<sub>2</sub>, a<sub>3</sub>}</i>. Using the described algorithm we grant that the maximum element of this set is as little as possible and the minimum element is as big as possible. Because the sum <i>a<sub>1</sub> + a<sub>2</sub> + a<sub>3</sub> = k</i> is fixed, we get the maximum product <i>(a<sub>1</sub> + 1) * (a<sub>2</sub> + 1) * (a<sub>3</sub> + 1)</i> which is the answer for the problem.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">2. <i>O(1) </i>solution</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Instead of simulation all the <i>k</i> actions we may quickly determine values of numbers <i>a<sub>i</sub></i> after using the algorithm described above.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Let <i>x</i> – the smallest value among <i>(x<sub>i </sub>– 1)</i>. When <i>x * 3 &gt;= k</i> on each of the algorithm iterations all three dimensions will be uncompleted. It means that during the first <i>(k / 3) * 3</i> steps each of numbers <i>a<sub>i</sub></i> will be increased by <i>(k / 3)</i>. Then 0, 1 or 2 numbers <i>a<sub>i</sub></i> will be increased by 1 subject to value of <i>k % 3</i>. So</span><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">, </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">we</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">have</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">found</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">values</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">a<sub>i</sub></span></i><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Otherwise (<i>x * 3 &lt; k</i>) during the first <i>x * 3</i> steps each of <i>a<sub>i</sub></i> will be increased by <i>x</i>. After that we will have at most two uncompleted dimensions which can be processed a similar way (we should choose the minimum value <i>x</i> among the remaining uncompleted dimensions).</span></p> <p><span lang="EN-US"> </span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"><b>Problem B.</b></span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">We may assume that we have exactly <i>n</i> awarded places but some of them give 0 points.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Let’s sort places by amount of points (<i>b<sub>i</sub></i>) and racers by amount of currently gained points (<i>a<sub>i</sub></i>). First let’s find the best place Vasya can reach. In the best case he will get <i>b<sub>0</sub></i> points (where <i>b<sub>0</sub></i> is the greatest number among <i>b<sub>i</sub></i>). So, let the total Vasya’s point is <i>v</i>. Now we should to distribute other prize points to racers so that the number of racers better than Vasya will be minimal. For doing that we are to give maximum number of prizes so that corresponding racers will have less than <i>v </i>points. Note that if we can give <i>k</i> prizes keeping this property, than we can give <i>k</i> “cheapest” prizes too. The following statement is also true: if we can get a prize with <i>t</i> points to racer <i>i</i> and to racer <i>j</i> , <i>a<sub>i</sub> &gt; a<sub>j</sub></i>, then it is better to give this prize to racer <i>i</i>. Formally: if there exists a way to give <i>k</i> prizes where this prize will get racer <i>j</i>, than there exists a way to give <i>k</i> prizes where this prize will get racer <i>i</i>. It can be proven the following way. Consider a way to give <i>k</i> prizes where racer <i>j</i> got prize with <i>t</i> points, racer <i>i</i> – <i>s</i> points or didn’t get prize at all. In the first case we can swap prizes for racers <i>i</i> and <i>j</i>: <i>a<sub>i</sub> &gt; a<sub>j</sub></i> and <i>a<sub>i</sub> + s &lt; v</i> (since racer <i>i</i> have got the prize), so <i>a<sub>j</sub> + s &lt; v</i>, and <i>a<sub>i</sub> + t &lt; v</i> i.e. this change is acceptable. In the second case we can just give the prize <i>t</i> to racer <i>i</i> instead of racer <i>j</i>. In the both cases we get a way to give <i>k</i> prizes where racer <i>i</i> receive prize<i> t</i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Now including this statement we may give prizes to racers using the following greedy algorithm. Let’s begin to give prizes starting from the cheapest one and check the racers starting from the best one (of course excluding Vasya and the best prize). For each prize <i>i</i> we will go through the racers until applicable racer (<i>j</i>) found: <i>b<sub>i</sub> + a<sub>j</sub> &lt; v</i>. If no such racers remain we are unable to give more prizes without violating the rule (racers should have less than <i>v</i> points). In this case we should stop the algorithm and the answer is <i>n – k </i>where <i>k</i> is the number of prizes we have given. If we have found such racer <i>j</i> we can give him prize <i>b<sub>i</sub></i> and go to the next prize. Complexity of this step is <i>O(n)</i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Similarly we can find the worst place for Vasya. For doing that we should give him the cheapest prize (note it may have positive points though). After that we should distribute the prizes iterating over prizes from the largest to cheapest and check racers from the worst to the best one trying to make sum of racer’s points more than <i>v</i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Total complexity of the described algorithm is <i>O(n * log(n))</i> because we have to sort prizes and racers.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"><b>Problem C.</b></span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">It is easy to see that if we put some symbol <i>c</i> at position <i>p</i> of the string <i>s</i> it will not affect symbols at positions (<i>p+2</i>) and greater. So</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">we</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">have a</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">standard</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">DP</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">problem</span><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">. </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">State of the dynamic is described by three parameters: <i>p</i> – the number of already processed symbols (or the index of currently processed symbol of the string), <i>c</i> – the previous symbol, <i>t</i> – the number of allowed symbol changes. To calculate the answer for a state we should choose the best value among all symbols for current position (when <i>t &gt; 0</i>) or just go to the index (<i>p + 1</i>) with current symbol <i>s[p]</i>. Thus we get the followings formulas:</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><i><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">d[n][*][*] = 0</span></i><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">d[p][c][t] = d[p + 1][s[p]][t] + bonus[c][s[p]] </span></i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">when<i> t = 0</i></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">d[p][c][t] = max(d[p + 1][c’][t – (c’ &lt;&gt; s[p])] + bonus[c][c’])</span></i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">where <i>n</i>  is the length of string <i>s</i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Computation complexity of the algorithm is <i>O(n * k * h^2)</i>, where <i>h</i> is the alphabet size (<i>h = 26</i> for current problem).<b></b></span></p></div><div /></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/73" class="notice" style="text-decoration: none;">Codeforces Beta Round 66</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-368-1700").click(function() { var that = this; 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line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/I_Remember_Olya_ashmelev"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/I_Remember_Olya_ashmelev"> I_Remember_Olya_ashmelev </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Apr/11/2011 05:48">12 years ago</span> </li> <li> <a href="/blog/entry/1700#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1700#comments"> 2 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; 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left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/time_14_07" style="position: relative;"> <img src='https://userpic.codeforces.org/1315340/avatar/caa9501b0e90f618.jpg'/> </a> <div><a href="/profile/time_14_07" title="Newbie time_14_07" class="rated-user user-gray">time_14_07</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/24/2020 15:40">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-628513" href="?#comment-628513" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="628513" class="CommentVoteFrame" data-commentRating="-8" data-commentUserId="1315340" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">-8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-628513"> <div class="moveup"> <div class="ttypography"><p>Please anyone explain problem C DP problem. It's states and recurrence relation.</p></div> </div> </div> <div class="reply info"> <a class="comment-628513 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-628513 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-628513"> <li> <div class="comment"> <table class="comment-table" commentId="781701" commentParentId="628513"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/arman.t" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/arman.t" title="Expert arman.t" class="rated-user user-blue">arman.t</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/18/2021 20:45">2 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-781701" href="?#comment-781701" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-628513" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="781701" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="208522" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-781701"> <div class="moveup"> <div class="ttypography"><p>You can take a look at solution <a href="/contest/73/submission/113434456" title="Submission 113434456 by arman.t">113434456</a>, I think it's a bit more intuitive than in the Editorial.</p></div> </div> </div> <div class="reply info"> <a class="comment-781701 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-781701 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-781701"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1710" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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73C
73
C
en
C. LionAge II
<div class="problem-statement"><div class="header"><div class="title">C. LionAge II</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Vasya plays the LionAge II. He was bored of playing with a stupid computer, so he installed this popular MMORPG, to fight with his friends. Vasya came up with the name of his character — non-empty string <span class="tex-span"><i>s</i></span>, consisting of a lowercase Latin letters. However, in order not to put up a front of friends, Vasya has decided to change no more than <span class="tex-span"><i>k</i></span> letters of the character name so that the new name sounded as good as possible. Euphony of the line is defined as follows: for each pair of adjacent letters <span class="tex-span"><i>x</i></span> and <span class="tex-span"><i>y</i></span> (<span class="tex-span"><i>x</i></span> immediately precedes <span class="tex-span"><i>y</i></span>) the bonus <span class="tex-span"><i>c</i>(<i>x</i>, <i>y</i>)</span> is added to the result. Your task is to determine what the greatest Euphony can be obtained by changing at most <span class="tex-span"><i>k</i></span> letters in the name of the Vasya's character.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains character's name <span class="tex-span"><i>s</i></span> and an integer number <span class="tex-span"><i>k</i></span> (<span class="tex-span">0 ≤ <i>k</i> ≤ 100</span>). The length of the nonempty string <span class="tex-span"><i>s</i></span> does not exceed <span class="tex-span">100</span>. The second line contains an integer number <span class="tex-span"><i>n</i></span> (<span class="tex-span">0 ≤ <i>n</i> ≤ 676</span>) — amount of pairs of letters, giving bonus to the euphony. The next <span class="tex-span"><i>n</i></span> lines contain description of these pairs «<span class="tex-span"><i>x</i></span> <span class="tex-span"><i>y</i></span> <span class="tex-span"><i>c</i></span>», which means that sequence <span class="tex-span"><i>xy</i></span> gives bonus <span class="tex-span"><i>c</i></span> (<span class="tex-span"><i>x</i>, <i>y</i></span> — lowercase Latin letters, <span class="tex-span"> - 1000 ≤ <i>c</i> ≤ 1000)</span>. It is guaranteed that no pair <span class="tex-span"><i>x</i></span> <span class="tex-span"><i>y</i></span> mentioned twice in the input data.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Output the only number — maximum possible euphony оf the new character's name.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>winner 4<br/>4<br/>s e 7<br/>o s 8<br/>l o 13<br/>o o 8<br/></pre></div><div class="output"><div class="title">Output</div><pre>36</pre></div><div class="input"><div class="title">Input</div><pre>abcdef 1<br/>5<br/>a b -10<br/>b c 5<br/>c d 5<br/>d e 5<br/>e f 5<br/></pre></div><div class="output"><div class="title">Output</div><pre>20</pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first example the most euphony name will be <span class="tex-span"><i>looser</i></span>. It is easy to calculate that its euphony is 36.</p></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/73">Codeforces Beta Round 66</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? 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If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="C" data-uuid="ps_f8b80b13cc31dfd9b7264231641391f1efbe0b2b"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. LionAge II</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Vasya plays the LionAge II. He was bored of playing with a stupid computer, so he installed this popular MMORPG, to fight with his friends. Vasya came up with the name of his character — non-empty string <span class="tex-span"><i>s</i></span>, consisting of a lowercase Latin letters. However, in order not to put up a front of friends, Vasya has decided to change no more than <span class="tex-span"><i>k</i></span> letters of the character name so that the new name sounded as good as possible. Euphony of the line is defined as follows: for each pair of adjacent letters <span class="tex-span"><i>x</i></span> and <span class="tex-span"><i>y</i></span> (<span class="tex-span"><i>x</i></span> immediately precedes <span class="tex-span"><i>y</i></span>) the bonus <span class="tex-span"><i>c</i>(<i>x</i>, <i>y</i>)</span> is added to the result. Your task is to determine what the greatest Euphony can be obtained by changing at most <span class="tex-span"><i>k</i></span> letters in the name of the Vasya's character.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains character's name <span class="tex-span"><i>s</i></span> and an integer number <span class="tex-span"><i>k</i></span> (<span class="tex-span">0 ≤ <i>k</i> ≤ 100</span>). The length of the nonempty string <span class="tex-span"><i>s</i></span> does not exceed <span class="tex-span">100</span>. The second line contains an integer number <span class="tex-span"><i>n</i></span> (<span class="tex-span">0 ≤ <i>n</i> ≤ 676</span>) — amount of pairs of letters, giving bonus to the euphony. The next <span class="tex-span"><i>n</i></span> lines contain description of these pairs «<span class="tex-span"><i>x</i></span> <span class="tex-span"><i>y</i></span> <span class="tex-span"><i>c</i></span>», which means that sequence <span class="tex-span"><i>xy</i></span> gives bonus <span class="tex-span"><i>c</i></span> (<span class="tex-span"><i>x</i>, <i>y</i></span> — lowercase Latin letters, <span class="tex-span"> - 1000 ≤ <i>c</i> ≤ 1000)</span>. It is guaranteed that no pair <span class="tex-span"><i>x</i></span> <span class="tex-span"><i>y</i></span> mentioned twice in the input data.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Output the only number — maximum possible euphony оf the new character's name.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>winner 4<br />4<br />s e 7<br />o s 8<br />l o 13<br />o o 8<br /></pre></div><div class="output"><div class="title">Output</div><pre>36</pre></div><div class="input"><div class="title">Input</div><pre>abcdef 1<br />5<br />a b -10<br />b c 5<br />c d 5<br />d e 5<br />e f 5<br /></pre></div><div class="output"><div class="title">Output</div><pre>20</pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first example the most euphony name will be <span class="tex-span"><i>looser</i></span>. 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["Dynamic programming"]
["dp", "*1800"]
https://codeforces.com/blog/entry/1700
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, serif;color: black;"><b>Problem A.</b></span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Let’s call the monster dimension sizes as <i>x<sub>1</sub>, x<sub>2</sub>, x<sub>3</sub></i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">1. <i>O(min(k, x<sub>1</sub> + x<sub>2</sub> + x<sub>3</sub>)) </i>solution</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">We can make at most <i>(x<sub>1</sub> – 1) + (x<sub>2</sub> – 1) + (x<sub>3</sub> – 1)</i> cuttings, so we may assume that <i>k &lt;= x<sub>1</sub> + x<sub>2</sub> + x<sub>3</sub> – 3</i>. For each of the three dimensions we will store an integer <i>a<sub>i</sub></i> – number of cuttings performed through the corresponding dimension. Let’s perform the following actions <i>k</i> times: consider all numbers <i>a<sub>i</sub> </i>which we may increase (<i>a<sub>i</sub> &lt;  x<sub>i</sub> - 1</i>) , call these dimensions “uncompleted”. Select the minimum number <i>a<sub>j</sub></i> among all uncompleted <i>a<sub>i</sub></i> and perform a cut through the corresponding dimension (<i>a<sub>j</sub></i> will be increased by 1 as the result). Now let’s consider the resulting set after <i>k</i> actions: <i>{a<sub>1</sub>, a<sub>2</sub>, a<sub>3</sub>}</i>. Using the described algorithm we grant that the maximum element of this set is as little as possible and the minimum element is as big as possible. Because the sum <i>a<sub>1</sub> + a<sub>2</sub> + a<sub>3</sub> = k</i> is fixed, we get the maximum product <i>(a<sub>1</sub> + 1) * (a<sub>2</sub> + 1) * (a<sub>3</sub> + 1)</i> which is the answer for the problem.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">2. <i>O(1) </i>solution</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Instead of simulation all the <i>k</i> actions we may quickly determine values of numbers <i>a<sub>i</sub></i> after using the algorithm described above.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Let <i>x</i> – the smallest value among <i>(x<sub>i </sub>– 1)</i>. When <i>x * 3 &gt;= k</i> on each of the algorithm iterations all three dimensions will be uncompleted. It means that during the first <i>(k / 3) * 3</i> steps each of numbers <i>a<sub>i</sub></i> will be increased by <i>(k / 3)</i>. Then 0, 1 or 2 numbers <i>a<sub>i</sub></i> will be increased by 1 subject to value of <i>k % 3</i>. So</span><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">, </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">we</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">have</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">found</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">values</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">a<sub>i</sub></span></i><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Otherwise (<i>x * 3 &lt; k</i>) during the first <i>x * 3</i> steps each of <i>a<sub>i</sub></i> will be increased by <i>x</i>. After that we will have at most two uncompleted dimensions which can be processed a similar way (we should choose the minimum value <i>x</i> among the remaining uncompleted dimensions).</span></p> <p><span lang="EN-US"> </span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"><b>Problem B.</b></span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">We may assume that we have exactly <i>n</i> awarded places but some of them give 0 points.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Let’s sort places by amount of points (<i>b<sub>i</sub></i>) and racers by amount of currently gained points (<i>a<sub>i</sub></i>). First let’s find the best place Vasya can reach. In the best case he will get <i>b<sub>0</sub></i> points (where <i>b<sub>0</sub></i> is the greatest number among <i>b<sub>i</sub></i>). So, let the total Vasya’s point is <i>v</i>. Now we should to distribute other prize points to racers so that the number of racers better than Vasya will be minimal. For doing that we are to give maximum number of prizes so that corresponding racers will have less than <i>v </i>points. Note that if we can give <i>k</i> prizes keeping this property, than we can give <i>k</i> “cheapest” prizes too. The following statement is also true: if we can get a prize with <i>t</i> points to racer <i>i</i> and to racer <i>j</i> , <i>a<sub>i</sub> &gt; a<sub>j</sub></i>, then it is better to give this prize to racer <i>i</i>. Formally: if there exists a way to give <i>k</i> prizes where this prize will get racer <i>j</i>, than there exists a way to give <i>k</i> prizes where this prize will get racer <i>i</i>. It can be proven the following way. Consider a way to give <i>k</i> prizes where racer <i>j</i> got prize with <i>t</i> points, racer <i>i</i> – <i>s</i> points or didn’t get prize at all. In the first case we can swap prizes for racers <i>i</i> and <i>j</i>: <i>a<sub>i</sub> &gt; a<sub>j</sub></i> and <i>a<sub>i</sub> + s &lt; v</i> (since racer <i>i</i> have got the prize), so <i>a<sub>j</sub> + s &lt; v</i>, and <i>a<sub>i</sub> + t &lt; v</i> i.e. this change is acceptable. In the second case we can just give the prize <i>t</i> to racer <i>i</i> instead of racer <i>j</i>. In the both cases we get a way to give <i>k</i> prizes where racer <i>i</i> receive prize<i> t</i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Now including this statement we may give prizes to racers using the following greedy algorithm. Let’s begin to give prizes starting from the cheapest one and check the racers starting from the best one (of course excluding Vasya and the best prize). For each prize <i>i</i> we will go through the racers until applicable racer (<i>j</i>) found: <i>b<sub>i</sub> + a<sub>j</sub> &lt; v</i>. If no such racers remain we are unable to give more prizes without violating the rule (racers should have less than <i>v</i> points). In this case we should stop the algorithm and the answer is <i>n – k </i>where <i>k</i> is the number of prizes we have given. If we have found such racer <i>j</i> we can give him prize <i>b<sub>i</sub></i> and go to the next prize. Complexity of this step is <i>O(n)</i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Similarly we can find the worst place for Vasya. For doing that we should give him the cheapest prize (note it may have positive points though). After that we should distribute the prizes iterating over prizes from the largest to cheapest and check racers from the worst to the best one trying to make sum of racer’s points more than <i>v</i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Total complexity of the described algorithm is <i>O(n * log(n))</i> because we have to sort prizes and racers.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"><b>Problem C.</b></span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">It is easy to see that if we put some symbol <i>c</i> at position <i>p</i> of the string <i>s</i> it will not affect symbols at positions (<i>p+2</i>) and greater. So</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">we</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">have a</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">standard</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">DP</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">problem</span><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">. </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">State of the dynamic is described by three parameters: <i>p</i> – the number of already processed symbols (or the index of currently processed symbol of the string), <i>c</i> – the previous symbol, <i>t</i> – the number of allowed symbol changes. To calculate the answer for a state we should choose the best value among all symbols for current position (when <i>t &gt; 0</i>) or just go to the index (<i>p + 1</i>) with current symbol <i>s[p]</i>. Thus we get the followings formulas:</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><i><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">d[n][*][*] = 0</span></i><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">d[p][c][t] = d[p + 1][s[p]][t] + bonus[c][s[p]] </span></i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">when<i> t = 0</i></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">d[p][c][t] = max(d[p + 1][c’][t – (c’ &lt;&gt; s[p])] + bonus[c][c’])</span></i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">where <i>n</i>  is the length of string <i>s</i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Computation complexity of the algorithm is <i>O(n * k * h^2)</i>, where <i>h</i> is the alphabet size (<i>h = 26</i> for current problem).<b></b></span></p></div><div /></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/73" class="notice" style="text-decoration: none;">Codeforces Beta Round 66</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-368-1700").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "368", blogEntryId: "1700", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces+round+66" class="tag notice" style="text-decoration: none;">codeforces round 66</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=editorial" class="tag notice" style="text-decoration: none;">editorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1700"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:gray'>-11</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1700"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; 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left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/time_14_07" style="position: relative;"> <img src='https://userpic.codeforces.org/1315340/avatar/caa9501b0e90f618.jpg'/> </a> <div><a href="/profile/time_14_07" title="Newbie time_14_07" class="rated-user user-gray">time_14_07</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/24/2020 15:40">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-628513" href="?#comment-628513" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="628513" class="CommentVoteFrame" data-commentRating="-8" data-commentUserId="1315340" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">-8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-628513"> <div class="moveup"> <div class="ttypography"><p>Please anyone explain problem C DP problem. It's states and recurrence relation.</p></div> </div> </div> <div class="reply info"> <a class="comment-628513 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-628513 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-628513"> <li> <div class="comment"> <table class="comment-table" commentId="781701" commentParentId="628513"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/arman.t" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/arman.t" title="Expert arman.t" class="rated-user user-blue">arman.t</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/18/2021 20:45">2 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-781701" href="?#comment-781701" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-628513" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="781701" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="208522" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-781701"> <div class="moveup"> <div class="ttypography"><p>You can take a look at solution <a href="/contest/73/submission/113434456" title="Submission 113434456 by arman.t">113434456</a>, I think it's a bit more intuitive than in the Editorial.</p></div> </div> </div> <div class="reply info"> <a class="comment-781701 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-781701 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-781701"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1710" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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73D
73
D
en
D. FreeDiv
<div class="problem-statement"><div class="header"><div class="title">D. FreeDiv</div><div class="time-limit"><div class="property-title">time limit per test</div>5 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Vasya plays FreeDiv. In this game he manages a huge state, which has <span class="tex-span"><i>n</i></span> cities and <span class="tex-span"><i>m</i></span> two-way roads between them. Unfortunately, not from every city you can reach any other one moving along these roads. Therefore Vasya decided to divide the state into provinces so that in every province, one could reach from every city all the cities of the province, but there are no roads between provinces. </p><p>Unlike other turn-based strategies, in FreeDiv a player has the opportunity to build tunnels between cities. The tunnels are two-way roads along which one can move armies undetected by the enemy. However, no more than one tunnel can be connected to each city. As for Vasya, he wants to build a network of tunnels so that any pair of cities in his state were reachable by some path consisting of roads and a tunnels. But at that no more than <span class="tex-span"><i>k</i></span> tunnels are connected to each province (otherwise, the province will be difficult to keep in case other provinces are captured by enemy armies).</p><p>Vasya discovered that maybe he will not be able to build such a network for the current condition of the state. Maybe he'll have first to build several roads between cities in different provinces to merge the provinces. Your task is to determine the minimum number of roads Vasya needs to build so that it was possible to build the required network of tunnels in the resulting state.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains three integers <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>m</i></span> and <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>n</i>, <i>k</i> ≤ 10<sup class="upper-index">6</sup>, 0 ≤ <i>m</i> ≤ 10<sup class="upper-index">6</sup></span>). Each of the next <span class="tex-span"><i>m</i></span> lines contains two integers. They are the numbers of cities connected by a corresponding road. No road connects city to itself and there is at most one road between each pair of cities.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single number, the minimum number of additional roads.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3 3 2<br/>1 2<br/>2 3<br/>3 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>0</pre></div><div class="input"><div class="title">Input</div><pre>4 2 2<br/>1 2<br/>3 4<br/></pre></div><div class="output"><div class="title">Output</div><pre>0</pre></div><div class="input"><div class="title">Input</div><pre>4 0 2<br/></pre></div><div class="output"><div class="title">Output</div><pre>1</pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first example only one province exists, so it is not necessary to build any tunnels or roads.</p><p>In the second example two provinces exist. It is possible to merge the provinces by building a tunnel between cities 1 and 3.</p><p>In the third example at least one additional road is necessary. For example it is possible to build additional road between cities 1 and 2 and build two tunnels between cities 1 and 3, 2 and 4 after that.</p></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="D" data-uuid="ps_6a1baf77c3bb54a21671d30c80c1e0b59e751262"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">D. FreeDiv</div><div class="time-limit"><div class="property-title">time limit per test</div>5 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Vasya plays FreeDiv. In this game he manages a huge state, which has <span class="tex-span"><i>n</i></span> cities and <span class="tex-span"><i>m</i></span> two-way roads between them. Unfortunately, not from every city you can reach any other one moving along these roads. Therefore Vasya decided to divide the state into provinces so that in every province, one could reach from every city all the cities of the province, but there are no roads between provinces. </p><p>Unlike other turn-based strategies, in FreeDiv a player has the opportunity to build tunnels between cities. The tunnels are two-way roads along which one can move armies undetected by the enemy. However, no more than one tunnel can be connected to each city. As for Vasya, he wants to build a network of tunnels so that any pair of cities in his state were reachable by some path consisting of roads and a tunnels. But at that no more than <span class="tex-span"><i>k</i></span> tunnels are connected to each province (otherwise, the province will be difficult to keep in case other provinces are captured by enemy armies).</p><p>Vasya discovered that maybe he will not be able to build such a network for the current condition of the state. Maybe he'll have first to build several roads between cities in different provinces to merge the provinces. Your task is to determine the minimum number of roads Vasya needs to build so that it was possible to build the required network of tunnels in the resulting state.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains three integers <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>m</i></span> and <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>n</i>, <i>k</i> ≤ 10<sup class="upper-index">6</sup>, 0 ≤ <i>m</i> ≤ 10<sup class="upper-index">6</sup></span>). Each of the next <span class="tex-span"><i>m</i></span> lines contains two integers. They are the numbers of cities connected by a corresponding road. No road connects city to itself and there is at most one road between each pair of cities.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single number, the minimum number of additional roads.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3 3 2<br />1 2<br />2 3<br />3 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>0</pre></div><div class="input"><div class="title">Input</div><pre>4 2 2<br />1 2<br />3 4<br /></pre></div><div class="output"><div class="title">Output</div><pre>0</pre></div><div class="input"><div class="title">Input</div><pre>4 0 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>1</pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first example only one province exists, so it is not necessary to build any tunnels or roads.</p><p>In the second example two provinces exist. It is possible to merge the provinces by building a tunnel between cities 1 and 3.</p><p>In the third example at least one additional road is necessary. 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["Dfs and similar", "Graphs", "Greedy algorithms"]
["dfs and similar", "graphs", "greedy", "*2200"]
https://codeforces.com/blog/entry/1700
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, serif;color: black;"><b>Problem A.</b></span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Let’s call the monster dimension sizes as <i>x<sub>1</sub>, x<sub>2</sub>, x<sub>3</sub></i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">1. <i>O(min(k, x<sub>1</sub> + x<sub>2</sub> + x<sub>3</sub>)) </i>solution</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">We can make at most <i>(x<sub>1</sub> – 1) + (x<sub>2</sub> – 1) + (x<sub>3</sub> – 1)</i> cuttings, so we may assume that <i>k &lt;= x<sub>1</sub> + x<sub>2</sub> + x<sub>3</sub> – 3</i>. For each of the three dimensions we will store an integer <i>a<sub>i</sub></i> – number of cuttings performed through the corresponding dimension. Let’s perform the following actions <i>k</i> times: consider all numbers <i>a<sub>i</sub> </i>which we may increase (<i>a<sub>i</sub> &lt;  x<sub>i</sub> - 1</i>) , call these dimensions “uncompleted”. Select the minimum number <i>a<sub>j</sub></i> among all uncompleted <i>a<sub>i</sub></i> and perform a cut through the corresponding dimension (<i>a<sub>j</sub></i> will be increased by 1 as the result). Now let’s consider the resulting set after <i>k</i> actions: <i>{a<sub>1</sub>, a<sub>2</sub>, a<sub>3</sub>}</i>. Using the described algorithm we grant that the maximum element of this set is as little as possible and the minimum element is as big as possible. Because the sum <i>a<sub>1</sub> + a<sub>2</sub> + a<sub>3</sub> = k</i> is fixed, we get the maximum product <i>(a<sub>1</sub> + 1) * (a<sub>2</sub> + 1) * (a<sub>3</sub> + 1)</i> which is the answer for the problem.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">2. <i>O(1) </i>solution</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Instead of simulation all the <i>k</i> actions we may quickly determine values of numbers <i>a<sub>i</sub></i> after using the algorithm described above.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Let <i>x</i> – the smallest value among <i>(x<sub>i </sub>– 1)</i>. When <i>x * 3 &gt;= k</i> on each of the algorithm iterations all three dimensions will be uncompleted. It means that during the first <i>(k / 3) * 3</i> steps each of numbers <i>a<sub>i</sub></i> will be increased by <i>(k / 3)</i>. Then 0, 1 or 2 numbers <i>a<sub>i</sub></i> will be increased by 1 subject to value of <i>k % 3</i>. So</span><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">, </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">we</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">have</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">found</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">values</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">a<sub>i</sub></span></i><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Otherwise (<i>x * 3 &lt; k</i>) during the first <i>x * 3</i> steps each of <i>a<sub>i</sub></i> will be increased by <i>x</i>. After that we will have at most two uncompleted dimensions which can be processed a similar way (we should choose the minimum value <i>x</i> among the remaining uncompleted dimensions).</span></p> <p><span lang="EN-US"> </span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"><b>Problem B.</b></span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">We may assume that we have exactly <i>n</i> awarded places but some of them give 0 points.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Let’s sort places by amount of points (<i>b<sub>i</sub></i>) and racers by amount of currently gained points (<i>a<sub>i</sub></i>). First let’s find the best place Vasya can reach. In the best case he will get <i>b<sub>0</sub></i> points (where <i>b<sub>0</sub></i> is the greatest number among <i>b<sub>i</sub></i>). So, let the total Vasya’s point is <i>v</i>. Now we should to distribute other prize points to racers so that the number of racers better than Vasya will be minimal. For doing that we are to give maximum number of prizes so that corresponding racers will have less than <i>v </i>points. Note that if we can give <i>k</i> prizes keeping this property, than we can give <i>k</i> “cheapest” prizes too. The following statement is also true: if we can get a prize with <i>t</i> points to racer <i>i</i> and to racer <i>j</i> , <i>a<sub>i</sub> &gt; a<sub>j</sub></i>, then it is better to give this prize to racer <i>i</i>. Formally: if there exists a way to give <i>k</i> prizes where this prize will get racer <i>j</i>, than there exists a way to give <i>k</i> prizes where this prize will get racer <i>i</i>. It can be proven the following way. Consider a way to give <i>k</i> prizes where racer <i>j</i> got prize with <i>t</i> points, racer <i>i</i> – <i>s</i> points or didn’t get prize at all. In the first case we can swap prizes for racers <i>i</i> and <i>j</i>: <i>a<sub>i</sub> &gt; a<sub>j</sub></i> and <i>a<sub>i</sub> + s &lt; v</i> (since racer <i>i</i> have got the prize), so <i>a<sub>j</sub> + s &lt; v</i>, and <i>a<sub>i</sub> + t &lt; v</i> i.e. this change is acceptable. In the second case we can just give the prize <i>t</i> to racer <i>i</i> instead of racer <i>j</i>. In the both cases we get a way to give <i>k</i> prizes where racer <i>i</i> receive prize<i> t</i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Now including this statement we may give prizes to racers using the following greedy algorithm. Let’s begin to give prizes starting from the cheapest one and check the racers starting from the best one (of course excluding Vasya and the best prize). For each prize <i>i</i> we will go through the racers until applicable racer (<i>j</i>) found: <i>b<sub>i</sub> + a<sub>j</sub> &lt; v</i>. If no such racers remain we are unable to give more prizes without violating the rule (racers should have less than <i>v</i> points). In this case we should stop the algorithm and the answer is <i>n – k </i>where <i>k</i> is the number of prizes we have given. If we have found such racer <i>j</i> we can give him prize <i>b<sub>i</sub></i> and go to the next prize. Complexity of this step is <i>O(n)</i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Similarly we can find the worst place for Vasya. For doing that we should give him the cheapest prize (note it may have positive points though). After that we should distribute the prizes iterating over prizes from the largest to cheapest and check racers from the worst to the best one trying to make sum of racer’s points more than <i>v</i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Total complexity of the described algorithm is <i>O(n * log(n))</i> because we have to sort prizes and racers.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"><b>Problem C.</b></span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">It is easy to see that if we put some symbol <i>c</i> at position <i>p</i> of the string <i>s</i> it will not affect symbols at positions (<i>p+2</i>) and greater. So</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">we</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">have a</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">standard</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">DP</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">problem</span><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">. </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">State of the dynamic is described by three parameters: <i>p</i> – the number of already processed symbols (or the index of currently processed symbol of the string), <i>c</i> – the previous symbol, <i>t</i> – the number of allowed symbol changes. To calculate the answer for a state we should choose the best value among all symbols for current position (when <i>t &gt; 0</i>) or just go to the index (<i>p + 1</i>) with current symbol <i>s[p]</i>. Thus we get the followings formulas:</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><i><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">d[n][*][*] = 0</span></i><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">d[p][c][t] = d[p + 1][s[p]][t] + bonus[c][s[p]] </span></i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">when<i> t = 0</i></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">d[p][c][t] = max(d[p + 1][c’][t – (c’ &lt;&gt; s[p])] + bonus[c][c’])</span></i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">where <i>n</i>  is the length of string <i>s</i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Computation complexity of the algorithm is <i>O(n * k * h^2)</i>, where <i>h</i> is the alphabet size (<i>h = 26</i> for current problem).<b></b></span></p></div><div /></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/73" class="notice" style="text-decoration: none;">Codeforces Beta Round 66</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-368-1700").click(function() { var that = this; 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line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/I_Remember_Olya_ashmelev"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/I_Remember_Olya_ashmelev"> I_Remember_Olya_ashmelev </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Apr/11/2011 05:48">12 years ago</span> </li> <li> <a href="/blog/entry/1700#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1700#comments"> 2 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; 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left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/time_14_07" style="position: relative;"> <img src='https://userpic.codeforces.org/1315340/avatar/caa9501b0e90f618.jpg'/> </a> <div><a href="/profile/time_14_07" title="Newbie time_14_07" class="rated-user user-gray">time_14_07</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/24/2020 15:40">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-628513" href="?#comment-628513" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="628513" class="CommentVoteFrame" data-commentRating="-8" data-commentUserId="1315340" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">-8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-628513"> <div class="moveup"> <div class="ttypography"><p>Please anyone explain problem C DP problem. It's states and recurrence relation.</p></div> </div> </div> <div class="reply info"> <a class="comment-628513 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-628513 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-628513"> <li> <div class="comment"> <table class="comment-table" commentId="781701" commentParentId="628513"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/arman.t" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/arman.t" title="Expert arman.t" class="rated-user user-blue">arman.t</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/18/2021 20:45">2 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-781701" href="?#comment-781701" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-628513" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="781701" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="208522" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-781701"> <div class="moveup"> <div class="ttypography"><p>You can take a look at solution <a href="/contest/73/submission/113434456" title="Submission 113434456 by arman.t">113434456</a>, I think it's a bit more intuitive than in the Editorial.</p></div> </div> </div> <div class="reply info"> <a class="comment-781701 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-781701 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-781701"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1710" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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73E
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E
en
E. Morrowindows
<div class="problem-statement"><div class="header"><div class="title">E. Morrowindows</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Vasya plays The Elder Trolls III: Morrowindows. He has a huge list of items in the inventory, however, there is no limits on the size of things. Vasya does not know the total amount of items but he is sure that are not more than <span class="tex-span"><i>x</i></span> and not less than <span class="tex-span">2</span> items in his inventory. A new patch for the game appeared to view inventory in <span class="tex-span"><i>n</i></span> different modes. Displaying in mode <span class="tex-span"><i>i</i></span> is a partition of all inventory items on pages, each of which (except for maybe the last one) shows exactly <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> items. In addition, each mode shows how many pages <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> is in a complete list. Great! Perhaps this information will be enough for Vasya to find the required number. Moreover, it is very interesting, what is the fewest number of modes in which Vasya can see inventory to determine the number of items in it?</p><p><span class="tex-font-style-bf">Vasya cannot use the information that was received while looking on inventory in some mode for selection of next actions. I. e. Vasya chooses some set of modes first, and then sees all the results and determines the size.</span></p><p>Knowing the number of <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>x</i></span> and assuming that Vasya is very smart, check whether he can uniquely determine the number of items in his inventory, and how many modes he will need to do that if he knows numbers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>x</i></span> and he is able to know number <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> after viewing items in mode <span class="tex-span"><i>i</i></span>.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>x</i></span> (<span class="tex-span">0 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup>, 2 ≤ <i>x</i> ≤ 10<sup class="upper-index">9</sup></span>). The second line contains integers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">9</sup></span>). Some numbers among all <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> may be equal.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Output the fewest amount of modes required to uniquely determine amount of items in the inventory. If there is no solution output <span class="tex-span"> - 1</span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2 4<br/>2 3<br/></pre></div><div class="output"><div class="title">Output</div><pre>2<br/></pre></div><div class="input"><div class="title">Input</div><pre>1 4<br/>2<br/></pre></div><div class="output"><div class="title">Output</div><pre>-1<br/></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the second example Vasya is not able to determine items count uniquely because 3 items, as well as 4 items, can be displayed on two pages.</p></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/73">Codeforces Beta Round 66</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? 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If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="E" data-uuid="ps_b37f1fa8fa5a6f2a5619a7dd987ccd9c87271790"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">E. Morrowindows</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Vasya plays The Elder Trolls III: Morrowindows. He has a huge list of items in the inventory, however, there is no limits on the size of things. Vasya does not know the total amount of items but he is sure that are not more than <span class="tex-span"><i>x</i></span> and not less than <span class="tex-span">2</span> items in his inventory. A new patch for the game appeared to view inventory in <span class="tex-span"><i>n</i></span> different modes. Displaying in mode <span class="tex-span"><i>i</i></span> is a partition of all inventory items on pages, each of which (except for maybe the last one) shows exactly <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> items. In addition, each mode shows how many pages <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> is in a complete list. Great! Perhaps this information will be enough for Vasya to find the required number. Moreover, it is very interesting, what is the fewest number of modes in which Vasya can see inventory to determine the number of items in it?</p><p><span class="tex-font-style-bf">Vasya cannot use the information that was received while looking on inventory in some mode for selection of next actions. I. e. Vasya chooses some set of modes first, and then sees all the results and determines the size.</span></p><p>Knowing the number of <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>x</i></span> and assuming that Vasya is very smart, check whether he can uniquely determine the number of items in his inventory, and how many modes he will need to do that if he knows numbers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>x</i></span> and he is able to know number <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> after viewing items in mode <span class="tex-span"><i>i</i></span>.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>x</i></span> (<span class="tex-span">0 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup>, 2 ≤ <i>x</i> ≤ 10<sup class="upper-index">9</sup></span>). The second line contains integers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">9</sup></span>). Some numbers among all <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> may be equal.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Output the fewest amount of modes required to uniquely determine amount of items in the inventory. If there is no solution output <span class="tex-span"> - 1</span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2 4<br />2 3<br /></pre></div><div class="output"><div class="title">Output</div><pre>2<br /></pre></div><div class="input"><div class="title">Input</div><pre>1 4<br />2<br /></pre></div><div class="output"><div class="title">Output</div><pre>-1<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the second example Vasya is not able to determine items count uniquely because 3 items, as well as 4 items, can be displayed on two pages.</p></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=E]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); 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["Mathematics including integration, differential equations, etc", "Number theory: Euler function, GCD, divisibility, etc"]
["math", "number theory", "*2400"]
https://codeforces.com/blog/entry/1700
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, serif;color: black;"><b>Problem A.</b></span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Let’s call the monster dimension sizes as <i>x<sub>1</sub>, x<sub>2</sub>, x<sub>3</sub></i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">1. <i>O(min(k, x<sub>1</sub> + x<sub>2</sub> + x<sub>3</sub>)) </i>solution</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">We can make at most <i>(x<sub>1</sub> – 1) + (x<sub>2</sub> – 1) + (x<sub>3</sub> – 1)</i> cuttings, so we may assume that <i>k &lt;= x<sub>1</sub> + x<sub>2</sub> + x<sub>3</sub> – 3</i>. For each of the three dimensions we will store an integer <i>a<sub>i</sub></i> – number of cuttings performed through the corresponding dimension. Let’s perform the following actions <i>k</i> times: consider all numbers <i>a<sub>i</sub> </i>which we may increase (<i>a<sub>i</sub> &lt;  x<sub>i</sub> - 1</i>) , call these dimensions “uncompleted”. Select the minimum number <i>a<sub>j</sub></i> among all uncompleted <i>a<sub>i</sub></i> and perform a cut through the corresponding dimension (<i>a<sub>j</sub></i> will be increased by 1 as the result). Now let’s consider the resulting set after <i>k</i> actions: <i>{a<sub>1</sub>, a<sub>2</sub>, a<sub>3</sub>}</i>. Using the described algorithm we grant that the maximum element of this set is as little as possible and the minimum element is as big as possible. Because the sum <i>a<sub>1</sub> + a<sub>2</sub> + a<sub>3</sub> = k</i> is fixed, we get the maximum product <i>(a<sub>1</sub> + 1) * (a<sub>2</sub> + 1) * (a<sub>3</sub> + 1)</i> which is the answer for the problem.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">2. <i>O(1) </i>solution</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Instead of simulation all the <i>k</i> actions we may quickly determine values of numbers <i>a<sub>i</sub></i> after using the algorithm described above.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Let <i>x</i> – the smallest value among <i>(x<sub>i </sub>– 1)</i>. When <i>x * 3 &gt;= k</i> on each of the algorithm iterations all three dimensions will be uncompleted. It means that during the first <i>(k / 3) * 3</i> steps each of numbers <i>a<sub>i</sub></i> will be increased by <i>(k / 3)</i>. Then 0, 1 or 2 numbers <i>a<sub>i</sub></i> will be increased by 1 subject to value of <i>k % 3</i>. So</span><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">, </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">we</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">have</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">found</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">values</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">a<sub>i</sub></span></i><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Otherwise (<i>x * 3 &lt; k</i>) during the first <i>x * 3</i> steps each of <i>a<sub>i</sub></i> will be increased by <i>x</i>. After that we will have at most two uncompleted dimensions which can be processed a similar way (we should choose the minimum value <i>x</i> among the remaining uncompleted dimensions).</span></p> <p><span lang="EN-US"> </span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"><b>Problem B.</b></span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">We may assume that we have exactly <i>n</i> awarded places but some of them give 0 points.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Let’s sort places by amount of points (<i>b<sub>i</sub></i>) and racers by amount of currently gained points (<i>a<sub>i</sub></i>). First let’s find the best place Vasya can reach. In the best case he will get <i>b<sub>0</sub></i> points (where <i>b<sub>0</sub></i> is the greatest number among <i>b<sub>i</sub></i>). So, let the total Vasya’s point is <i>v</i>. Now we should to distribute other prize points to racers so that the number of racers better than Vasya will be minimal. For doing that we are to give maximum number of prizes so that corresponding racers will have less than <i>v </i>points. Note that if we can give <i>k</i> prizes keeping this property, than we can give <i>k</i> “cheapest” prizes too. The following statement is also true: if we can get a prize with <i>t</i> points to racer <i>i</i> and to racer <i>j</i> , <i>a<sub>i</sub> &gt; a<sub>j</sub></i>, then it is better to give this prize to racer <i>i</i>. Formally: if there exists a way to give <i>k</i> prizes where this prize will get racer <i>j</i>, than there exists a way to give <i>k</i> prizes where this prize will get racer <i>i</i>. It can be proven the following way. Consider a way to give <i>k</i> prizes where racer <i>j</i> got prize with <i>t</i> points, racer <i>i</i> – <i>s</i> points or didn’t get prize at all. In the first case we can swap prizes for racers <i>i</i> and <i>j</i>: <i>a<sub>i</sub> &gt; a<sub>j</sub></i> and <i>a<sub>i</sub> + s &lt; v</i> (since racer <i>i</i> have got the prize), so <i>a<sub>j</sub> + s &lt; v</i>, and <i>a<sub>i</sub> + t &lt; v</i> i.e. this change is acceptable. In the second case we can just give the prize <i>t</i> to racer <i>i</i> instead of racer <i>j</i>. In the both cases we get a way to give <i>k</i> prizes where racer <i>i</i> receive prize<i> t</i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Now including this statement we may give prizes to racers using the following greedy algorithm. Let’s begin to give prizes starting from the cheapest one and check the racers starting from the best one (of course excluding Vasya and the best prize). For each prize <i>i</i> we will go through the racers until applicable racer (<i>j</i>) found: <i>b<sub>i</sub> + a<sub>j</sub> &lt; v</i>. If no such racers remain we are unable to give more prizes without violating the rule (racers should have less than <i>v</i> points). In this case we should stop the algorithm and the answer is <i>n – k </i>where <i>k</i> is the number of prizes we have given. If we have found such racer <i>j</i> we can give him prize <i>b<sub>i</sub></i> and go to the next prize. Complexity of this step is <i>O(n)</i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Similarly we can find the worst place for Vasya. For doing that we should give him the cheapest prize (note it may have positive points though). After that we should distribute the prizes iterating over prizes from the largest to cheapest and check racers from the worst to the best one trying to make sum of racer’s points more than <i>v</i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Total complexity of the described algorithm is <i>O(n * log(n))</i> because we have to sort prizes and racers.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"><b>Problem C.</b></span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">It is easy to see that if we put some symbol <i>c</i> at position <i>p</i> of the string <i>s</i> it will not affect symbols at positions (<i>p+2</i>) and greater. So</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">we</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">have a</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">standard</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">DP</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">problem</span><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">. </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">State of the dynamic is described by three parameters: <i>p</i> – the number of already processed symbols (or the index of currently processed symbol of the string), <i>c</i> – the previous symbol, <i>t</i> – the number of allowed symbol changes. To calculate the answer for a state we should choose the best value among all symbols for current position (when <i>t &gt; 0</i>) or just go to the index (<i>p + 1</i>) with current symbol <i>s[p]</i>. Thus we get the followings formulas:</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><i><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">d[n][*][*] = 0</span></i><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">d[p][c][t] = d[p + 1][s[p]][t] + bonus[c][s[p]] </span></i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">when<i> t = 0</i></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">d[p][c][t] = max(d[p + 1][c’][t – (c’ &lt;&gt; s[p])] + bonus[c][c’])</span></i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">where <i>n</i>  is the length of string <i>s</i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Computation complexity of the algorithm is <i>O(n * k * h^2)</i>, where <i>h</i> is the alphabet size (<i>h = 26</i> for current problem).<b></b></span></p></div><div /></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/73" class="notice" style="text-decoration: none;">Codeforces Beta Round 66</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-368-1700").click(function() { var that = this; 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line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/I_Remember_Olya_ashmelev"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/I_Remember_Olya_ashmelev"> I_Remember_Olya_ashmelev </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Apr/11/2011 05:48">12 years ago</span> </li> <li> <a href="/blog/entry/1700#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1700#comments"> 2 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; 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left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/time_14_07" style="position: relative;"> <img src='https://userpic.codeforces.org/1315340/avatar/caa9501b0e90f618.jpg'/> </a> <div><a href="/profile/time_14_07" title="Newbie time_14_07" class="rated-user user-gray">time_14_07</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/24/2020 15:40">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-628513" href="?#comment-628513" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="628513" class="CommentVoteFrame" data-commentRating="-8" data-commentUserId="1315340" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">-8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-628513"> <div class="moveup"> <div class="ttypography"><p>Please anyone explain problem C DP problem. It's states and recurrence relation.</p></div> </div> </div> <div class="reply info"> <a class="comment-628513 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-628513 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-628513"> <li> <div class="comment"> <table class="comment-table" commentId="781701" commentParentId="628513"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/arman.t" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/arman.t" title="Expert arman.t" class="rated-user user-blue">arman.t</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/18/2021 20:45">2 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-781701" href="?#comment-781701" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-628513" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="781701" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="208522" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-781701"> <div class="moveup"> <div class="ttypography"><p>You can take a look at solution <a href="/contest/73/submission/113434456" title="Submission 113434456 by arman.t">113434456</a>, I think it's a bit more intuitive than in the Editorial.</p></div> </div> </div> <div class="reply info"> <a class="comment-781701 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-781701 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-781701"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1710" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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73F
73
F
en
F. Plane of Tanks
<div class="problem-statement"><div class="header"><div class="title">F. Plane of Tanks</div><div class="time-limit"><div class="property-title">time limit per test</div>4 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Vasya plays the Plane of Tanks. The tanks in this game keep trying to finish each other off. But your "Pedalny" is not like that... He just needs to drive in a straight line from point <span class="tex-span"><i>A</i></span> to point B on the plane. Unfortunately, on the same plane are <span class="tex-span"><i>n</i></span> enemy tanks. We shall regard all the tanks as points. At the initial moment of time Pedalny is at the point <span class="tex-span"><i>A</i></span>. Enemy tanks would be happy to destroy it immediately, but initially their turrets are tuned in other directions. Specifically, for each tank we know the initial rotation of the turret <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> (the angle in radians relative to the <span class="tex-span"><i>OX</i></span> axis in the counterclockwise direction) and the maximum speed of rotation of the turret <span class="tex-span"><i>w</i><sub class="lower-index"><i>i</i></sub></span> (radians per second). If at any point of time a tank turret will be aimed precisely at the tank Pedalny, then the enemy fires and it never misses. Pedalny can endure no more than <span class="tex-span"><i>k</i></span> shots. Gun reloading takes very much time, so we can assume that every enemy will produce no more than one shot. Your task is to determine what minimum speed of <span class="tex-span"><i>v</i></span> Pedalny must have to get to the point <span class="tex-span"><i>B</i></span>. It is believed that Pedalny is able to instantly develop the speed of <span class="tex-span"><i>v</i></span>, and the first <span class="tex-span"><i>k</i></span> shots at him do not reduce the speed and do not change the coordinates of the tank.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains 4 numbers – the coordinates of points <span class="tex-span"><i>A</i></span> and <span class="tex-span"><i>B</i></span> (in meters), the points do not coincide. On the second line number <span class="tex-span"><i>n</i></span> is given (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">4</sup></span>). It is the number of enemy tanks. Each of the following <span class="tex-span"><i>n</i></span> lines contain the coordinates of a corresponding tank <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub>, <i>y</i><sub class="lower-index"><i>i</i></sub></span> and its parameters <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>w</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">0 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 2π</span>, <span class="tex-span">0 ≤ <i>w</i><sub class="lower-index"><i>i</i></sub> ≤ 100</span>). Numbers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>w</i><sub class="lower-index"><i>i</i></sub></span> contain at most 5 digits after the decimal point. All coordinates are integers and their absolute values do not exceed <span class="tex-span">10<sup class="upper-index">5</sup></span>. Enemy tanks can rotate a turret in the clockwise as well as in the counterclockwise direction at the angular speed of not more than <span class="tex-span"><i>w</i><sub class="lower-index"><i>i</i></sub></span>. It is guaranteed that each of the enemy tanks will need at least <span class="tex-span">0.1</span> seconds to aim at any point of the segment <span class="tex-span"><i>AB</i></span> and each of the enemy tanks is posistioned no closer than <span class="tex-span">0.1</span> meters to line <span class="tex-span"><i>AB</i></span>. On the last line is given the number <span class="tex-span"><i>k</i></span> (<span class="tex-span">0 ≤ <i>k</i> ≤ <i>n</i></span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single number with absolute or relative error no more than <span class="tex-span">10<sup class="upper-index"> - 4</sup></span> — the minimum required speed of Pedalny in meters per second.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>0 0 10 0<br/>1<br/>5 -5 4.71238 1<br/>0<br/></pre></div><div class="output"><div class="title">Output</div><pre>4.2441<br/></pre></div><div class="input"><div class="title">Input</div><pre>0 0 10 0<br/>1<br/>5 -5 4.71238 1<br/>1<br/></pre></div><div class="output"><div class="title">Output</div><pre>0.0000<br/></pre></div></div></div></div>
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Just register for practice and you will be able to submit solutions. </div> <div style="text-align:center;margin:1em;"> <form action="" method="post"><input type='hidden' name='csrf_token' value='54f22e2f4ff399a5061b40cc97bba6a2'/> <input type="hidden" name="action" value="registerForPractice"/> <input type="submit" name="submit" value="Register for practice" style="padding:0 0.5em;"> </form> </div> </div> </div> <div class="roundbox sidebox ContestVirtualFrame borderTopRound " style=""> <div class="caption titled">&rarr; Virtual participation <i class="sidebar-caption-icon las la-angle-down"></i> <div class="top-links"> </div> </div> <div style=" " data-page-url="/data/sidebarFrames" > <div style="margin:1em;font-size:0.8em;"> Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests. If you've seen these problems, a virtual contest is not for you - solve these problems in the archive. If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="F" data-uuid="ps_910cc2c73dd260688ef15c601b0bf2e71f962c64"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">F. Plane of Tanks</div><div class="time-limit"><div class="property-title">time limit per test</div>4 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Vasya plays the Plane of Tanks. The tanks in this game keep trying to finish each other off. But your &quot;Pedalny&quot; is not like that... He just needs to drive in a straight line from point <span class="tex-span"><i>A</i></span> to point B on the plane. Unfortunately, on the same plane are <span class="tex-span"><i>n</i></span> enemy tanks. We shall regard all the tanks as points. At the initial moment of time Pedalny is at the point <span class="tex-span"><i>A</i></span>. Enemy tanks would be happy to destroy it immediately, but initially their turrets are tuned in other directions. Specifically, for each tank we know the initial rotation of the turret <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> (the angle in radians relative to the <span class="tex-span"><i>OX</i></span> axis in the counterclockwise direction) and the maximum speed of rotation of the turret <span class="tex-span"><i>w</i><sub class="lower-index"><i>i</i></sub></span> (radians per second). If at any point of time a tank turret will be aimed precisely at the tank Pedalny, then the enemy fires and it never misses. Pedalny can endure no more than <span class="tex-span"><i>k</i></span> shots. Gun reloading takes very much time, so we can assume that every enemy will produce no more than one shot. Your task is to determine what minimum speed of <span class="tex-span"><i>v</i></span> Pedalny must have to get to the point <span class="tex-span"><i>B</i></span>. It is believed that Pedalny is able to instantly develop the speed of <span class="tex-span"><i>v</i></span>, and the first <span class="tex-span"><i>k</i></span> shots at him do not reduce the speed and do not change the coordinates of the tank.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains 4 numbers – the coordinates of points <span class="tex-span"><i>A</i></span> and <span class="tex-span"><i>B</i></span> (in meters), the points do not coincide. On the second line number <span class="tex-span"><i>n</i></span> is given (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">4</sup></span>). It is the number of enemy tanks. Each of the following <span class="tex-span"><i>n</i></span> lines contain the coordinates of a corresponding tank <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub>, <i>y</i><sub class="lower-index"><i>i</i></sub></span> and its parameters <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>w</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">0 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 2π</span>, <span class="tex-span">0 ≤ <i>w</i><sub class="lower-index"><i>i</i></sub> ≤ 100</span>). Numbers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>w</i><sub class="lower-index"><i>i</i></sub></span> contain at most 5 digits after the decimal point. All coordinates are integers and their absolute values do not exceed <span class="tex-span">10<sup class="upper-index">5</sup></span>. Enemy tanks can rotate a turret in the clockwise as well as in the counterclockwise direction at the angular speed of not more than <span class="tex-span"><i>w</i><sub class="lower-index"><i>i</i></sub></span>. It is guaranteed that each of the enemy tanks will need at least <span class="tex-span">0.1</span> seconds to aim at any point of the segment <span class="tex-span"><i>AB</i></span> and each of the enemy tanks is posistioned no closer than <span class="tex-span">0.1</span> meters to line <span class="tex-span"><i>AB</i></span>. On the last line is given the number <span class="tex-span"><i>k</i></span> (<span class="tex-span">0 ≤ <i>k</i> ≤ <i>n</i></span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single number with absolute or relative error no more than <span class="tex-span">10<sup class="upper-index"> - 4</sup></span> — the minimum required speed of Pedalny in meters per second.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>0 0 10 0<br />1<br />5 -5 4.71238 1<br />0<br /></pre></div><div class="output"><div class="title">Output</div><pre>4.2441<br /></pre></div><div class="input"><div class="title">Input</div><pre>0 0 10 0<br />1<br />5 -5 4.71238 1<br />1<br /></pre></div><div class="output"><div class="title">Output</div><pre>0.0000<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=F]"); 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["Brute force", "Geometry, computational geometry"]
["brute force", "geometry", "*2900"]
https://codeforces.com/blog/entry/1700
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, serif;color: black;"><b>Problem A.</b></span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Let’s call the monster dimension sizes as <i>x<sub>1</sub>, x<sub>2</sub>, x<sub>3</sub></i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">1. <i>O(min(k, x<sub>1</sub> + x<sub>2</sub> + x<sub>3</sub>)) </i>solution</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">We can make at most <i>(x<sub>1</sub> – 1) + (x<sub>2</sub> – 1) + (x<sub>3</sub> – 1)</i> cuttings, so we may assume that <i>k &lt;= x<sub>1</sub> + x<sub>2</sub> + x<sub>3</sub> – 3</i>. For each of the three dimensions we will store an integer <i>a<sub>i</sub></i> – number of cuttings performed through the corresponding dimension. Let’s perform the following actions <i>k</i> times: consider all numbers <i>a<sub>i</sub> </i>which we may increase (<i>a<sub>i</sub> &lt;  x<sub>i</sub> - 1</i>) , call these dimensions “uncompleted”. Select the minimum number <i>a<sub>j</sub></i> among all uncompleted <i>a<sub>i</sub></i> and perform a cut through the corresponding dimension (<i>a<sub>j</sub></i> will be increased by 1 as the result). Now let’s consider the resulting set after <i>k</i> actions: <i>{a<sub>1</sub>, a<sub>2</sub>, a<sub>3</sub>}</i>. Using the described algorithm we grant that the maximum element of this set is as little as possible and the minimum element is as big as possible. Because the sum <i>a<sub>1</sub> + a<sub>2</sub> + a<sub>3</sub> = k</i> is fixed, we get the maximum product <i>(a<sub>1</sub> + 1) * (a<sub>2</sub> + 1) * (a<sub>3</sub> + 1)</i> which is the answer for the problem.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">2. <i>O(1) </i>solution</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Instead of simulation all the <i>k</i> actions we may quickly determine values of numbers <i>a<sub>i</sub></i> after using the algorithm described above.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Let <i>x</i> – the smallest value among <i>(x<sub>i </sub>– 1)</i>. When <i>x * 3 &gt;= k</i> on each of the algorithm iterations all three dimensions will be uncompleted. It means that during the first <i>(k / 3) * 3</i> steps each of numbers <i>a<sub>i</sub></i> will be increased by <i>(k / 3)</i>. Then 0, 1 or 2 numbers <i>a<sub>i</sub></i> will be increased by 1 subject to value of <i>k % 3</i>. So</span><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">, </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">we</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">have</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">found</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">values</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">a<sub>i</sub></span></i><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Otherwise (<i>x * 3 &lt; k</i>) during the first <i>x * 3</i> steps each of <i>a<sub>i</sub></i> will be increased by <i>x</i>. After that we will have at most two uncompleted dimensions which can be processed a similar way (we should choose the minimum value <i>x</i> among the remaining uncompleted dimensions).</span></p> <p><span lang="EN-US"> </span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"><b>Problem B.</b></span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">We may assume that we have exactly <i>n</i> awarded places but some of them give 0 points.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Let’s sort places by amount of points (<i>b<sub>i</sub></i>) and racers by amount of currently gained points (<i>a<sub>i</sub></i>). First let’s find the best place Vasya can reach. In the best case he will get <i>b<sub>0</sub></i> points (where <i>b<sub>0</sub></i> is the greatest number among <i>b<sub>i</sub></i>). So, let the total Vasya’s point is <i>v</i>. Now we should to distribute other prize points to racers so that the number of racers better than Vasya will be minimal. For doing that we are to give maximum number of prizes so that corresponding racers will have less than <i>v </i>points. Note that if we can give <i>k</i> prizes keeping this property, than we can give <i>k</i> “cheapest” prizes too. The following statement is also true: if we can get a prize with <i>t</i> points to racer <i>i</i> and to racer <i>j</i> , <i>a<sub>i</sub> &gt; a<sub>j</sub></i>, then it is better to give this prize to racer <i>i</i>. Formally: if there exists a way to give <i>k</i> prizes where this prize will get racer <i>j</i>, than there exists a way to give <i>k</i> prizes where this prize will get racer <i>i</i>. It can be proven the following way. Consider a way to give <i>k</i> prizes where racer <i>j</i> got prize with <i>t</i> points, racer <i>i</i> – <i>s</i> points or didn’t get prize at all. In the first case we can swap prizes for racers <i>i</i> and <i>j</i>: <i>a<sub>i</sub> &gt; a<sub>j</sub></i> and <i>a<sub>i</sub> + s &lt; v</i> (since racer <i>i</i> have got the prize), so <i>a<sub>j</sub> + s &lt; v</i>, and <i>a<sub>i</sub> + t &lt; v</i> i.e. this change is acceptable. In the second case we can just give the prize <i>t</i> to racer <i>i</i> instead of racer <i>j</i>. In the both cases we get a way to give <i>k</i> prizes where racer <i>i</i> receive prize<i> t</i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Now including this statement we may give prizes to racers using the following greedy algorithm. Let’s begin to give prizes starting from the cheapest one and check the racers starting from the best one (of course excluding Vasya and the best prize). For each prize <i>i</i> we will go through the racers until applicable racer (<i>j</i>) found: <i>b<sub>i</sub> + a<sub>j</sub> &lt; v</i>. If no such racers remain we are unable to give more prizes without violating the rule (racers should have less than <i>v</i> points). In this case we should stop the algorithm and the answer is <i>n – k </i>where <i>k</i> is the number of prizes we have given. If we have found such racer <i>j</i> we can give him prize <i>b<sub>i</sub></i> and go to the next prize. Complexity of this step is <i>O(n)</i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Similarly we can find the worst place for Vasya. For doing that we should give him the cheapest prize (note it may have positive points though). After that we should distribute the prizes iterating over prizes from the largest to cheapest and check racers from the worst to the best one trying to make sum of racer’s points more than <i>v</i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Total complexity of the described algorithm is <i>O(n * log(n))</i> because we have to sort prizes and racers.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"><b>Problem C.</b></span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">It is easy to see that if we put some symbol <i>c</i> at position <i>p</i> of the string <i>s</i> it will not affect symbols at positions (<i>p+2</i>) and greater. So</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">we</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">have a</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">standard</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">DP</span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"> </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">problem</span><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">. </span><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">State of the dynamic is described by three parameters: <i>p</i> – the number of already processed symbols (or the index of currently processed symbol of the string), <i>c</i> – the previous symbol, <i>t</i> – the number of allowed symbol changes. To calculate the answer for a state we should choose the best value among all symbols for current position (when <i>t &gt; 0</i>) or just go to the index (<i>p + 1</i>) with current symbol <i>s[p]</i>. Thus we get the followings formulas:</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><i><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">d[n][*][*] = 0</span></i><span style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">d[p][c][t] = d[p + 1][s[p]][t] + bonus[c][s[p]] </span></i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">when<i> t = 0</i></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">d[p][c][t] = max(d[p + 1][c’][t – (c’ &lt;&gt; s[p])] + bonus[c][c’])</span></i><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;"></span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">where <i>n</i>  is the length of string <i>s</i>.</span></p> <p style="margin-top: 12.0pt;margin-right: 0.0cm;margin-bottom: 12.0pt;margin-left: 0.0cm;"><span lang="EN-US" style="font-size: 12.0pt;font-family: &quot;Times New Roman&quot; , serif;color: black;">Computation complexity of the algorithm is <i>O(n * k * h^2)</i>, where <i>h</i> is the alphabet size (<i>h = 26</i> for current problem).<b></b></span></p></div><div /></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/73" class="notice" style="text-decoration: none;">Codeforces Beta Round 66</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-368-1700").click(function() { var that = this; 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line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/I_Remember_Olya_ashmelev"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/I_Remember_Olya_ashmelev"> I_Remember_Olya_ashmelev </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Apr/11/2011 05:48">12 years ago</span> </li> <li> <a href="/blog/entry/1700#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1700#comments"> 2 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; 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left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/time_14_07" style="position: relative;"> <img src='https://userpic.codeforces.org/1315340/avatar/caa9501b0e90f618.jpg'/> </a> <div><a href="/profile/time_14_07" title="Newbie time_14_07" class="rated-user user-gray">time_14_07</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/24/2020 15:40">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-628513" href="?#comment-628513" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="628513" class="CommentVoteFrame" data-commentRating="-8" data-commentUserId="1315340" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">-8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-628513"> <div class="moveup"> <div class="ttypography"><p>Please anyone explain problem C DP problem. It's states and recurrence relation.</p></div> </div> </div> <div class="reply info"> <a class="comment-628513 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-628513 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-628513"> <li> <div class="comment"> <table class="comment-table" commentId="781701" commentParentId="628513"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/arman.t" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/arman.t" title="Expert arman.t" class="rated-user user-blue">arman.t</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/18/2021 20:45">2 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-781701" href="?#comment-781701" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-628513" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="781701" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="208522" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-781701"> <div class="moveup"> <div class="ttypography"><p>You can take a look at solution <a href="/contest/73/submission/113434456" title="Submission 113434456 by arman.t">113434456</a>, I think it's a bit more intuitive than in the Editorial.</p></div> </div> </div> <div class="reply info"> <a class="comment-781701 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-781701 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-781701"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1710" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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A. Room Leader
<div class="problem-statement"><div class="header"><div class="title">A. Room Leader</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Let us remind you part of the rules of Codeforces. The given rules slightly simplified, use the problem statement as a formal document.</p><p>In the beginning of the round the contestants are divided into rooms. Each room contains exactly <span class="tex-span"><i>n</i></span> participants. During the contest the participants are suggested to solve five problems, <span class="tex-span"><i>A</i></span>, <span class="tex-span"><i>B</i></span>, <span class="tex-span"><i>C</i></span>, <span class="tex-span"><i>D</i></span> and <span class="tex-span"><i>E</i></span>. For each of these problem, depending on when the given problem was solved and whether it was solved at all, the participants receive some points. Besides, a contestant can perform hacks on other contestants. For each successful hack a contestant earns <span class="tex-span">100</span> points, for each unsuccessful hack a contestant loses <span class="tex-span">50</span> points. The number of points for every contestant is represented by the sum of points he has received from all his problems, including hacks.</p><p>You are suggested to determine the leader for some room; the leader is a participant who has maximum points.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains an integer <span class="tex-span"><i>n</i></span>, which is the number of contestants in the room (<span class="tex-span">1 ≤ <i>n</i> ≤ 50</span>). The next <span class="tex-span"><i>n</i></span> lines contain the participants of a given room. The <span class="tex-span"><i>i</i></span>-th line has the format of "<span class="tex-span"><i>handle</i><sub class="lower-index"><i>i</i></sub></span> <span class="tex-span"><i>plus</i><sub class="lower-index"><i>i</i></sub></span> <span class="tex-span"><i>minus</i><sub class="lower-index"><i>i</i></sub></span> <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span> <span class="tex-span"><i>d</i><sub class="lower-index"><i>i</i></sub></span> <span class="tex-span"><i>e</i><sub class="lower-index"><i>i</i></sub></span>" — it is the handle of a contestant, the number of successful hacks, the number of unsuccessful hacks and the number of points he has received from problems <span class="tex-span"><i>A</i></span>, <span class="tex-span"><i>B</i></span>, <span class="tex-span"><i>C</i></span>, <span class="tex-span"><i>D</i></span>, <span class="tex-span"><i>E</i></span> correspondingly. The handle of each participant consists of Latin letters, digits and underscores and has the length from <span class="tex-span">1</span> to <span class="tex-span">20</span> characters. There are the following limitations imposed upon the numbers: </p><ul> <li> <span class="tex-span">0 ≤ <i>plus</i><sub class="lower-index"><i>i</i></sub>, <i>minus</i><sub class="lower-index"><i>i</i></sub> ≤ 50</span>; </li><li> <span class="tex-span">150 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 500</span> or <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub> = 0</span>, if problem <span class="tex-span"><i>A</i></span> is not solved; </li><li> <span class="tex-span">300 ≤ <i>b</i><sub class="lower-index"><i>i</i></sub> ≤ 1000</span> or <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub> = 0</span>, if problem <span class="tex-span"><i>B</i></span> is not solved; </li><li> <span class="tex-span">450 ≤ <i>c</i><sub class="lower-index"><i>i</i></sub> ≤ 1500</span> or <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub> = 0</span>, if problem <span class="tex-span"><i>C</i></span> is not solved; </li><li> <span class="tex-span">600 ≤ <i>d</i><sub class="lower-index"><i>i</i></sub> ≤ 2000</span> or <span class="tex-span"><i>d</i><sub class="lower-index"><i>i</i></sub> = 0</span>, if problem <span class="tex-span"><i>D</i></span> is not solved; </li><li> <span class="tex-span">750 ≤ <i>e</i><sub class="lower-index"><i>i</i></sub> ≤ 2500</span> or <span class="tex-span"><i>e</i><sub class="lower-index"><i>i</i></sub> = 0</span>, if problem <span class="tex-span"><i>E</i></span> is not solved. </li></ul><p>All the numbers are integer. All the participants have different handles. It is guaranteed that there is exactly one leader in the room (i.e. there are no two participants with the maximal number of points).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print on the single line the handle of the room leader.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>5<br/>Petr 3 1 490 920 1000 1200 0<br/>tourist 2 0 490 950 1100 1400 0<br/>Egor 7 0 480 900 950 0 1000<br/>c00lH4x0R 0 10 150 0 0 0 0<br/>some_participant 2 1 450 720 900 0 0<br/></pre></div><div class="output"><div class="title">Output</div><pre>tourist</pre></div></div></div><div class="note"><div class="section-title">Note</div><p>The number of points that each participant from the example earns, are as follows: </p><ul> <li> <span class="tex-font-style-tt">Petr</span> — <span class="tex-span">3860</span> </li><li> <span class="tex-font-style-tt">tourist</span> — <span class="tex-span">4140</span> </li><li> <span class="tex-font-style-tt">Egor</span> — <span class="tex-span">4030</span> </li><li> <span class="tex-font-style-tt">c00lH4x0R</span> — <span class="tex-span"> - 350</span> </li><li> <span class="tex-font-style-tt">some_participant</span> — <span class="tex-span">2220</span> </li></ul><p>Thus, the leader of the room is <span class="tex-font-style-tt">tourist</span>.</p></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/74">Codeforces Beta Round 68</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? 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If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="A" data-uuid="ps_2db7df5d344db7365ca26b103b02fa0370963619"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">A. Room Leader</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Let us remind you part of the rules of Codeforces. The given rules slightly simplified, use the problem statement as a formal document.</p><p>In the beginning of the round the contestants are divided into rooms. Each room contains exactly <span class="tex-span"><i>n</i></span> participants. During the contest the participants are suggested to solve five problems, <span class="tex-span"><i>A</i></span>, <span class="tex-span"><i>B</i></span>, <span class="tex-span"><i>C</i></span>, <span class="tex-span"><i>D</i></span> and <span class="tex-span"><i>E</i></span>. For each of these problem, depending on when the given problem was solved and whether it was solved at all, the participants receive some points. Besides, a contestant can perform hacks on other contestants. For each successful hack a contestant earns <span class="tex-span">100</span> points, for each unsuccessful hack a contestant loses <span class="tex-span">50</span> points. The number of points for every contestant is represented by the sum of points he has received from all his problems, including hacks.</p><p>You are suggested to determine the leader for some room; the leader is a participant who has maximum points.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains an integer <span class="tex-span"><i>n</i></span>, which is the number of contestants in the room (<span class="tex-span">1 ≤ <i>n</i> ≤ 50</span>). The next <span class="tex-span"><i>n</i></span> lines contain the participants of a given room. The <span class="tex-span"><i>i</i></span>-th line has the format of &quot;<span class="tex-span"><i>handle</i><sub class="lower-index"><i>i</i></sub></span> <span class="tex-span"><i>plus</i><sub class="lower-index"><i>i</i></sub></span> <span class="tex-span"><i>minus</i><sub class="lower-index"><i>i</i></sub></span> <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub></span> <span class="tex-span"><i>d</i><sub class="lower-index"><i>i</i></sub></span> <span class="tex-span"><i>e</i><sub class="lower-index"><i>i</i></sub></span>&quot; — it is the handle of a contestant, the number of successful hacks, the number of unsuccessful hacks and the number of points he has received from problems <span class="tex-span"><i>A</i></span>, <span class="tex-span"><i>B</i></span>, <span class="tex-span"><i>C</i></span>, <span class="tex-span"><i>D</i></span>, <span class="tex-span"><i>E</i></span> correspondingly. The handle of each participant consists of Latin letters, digits and underscores and has the length from <span class="tex-span">1</span> to <span class="tex-span">20</span> characters. There are the following limitations imposed upon the numbers: </p><ul> <li> <span class="tex-span">0 ≤ <i>plus</i><sub class="lower-index"><i>i</i></sub>, <i>minus</i><sub class="lower-index"><i>i</i></sub> ≤ 50</span>; </li><li> <span class="tex-span">150 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 500</span> or <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub> = 0</span>, if problem <span class="tex-span"><i>A</i></span> is not solved; </li><li> <span class="tex-span">300 ≤ <i>b</i><sub class="lower-index"><i>i</i></sub> ≤ 1000</span> or <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub> = 0</span>, if problem <span class="tex-span"><i>B</i></span> is not solved; </li><li> <span class="tex-span">450 ≤ <i>c</i><sub class="lower-index"><i>i</i></sub> ≤ 1500</span> or <span class="tex-span"><i>c</i><sub class="lower-index"><i>i</i></sub> = 0</span>, if problem <span class="tex-span"><i>C</i></span> is not solved; </li><li> <span class="tex-span">600 ≤ <i>d</i><sub class="lower-index"><i>i</i></sub> ≤ 2000</span> or <span class="tex-span"><i>d</i><sub class="lower-index"><i>i</i></sub> = 0</span>, if problem <span class="tex-span"><i>D</i></span> is not solved; </li><li> <span class="tex-span">750 ≤ <i>e</i><sub class="lower-index"><i>i</i></sub> ≤ 2500</span> or <span class="tex-span"><i>e</i><sub class="lower-index"><i>i</i></sub> = 0</span>, if problem <span class="tex-span"><i>E</i></span> is not solved. </li></ul><p>All the numbers are integer. All the participants have different handles. It is guaranteed that there is exactly one leader in the room (i.e. there are no two participants with the maximal number of points).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print on the single line the handle of the room leader.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>5<br />Petr 3 1 490 920 1000 1200 0<br />tourist 2 0 490 950 1100 1400 0<br />Egor 7 0 480 900 950 0 1000<br />c00lH4x0R 0 10 150 0 0 0 0<br />some_participant 2 1 450 720 900 0 0<br /></pre></div><div class="output"><div class="title">Output</div><pre>tourist</pre></div></div></div><div class="note"><div class="section-title">Note</div><p>The number of points that each participant from the example earns, are as follows: </p><ul> <li> <span class="tex-font-style-tt">Petr</span> — <span class="tex-span">3860</span> </li><li> <span class="tex-font-style-tt">tourist</span> — <span class="tex-span">4140</span> </li><li> <span class="tex-font-style-tt">Egor</span> — <span class="tex-span">4030</span> </li><li> <span class="tex-font-style-tt">c00lH4x0R</span> — <span class="tex-span"> - 350</span> </li><li> <span class="tex-font-style-tt">some_participant</span> — <span class="tex-span">2220</span> </li></ul><p>Thus, the leader of the room is <span class="tex-font-style-tt">tourist</span>.</p></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=A]"); 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["Implementation problems, programming technics, simulation"]
["implementation", "*1000"]
https://codeforces.com/blog/entry/1735
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left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/ayush19jul" style="position: relative;"> <img src='https://userpic.codeforces.org/2445411/avatar/299d1e7dd0d245e4.jpg'/> </a> <div><a href="/profile/ayush19jul" title="Newbie ayush19jul" class="rated-user user-gray">ayush19jul</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/30/2023 13:42">3 months ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-1042003" href="?#comment-1042003" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="1042003" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2445411" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-1042003"> <div class="moveup"> <div class="ttypography"><p>WTF!!!</p><p>worst editorial ever</p></div> </div> </div> <div class="reply info"> <a class="comment-1042003 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-1042003 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-1042003"> <li> <div class="comment"> <table class="comment-table" commentId="1042019" commentParentId="1042003"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Orifxon" style="position: relative;"> <img src='https://userpic.codeforces.org/2378398/avatar/1080506c7d3bef1.jpg'/> </a> <div><a href="/profile/Orifxon" title="Pupil Orifxon" class="rated-user user-green">Orifxon</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/30/2023 15:02">3 months ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-1042019" href="?#comment-1042019" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-1042003" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="1042019" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="1042019" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2378398" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-1042019"> <div class="moveup"> <div class="ttypography"><p>You are writing comment on the blog that was made 12 years ago</p></div> </div> </div> <div class="reply info"> <a class="comment-1042019 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-1042019 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-1042019"> <li> <div class="comment"> <table class="comment-table" commentId="1042072" commentParentId="1042019"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/adityagamer" style="position: relative;"> <img src='https://userpic.codeforces.org/1443750/avatar/448db22a71a7f0e5.jpg'/> </a> <div><a href="/profile/adityagamer" title="Candidate Master adityagamer" class="rated-user user-violet">adityagamer</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/30/2023 16:41">3 months ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-1042072" href="?#comment-1042072" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-1042019" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="1042072" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1443750" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-1042072"> <div class="moveup"> <div class="ttypography"><p>You too</p></div> </div> </div> <div class="reply info"> <a class="comment-1042072 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-1042072 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-1042072"> </ul> </div> </li> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1745" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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74B
74
B
en
B. Train
<div class="problem-statement"><div class="header"><div class="title">B. Train</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>A stowaway and a controller play the following game. </p><p>The train is represented by <span class="tex-span"><i>n</i></span> wagons which are numbered with positive integers from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span> from the head to the tail. The stowaway and the controller are initially in some two different wagons. Every minute the train can be in one of two conditions — moving or idle. Every minute the players move.</p><p>The controller's move is as follows. The controller has the movement direction — to the train's head or to its tail. During a move the controller moves to the neighbouring wagon correspondingly to its movement direction. If at the end of his move the controller enters the <span class="tex-span">1</span>-st or the <span class="tex-span"><i>n</i></span>-th wagon, that he changes the direction of his movement into the other one. In other words, the controller cyclically goes from the train's head to its tail and back again during all the time of a game, shifting during each move by one wagon. Note, that the controller always have exactly one possible move.</p><p>The stowaway's move depends from the state of the train. If the train is moving, then the stowaway can shift to one of neighbouring wagons or he can stay where he is without moving. If the train is at a station and is idle, then the stowaway leaves the train (i.e. he is now not present in any train wagon) and then, if it is not the terminal train station, he enters the train again into any of <span class="tex-span"><i>n</i></span> wagons (not necessarily into the one he's just left and not necessarily into the neighbouring one). If the train is idle for several minutes then each such minute the stowaway leaves the train and enters it back.</p><p>Let's determine the order of the players' moves. If at the given minute the train is moving, then first the stowaway moves and then the controller does. If at this minute the train is idle, then first the stowaway leaves the train, then the controller moves and then the stowaway enters the train.</p><p>If at some point in time the stowaway and the controller happen to be in one wagon, then the controller wins: he makes the stowaway pay fine. If after a while the stowaway reaches the terminal train station, then the stowaway wins: he simply leaves the station during his move and never returns there again.</p><p>At any moment of time the players know each other's positions. The players play in the optimal way. Specifically, if the controller wins, then the stowaway plays so as to lose as late as possible. As all the possible moves for the controller are determined uniquely, then he is considered to play optimally always. Determine the winner.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains three integers <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>m</i></span> and <span class="tex-span"><i>k</i></span>. They represent the number of wagons in the train, the stowaway's and the controller's initial positions correspondingly (<span class="tex-span">2 ≤ <i>n</i> ≤ 50</span>, <span class="tex-span">1 ≤ <i>m</i>, <i>k</i> ≤ <i>n</i></span>, <span class="tex-span"><i>m</i> ≠ <i>k</i></span>).</p><p>The second line contains the direction in which a controller moves. "to head" means that the controller moves to the train's head and "to tail" means that the controller moves to its tail. It is guaranteed that in the direction in which the controller is moving, there is at least one wagon. Wagon <span class="tex-span">1</span> is the head, and wagon <span class="tex-span"><i>n</i></span> is the tail.</p><p>The third line has the length from <span class="tex-span">1</span> to <span class="tex-span">200</span> and consists of symbols "0" and "1". The <span class="tex-span"><i>i</i></span>-th symbol contains information about the train's state at the <span class="tex-span"><i>i</i></span>-th minute of time. "0" means that in this very minute the train moves and "1" means that the train in this very minute stands idle. The last symbol of the third line is always "1" — that's the terminal train station.</p></div><div class="output-specification"><div class="section-title">Output</div><p>If the stowaway wins, print "Stowaway" without quotes. Otherwise, print "Controller" again without quotes, then, separated by a space, print the number of a minute, at which the stowaway will be caught.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>5 3 2<br/>to head<br/>0001001<br/></pre></div><div class="output"><div class="title">Output</div><pre>Stowaway</pre></div><div class="input"><div class="title">Input</div><pre>3 2 1<br/>to tail<br/>0001<br/></pre></div><div class="output"><div class="title">Output</div><pre>Controller 2</pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="B" data-uuid="ps_89c09480ceda0c5d8a7931f2a3317cdd5dc6e6c2"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">B. Train</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>A stowaway and a controller play the following game. </p><p>The train is represented by <span class="tex-span"><i>n</i></span> wagons which are numbered with positive integers from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span> from the head to the tail. The stowaway and the controller are initially in some two different wagons. Every minute the train can be in one of two conditions — moving or idle. Every minute the players move.</p><p>The controller's move is as follows. The controller has the movement direction — to the train's head or to its tail. During a move the controller moves to the neighbouring wagon correspondingly to its movement direction. If at the end of his move the controller enters the <span class="tex-span">1</span>-st or the <span class="tex-span"><i>n</i></span>-th wagon, that he changes the direction of his movement into the other one. In other words, the controller cyclically goes from the train's head to its tail and back again during all the time of a game, shifting during each move by one wagon. Note, that the controller always have exactly one possible move.</p><p>The stowaway's move depends from the state of the train. If the train is moving, then the stowaway can shift to one of neighbouring wagons or he can stay where he is without moving. If the train is at a station and is idle, then the stowaway leaves the train (i.e. he is now not present in any train wagon) and then, if it is not the terminal train station, he enters the train again into any of <span class="tex-span"><i>n</i></span> wagons (not necessarily into the one he's just left and not necessarily into the neighbouring one). If the train is idle for several minutes then each such minute the stowaway leaves the train and enters it back.</p><p>Let's determine the order of the players' moves. If at the given minute the train is moving, then first the stowaway moves and then the controller does. If at this minute the train is idle, then first the stowaway leaves the train, then the controller moves and then the stowaway enters the train.</p><p>If at some point in time the stowaway and the controller happen to be in one wagon, then the controller wins: he makes the stowaway pay fine. If after a while the stowaway reaches the terminal train station, then the stowaway wins: he simply leaves the station during his move and never returns there again.</p><p>At any moment of time the players know each other's positions. The players play in the optimal way. Specifically, if the controller wins, then the stowaway plays so as to lose as late as possible. As all the possible moves for the controller are determined uniquely, then he is considered to play optimally always. Determine the winner.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains three integers <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>m</i></span> and <span class="tex-span"><i>k</i></span>. They represent the number of wagons in the train, the stowaway's and the controller's initial positions correspondingly (<span class="tex-span">2 ≤ <i>n</i> ≤ 50</span>, <span class="tex-span">1 ≤ <i>m</i>, <i>k</i> ≤ <i>n</i></span>, <span class="tex-span"><i>m</i> ≠ <i>k</i></span>).</p><p>The second line contains the direction in which a controller moves. &quot;to head&quot; means that the controller moves to the train's head and &quot;to tail&quot; means that the controller moves to its tail. It is guaranteed that in the direction in which the controller is moving, there is at least one wagon. Wagon <span class="tex-span">1</span> is the head, and wagon <span class="tex-span"><i>n</i></span> is the tail.</p><p>The third line has the length from <span class="tex-span">1</span> to <span class="tex-span">200</span> and consists of symbols &quot;0&quot; and &quot;1&quot;. The <span class="tex-span"><i>i</i></span>-th symbol contains information about the train's state at the <span class="tex-span"><i>i</i></span>-th minute of time. &quot;0&quot; means that in this very minute the train moves and &quot;1&quot; means that the train in this very minute stands idle. The last symbol of the third line is always &quot;1&quot; — that's the terminal train station.</p></div><div class="output-specification"><div class="section-title">Output</div><p>If the stowaway wins, print &quot;Stowaway&quot; without quotes. Otherwise, print &quot;Controller&quot; again without quotes, then, separated by a space, print the number of a minute, at which the stowaway will be caught.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>5 3 2<br />to head<br />0001001<br /></pre></div><div class="output"><div class="title">Output</div><pre>Stowaway</pre></div><div class="input"><div class="title">Input</div><pre>3 2 1<br />to tail<br />0001<br /></pre></div><div class="output"><div class="title">Output</div><pre>Controller 2</pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=B]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); if (previousStatementText) { if (previousStatementText !== statementText) { $problem.find(".diff-notifier").show(); 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["Dynamic programming", "Games, Sprague\u2013Grundy theorem", "Greedy algorithms"]
["dp", "games", "greedy", "*1500"]
https://codeforces.com/blog/entry/1735
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left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/ayush19jul" style="position: relative;"> <img src='https://userpic.codeforces.org/2445411/avatar/299d1e7dd0d245e4.jpg'/> </a> <div><a href="/profile/ayush19jul" title="Newbie ayush19jul" class="rated-user user-gray">ayush19jul</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/30/2023 13:42">3 months ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-1042003" href="?#comment-1042003" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="1042003" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2445411" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-1042003"> <div class="moveup"> <div class="ttypography"><p>WTF!!!</p><p>worst editorial ever</p></div> </div> </div> <div class="reply info"> <a class="comment-1042003 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-1042003 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-1042003"> <li> <div class="comment"> <table class="comment-table" commentId="1042019" commentParentId="1042003"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Orifxon" style="position: relative;"> <img src='https://userpic.codeforces.org/2378398/avatar/1080506c7d3bef1.jpg'/> </a> <div><a href="/profile/Orifxon" title="Pupil Orifxon" class="rated-user user-green">Orifxon</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/30/2023 15:02">3 months ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-1042019" href="?#comment-1042019" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-1042003" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="1042019" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="1042019" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2378398" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-1042019"> <div class="moveup"> <div class="ttypography"><p>You are writing comment on the blog that was made 12 years ago</p></div> </div> </div> <div class="reply info"> <a class="comment-1042019 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-1042019 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-1042019"> <li> <div class="comment"> <table class="comment-table" commentId="1042072" commentParentId="1042019"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/adityagamer" style="position: relative;"> <img src='https://userpic.codeforces.org/1443750/avatar/448db22a71a7f0e5.jpg'/> </a> <div><a href="/profile/adityagamer" title="Candidate Master adityagamer" class="rated-user user-violet">adityagamer</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/30/2023 16:41">3 months ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-1042072" href="?#comment-1042072" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-1042019" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="1042072" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1443750" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-1042072"> <div class="moveup"> <div class="ttypography"><p>You too</p></div> </div> </div> <div class="reply info"> <a class="comment-1042072 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-1042072 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-1042072"> </ul> </div> </li> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1745" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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C. Chessboard Billiard
<div class="problem-statement"><div class="header"><div class="title">C. Chessboard Billiard</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Let's imagine: there is a chess piece <span class="tex-font-style-it">billiard ball</span>. Its movements resemble the ones of a bishop chess piece. The only difference is that when a billiard ball hits the board's border, it can reflect from it and continue moving.</p><p>More formally, first one of four diagonal directions is chosen and the billiard ball moves in that direction. When it reaches the square located on the board's edge, the billiard ball reflects from it; it changes the direction of its movement by 90 degrees and continues moving. Specifically, having reached a corner square, the billiard ball is reflected twice and starts to move the opposite way. While it moves, the billiard ball can make an infinite number of reflections. At any square of its trajectory the billiard ball can stop and on that the move is considered completed.</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/ec0cdb9bd6054853e9d9c88daebd39399a0de32e.png" style="max-width: 100.0%;max-height: 100.0%;"/> </center><p>It is considered that one billiard ball <span class="tex-span"><i>a</i></span> beats another billiard ball <span class="tex-span"><i>b</i></span> if <span class="tex-span"><i>a</i></span> can reach a point where <span class="tex-span"><i>b</i></span> is located.</p><p>You are suggested to find the maximal number of billiard balls, that pairwise do not beat each other and that can be positioned on a chessboard <span class="tex-span"><i>n</i> × <i>m</i></span> in size.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>m</i></span> (<span class="tex-span">2 ≤ <i>n</i>, <i>m</i> ≤ 10<sup class="upper-index">6</sup></span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single number, the maximum possible number of billiard balls that do not pairwise beat each other.</p><p>Please do not use the <span class="tex-font-style-tt">%lld</span> specificator to read or write 64-bit numbers in C++. It is preferred to use <span class="tex-font-style-tt">cin</span> (also you may use the <span class="tex-font-style-tt">%I64d</span> specificator).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3 4<br/></pre></div><div class="output"><div class="title">Output</div><pre>2</pre></div><div class="input"><div class="title">Input</div><pre>3 3<br/></pre></div><div class="output"><div class="title">Output</div><pre>3</pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="C" data-uuid="ps_ec6400abd11cc9f0598f8badbb610a18e15003da"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. Chessboard Billiard</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Let's imagine: there is a chess piece <span class="tex-font-style-it">billiard ball</span>. Its movements resemble the ones of a bishop chess piece. The only difference is that when a billiard ball hits the board's border, it can reflect from it and continue moving.</p><p>More formally, first one of four diagonal directions is chosen and the billiard ball moves in that direction. When it reaches the square located on the board's edge, the billiard ball reflects from it; it changes the direction of its movement by 90 degrees and continues moving. Specifically, having reached a corner square, the billiard ball is reflected twice and starts to move the opposite way. While it moves, the billiard ball can make an infinite number of reflections. At any square of its trajectory the billiard ball can stop and on that the move is considered completed.</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/ec0cdb9bd6054853e9d9c88daebd39399a0de32e.png" style="max-width: 100.0%;max-height: 100.0%;" /> </center><p>It is considered that one billiard ball <span class="tex-span"><i>a</i></span> beats another billiard ball <span class="tex-span"><i>b</i></span> if <span class="tex-span"><i>a</i></span> can reach a point where <span class="tex-span"><i>b</i></span> is located.</p><p>You are suggested to find the maximal number of billiard balls, that pairwise do not beat each other and that can be positioned on a chessboard <span class="tex-span"><i>n</i> × <i>m</i></span> in size.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>m</i></span> (<span class="tex-span">2 ≤ <i>n</i>, <i>m</i> ≤ 10<sup class="upper-index">6</sup></span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single number, the maximum possible number of billiard balls that do not pairwise beat each other.</p><p>Please do not use the <span class="tex-font-style-tt">%lld</span> specificator to read or write 64-bit numbers in C++. 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["Dfs and similar", "Disjoint set union", "Graphs", "Number theory: Euler function, GCD, divisibility, etc"]
["dfs and similar", "dsu", "graphs", "number theory", "*2100"]
https://codeforces.com/blog/entry/1735
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left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/ayush19jul" style="position: relative;"> <img src='https://userpic.codeforces.org/2445411/avatar/299d1e7dd0d245e4.jpg'/> </a> <div><a href="/profile/ayush19jul" title="Newbie ayush19jul" class="rated-user user-gray">ayush19jul</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/30/2023 13:42">3 months ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-1042003" href="?#comment-1042003" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="1042003" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2445411" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-1042003"> <div class="moveup"> <div class="ttypography"><p>WTF!!!</p><p>worst editorial ever</p></div> </div> </div> <div class="reply info"> <a class="comment-1042003 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-1042003 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-1042003"> <li> <div class="comment"> <table class="comment-table" commentId="1042019" commentParentId="1042003"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Orifxon" style="position: relative;"> <img src='https://userpic.codeforces.org/2378398/avatar/1080506c7d3bef1.jpg'/> </a> <div><a href="/profile/Orifxon" title="Pupil Orifxon" class="rated-user user-green">Orifxon</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/30/2023 15:02">3 months ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-1042019" href="?#comment-1042019" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-1042003" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="1042019" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="1042019" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2378398" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-1042019"> <div class="moveup"> <div class="ttypography"><p>You are writing comment on the blog that was made 12 years ago</p></div> </div> </div> <div class="reply info"> <a class="comment-1042019 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-1042019 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-1042019"> <li> <div class="comment"> <table class="comment-table" commentId="1042072" commentParentId="1042019"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/adityagamer" style="position: relative;"> <img src='https://userpic.codeforces.org/1443750/avatar/448db22a71a7f0e5.jpg'/> </a> <div><a href="/profile/adityagamer" title="Candidate Master adityagamer" class="rated-user user-violet">adityagamer</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/30/2023 16:41">3 months ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-1042072" href="?#comment-1042072" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-1042019" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="1042072" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1443750" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-1042072"> <div class="moveup"> <div class="ttypography"><p>You too</p></div> </div> </div> <div class="reply info"> <a class="comment-1042072 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-1042072 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-1042072"> </ul> </div> </li> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1745" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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74D
74
D
en
D. Hanger
<div class="problem-statement"><div class="header"><div class="title">D. Hanger</div><div class="time-limit"><div class="property-title">time limit per test</div>4 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>In one very large and very respectable company there is a cloakroom with a coat hanger. It is represented by <span class="tex-span"><i>n</i></span> hooks, positioned in a row. The hooks are numbered with positive integers from 1 to <span class="tex-span"><i>n</i></span> from the left to the right.</p><p>The company workers have a very complicated work schedule. At the beginning of a work day all the employees are not there and the coat hanger in the cloakroom is empty. At some moments of time the employees arrive and some of them leave.</p><p>When some employee arrives, he hangs his cloak on one of the available hooks. To be of as little discomfort to his colleagues as possible, the hook where the coat will hang, is chosen like this. First the employee chooses the longest segment among available hooks following in a row. If there are several of such segments, then he chooses the one closest to the right. After that the coat is hung on the hook located in the middle of this segment. If the segment has an even number of hooks, then among two central hooks we choose the one closest to the right.</p><p>When an employee leaves, he takes his coat. As all the company workers deeply respect each other, no one takes somebody else's coat.</p><p>From time to time the director of this respectable company gets bored and he sends his secretary to see how many coats hang on the coat hanger from the <span class="tex-span"><i>i</i></span>-th to the <span class="tex-span"><i>j</i></span>-th hook inclusive. And this whim is always to be fulfilled, otherwise the director gets angry and has a mental breakdown.</p><p>Not to spend too much time traversing from the director's office to the cloakroom and back again, the secretary asked you to write a program, emulating the company cloakroom's work.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>q</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">9</sup></span>, <span class="tex-span">1 ≤ <i>q</i> ≤ 10<sup class="upper-index">5</sup></span>), which are the number of hooks on the hanger and the number of requests correspondingly. Then follow <span class="tex-span"><i>q</i></span> lines with requests, sorted according to time. The request of the type "<span class="tex-span">0</span> <span class="tex-span"><i>i</i></span> <span class="tex-span"><i>j</i></span>" (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>j</i> ≤ <i>n</i></span>) — is the director's request. The input data has at least one director's request. In all other cases the request contains a positive integer not exceeding <span class="tex-span">10<sup class="upper-index">9</sup></span> — an employee identificator. Each odd appearance of the identificator of an employee in the request list is his arrival. Each even one is his leaving. All employees have distinct identificators. When any employee arrives, there is always at least one free hook.</p></div><div class="output-specification"><div class="section-title">Output</div><p>For each director's request in the input data print a single number on a single line — the number of coats hanging on the hooks from the <span class="tex-span"><i>i</i></span>-th one to the <span class="tex-span"><i>j</i></span>-th one inclusive.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>9 11<br/>1<br/>2<br/>0 5 8<br/>1<br/>1<br/>3<br/>0 3 8<br/>9<br/>0 6 9<br/>6<br/>0 1 9<br/></pre></div><div class="output"><div class="title">Output</div><pre>2<br/>3<br/>2<br/>5<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="D" data-uuid="ps_5b7d79f44e99cc71a9c4453b3465168ffc5c6614"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">D. Hanger</div><div class="time-limit"><div class="property-title">time limit per test</div>4 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>In one very large and very respectable company there is a cloakroom with a coat hanger. It is represented by <span class="tex-span"><i>n</i></span> hooks, positioned in a row. The hooks are numbered with positive integers from 1 to <span class="tex-span"><i>n</i></span> from the left to the right.</p><p>The company workers have a very complicated work schedule. At the beginning of a work day all the employees are not there and the coat hanger in the cloakroom is empty. At some moments of time the employees arrive and some of them leave.</p><p>When some employee arrives, he hangs his cloak on one of the available hooks. To be of as little discomfort to his colleagues as possible, the hook where the coat will hang, is chosen like this. First the employee chooses the longest segment among available hooks following in a row. If there are several of such segments, then he chooses the one closest to the right. After that the coat is hung on the hook located in the middle of this segment. If the segment has an even number of hooks, then among two central hooks we choose the one closest to the right.</p><p>When an employee leaves, he takes his coat. As all the company workers deeply respect each other, no one takes somebody else's coat.</p><p>From time to time the director of this respectable company gets bored and he sends his secretary to see how many coats hang on the coat hanger from the <span class="tex-span"><i>i</i></span>-th to the <span class="tex-span"><i>j</i></span>-th hook inclusive. And this whim is always to be fulfilled, otherwise the director gets angry and has a mental breakdown.</p><p>Not to spend too much time traversing from the director's office to the cloakroom and back again, the secretary asked you to write a program, emulating the company cloakroom's work.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>q</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">9</sup></span>, <span class="tex-span">1 ≤ <i>q</i> ≤ 10<sup class="upper-index">5</sup></span>), which are the number of hooks on the hanger and the number of requests correspondingly. Then follow <span class="tex-span"><i>q</i></span> lines with requests, sorted according to time. The request of the type &quot;<span class="tex-span">0</span> <span class="tex-span"><i>i</i></span> <span class="tex-span"><i>j</i></span>&quot; (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>j</i> ≤ <i>n</i></span>) — is the director's request. The input data has at least one director's request. In all other cases the request contains a positive integer not exceeding <span class="tex-span">10<sup class="upper-index">9</sup></span> — an employee identificator. Each odd appearance of the identificator of an employee in the request list is his arrival. Each even one is his leaving. All employees have distinct identificators. When any employee arrives, there is always at least one free hook.</p></div><div class="output-specification"><div class="section-title">Output</div><p>For each director's request in the input data print a single number on a single line — the number of coats hanging on the hooks from the <span class="tex-span"><i>i</i></span>-th one to the <span class="tex-span"><i>j</i></span>-th one inclusive.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>9 11<br />1<br />2<br />0 5 8<br />1<br />1<br />3<br />0 3 8<br />9<br />0 6 9<br />6<br />0 1 9<br /></pre></div><div class="output"><div class="title">Output</div><pre>2<br />3<br />2<br />5<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=D]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); 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["Heaps, binary search trees, segment trees, hash tables, etc"]
["data structures", "*2400"]
https://codeforces.com/blog/entry/1735
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left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/ayush19jul" style="position: relative;"> <img src='https://userpic.codeforces.org/2445411/avatar/299d1e7dd0d245e4.jpg'/> </a> <div><a href="/profile/ayush19jul" title="Newbie ayush19jul" class="rated-user user-gray">ayush19jul</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/30/2023 13:42">3 months ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-1042003" href="?#comment-1042003" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="1042003" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2445411" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-1042003"> <div class="moveup"> <div class="ttypography"><p>WTF!!!</p><p>worst editorial ever</p></div> </div> </div> <div class="reply info"> <a class="comment-1042003 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-1042003 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-1042003"> <li> <div class="comment"> <table class="comment-table" commentId="1042019" commentParentId="1042003"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Orifxon" style="position: relative;"> <img src='https://userpic.codeforces.org/2378398/avatar/1080506c7d3bef1.jpg'/> </a> <div><a href="/profile/Orifxon" title="Pupil Orifxon" class="rated-user user-green">Orifxon</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/30/2023 15:02">3 months ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-1042019" href="?#comment-1042019" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-1042003" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="1042019" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="1042019" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2378398" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-1042019"> <div class="moveup"> <div class="ttypography"><p>You are writing comment on the blog that was made 12 years ago</p></div> </div> </div> <div class="reply info"> <a class="comment-1042019 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-1042019 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-1042019"> <li> <div class="comment"> <table class="comment-table" commentId="1042072" commentParentId="1042019"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/adityagamer" style="position: relative;"> <img src='https://userpic.codeforces.org/1443750/avatar/448db22a71a7f0e5.jpg'/> </a> <div><a href="/profile/adityagamer" title="Candidate Master adityagamer" class="rated-user user-violet">adityagamer</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/30/2023 16:41">3 months ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-1042072" href="?#comment-1042072" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-1042019" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="1042072" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1443750" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-1042072"> <div class="moveup"> <div class="ttypography"><p>You too</p></div> </div> </div> <div class="reply info"> <a class="comment-1042072 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-1042072 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-1042072"> </ul> </div> </li> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1745" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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74E
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en
E. Shift It!
<div class="problem-statement"><div class="header"><div class="title">E. Shift It!</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>There is a square box <span class="tex-span">6 × 6</span> in size. It contains <span class="tex-span">36</span> chips <span class="tex-span">1 × 1</span> in size. Those chips contain 36 different characters — "<span class="tex-font-style-tt">0</span>"-"<span class="tex-font-style-tt">9</span>" and "<span class="tex-font-style-tt">A</span>"-"<span class="tex-font-style-tt">Z</span>". There is exactly one chip with each character.</p><p>You are allowed to make the following operations: you may choose one of <span class="tex-span">6</span> rows or one of <span class="tex-span">6</span> columns and cyclically shift the chips there to one position to the left or to the right (for the row) or upwards or downwards (for the column). Those operations are allowed to perform several times. </p><p>To solve the puzzle is to shift the chips using the above described operations so that they were written in the increasing order (exactly equal to the right picture). An example of solving the puzzle is shown on a picture below.</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/2a692c7742758fb73f054ef438bd545382d6b500.png" style="max-width: 100.0%;max-height: 100.0%;"/> </center><p>Write a program that finds the sequence of operations that solves the puzzle. That sequence <span class="tex-font-style-bf">should not necessarily be shortest</span>, but you should not exceed the limit of <span class="tex-span">10000</span> operations. It is guaranteed that the solution always exists.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The input data are represented by 6 lines containing 6 characters each. They are the puzzle's initial position. Those lines contain each character from the string "<span class="tex-font-style-tt">0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ</span>" exactly once.</p></div><div class="output-specification"><div class="section-title">Output</div><p>On the first line print number <span class="tex-span"><i>n</i></span>, which is the number of operations. On the next <span class="tex-span"><i>n</i></span> lines print the sequence of operations one per line. An operation is described by a word consisting of two characters. The first character shows the direction where the row or the column will be shifted. The possible directions are "<span class="tex-font-style-tt">L</span>", "<span class="tex-font-style-tt">R</span>" (to the left, to the right correspondingly, we shift a row), "<span class="tex-font-style-tt">U</span>", "<span class="tex-font-style-tt">D</span>" (upwards, downwards correspondingly, we shift a column). The second character is the number of the row (or the column), it is an integer from "<span class="tex-font-style-tt">1</span>" to "<span class="tex-font-style-tt">6</span>". The rows are numbered from the top to the bottom, the columns are numbered from the left to the right.</p><p>The number of operations should not exceed <span class="tex-span">10<sup class="upper-index">4</sup></span>. If there are several solutions, print any of them.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>01W345<br/>729AB6<br/>CD8FGH<br/>IJELMN<br/>OPKRST<br/>UVQXYZ<br/></pre></div><div class="output"><div class="title">Output</div><pre>2<br/>R2<br/>U3<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="E" data-uuid="ps_3d973155b84ee04ad1dd8dcd82cde03703d16951"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">E. Shift It!</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>There is a square box <span class="tex-span">6 × 6</span> in size. It contains <span class="tex-span">36</span> chips <span class="tex-span">1 × 1</span> in size. Those chips contain 36 different characters — &quot;<span class="tex-font-style-tt">0</span>&quot;-&quot;<span class="tex-font-style-tt">9</span>&quot; and &quot;<span class="tex-font-style-tt">A</span>&quot;-&quot;<span class="tex-font-style-tt">Z</span>&quot;. There is exactly one chip with each character.</p><p>You are allowed to make the following operations: you may choose one of <span class="tex-span">6</span> rows or one of <span class="tex-span">6</span> columns and cyclically shift the chips there to one position to the left or to the right (for the row) or upwards or downwards (for the column). Those operations are allowed to perform several times. </p><p>To solve the puzzle is to shift the chips using the above described operations so that they were written in the increasing order (exactly equal to the right picture). An example of solving the puzzle is shown on a picture below.</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/2a692c7742758fb73f054ef438bd545382d6b500.png" style="max-width: 100.0%;max-height: 100.0%;" /> </center><p>Write a program that finds the sequence of operations that solves the puzzle. That sequence <span class="tex-font-style-bf">should not necessarily be shortest</span>, but you should not exceed the limit of <span class="tex-span">10000</span> operations. It is guaranteed that the solution always exists.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The input data are represented by 6 lines containing 6 characters each. They are the puzzle's initial position. Those lines contain each character from the string &quot;<span class="tex-font-style-tt">0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ</span>&quot; exactly once.</p></div><div class="output-specification"><div class="section-title">Output</div><p>On the first line print number <span class="tex-span"><i>n</i></span>, which is the number of operations. On the next <span class="tex-span"><i>n</i></span> lines print the sequence of operations one per line. An operation is described by a word consisting of two characters. The first character shows the direction where the row or the column will be shifted. The possible directions are &quot;<span class="tex-font-style-tt">L</span>&quot;, &quot;<span class="tex-font-style-tt">R</span>&quot; (to the left, to the right correspondingly, we shift a row), &quot;<span class="tex-font-style-tt">U</span>&quot;, &quot;<span class="tex-font-style-tt">D</span>&quot; (upwards, downwards correspondingly, we shift a column). The second character is the number of the row (or the column), it is an integer from &quot;<span class="tex-font-style-tt">1</span>&quot; to &quot;<span class="tex-font-style-tt">6</span>&quot;. The rows are numbered from the top to the bottom, the columns are numbered from the left to the right.</p><p>The number of operations should not exceed <span class="tex-span">10<sup class="upper-index">4</sup></span>. If there are several solutions, print any of them.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>01W345<br />729AB6<br />CD8FGH<br />IJELMN<br />OPKRST<br />UVQXYZ<br /></pre></div><div class="output"><div class="title">Output</div><pre>2<br />R2<br />U3<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=E]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); if (previousStatementText) { if (previousStatementText !== statementText) { $problem.find(".diff-notifier").show(); $problem.find(".diff-notifier-close").click(function() { Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60); $problem.find(".diff-notifier").hide(); }); $problem.find("a.view-changes").click(function() { $.post("/data/diff", {action: "getDiff", a: previousStatementText, b: statementText}, function (result) { if (result["success"] === "true") { Codeforces.facebox(".diff-popup", "//codeforces.org/s/73366"); 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["Constructive algorithms"]
["constructive algorithms", "*2800"]
https://codeforces.com/blog/entry/1735
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left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/ayush19jul" style="position: relative;"> <img src='https://userpic.codeforces.org/2445411/avatar/299d1e7dd0d245e4.jpg'/> </a> <div><a href="/profile/ayush19jul" title="Newbie ayush19jul" class="rated-user user-gray">ayush19jul</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/30/2023 13:42">3 months ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-1042003" href="?#comment-1042003" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="1042003" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2445411" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-1042003"> <div class="moveup"> <div class="ttypography"><p>WTF!!!</p><p>worst editorial ever</p></div> </div> </div> <div class="reply info"> <a class="comment-1042003 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-1042003 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-1042003"> <li> <div class="comment"> <table class="comment-table" commentId="1042019" commentParentId="1042003"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Orifxon" style="position: relative;"> <img src='https://userpic.codeforces.org/2378398/avatar/1080506c7d3bef1.jpg'/> </a> <div><a href="/profile/Orifxon" title="Pupil Orifxon" class="rated-user user-green">Orifxon</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/30/2023 15:02">3 months ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-1042019" href="?#comment-1042019" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-1042003" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="1042019" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="1042019" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2378398" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-1042019"> <div class="moveup"> <div class="ttypography"><p>You are writing comment on the blog that was made 12 years ago</p></div> </div> </div> <div class="reply info"> <a class="comment-1042019 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-1042019 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-1042019"> <li> <div class="comment"> <table class="comment-table" commentId="1042072" commentParentId="1042019"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/adityagamer" style="position: relative;"> <img src='https://userpic.codeforces.org/1443750/avatar/448db22a71a7f0e5.jpg'/> </a> <div><a href="/profile/adityagamer" title="Candidate Master adityagamer" class="rated-user user-violet">adityagamer</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/30/2023 16:41">3 months ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-1042072" href="?#comment-1042072" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-1042019" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="1042072" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1443750" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-1042072"> <div class="moveup"> <div class="ttypography"><p>You too</p></div> </div> </div> <div class="reply info"> <a class="comment-1042072 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-1042072 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-1042072"> </ul> </div> </li> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1745" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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75A
75
A
en
A. Life Without Zeros
<div class="problem-statement"><div class="header"><div class="title">A. Life Without Zeros</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Can you imagine our life if we removed all zeros from it? For sure we will have many problems.</p><p>In this problem we will have a simple example if we removed all zeros from our life, it's the addition operation. Let's assume you are given this equation <span class="tex-span"><i>a</i> + <i>b</i> = <i>c</i></span>, where <span class="tex-span"><i>a</i></span> and <span class="tex-span"><i>b</i></span> are positive integers, and <span class="tex-span"><i>c</i></span> is the sum of <span class="tex-span"><i>a</i></span> and <span class="tex-span"><i>b</i></span>. Now let's remove all zeros from this equation. Will the equation remain correct after removing all zeros?</p><p>For example if the equation is <span class="tex-span">101 + 102 = 203</span>, if we removed all zeros it will be <span class="tex-span">11 + 12 = 23</span> which is still a correct equation.</p><p>But if the equation is <span class="tex-span">105 + 106 = 211</span>, if we removed all zeros it will be <span class="tex-span">15 + 16 = 211</span> which is not a correct equation.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The input will consist of two lines, the first line will contain the integer <span class="tex-span"><i>a</i></span>, and the second line will contain the integer <span class="tex-span"><i>b</i></span> which are in the equation as described above (<span class="tex-span">1 ≤ <i>a</i>, <i>b</i> ≤ 10<sup class="upper-index">9</sup></span>). There won't be any leading zeros in both. The value of <span class="tex-span"><i>c</i></span> should be calculated as <span class="tex-span"><i>c</i> = <i>a</i> + <i>b</i></span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>The output will be just one line, you should print "<span class="tex-font-style-tt">YES</span>" if the equation will remain correct after removing all zeros, and print "<span class="tex-font-style-tt">NO</span>" otherwise.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>101<br/>102<br/></pre></div><div class="output"><div class="title">Output</div><pre>YES<br/></pre></div><div class="input"><div class="title">Input</div><pre>105<br/>106<br/></pre></div><div class="output"><div class="title">Output</div><pre>NO<br/></pre></div></div></div></div>
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} </style> <div class="roundbox sidebox sidebar-menu borderTopRound " style=""> <div class="caption titled">&rarr; Contest materials <div class="top-links"> </div> </div> <ul> <li> <span> <a href="/blog/entry/1713" title="Codeforces Beta Round #67 (Div. 2)" target="_blank">Announcement</a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="254:255" resourceName="Announcement" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1715" title="Codeforces Beta Round #67 (Div. 2) Editorial" target="_blank">Tutorial #1 <span class="resource-locale">(en)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="841" resourceName="Codeforces Beta Round #67 (Div. 2) Editorial" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1717" title="Codeforces Beta Round #67 (Div. 2), my solutions" target="_blank">Tutorial #2 <span class="resource-locale">(en)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="842" resourceName="Codeforces Beta Round #67 (Div. 2), my solutions" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> </ul> </div></div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li class="current selectedLava"><a href="/contest/75">Problems</a></li> <li><a href="/contest/75/submit">Submit Code</a></li> <li><a href="/contest/75/my">My Submissions</a></li> <li><a href="/contest/75/status">Status</a></li> <li><a href="/contest/75/hacks">Hacks</a></li> <li><a href="/contest/75/room/1">Room</a></li> <li><a href="/contest/75/standings">Standings</a></li> <li><a href="/contest/75/customtest">Custom Invocation</a></li> </ul> </div> <style> #facebox .content:has(.diff-popup) { width: 90vw; 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="A" data-uuid="ps_4c93cd93cfd3e918461bf443217be4d03c9c4e27"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">A. Life Without Zeros</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Can you imagine our life if we removed all zeros from it? For sure we will have many problems.</p><p>In this problem we will have a simple example if we removed all zeros from our life, it's the addition operation. Let's assume you are given this equation <span class="tex-span"><i>a</i> + <i>b</i> = <i>c</i></span>, where <span class="tex-span"><i>a</i></span> and <span class="tex-span"><i>b</i></span> are positive integers, and <span class="tex-span"><i>c</i></span> is the sum of <span class="tex-span"><i>a</i></span> and <span class="tex-span"><i>b</i></span>. Now let's remove all zeros from this equation. Will the equation remain correct after removing all zeros?</p><p>For example if the equation is <span class="tex-span">101 + 102 = 203</span>, if we removed all zeros it will be <span class="tex-span">11 + 12 = 23</span> which is still a correct equation.</p><p>But if the equation is <span class="tex-span">105 + 106 = 211</span>, if we removed all zeros it will be <span class="tex-span">15 + 16 = 211</span> which is not a correct equation.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The input will consist of two lines, the first line will contain the integer <span class="tex-span"><i>a</i></span>, and the second line will contain the integer <span class="tex-span"><i>b</i></span> which are in the equation as described above (<span class="tex-span">1 ≤ <i>a</i>, <i>b</i> ≤ 10<sup class="upper-index">9</sup></span>). There won't be any leading zeros in both. The value of <span class="tex-span"><i>c</i></span> should be calculated as <span class="tex-span"><i>c</i> = <i>a</i> + <i>b</i></span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>The output will be just one line, you should print &quot;<span class="tex-font-style-tt">YES</span>&quot; if the equation will remain correct after removing all zeros, and print &quot;<span class="tex-font-style-tt">NO</span>&quot; otherwise.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>101<br />102<br /></pre></div><div class="output"><div class="title">Output</div><pre>YES<br /></pre></div><div class="input"><div class="title">Input</div><pre>105<br />106<br /></pre></div><div class="output"><div class="title">Output</div><pre>NO<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=A]"); 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["Implementation problems, programming technics, simulation"]
["implementation", "*1000"]
https://codeforces.com/blog/entry/1715
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<a href="/blog/entry/120644">Codeforces Round 899 (Div. 2)</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/Misa-Misa" title="Expert Misa-Misa" class="rated-user user-blue">Misa-Misa</a> &rarr; <a href="/blog/entry/121157">Someone please help me understand this.</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/shivam565" title="Specialist shivam565" class="rated-user user-cyan">shivam565</a> &rarr; <a href="/blog/entry/108348">Total number of subarrays with sum atmost k</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> </ul> </div> <div class="bottom-links"> <table style="width:100%;"> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:right;"> <a href="/recent-actions">Detailed &rarr;</a> </td> </tr> </tbody> </table> </div> </div> </div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li><a href="/profile/ahmed_aly">ahmed_aly</a></li> <li class="current selectedLava"><a href="/blog/ahmed_aly">Blog</a></li> <li><a href="/teams/with/ahmed_aly">Teams</a></li> <li><a href="/submissions/ahmed_aly">Submissions</a></li> <li><a href="/groups/with/ahmed_aly">Groups</a></li> <li><a href="/contests/with/ahmed_aly">Contests</a></li> <li><a href="/contests/writer/ahmed_aly">Problemsetting</a></li> </ul> </div> <div style="margin-top:0;"> <div> <h3><a href="/blog/ahmed_aly" style="text-decoration:none;color:black !important;">ahmed_aly's blog</a></h3> </div> <div style="margin-top:2em;"> <div class="has-topic-id topic" topicId="1715"> <div class="title"> <a href="/blog/entry/1715"> Codeforces Beta Round #67 (Div. 2) Editorial </a> </div> <div class="info" style="position:relative;"> By&nbsp;<a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a>, <span class="format-humantime" title="Apr/13/2011 21:46">12 years ago</span>, <img style="position: relative;top: 5px;" src="//codeforces.org/s/81027/images/flags/24/gb.png" alt="In English" title="In English"/> <span style="position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;"> <div style="margin-top:0.25em;"> </div> </span> </div> <div class="content"> <div class="ttypography"><b>Problem A:</b><br />In this problem you need to do what is written in the statement. You can do it in the following 3 steps:<br />1- Calculate C.<br />2- Remove all zeros from A, B and C.<br />3- Check if the new values form a correct equation.<br /><br /><a href="http://pastebin.com/1cc1xKNW">C++ solution for problem A.</a><br /><br /><br /><b>Problem B:</b><br />This problem is a direct simulation to the rules written in the problem statement.<br />You need to iterate over all actions and parse each one to know the type of the action, and the 2 names X and Y, and if your name is X or Y then update your priority factor with this person with the action corresponding value. And take care about some special names like &quot;post&quot;, &quot;wall&quot;, &quot;commented&quot; and &quot;on&quot;.<br />Then sort all names according to the sorting criteria mentioned in the statement.<br />Just make sure to print all names which are mentioned in the input (excluding yourself), even if the priority factor with you is 0.<br /><br /><a href="http://pastebin.com/cGHAv8qs">C++ solution for problem B.</a><br /><br /><br /><b>Problem C:</b><br />In this problem you will need to generate all common divisors between a and b before answering any query.<br />The first step in this problem is to factorize a and b, you can use the trial division technique which runs in O(sqrt(N)), you can check getFactors function in my solutions.<br />Then using a recursive function you can generate all divisors for a and b from their prime factors, you can check getDivisors function in my solutions.<br />Then intersect the 2 sets of divisors for both to get all common divisors, you can do this in O(N+M) where N and M are the lengths of the 2 sets, and also you can do a trivial O(N*M) intersection algorithm, because the maximum number of divisors is not too big (it's 1344).<br />Now for each query you need to find the largest common divisor which lies in the given range, you can do this by sorting all common divisors and do binary search for the largest one which lies in the given range. Also you can do this using linear search, because the total number of queries is not too big.<br /><br />Also there is much shorter solution for this problem. Here is a hint for it, the GCD between a and b should be dividable by all common divisors of a and b.<br /><br /><a href="http://pastebin.com/zcEGkKhw">C++ solution for problem C (with binary search).</a><br /><a href="http://pastebin.com/Uw4rG7Ar">C++ solution for problem C (without binary search).</a><br /><a href="http://pastebin.com/Nd54H6em">Java solution for problem C (with binary search).</a><br /><br /><br /><b>Problem D:</b><br />This problem is my favorite one in this problem set. Maybe it will be easier to solve this problem if you know how to solve the standard one.<br />But because we can't construct the big array, so we can't apply the standard solution for this problem.<br />Let's see first how to solve the standard problem, the following code solves it for a given array arr with length len:<br /><br />int mx = -(1 &lt;&lt; 30);<br />int sum = 0;<br />for (int j = 0; j &lt; len; j++) {<br />    mx = max(mx, arr[i]); // we need this for the case where all elements in the array are negatives<br />    sum += arr[i];<br />    if (sum &lt; 0)<br />        sum = 0;<br />    else<br />        mx = max(mx, sum);<br />}<br /><br />Now let's solve the big array problem, the first step is to calculate 4 values for each small array:<br />1- The total sum of it, let's call it tot.<br />2- The maximum sum of 0 or more consecutive elements starting from the first element in the array, let's call it lft.<br />3- The maximum sum of 0 or more consecutive elements ending at the last element in the array, let's call it rght.<br />4- The maximum sum of 1 or more consecutive elements, let's call it gen.<br /><br />The final result will be 1 of 2 cases:<br />1- The consecutive elements with the maximum sum will start and end inside the same small array.<br />2- The consecutive elements with the maximum sum will start and end inside different small arrays.<br /><br />For the first case, we can simply pick the maximum gen for all small arrays which exist in the big array.<br />For the second case, we can apply something similar to the standard solution, we will keep a variable called sum, and it's initialized to 0, this will be the maximum sum of 0 or more consecutive elements ending at the last element in the previous small array. Now for each small array, if the maximum possible sum will end in this small array, so it will be sum+lft and maximize over this value (make sure this will be for 1 or more elements). And we need to update sum to be the maximum of the following 3 values:<br />1- sum+tot (we will include all elements of this small array to the old sum).<br />2- rght (we will take the maximum sum ending at the last element in the current small array).<br />3- 0 (we will not take any elements in sum).<br /><br />The running time for this solution will be just for reading the input, in my solutions I have no iterations except for reading the input.<br /><br />You can check my solutions for more clarification.<br /><br /><a href="http://pastebin.com/bsxvF4aC">C++ solution for problem D.</a><br /><a href="http://pastebin.com/k1hzX5XD">Java solution for problem D.</a><br /><br /><br /><b>Problem E:</b><br />The main idea for this problem is not hard, but maybe the hard part is implementing it.<br />First we need to know if the straight line segment between the source and destination points intersect with the island or not. So we will intersect this line segment with all the polygon sides. If there are 2 segments intersect in more than 1 point we will consider as they don't intersect, because it's mentioned in the problem statement that you can move on the island's edge and it will be considered in the sea.<br />Now we have a set of all distinct intersection points of the polygon and the straight line segment between the source and destination points. Because the polygon is convex, this set will contain at most 2 points. We have 3 different cases now:<br />1- This set contains less than 2 points.<br />2- This set contains 2 points and they are on the same polygon side.<br />3- This set contains 2 points and they are not on the same polygon side.<br /><br />In the first 2 cases the result will be simply the length of the straight line segment.<br />In the 3rd case you can do the following:<br />1- Move from the source point to the nearest point of the 2 intersection points.<br />2- You have 3 options here:<br />    a- Move inside the island to the other intersection point.<br />    b- Move in clockwise direction on the island's edge to the other intersection point.<br />    c- Move in anti-clockwise direction on the island's edge to the other intersection point.<br />    First option will be considered moving inside the island, and the other 2 options will be considered moving in the sea.<br />    You should pick the minimum one.<br />3- Move from the 2nd intersection point to the destination point.<br /><br />Another solution:<br />You can construct a graph where the nodes are the source point, the destination point, the intersection points and the polygon corner points. Then add an edge between any 2 points which you can move between them with the corresponding cost. Then run any shortest path algorithm, Floyd Warshall for example.<br /><br />You can check my solutions for more clarification.<br /><br /><a href="http://pastebin.com/7jgsu40r">C++ solution for problem E.</a><br /><a href="http://pastebin.com/cZVCifwt">C++ solution for problem E (with Floyd Warshall).</a></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/75" class="notice" style="text-decoration: none;">Codeforces Beta Round 67 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-229-1715").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "229", blogEntryId: "1715", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces+round+%2367" class="tag notice" style="text-decoration: none;">codeforces round #67</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=editorial" class="tag notice" style="text-decoration: none;">editorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1715"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+44</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1715"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/ahmed_aly"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/ahmed_aly"> ahmed_aly </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Apr/13/2011 21:46">12 years ago</span> </li> <li> <a href="/blog/entry/1715#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1715#comments"> 25 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1725"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (21)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="32752" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/eik0u" style="position: relative;"> <img src='https://userpic.codeforces.org/1231/avatar/7637a0d6900a713b.jpg'/> </a> <div><a href="/profile/eik0u" title="Expert eik0u" class="rated-user user-blue">eik0u</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/13/2011 22:26">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32752" href="?#comment-32752" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32752" class="CommentVoteFrame" data-commentRating="11" data-commentUserId="1231" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+11</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32752"> <div class="moveup"> <div class="ttypography">D is also my favourite problem in this problem set :)<div>And the whole problem set is very nice. It is very diverse: easy implementation, math, dp/classic, geometry. And problems do not require extraodinary knowledge in algorithms.</div><div>This round was very suitable for Div2.</div></div> </div> </div> <div class="reply info"> <a class="comment-32752 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32752 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32752"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32770" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/iman_MC" style="position: relative;"> <img src='https://userpic.codeforces.org/2447/avatar/b2ab3e48d7eb8c6.jpg'/> </a> <div><a href="/profile/iman_MC" title="Pupil iman_MC" class="rated-user user-green">iman_MC</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/13/2011 23:43">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32770" href="?#comment-32770" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32770" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="2447" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32770"> <div class="moveup"> <div class="ttypography">Excellent Tutorial's ,  several ways several code for each one , good luck <a class="rated-user user-orange" href="../../profile/ahmed_aly" title="Major ahmed_aly">ahmed_aly</a></div> </div> </div> <div class="reply info"> <a class="comment-32770 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32770 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32770"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32800" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Egor" style="position: relative;"> <img src='https://userpic.codeforces.org/838/avatar/6976bef0cdef7d5c.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/Egor" title="International Grandmaster Egor" class="rated-user user-red">Egor</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 01:30">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32800" href="?#comment-32800" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32800" class="CommentVoteFrame" data-commentRating="4" data-commentUserId="838" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+4</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32800"> <div class="moveup"> <div class="ttypography">(In English)<div><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;">Very nice contest</span><div style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;">B can be also solved using regexps</div></div><div style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;"><br /></div><div style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;">Also in Java we use List, Vector is deprecated ;)</div></div> </div> </div> <div class="reply info"> <a class="comment-32800 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32800 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32800"> <li> <div class="comment"> <table class="comment-table" commentId="32801" commentParentId="32800"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 01:56">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32801" href="?#comment-32801" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32800" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="32801" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="32801" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32801"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">Thanks, but I'm not very good Java coder. :)</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-32801 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32801 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32801"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32844" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ACCEPT" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/ACCEPT" title="Unrated, ACCEPT" class="rated-user user-black">ACCEPT</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 16:02">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32844" href="?#comment-32844" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32844" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14879" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32844"> <div class="moveup"> <div class="ttypography">thank's for your nice contest and tutorial.<div>I have a question for problem E:</div><div>why your algo is correct?</div></div> </div> </div> <div class="reply info"> <a class="comment-32844 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32844 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32844"> <li> <div class="comment"> <table class="comment-table" commentId="32913" commentParentId="32844"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 23:46">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32913" href="?#comment-32913" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32844" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32913" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32913"> <div class="moveup"> <div class="ttypography">Because you can only move to safe points, so you don't have any other choice.</div> </div> </div> <div class="reply info"> <a class="comment-32913 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32913 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32913"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32855" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/novkostya" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/novkostya" title="Expert novkostya" class="rated-user user-blue">novkostya</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 18:30">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32855" href="?#comment-32855" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32855" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5985" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32855"> <div class="moveup"> <div class="ttypography">(C++ solution for problem C)<br />std::back_inserter(cd) seems to be more applicable than std::inserter(cd, cd.begin())</div> </div> </div> <div class="reply info"> <a class="comment-32855 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32855 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32855"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32861" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/lantimilan" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/lantimilan" title="Expert lantimilan" class="rated-user user-blue">lantimilan</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 21:03">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32861" href="?#comment-32861" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32861" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="15561" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32861"> <div class="moveup"> <div class="ttypography">The c++ code for problem A has integer overflow, since a and b can be up to 999999999, c=a+b cannot fit into 32-bit int. My solution had the same issue and got hacked.</div> </div> </div> <div class="reply info"> <a class="comment-32861 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32861 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32861"> <li> <div class="comment"> <table class="comment-table" commentId="32863" commentParentId="32861"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Egor" style="position: relative;"> <img src='https://userpic.codeforces.org/838/avatar/6976bef0cdef7d5c.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/Egor" title="International Grandmaster Egor" class="rated-user user-red">Egor</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 21:05">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32863" href="?#comment-32863" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32861" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32863" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="838" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32863"> <div class="moveup"> <div class="ttypography">Actually 1999999998 fits into 32bit signed integer</div> </div> </div> <div class="reply info"> <a class="comment-32863 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32863 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32863"> <li> <div class="comment"> <table class="comment-table" commentId="32891" commentParentId="32863"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/lantimilan" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/lantimilan" title="Expert lantimilan" class="rated-user user-blue">lantimilan</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 22:21">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32891" href="?#comment-32891" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32863" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32891" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="15561" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32891"> <div class="moveup"> <div class="ttypography">That's right. Just realized that my overflow is due to 8999999991, the reverse of 1999999998.</div> </div> </div> <div class="reply info"> <a class="comment-32891 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32891 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32891"> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32868" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/philolo1" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/philolo1" title="Expert philolo1" class="rated-user user-blue">philolo1</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 21:12">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32868" href="?#comment-32868" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32868" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5296" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32868"> <div class="moveup"> <div class="ttypography">what does the instruction factor[name1] do?</div> </div> </div> <div class="reply info"> <a class="comment-32868 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32868 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32868"> <li> <div class="comment"> <table class="comment-table" commentId="32915" commentParentId="32868"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 23:48">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32915" href="?#comment-32915" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32868" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32915" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32915"> <div class="moveup"> <div class="ttypography">Just to make an entry for name1 in the map, and it will be 0. Because I have to print all names even if the factor is 0.<br />If there is no entry for name1, nothing will happen. If there is no entry, it will be the same as factor[name1] = 0.</div> </div> </div> <div class="reply info"> <a class="comment-32915 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32915 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32915"> <li> <div class="comment"> <table class="comment-table" commentId="32937" commentParentId="32915"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/philolo1" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/philolo1" title="Expert philolo1" class="rated-user user-blue">philolo1</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 00:51">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32937" href="?#comment-32937" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32915" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32937" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5296" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32937"> <div class="moveup"> <div class="ttypography">interesting, I just did map.find()==map.end(), but this is much cooler.</div> </div> </div> <div class="reply info"> <a class="comment-32937 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32937 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32937"> <li> <div class="comment"> <table class="comment-table" commentId="32946" commentParentId="32937"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/smilitude" style="position: relative;"> <img src='https://userpic.codeforces.org/68/avatar/e81e4a6fe0f7bdd8.jpg'/> </a> <div><a href="/profile/smilitude" title="Expert smilitude" class="rated-user user-blue">smilitude</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 02:12">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32946" href="?#comment-32946" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32937" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32946" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="68" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32946"> <div class="moveup"> <div class="ttypography">It's actually safer that way. If you search with if( map[ name1 ] ), every time you do the query, the size of the map increases by 1. Try this - <br /> <pre> map&lt; int,int &gt; one, two; for(int i=1;i&lt;=100; i++) if( one[i] ); for(int i=1;i&lt;=100; i++) if( two.find(i) == two.end() ); cout &lt;&lt; one.size() &lt;&lt; &quot; &quot; &lt;&lt; two.size() &lt;&lt; endl; </pre></div> </div> </div> <div class="reply info"> <a class="comment-32946 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32946 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32946"> <li> <div class="comment"> <table class="comment-table" commentId="32948" commentParentId="32946"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 02:22">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32948" href="?#comment-32948" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32946" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32948" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32948"> <div class="moveup"> <div class="ttypography">In this problem it's the same, because I wanted to make an entry anyway if it doesn't exist.<br />I didn't write this statement as an if condition.</div> </div> </div> <div class="reply info"> <a class="comment-32948 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32948 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32948"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="278325" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/shubhamgoyal__" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/shubhamgoyal__" title="Candidate Master shubhamgoyal__" class="rated-user user-violet">shubhamgoyal__</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/13/2016 17:17">8 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-278325" href="?#comment-278325" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="278325" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="321533" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-278325"> <div class="moveup"> <div class="ttypography"><p>great explanation for problem D!!!</p></div> </div> </div> <div class="reply info"> <a class="comment-278325 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-278325 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-278325"> <li> <div class="comment"> <table class="comment-table" commentId="278326" commentParentId="278325"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/P_Nyagolov" style="position: relative;"> <img src='https://userpic.codeforces.org/239110/avatar/9494c230dc159315.jpg'/> </a> <div><a href="/profile/P_Nyagolov" title="Expert P_Nyagolov" class="rated-user user-blue">P_Nyagolov</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/13/2016 17:26">8 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-278326" href="?#comment-278326" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-278325" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="278326" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="239110" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-278326"> <div class="moveup"> <div class="ttypography"><p>Seriously, guys, what's wrong with you?</p></div> </div> </div> <div class="reply info"> <a class="comment-278326 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-278326 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-278326"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="599691" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Amr-Fahmy" style="position: relative;"> <img src='https://userpic.codeforces.org/858870/avatar/5c5b1d238b408975.jpg'/> </a> <div><a href="/profile/Amr-Fahmy" title="Expert Amr-Fahmy" class="rated-user user-blue">Amr-Fahmy</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/09/2020 07:21">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-599691" href="?#comment-599691" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="599691" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="858870" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-599691"> <div class="moveup"> <div class="ttypography"><p>I am here after 9 years, The explanation of problem D is the best explanation i have ever read on codeforces ! Thank you</p></div> </div> </div> <div class="reply info"> <a class="comment-599691 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-599691 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-599691"> <li> <div class="comment"> <table class="comment-table" commentId="599695" commentParentId="599691"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/09/2020 07:45">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-599695" href="?#comment-599695" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-599691" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="599695" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-599695"> <div class="moveup"> <div class="ttypography"><p>Thanks!</p></div> </div> </div> <div class="reply info"> <a class="comment-599695 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-599695 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-599695"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="612647" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/hereForFun" style="position: relative;"> <img src='https://userpic.codeforces.org/695688/avatar/5e5b50c23f422942.jpg'/> </a> <div><a href="/profile/hereForFun" title="Pupil hereForFun" class="rated-user user-green">hereForFun</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/29/2020 08:06">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-612647" href="?#comment-612647" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="612647" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="695688" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-612647"> <div class="moveup"> <div class="ttypography"><p>Hello! I am here from the a2oj ladder. I received a WA on test case 14 in problem A. When I checked the test case and ran it locally, it is giving the correct answer. Why is the output different here? <a href="https://codeforces.com/contest/75/submission/78440577">https://codeforces.com/contest/75/submission/78440577</a> Here is my submission.</p></div> </div> </div> <div class="reply info"> <a class="comment-612647 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-612647 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-612647"> <li> <div class="comment"> <table class="comment-table" commentId="612658" commentParentId="612647"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/qpwoeirut" style="position: relative;"> <img src='https://userpic.codeforces.org/1165565/avatar/71d9b6b641fb567b.jpg'/> </a> <div><a href="/profile/qpwoeirut" title="Candidate Master qpwoeirut" class="rated-user user-violet">qpwoeirut</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/29/2020 08:56">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-612658" href="?#comment-612658" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-612647" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="612658" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1165565" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-612658"> <div class="moveup"> <div class="ttypography"><p>It looks like you're getting overflow from <code>(digit*pow(10,nonZero))</code>. This can be fixed by using a running place multiplier instead of <code>pow</code>.</p><p>See <a href="/contest/75/submission/78443731" title="Submission 78443731 by qpwoeirut">78443731</a> for an accepted version of your code with that change.</p></div> </div> </div> <div class="reply info"> <a class="comment-612658 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-612658 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-612658"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1725" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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75B
75
B
en
B. Facetook Priority Wall
<div class="problem-statement"><div class="header"><div class="title">B. Facetook Priority Wall</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Facetook is a well known social network website, and it will launch a new feature called Facetook Priority Wall. This feature will sort all posts from your friends according to the priority factor (it will be described).</p><p>This priority factor will be affected by three types of actions: </p><ul> <li> 1. "<span class="tex-font-style-tt"><span class="tex-span"><i>X</i></span> posted on <span class="tex-span"><i>Y</i></span>'s wall</span>" (15 points), </li><li> 2. "<span class="tex-font-style-tt"><span class="tex-span"><i>X</i></span> commented on <span class="tex-span"><i>Y</i></span>'s post</span>" (10 points), </li><li> 3. "<span class="tex-font-style-tt"><span class="tex-span"><i>X</i></span> likes <span class="tex-span"><i>Y</i></span>'s post</span>" (5 points). </li></ul><p><span class="tex-span"><i>X</i></span> and <span class="tex-span"><i>Y</i></span> will be two distinct names. And each action will increase the priority factor between <span class="tex-span"><i>X</i></span> and <span class="tex-span"><i>Y</i></span> (and vice versa) by the above value of points (the priority factor between <span class="tex-span"><i>X</i></span> and <span class="tex-span"><i>Y</i></span> is the same as the priority factor between <span class="tex-span"><i>Y</i></span> and <span class="tex-span"><i>X</i></span>).</p><p>You will be given <span class="tex-span"><i>n</i></span> actions with the above format (without the action number and the number of points), and you have to print all the distinct names in these actions sorted according to the priority factor with you.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains your name. The second line contains an integer <span class="tex-span"><i>n</i></span>, which is the number of actions (<span class="tex-span">1 ≤ <i>n</i> ≤ 100</span>). Then <span class="tex-span"><i>n</i></span> lines follow, it is guaranteed that each one contains exactly 1 action in the format given above. There is exactly one space between each two words in a line, and there are no extra spaces. All the letters are lowercase. All names in the input will consist of at least 1 letter and at most 10 small Latin letters.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span"><i>m</i></span> lines, where <span class="tex-span"><i>m</i></span> is the number of distinct names in the input (excluding yourself). Each line should contain just 1 name. The names should be sorted according to the priority factor with you in the descending order (the highest priority factor should come first). If two or more names have the same priority factor, print them in the alphabetical (lexicographical) order.</p><p>Note, that you should output all the names that are present in the input data (excluding yourself), even if that person has a zero priority factor.</p><p>The lexicographical comparison is performed by the standard "<span class="tex-font-style-tt">&lt;</span>" operator in modern programming languages. The line <span class="tex-span"><i>a</i></span> is lexicographically smaller than the line <span class="tex-span"><i>b</i></span>, if either <span class="tex-span"><i>a</i></span> is the prefix of <span class="tex-span"><i>b</i></span>, or if exists such an <span class="tex-span"><i>i</i></span> (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>min</i>(|<i>a</i>|, |<i>b</i>|)</span>), that <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub> &lt; <i>b</i><sub class="lower-index"><i>i</i></sub></span>, and for any <span class="tex-span"><i>j</i></span> (<span class="tex-span">1 ≤ <i>j</i> &lt; <i>i</i></span>) <span class="tex-span"><i>a</i><sub class="lower-index"><i>j</i></sub> = <i>b</i><sub class="lower-index"><i>j</i></sub></span>, where <span class="tex-span">|<i>a</i>|</span> and <span class="tex-span">|<i>b</i>|</span> stand for the lengths of strings <span class="tex-span"><i>a</i></span> and <span class="tex-span"><i>b</i></span> correspondently.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>ahmed<br/>3<br/>ahmed posted on fatma's wall<br/>fatma commented on ahmed's post<br/>mona likes ahmed's post<br/></pre></div><div class="output"><div class="title">Output</div><pre>fatma<br/>mona<br/></pre></div><div class="input"><div class="title">Input</div><pre>aba<br/>1<br/>likes likes posted's post<br/></pre></div><div class="output"><div class="title">Output</div><pre>likes<br/>posted<br/></pre></div></div></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/75">Codeforces Beta Round 67 (Div. 2)</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? 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If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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} </style> <div class="roundbox sidebox sidebar-menu borderTopRound " style=""> <div class="caption titled">&rarr; Contest materials <div class="top-links"> </div> </div> <ul> <li> <span> <a href="/blog/entry/1713" title="Codeforces Beta Round #67 (Div. 2)" target="_blank">Announcement</a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="254:255" resourceName="Announcement" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1715" title="Codeforces Beta Round #67 (Div. 2) Editorial" target="_blank">Tutorial #1 <span class="resource-locale">(en)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="841" resourceName="Codeforces Beta Round #67 (Div. 2) Editorial" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1717" title="Codeforces Beta Round #67 (Div. 2), my solutions" target="_blank">Tutorial #2 <span class="resource-locale">(en)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="842" resourceName="Codeforces Beta Round #67 (Div. 2), my solutions" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> </ul> </div></div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li class="current selectedLava"><a href="/contest/75">Problems</a></li> <li><a href="/contest/75/submit">Submit Code</a></li> <li><a href="/contest/75/my">My Submissions</a></li> <li><a href="/contest/75/status">Status</a></li> <li><a href="/contest/75/hacks">Hacks</a></li> <li><a href="/contest/75/room/1">Room</a></li> <li><a href="/contest/75/standings">Standings</a></li> <li><a href="/contest/75/customtest">Custom Invocation</a></li> </ul> </div> <style> #facebox .content:has(.diff-popup) { width: 90vw; 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="B" data-uuid="ps_0c2917f234859576d54d239dfe4d6dfe1aff02fc"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">B. Facetook Priority Wall</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Facetook is a well known social network website, and it will launch a new feature called Facetook Priority Wall. This feature will sort all posts from your friends according to the priority factor (it will be described).</p><p>This priority factor will be affected by three types of actions: </p><ul> <li> 1. &quot;<span class="tex-font-style-tt"><span class="tex-span"><i>X</i></span> posted on <span class="tex-span"><i>Y</i></span>'s wall</span>&quot; (15 points), </li><li> 2. &quot;<span class="tex-font-style-tt"><span class="tex-span"><i>X</i></span> commented on <span class="tex-span"><i>Y</i></span>'s post</span>&quot; (10 points), </li><li> 3. &quot;<span class="tex-font-style-tt"><span class="tex-span"><i>X</i></span> likes <span class="tex-span"><i>Y</i></span>'s post</span>&quot; (5 points). </li></ul><p><span class="tex-span"><i>X</i></span> and <span class="tex-span"><i>Y</i></span> will be two distinct names. And each action will increase the priority factor between <span class="tex-span"><i>X</i></span> and <span class="tex-span"><i>Y</i></span> (and vice versa) by the above value of points (the priority factor between <span class="tex-span"><i>X</i></span> and <span class="tex-span"><i>Y</i></span> is the same as the priority factor between <span class="tex-span"><i>Y</i></span> and <span class="tex-span"><i>X</i></span>).</p><p>You will be given <span class="tex-span"><i>n</i></span> actions with the above format (without the action number and the number of points), and you have to print all the distinct names in these actions sorted according to the priority factor with you.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains your name. The second line contains an integer <span class="tex-span"><i>n</i></span>, which is the number of actions (<span class="tex-span">1 ≤ <i>n</i> ≤ 100</span>). Then <span class="tex-span"><i>n</i></span> lines follow, it is guaranteed that each one contains exactly 1 action in the format given above. There is exactly one space between each two words in a line, and there are no extra spaces. All the letters are lowercase. All names in the input will consist of at least 1 letter and at most 10 small Latin letters.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span"><i>m</i></span> lines, where <span class="tex-span"><i>m</i></span> is the number of distinct names in the input (excluding yourself). Each line should contain just 1 name. The names should be sorted according to the priority factor with you in the descending order (the highest priority factor should come first). If two or more names have the same priority factor, print them in the alphabetical (lexicographical) order.</p><p>Note, that you should output all the names that are present in the input data (excluding yourself), even if that person has a zero priority factor.</p><p>The lexicographical comparison is performed by the standard &quot;<span class="tex-font-style-tt">&lt;</span>&quot; operator in modern programming languages. The line <span class="tex-span"><i>a</i></span> is lexicographically smaller than the line <span class="tex-span"><i>b</i></span>, if either <span class="tex-span"><i>a</i></span> is the prefix of <span class="tex-span"><i>b</i></span>, or if exists such an <span class="tex-span"><i>i</i></span> (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>min</i>(|<i>a</i>|, |<i>b</i>|)</span>), that <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub> &lt; <i>b</i><sub class="lower-index"><i>i</i></sub></span>, and for any <span class="tex-span"><i>j</i></span> (<span class="tex-span">1 ≤ <i>j</i> &lt; <i>i</i></span>) <span class="tex-span"><i>a</i><sub class="lower-index"><i>j</i></sub> = <i>b</i><sub class="lower-index"><i>j</i></sub></span>, where <span class="tex-span">|<i>a</i>|</span> and <span class="tex-span">|<i>b</i>|</span> stand for the lengths of strings <span class="tex-span"><i>a</i></span> and <span class="tex-span"><i>b</i></span> correspondently.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>ahmed<br />3<br />ahmed posted on fatma's wall<br />fatma commented on ahmed's post<br />mona likes ahmed's post<br /></pre></div><div class="output"><div class="title">Output</div><pre>fatma<br />mona<br /></pre></div><div class="input"><div class="title">Input</div><pre>aba<br />1<br />likes likes posted's post<br /></pre></div><div class="output"><div class="title">Output</div><pre>likes<br />posted<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=B]"); 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["Parsing expression grammar", "Implementation problems, programming technics, simulation", "Prefix- and Z-functions, suffix structures, Knuth\u2013Morris\u2013Pratt algorithm, etc"]
["expression parsing", "implementation", "strings", "*1500"]
https://codeforces.com/blog/entry/1715
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<a href="/blog/entry/120644">Codeforces Round 899 (Div. 2)</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/Misa-Misa" title="Expert Misa-Misa" class="rated-user user-blue">Misa-Misa</a> &rarr; <a href="/blog/entry/121157">Someone please help me understand this.</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/shivam565" title="Specialist shivam565" class="rated-user user-cyan">shivam565</a> &rarr; <a href="/blog/entry/108348">Total number of subarrays with sum atmost k</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> </ul> </div> <div class="bottom-links"> <table style="width:100%;"> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:right;"> <a href="/recent-actions">Detailed &rarr;</a> </td> </tr> </tbody> </table> </div> </div> </div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li><a href="/profile/ahmed_aly">ahmed_aly</a></li> <li class="current selectedLava"><a href="/blog/ahmed_aly">Blog</a></li> <li><a href="/teams/with/ahmed_aly">Teams</a></li> <li><a href="/submissions/ahmed_aly">Submissions</a></li> <li><a href="/groups/with/ahmed_aly">Groups</a></li> <li><a href="/contests/with/ahmed_aly">Contests</a></li> <li><a href="/contests/writer/ahmed_aly">Problemsetting</a></li> </ul> </div> <div style="margin-top:0;"> <div> <h3><a href="/blog/ahmed_aly" style="text-decoration:none;color:black !important;">ahmed_aly's blog</a></h3> </div> <div style="margin-top:2em;"> <div class="has-topic-id topic" topicId="1715"> <div class="title"> <a href="/blog/entry/1715"> Codeforces Beta Round #67 (Div. 2) Editorial </a> </div> <div class="info" style="position:relative;"> By&nbsp;<a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a>, <span class="format-humantime" title="Apr/13/2011 21:46">12 years ago</span>, <img style="position: relative;top: 5px;" src="//codeforces.org/s/81027/images/flags/24/gb.png" alt="In English" title="In English"/> <span style="position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;"> <div style="margin-top:0.25em;"> </div> </span> </div> <div class="content"> <div class="ttypography"><b>Problem A:</b><br />In this problem you need to do what is written in the statement. You can do it in the following 3 steps:<br />1- Calculate C.<br />2- Remove all zeros from A, B and C.<br />3- Check if the new values form a correct equation.<br /><br /><a href="http://pastebin.com/1cc1xKNW">C++ solution for problem A.</a><br /><br /><br /><b>Problem B:</b><br />This problem is a direct simulation to the rules written in the problem statement.<br />You need to iterate over all actions and parse each one to know the type of the action, and the 2 names X and Y, and if your name is X or Y then update your priority factor with this person with the action corresponding value. And take care about some special names like &quot;post&quot;, &quot;wall&quot;, &quot;commented&quot; and &quot;on&quot;.<br />Then sort all names according to the sorting criteria mentioned in the statement.<br />Just make sure to print all names which are mentioned in the input (excluding yourself), even if the priority factor with you is 0.<br /><br /><a href="http://pastebin.com/cGHAv8qs">C++ solution for problem B.</a><br /><br /><br /><b>Problem C:</b><br />In this problem you will need to generate all common divisors between a and b before answering any query.<br />The first step in this problem is to factorize a and b, you can use the trial division technique which runs in O(sqrt(N)), you can check getFactors function in my solutions.<br />Then using a recursive function you can generate all divisors for a and b from their prime factors, you can check getDivisors function in my solutions.<br />Then intersect the 2 sets of divisors for both to get all common divisors, you can do this in O(N+M) where N and M are the lengths of the 2 sets, and also you can do a trivial O(N*M) intersection algorithm, because the maximum number of divisors is not too big (it's 1344).<br />Now for each query you need to find the largest common divisor which lies in the given range, you can do this by sorting all common divisors and do binary search for the largest one which lies in the given range. Also you can do this using linear search, because the total number of queries is not too big.<br /><br />Also there is much shorter solution for this problem. Here is a hint for it, the GCD between a and b should be dividable by all common divisors of a and b.<br /><br /><a href="http://pastebin.com/zcEGkKhw">C++ solution for problem C (with binary search).</a><br /><a href="http://pastebin.com/Uw4rG7Ar">C++ solution for problem C (without binary search).</a><br /><a href="http://pastebin.com/Nd54H6em">Java solution for problem C (with binary search).</a><br /><br /><br /><b>Problem D:</b><br />This problem is my favorite one in this problem set. Maybe it will be easier to solve this problem if you know how to solve the standard one.<br />But because we can't construct the big array, so we can't apply the standard solution for this problem.<br />Let's see first how to solve the standard problem, the following code solves it for a given array arr with length len:<br /><br />int mx = -(1 &lt;&lt; 30);<br />int sum = 0;<br />for (int j = 0; j &lt; len; j++) {<br />    mx = max(mx, arr[i]); // we need this for the case where all elements in the array are negatives<br />    sum += arr[i];<br />    if (sum &lt; 0)<br />        sum = 0;<br />    else<br />        mx = max(mx, sum);<br />}<br /><br />Now let's solve the big array problem, the first step is to calculate 4 values for each small array:<br />1- The total sum of it, let's call it tot.<br />2- The maximum sum of 0 or more consecutive elements starting from the first element in the array, let's call it lft.<br />3- The maximum sum of 0 or more consecutive elements ending at the last element in the array, let's call it rght.<br />4- The maximum sum of 1 or more consecutive elements, let's call it gen.<br /><br />The final result will be 1 of 2 cases:<br />1- The consecutive elements with the maximum sum will start and end inside the same small array.<br />2- The consecutive elements with the maximum sum will start and end inside different small arrays.<br /><br />For the first case, we can simply pick the maximum gen for all small arrays which exist in the big array.<br />For the second case, we can apply something similar to the standard solution, we will keep a variable called sum, and it's initialized to 0, this will be the maximum sum of 0 or more consecutive elements ending at the last element in the previous small array. Now for each small array, if the maximum possible sum will end in this small array, so it will be sum+lft and maximize over this value (make sure this will be for 1 or more elements). And we need to update sum to be the maximum of the following 3 values:<br />1- sum+tot (we will include all elements of this small array to the old sum).<br />2- rght (we will take the maximum sum ending at the last element in the current small array).<br />3- 0 (we will not take any elements in sum).<br /><br />The running time for this solution will be just for reading the input, in my solutions I have no iterations except for reading the input.<br /><br />You can check my solutions for more clarification.<br /><br /><a href="http://pastebin.com/bsxvF4aC">C++ solution for problem D.</a><br /><a href="http://pastebin.com/k1hzX5XD">Java solution for problem D.</a><br /><br /><br /><b>Problem E:</b><br />The main idea for this problem is not hard, but maybe the hard part is implementing it.<br />First we need to know if the straight line segment between the source and destination points intersect with the island or not. So we will intersect this line segment with all the polygon sides. If there are 2 segments intersect in more than 1 point we will consider as they don't intersect, because it's mentioned in the problem statement that you can move on the island's edge and it will be considered in the sea.<br />Now we have a set of all distinct intersection points of the polygon and the straight line segment between the source and destination points. Because the polygon is convex, this set will contain at most 2 points. We have 3 different cases now:<br />1- This set contains less than 2 points.<br />2- This set contains 2 points and they are on the same polygon side.<br />3- This set contains 2 points and they are not on the same polygon side.<br /><br />In the first 2 cases the result will be simply the length of the straight line segment.<br />In the 3rd case you can do the following:<br />1- Move from the source point to the nearest point of the 2 intersection points.<br />2- You have 3 options here:<br />    a- Move inside the island to the other intersection point.<br />    b- Move in clockwise direction on the island's edge to the other intersection point.<br />    c- Move in anti-clockwise direction on the island's edge to the other intersection point.<br />    First option will be considered moving inside the island, and the other 2 options will be considered moving in the sea.<br />    You should pick the minimum one.<br />3- Move from the 2nd intersection point to the destination point.<br /><br />Another solution:<br />You can construct a graph where the nodes are the source point, the destination point, the intersection points and the polygon corner points. Then add an edge between any 2 points which you can move between them with the corresponding cost. Then run any shortest path algorithm, Floyd Warshall for example.<br /><br />You can check my solutions for more clarification.<br /><br /><a href="http://pastebin.com/7jgsu40r">C++ solution for problem E.</a><br /><a href="http://pastebin.com/cZVCifwt">C++ solution for problem E (with Floyd Warshall).</a></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/75" class="notice" style="text-decoration: none;">Codeforces Beta Round 67 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-229-1715").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "229", blogEntryId: "1715", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces+round+%2367" class="tag notice" style="text-decoration: none;">codeforces round #67</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=editorial" class="tag notice" style="text-decoration: none;">editorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1715"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+44</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1715"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/ahmed_aly"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/ahmed_aly"> ahmed_aly </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Apr/13/2011 21:46">12 years ago</span> </li> <li> <a href="/blog/entry/1715#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1715#comments"> 25 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1725"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (21)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="32752" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/eik0u" style="position: relative;"> <img src='https://userpic.codeforces.org/1231/avatar/7637a0d6900a713b.jpg'/> </a> <div><a href="/profile/eik0u" title="Expert eik0u" class="rated-user user-blue">eik0u</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/13/2011 22:26">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32752" href="?#comment-32752" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32752" class="CommentVoteFrame" data-commentRating="11" data-commentUserId="1231" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+11</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32752"> <div class="moveup"> <div class="ttypography">D is also my favourite problem in this problem set :)<div>And the whole problem set is very nice. It is very diverse: easy implementation, math, dp/classic, geometry. And problems do not require extraodinary knowledge in algorithms.</div><div>This round was very suitable for Div2.</div></div> </div> </div> <div class="reply info"> <a class="comment-32752 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32752 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32752"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32770" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/iman_MC" style="position: relative;"> <img src='https://userpic.codeforces.org/2447/avatar/b2ab3e48d7eb8c6.jpg'/> </a> <div><a href="/profile/iman_MC" title="Pupil iman_MC" class="rated-user user-green">iman_MC</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/13/2011 23:43">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32770" href="?#comment-32770" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32770" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="2447" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32770"> <div class="moveup"> <div class="ttypography">Excellent Tutorial's ,  several ways several code for each one , good luck <a class="rated-user user-orange" href="../../profile/ahmed_aly" title="Major ahmed_aly">ahmed_aly</a></div> </div> </div> <div class="reply info"> <a class="comment-32770 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32770 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32770"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32800" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Egor" style="position: relative;"> <img src='https://userpic.codeforces.org/838/avatar/6976bef0cdef7d5c.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/Egor" title="International Grandmaster Egor" class="rated-user user-red">Egor</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 01:30">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32800" href="?#comment-32800" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32800" class="CommentVoteFrame" data-commentRating="4" data-commentUserId="838" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+4</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32800"> <div class="moveup"> <div class="ttypography">(In English)<div><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;">Very nice contest</span><div style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;">B can be also solved using regexps</div></div><div style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;"><br /></div><div style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;">Also in Java we use List, Vector is deprecated ;)</div></div> </div> </div> <div class="reply info"> <a class="comment-32800 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32800 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32800"> <li> <div class="comment"> <table class="comment-table" commentId="32801" commentParentId="32800"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 01:56">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32801" href="?#comment-32801" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32800" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="32801" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="32801" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32801"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">Thanks, but I'm not very good Java coder. :)</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-32801 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32801 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32801"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32844" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ACCEPT" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/ACCEPT" title="Unrated, ACCEPT" class="rated-user user-black">ACCEPT</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 16:02">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32844" href="?#comment-32844" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32844" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14879" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32844"> <div class="moveup"> <div class="ttypography">thank's for your nice contest and tutorial.<div>I have a question for problem E:</div><div>why your algo is correct?</div></div> </div> </div> <div class="reply info"> <a class="comment-32844 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32844 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32844"> <li> <div class="comment"> <table class="comment-table" commentId="32913" commentParentId="32844"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 23:46">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32913" href="?#comment-32913" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32844" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32913" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32913"> <div class="moveup"> <div class="ttypography">Because you can only move to safe points, so you don't have any other choice.</div> </div> </div> <div class="reply info"> <a class="comment-32913 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32913 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32913"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32855" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/novkostya" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/novkostya" title="Expert novkostya" class="rated-user user-blue">novkostya</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 18:30">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32855" href="?#comment-32855" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32855" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5985" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32855"> <div class="moveup"> <div class="ttypography">(C++ solution for problem C)<br />std::back_inserter(cd) seems to be more applicable than std::inserter(cd, cd.begin())</div> </div> </div> <div class="reply info"> <a class="comment-32855 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32855 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32855"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32861" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/lantimilan" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/lantimilan" title="Expert lantimilan" class="rated-user user-blue">lantimilan</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 21:03">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32861" href="?#comment-32861" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32861" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="15561" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32861"> <div class="moveup"> <div class="ttypography">The c++ code for problem A has integer overflow, since a and b can be up to 999999999, c=a+b cannot fit into 32-bit int. My solution had the same issue and got hacked.</div> </div> </div> <div class="reply info"> <a class="comment-32861 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32861 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32861"> <li> <div class="comment"> <table class="comment-table" commentId="32863" commentParentId="32861"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Egor" style="position: relative;"> <img src='https://userpic.codeforces.org/838/avatar/6976bef0cdef7d5c.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/Egor" title="International Grandmaster Egor" class="rated-user user-red">Egor</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 21:05">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32863" href="?#comment-32863" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32861" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32863" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="838" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32863"> <div class="moveup"> <div class="ttypography">Actually 1999999998 fits into 32bit signed integer</div> </div> </div> <div class="reply info"> <a class="comment-32863 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32863 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32863"> <li> <div class="comment"> <table class="comment-table" commentId="32891" commentParentId="32863"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/lantimilan" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/lantimilan" title="Expert lantimilan" class="rated-user user-blue">lantimilan</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 22:21">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32891" href="?#comment-32891" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32863" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32891" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="15561" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32891"> <div class="moveup"> <div class="ttypography">That's right. Just realized that my overflow is due to 8999999991, the reverse of 1999999998.</div> </div> </div> <div class="reply info"> <a class="comment-32891 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32891 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32891"> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32868" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/philolo1" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/philolo1" title="Expert philolo1" class="rated-user user-blue">philolo1</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 21:12">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32868" href="?#comment-32868" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32868" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5296" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32868"> <div class="moveup"> <div class="ttypography">what does the instruction factor[name1] do?</div> </div> </div> <div class="reply info"> <a class="comment-32868 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32868 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32868"> <li> <div class="comment"> <table class="comment-table" commentId="32915" commentParentId="32868"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 23:48">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32915" href="?#comment-32915" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32868" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32915" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32915"> <div class="moveup"> <div class="ttypography">Just to make an entry for name1 in the map, and it will be 0. Because I have to print all names even if the factor is 0.<br />If there is no entry for name1, nothing will happen. If there is no entry, it will be the same as factor[name1] = 0.</div> </div> </div> <div class="reply info"> <a class="comment-32915 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32915 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32915"> <li> <div class="comment"> <table class="comment-table" commentId="32937" commentParentId="32915"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/philolo1" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/philolo1" title="Expert philolo1" class="rated-user user-blue">philolo1</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 00:51">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32937" href="?#comment-32937" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32915" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32937" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5296" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32937"> <div class="moveup"> <div class="ttypography">interesting, I just did map.find()==map.end(), but this is much cooler.</div> </div> </div> <div class="reply info"> <a class="comment-32937 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32937 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32937"> <li> <div class="comment"> <table class="comment-table" commentId="32946" commentParentId="32937"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/smilitude" style="position: relative;"> <img src='https://userpic.codeforces.org/68/avatar/e81e4a6fe0f7bdd8.jpg'/> </a> <div><a href="/profile/smilitude" title="Expert smilitude" class="rated-user user-blue">smilitude</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 02:12">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32946" href="?#comment-32946" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32937" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32946" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="68" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32946"> <div class="moveup"> <div class="ttypography">It's actually safer that way. If you search with if( map[ name1 ] ), every time you do the query, the size of the map increases by 1. Try this - <br /> <pre> map&lt; int,int &gt; one, two; for(int i=1;i&lt;=100; i++) if( one[i] ); for(int i=1;i&lt;=100; i++) if( two.find(i) == two.end() ); cout &lt;&lt; one.size() &lt;&lt; &quot; &quot; &lt;&lt; two.size() &lt;&lt; endl; </pre></div> </div> </div> <div class="reply info"> <a class="comment-32946 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32946 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32946"> <li> <div class="comment"> <table class="comment-table" commentId="32948" commentParentId="32946"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 02:22">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32948" href="?#comment-32948" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32946" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32948" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32948"> <div class="moveup"> <div class="ttypography">In this problem it's the same, because I wanted to make an entry anyway if it doesn't exist.<br />I didn't write this statement as an if condition.</div> </div> </div> <div class="reply info"> <a class="comment-32948 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32948 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32948"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="278325" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/shubhamgoyal__" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/shubhamgoyal__" title="Candidate Master shubhamgoyal__" class="rated-user user-violet">shubhamgoyal__</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/13/2016 17:17">8 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-278325" href="?#comment-278325" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="278325" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="321533" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-278325"> <div class="moveup"> <div class="ttypography"><p>great explanation for problem D!!!</p></div> </div> </div> <div class="reply info"> <a class="comment-278325 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-278325 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-278325"> <li> <div class="comment"> <table class="comment-table" commentId="278326" commentParentId="278325"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/P_Nyagolov" style="position: relative;"> <img src='https://userpic.codeforces.org/239110/avatar/9494c230dc159315.jpg'/> </a> <div><a href="/profile/P_Nyagolov" title="Expert P_Nyagolov" class="rated-user user-blue">P_Nyagolov</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/13/2016 17:26">8 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-278326" href="?#comment-278326" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-278325" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="278326" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="239110" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-278326"> <div class="moveup"> <div class="ttypography"><p>Seriously, guys, what's wrong with you?</p></div> </div> </div> <div class="reply info"> <a class="comment-278326 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-278326 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-278326"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="599691" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Amr-Fahmy" style="position: relative;"> <img src='https://userpic.codeforces.org/858870/avatar/5c5b1d238b408975.jpg'/> </a> <div><a href="/profile/Amr-Fahmy" title="Expert Amr-Fahmy" class="rated-user user-blue">Amr-Fahmy</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/09/2020 07:21">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-599691" href="?#comment-599691" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="599691" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="858870" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-599691"> <div class="moveup"> <div class="ttypography"><p>I am here after 9 years, The explanation of problem D is the best explanation i have ever read on codeforces ! Thank you</p></div> </div> </div> <div class="reply info"> <a class="comment-599691 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-599691 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-599691"> <li> <div class="comment"> <table class="comment-table" commentId="599695" commentParentId="599691"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/09/2020 07:45">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-599695" href="?#comment-599695" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-599691" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="599695" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-599695"> <div class="moveup"> <div class="ttypography"><p>Thanks!</p></div> </div> </div> <div class="reply info"> <a class="comment-599695 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-599695 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-599695"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="612647" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/hereForFun" style="position: relative;"> <img src='https://userpic.codeforces.org/695688/avatar/5e5b50c23f422942.jpg'/> </a> <div><a href="/profile/hereForFun" title="Pupil hereForFun" class="rated-user user-green">hereForFun</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/29/2020 08:06">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-612647" href="?#comment-612647" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="612647" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="695688" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-612647"> <div class="moveup"> <div class="ttypography"><p>Hello! I am here from the a2oj ladder. I received a WA on test case 14 in problem A. When I checked the test case and ran it locally, it is giving the correct answer. Why is the output different here? <a href="https://codeforces.com/contest/75/submission/78440577">https://codeforces.com/contest/75/submission/78440577</a> Here is my submission.</p></div> </div> </div> <div class="reply info"> <a class="comment-612647 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-612647 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-612647"> <li> <div class="comment"> <table class="comment-table" commentId="612658" commentParentId="612647"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/qpwoeirut" style="position: relative;"> <img src='https://userpic.codeforces.org/1165565/avatar/71d9b6b641fb567b.jpg'/> </a> <div><a href="/profile/qpwoeirut" title="Candidate Master qpwoeirut" class="rated-user user-violet">qpwoeirut</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/29/2020 08:56">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-612658" href="?#comment-612658" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-612647" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="612658" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1165565" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-612658"> <div class="moveup"> <div class="ttypography"><p>It looks like you're getting overflow from <code>(digit*pow(10,nonZero))</code>. This can be fixed by using a running place multiplier instead of <code>pow</code>.</p><p>See <a href="/contest/75/submission/78443731" title="Submission 78443731 by qpwoeirut">78443731</a> for an accepted version of your code with that change.</p></div> </div> </div> <div class="reply info"> <a class="comment-612658 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-612658 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-612658"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1725" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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75C
75
C
en
C. Modified GCD
<div class="problem-statement"><div class="header"><div class="title">C. Modified GCD</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Well, here is another math class task. In mathematics, GCD is the greatest common divisor, and it's an easy task to calculate the GCD between two positive integers.</p><p>A common divisor for two positive numbers is a number which both numbers are divisible by.</p><p>But your teacher wants to give you a harder task, in this task you have to find the greatest common divisor <span class="tex-span"><i>d</i></span> between two integers <span class="tex-span"><i>a</i></span> and <span class="tex-span"><i>b</i></span> that is in a given range from <span class="tex-span"><i>low</i></span> to <span class="tex-span"><i>high</i></span> (inclusive), i.e. <span class="tex-span"><i>low</i> ≤ <i>d</i> ≤ <i>high</i></span>. It is possible that there is no common divisor in the given range.</p><p>You will be given the two integers <span class="tex-span"><i>a</i></span> and <span class="tex-span"><i>b</i></span>, then <span class="tex-span"><i>n</i></span> queries. Each query is a range from <span class="tex-span"><i>low</i></span> to <span class="tex-span"><i>high</i></span> and you have to answer each query.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>a</i></span> and <span class="tex-span"><i>b</i></span>, the two integers as described above (<span class="tex-span">1 ≤ <i>a</i>, <i>b</i> ≤ 10<sup class="upper-index">9</sup></span>). The second line contains one integer <span class="tex-span"><i>n</i></span>, the number of queries (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">4</sup></span>). Then <span class="tex-span"><i>n</i></span> lines follow, each line contains one query consisting of two integers, <span class="tex-span"><i>low</i></span> and <span class="tex-span"><i>high</i></span> (<span class="tex-span">1 ≤ <i>low</i> ≤ <i>high</i> ≤ 10<sup class="upper-index">9</sup></span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span"><i>n</i></span> lines. The <span class="tex-span"><i>i</i></span>-th of them should contain the result of the <span class="tex-span"><i>i</i></span>-th query in the input. If there is no common divisor in the given range for any query, you should print <span class="tex-font-style-tt">-1</span> as a result for this query.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>9 27<br/>3<br/>1 5<br/>10 11<br/>9 11<br/></pre></div><div class="output"><div class="title">Output</div><pre>3<br/>-1<br/>9<br/></pre></div></div></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/75">Codeforces Beta Round 67 (Div. 2)</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? 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If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="C" data-uuid="ps_be966a026241b7bfcb35955be845cb582640b9b5"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. Modified GCD</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Well, here is another math class task. In mathematics, GCD is the greatest common divisor, and it's an easy task to calculate the GCD between two positive integers.</p><p>A common divisor for two positive numbers is a number which both numbers are divisible by.</p><p>But your teacher wants to give you a harder task, in this task you have to find the greatest common divisor <span class="tex-span"><i>d</i></span> between two integers <span class="tex-span"><i>a</i></span> and <span class="tex-span"><i>b</i></span> that is in a given range from <span class="tex-span"><i>low</i></span> to <span class="tex-span"><i>high</i></span> (inclusive), i.e. <span class="tex-span"><i>low</i> ≤ <i>d</i> ≤ <i>high</i></span>. It is possible that there is no common divisor in the given range.</p><p>You will be given the two integers <span class="tex-span"><i>a</i></span> and <span class="tex-span"><i>b</i></span>, then <span class="tex-span"><i>n</i></span> queries. Each query is a range from <span class="tex-span"><i>low</i></span> to <span class="tex-span"><i>high</i></span> and you have to answer each query.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>a</i></span> and <span class="tex-span"><i>b</i></span>, the two integers as described above (<span class="tex-span">1 ≤ <i>a</i>, <i>b</i> ≤ 10<sup class="upper-index">9</sup></span>). The second line contains one integer <span class="tex-span"><i>n</i></span>, the number of queries (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">4</sup></span>). Then <span class="tex-span"><i>n</i></span> lines follow, each line contains one query consisting of two integers, <span class="tex-span"><i>low</i></span> and <span class="tex-span"><i>high</i></span> (<span class="tex-span">1 ≤ <i>low</i> ≤ <i>high</i> ≤ 10<sup class="upper-index">9</sup></span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span"><i>n</i></span> lines. The <span class="tex-span"><i>i</i></span>-th of them should contain the result of the <span class="tex-span"><i>i</i></span>-th query in the input. 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["Binary search", "Number theory: Euler function, GCD, divisibility, etc"]
["binary search", "number theory", "*1600"]
https://codeforces.com/blog/entry/1715
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You can do it in the following 3 steps:<br />1- Calculate C.<br />2- Remove all zeros from A, B and C.<br />3- Check if the new values form a correct equation.<br /><br /><a href="http://pastebin.com/1cc1xKNW">C++ solution for problem A.</a><br /><br /><br /><b>Problem B:</b><br />This problem is a direct simulation to the rules written in the problem statement.<br />You need to iterate over all actions and parse each one to know the type of the action, and the 2 names X and Y, and if your name is X or Y then update your priority factor with this person with the action corresponding value. And take care about some special names like &quot;post&quot;, &quot;wall&quot;, &quot;commented&quot; and &quot;on&quot;.<br />Then sort all names according to the sorting criteria mentioned in the statement.<br />Just make sure to print all names which are mentioned in the input (excluding yourself), even if the priority factor with you is 0.<br /><br /><a href="http://pastebin.com/cGHAv8qs">C++ solution for problem B.</a><br /><br /><br /><b>Problem C:</b><br />In this problem you will need to generate all common divisors between a and b before answering any query.<br />The first step in this problem is to factorize a and b, you can use the trial division technique which runs in O(sqrt(N)), you can check getFactors function in my solutions.<br />Then using a recursive function you can generate all divisors for a and b from their prime factors, you can check getDivisors function in my solutions.<br />Then intersect the 2 sets of divisors for both to get all common divisors, you can do this in O(N+M) where N and M are the lengths of the 2 sets, and also you can do a trivial O(N*M) intersection algorithm, because the maximum number of divisors is not too big (it's 1344).<br />Now for each query you need to find the largest common divisor which lies in the given range, you can do this by sorting all common divisors and do binary search for the largest one which lies in the given range. Also you can do this using linear search, because the total number of queries is not too big.<br /><br />Also there is much shorter solution for this problem. Here is a hint for it, the GCD between a and b should be dividable by all common divisors of a and b.<br /><br /><a href="http://pastebin.com/zcEGkKhw">C++ solution for problem C (with binary search).</a><br /><a href="http://pastebin.com/Uw4rG7Ar">C++ solution for problem C (without binary search).</a><br /><a href="http://pastebin.com/Nd54H6em">Java solution for problem C (with binary search).</a><br /><br /><br /><b>Problem D:</b><br />This problem is my favorite one in this problem set. Maybe it will be easier to solve this problem if you know how to solve the standard one.<br />But because we can't construct the big array, so we can't apply the standard solution for this problem.<br />Let's see first how to solve the standard problem, the following code solves it for a given array arr with length len:<br /><br />int mx = -(1 &lt;&lt; 30);<br />int sum = 0;<br />for (int j = 0; j &lt; len; j++) {<br />    mx = max(mx, arr[i]); // we need this for the case where all elements in the array are negatives<br />    sum += arr[i];<br />    if (sum &lt; 0)<br />        sum = 0;<br />    else<br />        mx = max(mx, sum);<br />}<br /><br />Now let's solve the big array problem, the first step is to calculate 4 values for each small array:<br />1- The total sum of it, let's call it tot.<br />2- The maximum sum of 0 or more consecutive elements starting from the first element in the array, let's call it lft.<br />3- The maximum sum of 0 or more consecutive elements ending at the last element in the array, let's call it rght.<br />4- The maximum sum of 1 or more consecutive elements, let's call it gen.<br /><br />The final result will be 1 of 2 cases:<br />1- The consecutive elements with the maximum sum will start and end inside the same small array.<br />2- The consecutive elements with the maximum sum will start and end inside different small arrays.<br /><br />For the first case, we can simply pick the maximum gen for all small arrays which exist in the big array.<br />For the second case, we can apply something similar to the standard solution, we will keep a variable called sum, and it's initialized to 0, this will be the maximum sum of 0 or more consecutive elements ending at the last element in the previous small array. Now for each small array, if the maximum possible sum will end in this small array, so it will be sum+lft and maximize over this value (make sure this will be for 1 or more elements). And we need to update sum to be the maximum of the following 3 values:<br />1- sum+tot (we will include all elements of this small array to the old sum).<br />2- rght (we will take the maximum sum ending at the last element in the current small array).<br />3- 0 (we will not take any elements in sum).<br /><br />The running time for this solution will be just for reading the input, in my solutions I have no iterations except for reading the input.<br /><br />You can check my solutions for more clarification.<br /><br /><a href="http://pastebin.com/bsxvF4aC">C++ solution for problem D.</a><br /><a href="http://pastebin.com/k1hzX5XD">Java solution for problem D.</a><br /><br /><br /><b>Problem E:</b><br />The main idea for this problem is not hard, but maybe the hard part is implementing it.<br />First we need to know if the straight line segment between the source and destination points intersect with the island or not. So we will intersect this line segment with all the polygon sides. If there are 2 segments intersect in more than 1 point we will consider as they don't intersect, because it's mentioned in the problem statement that you can move on the island's edge and it will be considered in the sea.<br />Now we have a set of all distinct intersection points of the polygon and the straight line segment between the source and destination points. Because the polygon is convex, this set will contain at most 2 points. We have 3 different cases now:<br />1- This set contains less than 2 points.<br />2- This set contains 2 points and they are on the same polygon side.<br />3- This set contains 2 points and they are not on the same polygon side.<br /><br />In the first 2 cases the result will be simply the length of the straight line segment.<br />In the 3rd case you can do the following:<br />1- Move from the source point to the nearest point of the 2 intersection points.<br />2- You have 3 options here:<br />    a- Move inside the island to the other intersection point.<br />    b- Move in clockwise direction on the island's edge to the other intersection point.<br />    c- Move in anti-clockwise direction on the island's edge to the other intersection point.<br />    First option will be considered moving inside the island, and the other 2 options will be considered moving in the sea.<br />    You should pick the minimum one.<br />3- Move from the 2nd intersection point to the destination point.<br /><br />Another solution:<br />You can construct a graph where the nodes are the source point, the destination point, the intersection points and the polygon corner points. Then add an edge between any 2 points which you can move between them with the corresponding cost. Then run any shortest path algorithm, Floyd Warshall for example.<br /><br />You can check my solutions for more clarification.<br /><br /><a href="http://pastebin.com/7jgsu40r">C++ solution for problem E.</a><br /><a href="http://pastebin.com/cZVCifwt">C++ solution for problem E (with Floyd Warshall).</a></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/75" class="notice" style="text-decoration: none;">Codeforces Beta Round 67 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-229-1715").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "229", blogEntryId: "1715", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces+round+%2367" class="tag notice" style="text-decoration: none;">codeforces round #67</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=editorial" class="tag notice" style="text-decoration: none;">editorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1715"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+44</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1715"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/ahmed_aly"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/ahmed_aly"> ahmed_aly </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Apr/13/2011 21:46">12 years ago</span> </li> <li> <a href="/blog/entry/1715#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1715#comments"> 25 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1725"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (21)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="32752" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/eik0u" style="position: relative;"> <img src='https://userpic.codeforces.org/1231/avatar/7637a0d6900a713b.jpg'/> </a> <div><a href="/profile/eik0u" title="Expert eik0u" class="rated-user user-blue">eik0u</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/13/2011 22:26">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32752" href="?#comment-32752" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32752" class="CommentVoteFrame" data-commentRating="11" data-commentUserId="1231" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+11</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32752"> <div class="moveup"> <div class="ttypography">D is also my favourite problem in this problem set :)<div>And the whole problem set is very nice. It is very diverse: easy implementation, math, dp/classic, geometry. And problems do not require extraodinary knowledge in algorithms.</div><div>This round was very suitable for Div2.</div></div> </div> </div> <div class="reply info"> <a class="comment-32752 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32752 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32752"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32770" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/iman_MC" style="position: relative;"> <img src='https://userpic.codeforces.org/2447/avatar/b2ab3e48d7eb8c6.jpg'/> </a> <div><a href="/profile/iman_MC" title="Pupil iman_MC" class="rated-user user-green">iman_MC</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/13/2011 23:43">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32770" href="?#comment-32770" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32770" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="2447" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32770"> <div class="moveup"> <div class="ttypography">Excellent Tutorial's ,  several ways several code for each one , good luck <a class="rated-user user-orange" href="../../profile/ahmed_aly" title="Major ahmed_aly">ahmed_aly</a></div> </div> </div> <div class="reply info"> <a class="comment-32770 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32770 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32770"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32800" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Egor" style="position: relative;"> <img src='https://userpic.codeforces.org/838/avatar/6976bef0cdef7d5c.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/Egor" title="International Grandmaster Egor" class="rated-user user-red">Egor</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 01:30">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32800" href="?#comment-32800" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32800" class="CommentVoteFrame" data-commentRating="4" data-commentUserId="838" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+4</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32800"> <div class="moveup"> <div class="ttypography">(In English)<div><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;">Very nice contest</span><div style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;">B can be also solved using regexps</div></div><div style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;"><br /></div><div style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;">Also in Java we use List, Vector is deprecated ;)</div></div> </div> </div> <div class="reply info"> <a class="comment-32800 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32800 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32800"> <li> <div class="comment"> <table class="comment-table" commentId="32801" commentParentId="32800"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 01:56">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32801" href="?#comment-32801" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32800" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="32801" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="32801" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32801"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">Thanks, but I'm not very good Java coder. :)</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-32801 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32801 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32801"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32844" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ACCEPT" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/ACCEPT" title="Unrated, ACCEPT" class="rated-user user-black">ACCEPT</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 16:02">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32844" href="?#comment-32844" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32844" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14879" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32844"> <div class="moveup"> <div class="ttypography">thank's for your nice contest and tutorial.<div>I have a question for problem E:</div><div>why your algo is correct?</div></div> </div> </div> <div class="reply info"> <a class="comment-32844 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32844 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32844"> <li> <div class="comment"> <table class="comment-table" commentId="32913" commentParentId="32844"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 23:46">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32913" href="?#comment-32913" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32844" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32913" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32913"> <div class="moveup"> <div class="ttypography">Because you can only move to safe points, so you don't have any other choice.</div> </div> </div> <div class="reply info"> <a class="comment-32913 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32913 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32913"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32855" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/novkostya" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/novkostya" title="Expert novkostya" class="rated-user user-blue">novkostya</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 18:30">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32855" href="?#comment-32855" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32855" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5985" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32855"> <div class="moveup"> <div class="ttypography">(C++ solution for problem C)<br />std::back_inserter(cd) seems to be more applicable than std::inserter(cd, cd.begin())</div> </div> </div> <div class="reply info"> <a class="comment-32855 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32855 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32855"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32861" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/lantimilan" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/lantimilan" title="Expert lantimilan" class="rated-user user-blue">lantimilan</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 21:03">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32861" href="?#comment-32861" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32861" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="15561" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32861"> <div class="moveup"> <div class="ttypography">The c++ code for problem A has integer overflow, since a and b can be up to 999999999, c=a+b cannot fit into 32-bit int. My solution had the same issue and got hacked.</div> </div> </div> <div class="reply info"> <a class="comment-32861 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32861 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32861"> <li> <div class="comment"> <table class="comment-table" commentId="32863" commentParentId="32861"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Egor" style="position: relative;"> <img src='https://userpic.codeforces.org/838/avatar/6976bef0cdef7d5c.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/Egor" title="International Grandmaster Egor" class="rated-user user-red">Egor</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 21:05">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32863" href="?#comment-32863" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32861" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32863" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="838" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32863"> <div class="moveup"> <div class="ttypography">Actually 1999999998 fits into 32bit signed integer</div> </div> </div> <div class="reply info"> <a class="comment-32863 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32863 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32863"> <li> <div class="comment"> <table class="comment-table" commentId="32891" commentParentId="32863"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/lantimilan" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/lantimilan" title="Expert lantimilan" class="rated-user user-blue">lantimilan</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 22:21">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32891" href="?#comment-32891" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32863" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32891" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="15561" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32891"> <div class="moveup"> <div class="ttypography">That's right. Just realized that my overflow is due to 8999999991, the reverse of 1999999998.</div> </div> </div> <div class="reply info"> <a class="comment-32891 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32891 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32891"> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32868" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/philolo1" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/philolo1" title="Expert philolo1" class="rated-user user-blue">philolo1</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 21:12">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32868" href="?#comment-32868" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32868" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5296" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32868"> <div class="moveup"> <div class="ttypography">what does the instruction factor[name1] do?</div> </div> </div> <div class="reply info"> <a class="comment-32868 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32868 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32868"> <li> <div class="comment"> <table class="comment-table" commentId="32915" commentParentId="32868"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 23:48">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32915" href="?#comment-32915" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32868" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32915" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32915"> <div class="moveup"> <div class="ttypography">Just to make an entry for name1 in the map, and it will be 0. Because I have to print all names even if the factor is 0.<br />If there is no entry for name1, nothing will happen. If there is no entry, it will be the same as factor[name1] = 0.</div> </div> </div> <div class="reply info"> <a class="comment-32915 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32915 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32915"> <li> <div class="comment"> <table class="comment-table" commentId="32937" commentParentId="32915"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/philolo1" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/philolo1" title="Expert philolo1" class="rated-user user-blue">philolo1</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 00:51">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32937" href="?#comment-32937" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32915" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32937" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5296" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32937"> <div class="moveup"> <div class="ttypography">interesting, I just did map.find()==map.end(), but this is much cooler.</div> </div> </div> <div class="reply info"> <a class="comment-32937 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32937 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32937"> <li> <div class="comment"> <table class="comment-table" commentId="32946" commentParentId="32937"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/smilitude" style="position: relative;"> <img src='https://userpic.codeforces.org/68/avatar/e81e4a6fe0f7bdd8.jpg'/> </a> <div><a href="/profile/smilitude" title="Expert smilitude" class="rated-user user-blue">smilitude</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 02:12">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32946" href="?#comment-32946" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32937" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32946" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="68" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32946"> <div class="moveup"> <div class="ttypography">It's actually safer that way. If you search with if( map[ name1 ] ), every time you do the query, the size of the map increases by 1. Try this - <br /> <pre> map&lt; int,int &gt; one, two; for(int i=1;i&lt;=100; i++) if( one[i] ); for(int i=1;i&lt;=100; i++) if( two.find(i) == two.end() ); cout &lt;&lt; one.size() &lt;&lt; &quot; &quot; &lt;&lt; two.size() &lt;&lt; endl; </pre></div> </div> </div> <div class="reply info"> <a class="comment-32946 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32946 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32946"> <li> <div class="comment"> <table class="comment-table" commentId="32948" commentParentId="32946"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 02:22">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32948" href="?#comment-32948" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32946" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32948" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32948"> <div class="moveup"> <div class="ttypography">In this problem it's the same, because I wanted to make an entry anyway if it doesn't exist.<br />I didn't write this statement as an if condition.</div> </div> </div> <div class="reply info"> <a class="comment-32948 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32948 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32948"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="278325" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/shubhamgoyal__" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/shubhamgoyal__" title="Candidate Master shubhamgoyal__" class="rated-user user-violet">shubhamgoyal__</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/13/2016 17:17">8 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-278325" href="?#comment-278325" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="278325" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="321533" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-278325"> <div class="moveup"> <div class="ttypography"><p>great explanation for problem D!!!</p></div> </div> </div> <div class="reply info"> <a class="comment-278325 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-278325 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-278325"> <li> <div class="comment"> <table class="comment-table" commentId="278326" commentParentId="278325"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/P_Nyagolov" style="position: relative;"> <img src='https://userpic.codeforces.org/239110/avatar/9494c230dc159315.jpg'/> </a> <div><a href="/profile/P_Nyagolov" title="Expert P_Nyagolov" class="rated-user user-blue">P_Nyagolov</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/13/2016 17:26">8 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-278326" href="?#comment-278326" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-278325" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="278326" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="239110" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-278326"> <div class="moveup"> <div class="ttypography"><p>Seriously, guys, what's wrong with you?</p></div> </div> </div> <div class="reply info"> <a class="comment-278326 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-278326 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-278326"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="599691" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Amr-Fahmy" style="position: relative;"> <img src='https://userpic.codeforces.org/858870/avatar/5c5b1d238b408975.jpg'/> </a> <div><a href="/profile/Amr-Fahmy" title="Expert Amr-Fahmy" class="rated-user user-blue">Amr-Fahmy</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/09/2020 07:21">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-599691" href="?#comment-599691" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="599691" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="858870" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-599691"> <div class="moveup"> <div class="ttypography"><p>I am here after 9 years, The explanation of problem D is the best explanation i have ever read on codeforces ! Thank you</p></div> </div> </div> <div class="reply info"> <a class="comment-599691 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-599691 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-599691"> <li> <div class="comment"> <table class="comment-table" commentId="599695" commentParentId="599691"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/09/2020 07:45">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-599695" href="?#comment-599695" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-599691" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="599695" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-599695"> <div class="moveup"> <div class="ttypography"><p>Thanks!</p></div> </div> </div> <div class="reply info"> <a class="comment-599695 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-599695 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-599695"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="612647" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/hereForFun" style="position: relative;"> <img src='https://userpic.codeforces.org/695688/avatar/5e5b50c23f422942.jpg'/> </a> <div><a href="/profile/hereForFun" title="Pupil hereForFun" class="rated-user user-green">hereForFun</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/29/2020 08:06">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-612647" href="?#comment-612647" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="612647" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="695688" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-612647"> <div class="moveup"> <div class="ttypography"><p>Hello! I am here from the a2oj ladder. I received a WA on test case 14 in problem A. When I checked the test case and ran it locally, it is giving the correct answer. Why is the output different here? <a href="https://codeforces.com/contest/75/submission/78440577">https://codeforces.com/contest/75/submission/78440577</a> Here is my submission.</p></div> </div> </div> <div class="reply info"> <a class="comment-612647 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-612647 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-612647"> <li> <div class="comment"> <table class="comment-table" commentId="612658" commentParentId="612647"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/qpwoeirut" style="position: relative;"> <img src='https://userpic.codeforces.org/1165565/avatar/71d9b6b641fb567b.jpg'/> </a> <div><a href="/profile/qpwoeirut" title="Candidate Master qpwoeirut" class="rated-user user-violet">qpwoeirut</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/29/2020 08:56">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-612658" href="?#comment-612658" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-612647" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="612658" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1165565" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-612658"> <div class="moveup"> <div class="ttypography"><p>It looks like you're getting overflow from <code>(digit*pow(10,nonZero))</code>. This can be fixed by using a running place multiplier instead of <code>pow</code>.</p><p>See <a href="/contest/75/submission/78443731" title="Submission 78443731 by qpwoeirut">78443731</a> for an accepted version of your code with that change.</p></div> </div> </div> <div class="reply info"> <a class="comment-612658 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-612658 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-612658"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1725" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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75D
75
D
en
D. Big Maximum Sum
<div class="problem-statement"><div class="header"><div class="title">D. Big Maximum Sum</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Ahmed and Mostafa used to compete together in many programming contests for several years. Their coach Fegla asked them to solve one challenging problem, of course Ahmed was able to solve it but Mostafa couldn't.</p><p>This problem is similar to a standard problem but it has a different format and constraints.</p><p>In the standard problem you are given an array of integers, and you have to find one or more consecutive elements in this array where their sum is the maximum possible sum.</p><p>But in this problem you are given <span class="tex-span"><i>n</i></span> small arrays, and you will create one big array from the concatenation of one or more instances of the small arrays (each small array could occur more than once). The big array will be given as an array of indexes (1-based) of the small arrays, and the concatenation should be done in the same order as in this array. Then you should apply the standard problem mentioned above on the resulting big array.</p><p>For example let's suppose that the small arrays are {1, 6, -2}, {3, 3} and {-5, 1}. And the indexes in the big array are {2, 3, 1, 3}. So the actual values in the big array after formatting it as concatenation of the small arrays will be {3, 3, -5, 1, 1, 6, -2, -5, 1}. In this example the maximum sum is 9.</p><p>Can you help Mostafa solve this problem?</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>m</i></span>, <span class="tex-span"><i>n</i></span> is the number of the small arrays (<span class="tex-span">1 ≤ <i>n</i> ≤ 50</span>), and <span class="tex-span"><i>m</i></span> is the number of indexes in the big array (<span class="tex-span">1 ≤ <i>m</i> ≤ 250000</span>). Then follow <span class="tex-span"><i>n</i></span> lines, the <span class="tex-span"><i>i</i></span>-th line starts with one integer <span class="tex-span"><i>l</i></span> which is the size of the <span class="tex-span"><i>i</i></span>-th array (<span class="tex-span">1 ≤ <i>l</i> ≤ 5000</span>), followed by <span class="tex-span"><i>l</i></span> integers each one will be greater than or equal -1000 and less than or equal 1000. The last line contains <span class="tex-span"><i>m</i></span> integers which are the indexes in the big array, and you should concatenate the small arrays in the same order, and each index will be greater than or equal to 1 and less than or equal to <span class="tex-span"><i>n</i></span>.</p><p>The small arrays are numbered from 1 to <span class="tex-span"><i>n</i></span> in the same order as given in the input. Some of the given small arrays may not be used in big array.</p><p>Note, that the array is very big. So if you try to build it straightforwardly, you will probably get time or/and memory limit exceeded.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print one line containing the maximum sum in the big array after formatting it as described above. You must choose at least one element for the sum, i. e. it cannot be empty.</p><p>Please, do not use <span class="tex-font-style-tt">%lld</span> specificator to write 64-bit integers in C++. It is preferred to use <span class="tex-font-style-tt">cout</span> (also you may use <span class="tex-font-style-tt">%I64d</span>).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3 4<br/>3 1 6 -2<br/>2 3 3<br/>2 -5 1<br/>2 3 1 3<br/></pre></div><div class="output"><div class="title">Output</div><pre>9<br/></pre></div><div class="input"><div class="title">Input</div><pre>6 1<br/>4 0 8 -3 -10<br/>8 3 -2 -5 10 8 -9 -5 -4<br/>1 0<br/>1 -3<br/>3 -8 5 6<br/>2 9 6<br/>1<br/></pre></div><div class="output"><div class="title">Output</div><pre>8<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="D" data-uuid="ps_a8f2f889657154cc5db337ece8d03f25ee6007a0"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">D. Big Maximum Sum</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Ahmed and Mostafa used to compete together in many programming contests for several years. Their coach Fegla asked them to solve one challenging problem, of course Ahmed was able to solve it but Mostafa couldn't.</p><p>This problem is similar to a standard problem but it has a different format and constraints.</p><p>In the standard problem you are given an array of integers, and you have to find one or more consecutive elements in this array where their sum is the maximum possible sum.</p><p>But in this problem you are given <span class="tex-span"><i>n</i></span> small arrays, and you will create one big array from the concatenation of one or more instances of the small arrays (each small array could occur more than once). The big array will be given as an array of indexes (1-based) of the small arrays, and the concatenation should be done in the same order as in this array. Then you should apply the standard problem mentioned above on the resulting big array.</p><p>For example let's suppose that the small arrays are {1, 6, -2}, {3, 3} and {-5, 1}. And the indexes in the big array are {2, 3, 1, 3}. So the actual values in the big array after formatting it as concatenation of the small arrays will be {3, 3, -5, 1, 1, 6, -2, -5, 1}. In this example the maximum sum is 9.</p><p>Can you help Mostafa solve this problem?</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>m</i></span>, <span class="tex-span"><i>n</i></span> is the number of the small arrays (<span class="tex-span">1 ≤ <i>n</i> ≤ 50</span>), and <span class="tex-span"><i>m</i></span> is the number of indexes in the big array (<span class="tex-span">1 ≤ <i>m</i> ≤ 250000</span>). Then follow <span class="tex-span"><i>n</i></span> lines, the <span class="tex-span"><i>i</i></span>-th line starts with one integer <span class="tex-span"><i>l</i></span> which is the size of the <span class="tex-span"><i>i</i></span>-th array (<span class="tex-span">1 ≤ <i>l</i> ≤ 5000</span>), followed by <span class="tex-span"><i>l</i></span> integers each one will be greater than or equal -1000 and less than or equal 1000. The last line contains <span class="tex-span"><i>m</i></span> integers which are the indexes in the big array, and you should concatenate the small arrays in the same order, and each index will be greater than or equal to 1 and less than or equal to <span class="tex-span"><i>n</i></span>.</p><p>The small arrays are numbered from 1 to <span class="tex-span"><i>n</i></span> in the same order as given in the input. Some of the given small arrays may not be used in big array.</p><p>Note, that the array is very big. So if you try to build it straightforwardly, you will probably get time or/and memory limit exceeded.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print one line containing the maximum sum in the big array after formatting it as described above. You must choose at least one element for the sum, i. e. it cannot be empty.</p><p>Please, do not use <span class="tex-font-style-tt">%lld</span> specificator to write 64-bit integers in C++. It is preferred to use <span class="tex-font-style-tt">cout</span> (also you may use <span class="tex-font-style-tt">%I64d</span>).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3 4<br />3 1 6 -2<br />2 3 3<br />2 -5 1<br />2 3 1 3<br /></pre></div><div class="output"><div class="title">Output</div><pre>9<br /></pre></div><div class="input"><div class="title">Input</div><pre>6 1<br />4 0 8 -3 -10<br />8 3 -2 -5 10 8 -9 -5 -4<br />1 0<br />1 -3<br />3 -8 5 6<br />2 9 6<br />1<br /></pre></div><div class="output"><div class="title">Output</div><pre>8<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=D]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); 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["Heaps, binary search trees, segment trees, hash tables, etc", "Dynamic programming", "Greedy algorithms", "Implementation problems, programming technics, simulation", "Mathematics including integration, differential equations, etc", "Trees"]
["data structures", "dp", "greedy", "implementation", "math", "trees", "*2000"]
https://codeforces.com/blog/entry/1715
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You can do it in the following 3 steps:<br />1- Calculate C.<br />2- Remove all zeros from A, B and C.<br />3- Check if the new values form a correct equation.<br /><br /><a href="http://pastebin.com/1cc1xKNW">C++ solution for problem A.</a><br /><br /><br /><b>Problem B:</b><br />This problem is a direct simulation to the rules written in the problem statement.<br />You need to iterate over all actions and parse each one to know the type of the action, and the 2 names X and Y, and if your name is X or Y then update your priority factor with this person with the action corresponding value. And take care about some special names like &quot;post&quot;, &quot;wall&quot;, &quot;commented&quot; and &quot;on&quot;.<br />Then sort all names according to the sorting criteria mentioned in the statement.<br />Just make sure to print all names which are mentioned in the input (excluding yourself), even if the priority factor with you is 0.<br /><br /><a href="http://pastebin.com/cGHAv8qs">C++ solution for problem B.</a><br /><br /><br /><b>Problem C:</b><br />In this problem you will need to generate all common divisors between a and b before answering any query.<br />The first step in this problem is to factorize a and b, you can use the trial division technique which runs in O(sqrt(N)), you can check getFactors function in my solutions.<br />Then using a recursive function you can generate all divisors for a and b from their prime factors, you can check getDivisors function in my solutions.<br />Then intersect the 2 sets of divisors for both to get all common divisors, you can do this in O(N+M) where N and M are the lengths of the 2 sets, and also you can do a trivial O(N*M) intersection algorithm, because the maximum number of divisors is not too big (it's 1344).<br />Now for each query you need to find the largest common divisor which lies in the given range, you can do this by sorting all common divisors and do binary search for the largest one which lies in the given range. Also you can do this using linear search, because the total number of queries is not too big.<br /><br />Also there is much shorter solution for this problem. Here is a hint for it, the GCD between a and b should be dividable by all common divisors of a and b.<br /><br /><a href="http://pastebin.com/zcEGkKhw">C++ solution for problem C (with binary search).</a><br /><a href="http://pastebin.com/Uw4rG7Ar">C++ solution for problem C (without binary search).</a><br /><a href="http://pastebin.com/Nd54H6em">Java solution for problem C (with binary search).</a><br /><br /><br /><b>Problem D:</b><br />This problem is my favorite one in this problem set. Maybe it will be easier to solve this problem if you know how to solve the standard one.<br />But because we can't construct the big array, so we can't apply the standard solution for this problem.<br />Let's see first how to solve the standard problem, the following code solves it for a given array arr with length len:<br /><br />int mx = -(1 &lt;&lt; 30);<br />int sum = 0;<br />for (int j = 0; j &lt; len; j++) {<br />    mx = max(mx, arr[i]); // we need this for the case where all elements in the array are negatives<br />    sum += arr[i];<br />    if (sum &lt; 0)<br />        sum = 0;<br />    else<br />        mx = max(mx, sum);<br />}<br /><br />Now let's solve the big array problem, the first step is to calculate 4 values for each small array:<br />1- The total sum of it, let's call it tot.<br />2- The maximum sum of 0 or more consecutive elements starting from the first element in the array, let's call it lft.<br />3- The maximum sum of 0 or more consecutive elements ending at the last element in the array, let's call it rght.<br />4- The maximum sum of 1 or more consecutive elements, let's call it gen.<br /><br />The final result will be 1 of 2 cases:<br />1- The consecutive elements with the maximum sum will start and end inside the same small array.<br />2- The consecutive elements with the maximum sum will start and end inside different small arrays.<br /><br />For the first case, we can simply pick the maximum gen for all small arrays which exist in the big array.<br />For the second case, we can apply something similar to the standard solution, we will keep a variable called sum, and it's initialized to 0, this will be the maximum sum of 0 or more consecutive elements ending at the last element in the previous small array. Now for each small array, if the maximum possible sum will end in this small array, so it will be sum+lft and maximize over this value (make sure this will be for 1 or more elements). And we need to update sum to be the maximum of the following 3 values:<br />1- sum+tot (we will include all elements of this small array to the old sum).<br />2- rght (we will take the maximum sum ending at the last element in the current small array).<br />3- 0 (we will not take any elements in sum).<br /><br />The running time for this solution will be just for reading the input, in my solutions I have no iterations except for reading the input.<br /><br />You can check my solutions for more clarification.<br /><br /><a href="http://pastebin.com/bsxvF4aC">C++ solution for problem D.</a><br /><a href="http://pastebin.com/k1hzX5XD">Java solution for problem D.</a><br /><br /><br /><b>Problem E:</b><br />The main idea for this problem is not hard, but maybe the hard part is implementing it.<br />First we need to know if the straight line segment between the source and destination points intersect with the island or not. So we will intersect this line segment with all the polygon sides. If there are 2 segments intersect in more than 1 point we will consider as they don't intersect, because it's mentioned in the problem statement that you can move on the island's edge and it will be considered in the sea.<br />Now we have a set of all distinct intersection points of the polygon and the straight line segment between the source and destination points. Because the polygon is convex, this set will contain at most 2 points. We have 3 different cases now:<br />1- This set contains less than 2 points.<br />2- This set contains 2 points and they are on the same polygon side.<br />3- This set contains 2 points and they are not on the same polygon side.<br /><br />In the first 2 cases the result will be simply the length of the straight line segment.<br />In the 3rd case you can do the following:<br />1- Move from the source point to the nearest point of the 2 intersection points.<br />2- You have 3 options here:<br />    a- Move inside the island to the other intersection point.<br />    b- Move in clockwise direction on the island's edge to the other intersection point.<br />    c- Move in anti-clockwise direction on the island's edge to the other intersection point.<br />    First option will be considered moving inside the island, and the other 2 options will be considered moving in the sea.<br />    You should pick the minimum one.<br />3- Move from the 2nd intersection point to the destination point.<br /><br />Another solution:<br />You can construct a graph where the nodes are the source point, the destination point, the intersection points and the polygon corner points. Then add an edge between any 2 points which you can move between them with the corresponding cost. Then run any shortest path algorithm, Floyd Warshall for example.<br /><br />You can check my solutions for more clarification.<br /><br /><a href="http://pastebin.com/7jgsu40r">C++ solution for problem E.</a><br /><a href="http://pastebin.com/cZVCifwt">C++ solution for problem E (with Floyd Warshall).</a></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/75" class="notice" style="text-decoration: none;">Codeforces Beta Round 67 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-229-1715").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "229", blogEntryId: "1715", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces+round+%2367" class="tag notice" style="text-decoration: none;">codeforces round #67</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=editorial" class="tag notice" style="text-decoration: none;">editorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1715"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+44</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1715"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/ahmed_aly"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/ahmed_aly"> ahmed_aly </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Apr/13/2011 21:46">12 years ago</span> </li> <li> <a href="/blog/entry/1715#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1715#comments"> 25 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1725"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (21)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="32752" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/eik0u" style="position: relative;"> <img src='https://userpic.codeforces.org/1231/avatar/7637a0d6900a713b.jpg'/> </a> <div><a href="/profile/eik0u" title="Expert eik0u" class="rated-user user-blue">eik0u</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/13/2011 22:26">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32752" href="?#comment-32752" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32752" class="CommentVoteFrame" data-commentRating="11" data-commentUserId="1231" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+11</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32752"> <div class="moveup"> <div class="ttypography">D is also my favourite problem in this problem set :)<div>And the whole problem set is very nice. It is very diverse: easy implementation, math, dp/classic, geometry. And problems do not require extraodinary knowledge in algorithms.</div><div>This round was very suitable for Div2.</div></div> </div> </div> <div class="reply info"> <a class="comment-32752 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32752 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32752"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32770" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/iman_MC" style="position: relative;"> <img src='https://userpic.codeforces.org/2447/avatar/b2ab3e48d7eb8c6.jpg'/> </a> <div><a href="/profile/iman_MC" title="Pupil iman_MC" class="rated-user user-green">iman_MC</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/13/2011 23:43">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32770" href="?#comment-32770" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32770" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="2447" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32770"> <div class="moveup"> <div class="ttypography">Excellent Tutorial's ,  several ways several code for each one , good luck <a class="rated-user user-orange" href="../../profile/ahmed_aly" title="Major ahmed_aly">ahmed_aly</a></div> </div> </div> <div class="reply info"> <a class="comment-32770 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32770 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32770"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32800" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Egor" style="position: relative;"> <img src='https://userpic.codeforces.org/838/avatar/6976bef0cdef7d5c.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/Egor" title="International Grandmaster Egor" class="rated-user user-red">Egor</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 01:30">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32800" href="?#comment-32800" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32800" class="CommentVoteFrame" data-commentRating="4" data-commentUserId="838" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+4</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32800"> <div class="moveup"> <div class="ttypography">(In English)<div><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;">Very nice contest</span><div style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;">B can be also solved using regexps</div></div><div style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;"><br /></div><div style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;">Also in Java we use List, Vector is deprecated ;)</div></div> </div> </div> <div class="reply info"> <a class="comment-32800 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32800 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32800"> <li> <div class="comment"> <table class="comment-table" commentId="32801" commentParentId="32800"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 01:56">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32801" href="?#comment-32801" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32800" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="32801" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="32801" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32801"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">Thanks, but I'm not very good Java coder. :)</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-32801 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32801 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32801"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32844" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ACCEPT" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/ACCEPT" title="Unrated, ACCEPT" class="rated-user user-black">ACCEPT</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 16:02">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32844" href="?#comment-32844" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32844" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14879" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32844"> <div class="moveup"> <div class="ttypography">thank's for your nice contest and tutorial.<div>I have a question for problem E:</div><div>why your algo is correct?</div></div> </div> </div> <div class="reply info"> <a class="comment-32844 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32844 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32844"> <li> <div class="comment"> <table class="comment-table" commentId="32913" commentParentId="32844"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 23:46">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32913" href="?#comment-32913" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32844" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32913" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32913"> <div class="moveup"> <div class="ttypography">Because you can only move to safe points, so you don't have any other choice.</div> </div> </div> <div class="reply info"> <a class="comment-32913 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32913 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32913"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32855" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/novkostya" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/novkostya" title="Expert novkostya" class="rated-user user-blue">novkostya</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 18:30">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32855" href="?#comment-32855" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32855" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5985" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32855"> <div class="moveup"> <div class="ttypography">(C++ solution for problem C)<br />std::back_inserter(cd) seems to be more applicable than std::inserter(cd, cd.begin())</div> </div> </div> <div class="reply info"> <a class="comment-32855 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32855 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32855"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32861" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/lantimilan" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/lantimilan" title="Expert lantimilan" class="rated-user user-blue">lantimilan</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 21:03">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32861" href="?#comment-32861" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32861" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="15561" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32861"> <div class="moveup"> <div class="ttypography">The c++ code for problem A has integer overflow, since a and b can be up to 999999999, c=a+b cannot fit into 32-bit int. My solution had the same issue and got hacked.</div> </div> </div> <div class="reply info"> <a class="comment-32861 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32861 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32861"> <li> <div class="comment"> <table class="comment-table" commentId="32863" commentParentId="32861"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Egor" style="position: relative;"> <img src='https://userpic.codeforces.org/838/avatar/6976bef0cdef7d5c.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/Egor" title="International Grandmaster Egor" class="rated-user user-red">Egor</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 21:05">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32863" href="?#comment-32863" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32861" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32863" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="838" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32863"> <div class="moveup"> <div class="ttypography">Actually 1999999998 fits into 32bit signed integer</div> </div> </div> <div class="reply info"> <a class="comment-32863 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32863 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32863"> <li> <div class="comment"> <table class="comment-table" commentId="32891" commentParentId="32863"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/lantimilan" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/lantimilan" title="Expert lantimilan" class="rated-user user-blue">lantimilan</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 22:21">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32891" href="?#comment-32891" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32863" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32891" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="15561" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32891"> <div class="moveup"> <div class="ttypography">That's right. Just realized that my overflow is due to 8999999991, the reverse of 1999999998.</div> </div> </div> <div class="reply info"> <a class="comment-32891 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32891 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32891"> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32868" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/philolo1" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/philolo1" title="Expert philolo1" class="rated-user user-blue">philolo1</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 21:12">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32868" href="?#comment-32868" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32868" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5296" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32868"> <div class="moveup"> <div class="ttypography">what does the instruction factor[name1] do?</div> </div> </div> <div class="reply info"> <a class="comment-32868 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32868 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32868"> <li> <div class="comment"> <table class="comment-table" commentId="32915" commentParentId="32868"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 23:48">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32915" href="?#comment-32915" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32868" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32915" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32915"> <div class="moveup"> <div class="ttypography">Just to make an entry for name1 in the map, and it will be 0. Because I have to print all names even if the factor is 0.<br />If there is no entry for name1, nothing will happen. If there is no entry, it will be the same as factor[name1] = 0.</div> </div> </div> <div class="reply info"> <a class="comment-32915 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32915 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32915"> <li> <div class="comment"> <table class="comment-table" commentId="32937" commentParentId="32915"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/philolo1" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/philolo1" title="Expert philolo1" class="rated-user user-blue">philolo1</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 00:51">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32937" href="?#comment-32937" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32915" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32937" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5296" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32937"> <div class="moveup"> <div class="ttypography">interesting, I just did map.find()==map.end(), but this is much cooler.</div> </div> </div> <div class="reply info"> <a class="comment-32937 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32937 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32937"> <li> <div class="comment"> <table class="comment-table" commentId="32946" commentParentId="32937"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/smilitude" style="position: relative;"> <img src='https://userpic.codeforces.org/68/avatar/e81e4a6fe0f7bdd8.jpg'/> </a> <div><a href="/profile/smilitude" title="Expert smilitude" class="rated-user user-blue">smilitude</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 02:12">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32946" href="?#comment-32946" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32937" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32946" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="68" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32946"> <div class="moveup"> <div class="ttypography">It's actually safer that way. If you search with if( map[ name1 ] ), every time you do the query, the size of the map increases by 1. Try this - <br /> <pre> map&lt; int,int &gt; one, two; for(int i=1;i&lt;=100; i++) if( one[i] ); for(int i=1;i&lt;=100; i++) if( two.find(i) == two.end() ); cout &lt;&lt; one.size() &lt;&lt; &quot; &quot; &lt;&lt; two.size() &lt;&lt; endl; </pre></div> </div> </div> <div class="reply info"> <a class="comment-32946 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32946 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32946"> <li> <div class="comment"> <table class="comment-table" commentId="32948" commentParentId="32946"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 02:22">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32948" href="?#comment-32948" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32946" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32948" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32948"> <div class="moveup"> <div class="ttypography">In this problem it's the same, because I wanted to make an entry anyway if it doesn't exist.<br />I didn't write this statement as an if condition.</div> </div> </div> <div class="reply info"> <a class="comment-32948 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32948 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32948"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="278325" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/shubhamgoyal__" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/shubhamgoyal__" title="Candidate Master shubhamgoyal__" class="rated-user user-violet">shubhamgoyal__</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/13/2016 17:17">8 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-278325" href="?#comment-278325" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="278325" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="321533" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-278325"> <div class="moveup"> <div class="ttypography"><p>great explanation for problem D!!!</p></div> </div> </div> <div class="reply info"> <a class="comment-278325 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-278325 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-278325"> <li> <div class="comment"> <table class="comment-table" commentId="278326" commentParentId="278325"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/P_Nyagolov" style="position: relative;"> <img src='https://userpic.codeforces.org/239110/avatar/9494c230dc159315.jpg'/> </a> <div><a href="/profile/P_Nyagolov" title="Expert P_Nyagolov" class="rated-user user-blue">P_Nyagolov</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/13/2016 17:26">8 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-278326" href="?#comment-278326" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-278325" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="278326" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="239110" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-278326"> <div class="moveup"> <div class="ttypography"><p>Seriously, guys, what's wrong with you?</p></div> </div> </div> <div class="reply info"> <a class="comment-278326 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-278326 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-278326"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="599691" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Amr-Fahmy" style="position: relative;"> <img src='https://userpic.codeforces.org/858870/avatar/5c5b1d238b408975.jpg'/> </a> <div><a href="/profile/Amr-Fahmy" title="Expert Amr-Fahmy" class="rated-user user-blue">Amr-Fahmy</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/09/2020 07:21">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-599691" href="?#comment-599691" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="599691" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="858870" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-599691"> <div class="moveup"> <div class="ttypography"><p>I am here after 9 years, The explanation of problem D is the best explanation i have ever read on codeforces ! Thank you</p></div> </div> </div> <div class="reply info"> <a class="comment-599691 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-599691 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-599691"> <li> <div class="comment"> <table class="comment-table" commentId="599695" commentParentId="599691"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/09/2020 07:45">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-599695" href="?#comment-599695" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-599691" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="599695" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-599695"> <div class="moveup"> <div class="ttypography"><p>Thanks!</p></div> </div> </div> <div class="reply info"> <a class="comment-599695 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-599695 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-599695"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="612647" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/hereForFun" style="position: relative;"> <img src='https://userpic.codeforces.org/695688/avatar/5e5b50c23f422942.jpg'/> </a> <div><a href="/profile/hereForFun" title="Pupil hereForFun" class="rated-user user-green">hereForFun</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/29/2020 08:06">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-612647" href="?#comment-612647" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="612647" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="695688" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-612647"> <div class="moveup"> <div class="ttypography"><p>Hello! I am here from the a2oj ladder. I received a WA on test case 14 in problem A. When I checked the test case and ran it locally, it is giving the correct answer. Why is the output different here? <a href="https://codeforces.com/contest/75/submission/78440577">https://codeforces.com/contest/75/submission/78440577</a> Here is my submission.</p></div> </div> </div> <div class="reply info"> <a class="comment-612647 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-612647 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-612647"> <li> <div class="comment"> <table class="comment-table" commentId="612658" commentParentId="612647"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/qpwoeirut" style="position: relative;"> <img src='https://userpic.codeforces.org/1165565/avatar/71d9b6b641fb567b.jpg'/> </a> <div><a href="/profile/qpwoeirut" title="Candidate Master qpwoeirut" class="rated-user user-violet">qpwoeirut</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/29/2020 08:56">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-612658" href="?#comment-612658" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-612647" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="612658" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1165565" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-612658"> <div class="moveup"> <div class="ttypography"><p>It looks like you're getting overflow from <code>(digit*pow(10,nonZero))</code>. This can be fixed by using a running place multiplier instead of <code>pow</code>.</p><p>See <a href="/contest/75/submission/78443731" title="Submission 78443731 by qpwoeirut">78443731</a> for an accepted version of your code with that change.</p></div> </div> </div> <div class="reply info"> <a class="comment-612658 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-612658 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-612658"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1725" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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75E
75
E
en
E. Ship's Shortest Path
<div class="problem-statement"><div class="header"><div class="title">E. Ship's Shortest Path</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>You have got a new job, and it's very interesting, you are a ship captain. Your first task is to move your ship from one point to another point, and for sure you want to move it at the minimum cost.</p><p>And it's well known that the shortest distance between any 2 points is the length of the line segment between these 2 points. But unfortunately there is an island in the sea, so sometimes you won't be able to move your ship in the line segment between the 2 points.</p><p>You can <span class="tex-font-style-bf">only</span> move to safe points. A point is called safe if it's on the line segment between the start and end points, or if it's on the island's edge.</p><p>But you are too lucky, you have got some clever and strong workers and they can help you in your trip, they can help you move the ship in the sea and they will take 1 Egyptian pound for each moving unit in the sea, and they can carry the ship (yes, they are very strong) and walk on the island and they will take 2 Egyptian pounds for each moving unit in the island. The money which you will give to them will be divided between all workers, so the number of workers does not matter here.</p><p>You can move your ship on the island edge, and it will be considered moving in the sea.</p><p>Now you have a sea map, and you have to decide what is the minimum cost for your trip.</p><p>Your starting point is (<span class="tex-span"><i>xStart</i></span>, <span class="tex-span"><i>yStart</i></span>), and the end point is (<span class="tex-span"><i>xEnd</i></span>, <span class="tex-span"><i>yEnd</i></span>), both points will be different.</p><p>The island will be a convex polygon and there will be no more than 2 polygon points on the same line, also the starting and the end points won't be inside or on the boundary of the island. The points for the polygon will be given in the anti-clockwise order.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains 4 integers, <span class="tex-span"><i>xStart</i></span>, <span class="tex-span"><i>yStart</i></span>, <span class="tex-span"><i>xEnd</i></span> and <span class="tex-span"><i>yEnd</i></span> (<span class="tex-span"> - 100 ≤ <i>xStart</i>, <i>yStart</i>, <i>xEnd</i>, <i>yEnd</i> ≤ 100</span>). The second line contains an integer <span class="tex-span"><i>n</i></span>, which is the number of points in the polygon (<span class="tex-span">3 ≤ <i>n</i> ≤ 30</span>), followed by a line containing <span class="tex-span"><i>n</i></span> pairs of integers <span class="tex-span"><i>x</i></span> and <span class="tex-span"><i>y</i></span>, which are the coordinates of the points (<span class="tex-span"> - 100 ≤ <i>x</i>, <i>y</i> ≤ 100</span>), the polygon points will be distinct.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print one line which contains the minimum possible cost. The absolute or relative error in the answer should not exceed <span class="tex-span">10<sup class="upper-index"> - 6</sup></span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>1 7 6 7<br/>4<br/>4 2 4 12 3 12 3 2<br/></pre></div><div class="output"><div class="title">Output</div><pre>6.000000000<br/></pre></div><div class="input"><div class="title">Input</div><pre>-1 0 2 0<br/>4<br/>0 0 1 0 1 1 0 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>3.000000000<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="E" data-uuid="ps_3365d70ba65a3101d874fed5ec72bccc6c7394e0"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">E. Ship's Shortest Path</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>You have got a new job, and it's very interesting, you are a ship captain. Your first task is to move your ship from one point to another point, and for sure you want to move it at the minimum cost.</p><p>And it's well known that the shortest distance between any 2 points is the length of the line segment between these 2 points. But unfortunately there is an island in the sea, so sometimes you won't be able to move your ship in the line segment between the 2 points.</p><p>You can <span class="tex-font-style-bf">only</span> move to safe points. A point is called safe if it's on the line segment between the start and end points, or if it's on the island's edge.</p><p>But you are too lucky, you have got some clever and strong workers and they can help you in your trip, they can help you move the ship in the sea and they will take 1 Egyptian pound for each moving unit in the sea, and they can carry the ship (yes, they are very strong) and walk on the island and they will take 2 Egyptian pounds for each moving unit in the island. The money which you will give to them will be divided between all workers, so the number of workers does not matter here.</p><p>You can move your ship on the island edge, and it will be considered moving in the sea.</p><p>Now you have a sea map, and you have to decide what is the minimum cost for your trip.</p><p>Your starting point is (<span class="tex-span"><i>xStart</i></span>, <span class="tex-span"><i>yStart</i></span>), and the end point is (<span class="tex-span"><i>xEnd</i></span>, <span class="tex-span"><i>yEnd</i></span>), both points will be different.</p><p>The island will be a convex polygon and there will be no more than 2 polygon points on the same line, also the starting and the end points won't be inside or on the boundary of the island. The points for the polygon will be given in the anti-clockwise order.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains 4 integers, <span class="tex-span"><i>xStart</i></span>, <span class="tex-span"><i>yStart</i></span>, <span class="tex-span"><i>xEnd</i></span> and <span class="tex-span"><i>yEnd</i></span> (<span class="tex-span"> - 100 ≤ <i>xStart</i>, <i>yStart</i>, <i>xEnd</i>, <i>yEnd</i> ≤ 100</span>). The second line contains an integer <span class="tex-span"><i>n</i></span>, which is the number of points in the polygon (<span class="tex-span">3 ≤ <i>n</i> ≤ 30</span>), followed by a line containing <span class="tex-span"><i>n</i></span> pairs of integers <span class="tex-span"><i>x</i></span> and <span class="tex-span"><i>y</i></span>, which are the coordinates of the points (<span class="tex-span"> - 100 ≤ <i>x</i>, <i>y</i> ≤ 100</span>), the polygon points will be distinct.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print one line which contains the minimum possible cost. The absolute or relative error in the answer should not exceed <span class="tex-span">10<sup class="upper-index"> - 6</sup></span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>1 7 6 7<br />4<br />4 2 4 12 3 12 3 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>6.000000000<br /></pre></div><div class="input"><div class="title">Input</div><pre>-1 0 2 0<br />4<br />0 0 1 0 1 1 0 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>3.000000000<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=E]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); if (previousStatementText) { if (previousStatementText !== statementText) { $problem.find(".diff-notifier").show(); 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["Geometry, computational geometry", "Shortest paths on weighted and unweighted graphs"]
["geometry", "shortest paths", "*2400"]
https://codeforces.com/blog/entry/1715
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You can do it in the following 3 steps:<br />1- Calculate C.<br />2- Remove all zeros from A, B and C.<br />3- Check if the new values form a correct equation.<br /><br /><a href="http://pastebin.com/1cc1xKNW">C++ solution for problem A.</a><br /><br /><br /><b>Problem B:</b><br />This problem is a direct simulation to the rules written in the problem statement.<br />You need to iterate over all actions and parse each one to know the type of the action, and the 2 names X and Y, and if your name is X or Y then update your priority factor with this person with the action corresponding value. And take care about some special names like &quot;post&quot;, &quot;wall&quot;, &quot;commented&quot; and &quot;on&quot;.<br />Then sort all names according to the sorting criteria mentioned in the statement.<br />Just make sure to print all names which are mentioned in the input (excluding yourself), even if the priority factor with you is 0.<br /><br /><a href="http://pastebin.com/cGHAv8qs">C++ solution for problem B.</a><br /><br /><br /><b>Problem C:</b><br />In this problem you will need to generate all common divisors between a and b before answering any query.<br />The first step in this problem is to factorize a and b, you can use the trial division technique which runs in O(sqrt(N)), you can check getFactors function in my solutions.<br />Then using a recursive function you can generate all divisors for a and b from their prime factors, you can check getDivisors function in my solutions.<br />Then intersect the 2 sets of divisors for both to get all common divisors, you can do this in O(N+M) where N and M are the lengths of the 2 sets, and also you can do a trivial O(N*M) intersection algorithm, because the maximum number of divisors is not too big (it's 1344).<br />Now for each query you need to find the largest common divisor which lies in the given range, you can do this by sorting all common divisors and do binary search for the largest one which lies in the given range. Also you can do this using linear search, because the total number of queries is not too big.<br /><br />Also there is much shorter solution for this problem. Here is a hint for it, the GCD between a and b should be dividable by all common divisors of a and b.<br /><br /><a href="http://pastebin.com/zcEGkKhw">C++ solution for problem C (with binary search).</a><br /><a href="http://pastebin.com/Uw4rG7Ar">C++ solution for problem C (without binary search).</a><br /><a href="http://pastebin.com/Nd54H6em">Java solution for problem C (with binary search).</a><br /><br /><br /><b>Problem D:</b><br />This problem is my favorite one in this problem set. Maybe it will be easier to solve this problem if you know how to solve the standard one.<br />But because we can't construct the big array, so we can't apply the standard solution for this problem.<br />Let's see first how to solve the standard problem, the following code solves it for a given array arr with length len:<br /><br />int mx = -(1 &lt;&lt; 30);<br />int sum = 0;<br />for (int j = 0; j &lt; len; j++) {<br />    mx = max(mx, arr[i]); // we need this for the case where all elements in the array are negatives<br />    sum += arr[i];<br />    if (sum &lt; 0)<br />        sum = 0;<br />    else<br />        mx = max(mx, sum);<br />}<br /><br />Now let's solve the big array problem, the first step is to calculate 4 values for each small array:<br />1- The total sum of it, let's call it tot.<br />2- The maximum sum of 0 or more consecutive elements starting from the first element in the array, let's call it lft.<br />3- The maximum sum of 0 or more consecutive elements ending at the last element in the array, let's call it rght.<br />4- The maximum sum of 1 or more consecutive elements, let's call it gen.<br /><br />The final result will be 1 of 2 cases:<br />1- The consecutive elements with the maximum sum will start and end inside the same small array.<br />2- The consecutive elements with the maximum sum will start and end inside different small arrays.<br /><br />For the first case, we can simply pick the maximum gen for all small arrays which exist in the big array.<br />For the second case, we can apply something similar to the standard solution, we will keep a variable called sum, and it's initialized to 0, this will be the maximum sum of 0 or more consecutive elements ending at the last element in the previous small array. Now for each small array, if the maximum possible sum will end in this small array, so it will be sum+lft and maximize over this value (make sure this will be for 1 or more elements). And we need to update sum to be the maximum of the following 3 values:<br />1- sum+tot (we will include all elements of this small array to the old sum).<br />2- rght (we will take the maximum sum ending at the last element in the current small array).<br />3- 0 (we will not take any elements in sum).<br /><br />The running time for this solution will be just for reading the input, in my solutions I have no iterations except for reading the input.<br /><br />You can check my solutions for more clarification.<br /><br /><a href="http://pastebin.com/bsxvF4aC">C++ solution for problem D.</a><br /><a href="http://pastebin.com/k1hzX5XD">Java solution for problem D.</a><br /><br /><br /><b>Problem E:</b><br />The main idea for this problem is not hard, but maybe the hard part is implementing it.<br />First we need to know if the straight line segment between the source and destination points intersect with the island or not. So we will intersect this line segment with all the polygon sides. If there are 2 segments intersect in more than 1 point we will consider as they don't intersect, because it's mentioned in the problem statement that you can move on the island's edge and it will be considered in the sea.<br />Now we have a set of all distinct intersection points of the polygon and the straight line segment between the source and destination points. Because the polygon is convex, this set will contain at most 2 points. We have 3 different cases now:<br />1- This set contains less than 2 points.<br />2- This set contains 2 points and they are on the same polygon side.<br />3- This set contains 2 points and they are not on the same polygon side.<br /><br />In the first 2 cases the result will be simply the length of the straight line segment.<br />In the 3rd case you can do the following:<br />1- Move from the source point to the nearest point of the 2 intersection points.<br />2- You have 3 options here:<br />    a- Move inside the island to the other intersection point.<br />    b- Move in clockwise direction on the island's edge to the other intersection point.<br />    c- Move in anti-clockwise direction on the island's edge to the other intersection point.<br />    First option will be considered moving inside the island, and the other 2 options will be considered moving in the sea.<br />    You should pick the minimum one.<br />3- Move from the 2nd intersection point to the destination point.<br /><br />Another solution:<br />You can construct a graph where the nodes are the source point, the destination point, the intersection points and the polygon corner points. Then add an edge between any 2 points which you can move between them with the corresponding cost. Then run any shortest path algorithm, Floyd Warshall for example.<br /><br />You can check my solutions for more clarification.<br /><br /><a href="http://pastebin.com/7jgsu40r">C++ solution for problem E.</a><br /><a href="http://pastebin.com/cZVCifwt">C++ solution for problem E (with Floyd Warshall).</a></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/75" class="notice" style="text-decoration: none;">Codeforces Beta Round 67 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-229-1715").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "229", blogEntryId: "1715", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces+round+%2367" class="tag notice" style="text-decoration: none;">codeforces round #67</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=editorial" class="tag notice" style="text-decoration: none;">editorial</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1715"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+44</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1715"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/ahmed_aly"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/ahmed_aly"> ahmed_aly </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Apr/13/2011 21:46">12 years ago</span> </li> <li> <a href="/blog/entry/1715#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1715#comments"> 25 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1725"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (21)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="32752" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/eik0u" style="position: relative;"> <img src='https://userpic.codeforces.org/1231/avatar/7637a0d6900a713b.jpg'/> </a> <div><a href="/profile/eik0u" title="Expert eik0u" class="rated-user user-blue">eik0u</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/13/2011 22:26">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32752" href="?#comment-32752" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32752" class="CommentVoteFrame" data-commentRating="11" data-commentUserId="1231" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+11</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32752"> <div class="moveup"> <div class="ttypography">D is also my favourite problem in this problem set :)<div>And the whole problem set is very nice. It is very diverse: easy implementation, math, dp/classic, geometry. And problems do not require extraodinary knowledge in algorithms.</div><div>This round was very suitable for Div2.</div></div> </div> </div> <div class="reply info"> <a class="comment-32752 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32752 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32752"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32770" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/iman_MC" style="position: relative;"> <img src='https://userpic.codeforces.org/2447/avatar/b2ab3e48d7eb8c6.jpg'/> </a> <div><a href="/profile/iman_MC" title="Pupil iman_MC" class="rated-user user-green">iman_MC</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/13/2011 23:43">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32770" href="?#comment-32770" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32770" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="2447" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32770"> <div class="moveup"> <div class="ttypography">Excellent Tutorial's ,  several ways several code for each one , good luck <a class="rated-user user-orange" href="../../profile/ahmed_aly" title="Major ahmed_aly">ahmed_aly</a></div> </div> </div> <div class="reply info"> <a class="comment-32770 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32770 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32770"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32800" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Egor" style="position: relative;"> <img src='https://userpic.codeforces.org/838/avatar/6976bef0cdef7d5c.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/Egor" title="International Grandmaster Egor" class="rated-user user-red">Egor</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 01:30">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32800" href="?#comment-32800" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32800" class="CommentVoteFrame" data-commentRating="4" data-commentUserId="838" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+4</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32800"> <div class="moveup"> <div class="ttypography">(In English)<div><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;">Very nice contest</span><div style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;">B can be also solved using regexps</div></div><div style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;"><br /></div><div style="margin-top: 0.0px;margin-right: 0.0px;margin-bottom: 0.0px;margin-left: 0.0px;padding-top: 0.0px;padding-right: 0.0px;padding-bottom: 0.0px;padding-left: 0.0px;border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 14.0px;">Also in Java we use List, Vector is deprecated ;)</div></div> </div> </div> <div class="reply info"> <a class="comment-32800 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32800 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32800"> <li> <div class="comment"> <table class="comment-table" commentId="32801" commentParentId="32800"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 01:56">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32801" href="?#comment-32801" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32800" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="32801" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="32801" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32801"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">Thanks, but I'm not very good Java coder. :)</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-32801 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32801 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32801"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32844" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ACCEPT" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/ACCEPT" title="Unrated, ACCEPT" class="rated-user user-black">ACCEPT</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 16:02">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32844" href="?#comment-32844" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32844" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="14879" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32844"> <div class="moveup"> <div class="ttypography">thank's for your nice contest and tutorial.<div>I have a question for problem E:</div><div>why your algo is correct?</div></div> </div> </div> <div class="reply info"> <a class="comment-32844 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32844 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32844"> <li> <div class="comment"> <table class="comment-table" commentId="32913" commentParentId="32844"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 23:46">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32913" href="?#comment-32913" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32844" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32913" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32913"> <div class="moveup"> <div class="ttypography">Because you can only move to safe points, so you don't have any other choice.</div> </div> </div> <div class="reply info"> <a class="comment-32913 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32913 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32913"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32855" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/novkostya" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/novkostya" title="Expert novkostya" class="rated-user user-blue">novkostya</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 18:30">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32855" href="?#comment-32855" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32855" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5985" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32855"> <div class="moveup"> <div class="ttypography">(C++ solution for problem C)<br />std::back_inserter(cd) seems to be more applicable than std::inserter(cd, cd.begin())</div> </div> </div> <div class="reply info"> <a class="comment-32855 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32855 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32855"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32861" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/lantimilan" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/lantimilan" title="Expert lantimilan" class="rated-user user-blue">lantimilan</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 21:03">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32861" href="?#comment-32861" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32861" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="15561" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32861"> <div class="moveup"> <div class="ttypography">The c++ code for problem A has integer overflow, since a and b can be up to 999999999, c=a+b cannot fit into 32-bit int. My solution had the same issue and got hacked.</div> </div> </div> <div class="reply info"> <a class="comment-32861 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32861 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32861"> <li> <div class="comment"> <table class="comment-table" commentId="32863" commentParentId="32861"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Egor" style="position: relative;"> <img src='https://userpic.codeforces.org/838/avatar/6976bef0cdef7d5c.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/Egor" title="International Grandmaster Egor" class="rated-user user-red">Egor</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 21:05">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32863" href="?#comment-32863" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32861" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32863" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="838" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32863"> <div class="moveup"> <div class="ttypography">Actually 1999999998 fits into 32bit signed integer</div> </div> </div> <div class="reply info"> <a class="comment-32863 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32863 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32863"> <li> <div class="comment"> <table class="comment-table" commentId="32891" commentParentId="32863"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/lantimilan" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/lantimilan" title="Expert lantimilan" class="rated-user user-blue">lantimilan</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 22:21">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32891" href="?#comment-32891" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32863" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32891" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="15561" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32891"> <div class="moveup"> <div class="ttypography">That's right. Just realized that my overflow is due to 8999999991, the reverse of 1999999998.</div> </div> </div> <div class="reply info"> <a class="comment-32891 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32891 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32891"> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="32868" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/philolo1" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/philolo1" title="Expert philolo1" class="rated-user user-blue">philolo1</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 21:12">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32868" href="?#comment-32868" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32868" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5296" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32868"> <div class="moveup"> <div class="ttypography">what does the instruction factor[name1] do?</div> </div> </div> <div class="reply info"> <a class="comment-32868 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32868 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32868"> <li> <div class="comment"> <table class="comment-table" commentId="32915" commentParentId="32868"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/14/2011 23:48">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32915" href="?#comment-32915" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32868" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32915" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32915"> <div class="moveup"> <div class="ttypography">Just to make an entry for name1 in the map, and it will be 0. Because I have to print all names even if the factor is 0.<br />If there is no entry for name1, nothing will happen. If there is no entry, it will be the same as factor[name1] = 0.</div> </div> </div> <div class="reply info"> <a class="comment-32915 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32915 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32915"> <li> <div class="comment"> <table class="comment-table" commentId="32937" commentParentId="32915"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/philolo1" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/philolo1" title="Expert philolo1" class="rated-user user-blue">philolo1</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 00:51">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32937" href="?#comment-32937" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32915" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32937" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="5296" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32937"> <div class="moveup"> <div class="ttypography">interesting, I just did map.find()==map.end(), but this is much cooler.</div> </div> </div> <div class="reply info"> <a class="comment-32937 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32937 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32937"> <li> <div class="comment"> <table class="comment-table" commentId="32946" commentParentId="32937"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/smilitude" style="position: relative;"> <img src='https://userpic.codeforces.org/68/avatar/e81e4a6fe0f7bdd8.jpg'/> </a> <div><a href="/profile/smilitude" title="Expert smilitude" class="rated-user user-blue">smilitude</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 02:12">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32946" href="?#comment-32946" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32937" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32946" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="68" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32946"> <div class="moveup"> <div class="ttypography">It's actually safer that way. If you search with if( map[ name1 ] ), every time you do the query, the size of the map increases by 1. Try this - <br /> <pre> map&lt; int,int &gt; one, two; for(int i=1;i&lt;=100; i++) if( one[i] ); for(int i=1;i&lt;=100; i++) if( two.find(i) == two.end() ); cout &lt;&lt; one.size() &lt;&lt; &quot; &quot; &lt;&lt; two.size() &lt;&lt; endl; </pre></div> </div> </div> <div class="reply info"> <a class="comment-32946 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32946 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32946"> <li> <div class="comment"> <table class="comment-table" commentId="32948" commentParentId="32946"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 02:22">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32948" href="?#comment-32948" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-32946" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32948" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32948"> <div class="moveup"> <div class="ttypography">In this problem it's the same, because I wanted to make an entry anyway if it doesn't exist.<br />I didn't write this statement as an if condition.</div> </div> </div> <div class="reply info"> <a class="comment-32948 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32948 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32948"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="278325" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/shubhamgoyal__" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/shubhamgoyal__" title="Candidate Master shubhamgoyal__" class="rated-user user-violet">shubhamgoyal__</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/13/2016 17:17">8 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-278325" href="?#comment-278325" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="278325" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="321533" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-278325"> <div class="moveup"> <div class="ttypography"><p>great explanation for problem D!!!</p></div> </div> </div> <div class="reply info"> <a class="comment-278325 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-278325 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-278325"> <li> <div class="comment"> <table class="comment-table" commentId="278326" commentParentId="278325"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/P_Nyagolov" style="position: relative;"> <img src='https://userpic.codeforces.org/239110/avatar/9494c230dc159315.jpg'/> </a> <div><a href="/profile/P_Nyagolov" title="Expert P_Nyagolov" class="rated-user user-blue">P_Nyagolov</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/13/2016 17:26">8 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-278326" href="?#comment-278326" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-278325" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="278326" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="239110" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-278326"> <div class="moveup"> <div class="ttypography"><p>Seriously, guys, what's wrong with you?</p></div> </div> </div> <div class="reply info"> <a class="comment-278326 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-278326 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-278326"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="599691" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Amr-Fahmy" style="position: relative;"> <img src='https://userpic.codeforces.org/858870/avatar/5c5b1d238b408975.jpg'/> </a> <div><a href="/profile/Amr-Fahmy" title="Expert Amr-Fahmy" class="rated-user user-blue">Amr-Fahmy</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/09/2020 07:21">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-599691" href="?#comment-599691" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="599691" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="858870" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-599691"> <div class="moveup"> <div class="ttypography"><p>I am here after 9 years, The explanation of problem D is the best explanation i have ever read on codeforces ! Thank you</p></div> </div> </div> <div class="reply info"> <a class="comment-599691 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-599691 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-599691"> <li> <div class="comment"> <table class="comment-table" commentId="599695" commentParentId="599691"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/ahmed_aly" style="position: relative;"> <img src='https://userpic.codeforces.org/539/avatar/520d78429a76e908.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/ahmed_aly" title="Expert ahmed_aly" class="rated-user user-blue">ahmed_aly</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/09/2020 07:45">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-599695" href="?#comment-599695" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-599691" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="599695" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="539" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-599695"> <div class="moveup"> <div class="ttypography"><p>Thanks!</p></div> </div> </div> <div class="reply info"> <a class="comment-599695 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-599695 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-599695"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="612647" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/hereForFun" style="position: relative;"> <img src='https://userpic.codeforces.org/695688/avatar/5e5b50c23f422942.jpg'/> </a> <div><a href="/profile/hereForFun" title="Pupil hereForFun" class="rated-user user-green">hereForFun</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/29/2020 08:06">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-612647" href="?#comment-612647" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="612647" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="695688" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-612647"> <div class="moveup"> <div class="ttypography"><p>Hello! I am here from the a2oj ladder. I received a WA on test case 14 in problem A. When I checked the test case and ran it locally, it is giving the correct answer. Why is the output different here? <a href="https://codeforces.com/contest/75/submission/78440577">https://codeforces.com/contest/75/submission/78440577</a> Here is my submission.</p></div> </div> </div> <div class="reply info"> <a class="comment-612647 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-612647 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-612647"> <li> <div class="comment"> <table class="comment-table" commentId="612658" commentParentId="612647"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/qpwoeirut" style="position: relative;"> <img src='https://userpic.codeforces.org/1165565/avatar/71d9b6b641fb567b.jpg'/> </a> <div><a href="/profile/qpwoeirut" title="Candidate Master qpwoeirut" class="rated-user user-violet">qpwoeirut</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/29/2020 08:56">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-612658" href="?#comment-612658" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-612647" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="612658" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1165565" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-612658"> <div class="moveup"> <div class="ttypography"><p>It looks like you're getting overflow from <code>(digit*pow(10,nonZero))</code>. This can be fixed by using a running place multiplier instead of <code>pow</code>.</p><p>See <a href="/contest/75/submission/78443731" title="Submission 78443731 by qpwoeirut">78443731</a> for an accepted version of your code with that change.</p></div> </div> </div> <div class="reply info"> <a class="comment-612658 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-612658 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-612658"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1725" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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76A
76
A
en
A. Gift
<div class="problem-statement"><div class="header"><div class="title">A. Gift</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>The kingdom of Olympia consists of <span class="tex-span"><i>N</i></span> cities and <span class="tex-span"><i>M</i></span> bidirectional roads. Each road connects exactly two cities and two cities can be connected with more than one road. Also it possible that some roads connect city with itself making a loop.</p><p>All roads are constantly plundered with bandits. After a while bandits became bored of wasting time in road robberies, so they suggested the king of Olympia to pay off. According to the offer, bandits want to get a gift consisted of gold and silver coins. Offer also contains a list of restrictions: for each road it is known <span class="tex-span"><i>g</i><sub class="lower-index"><i>i</i></sub></span> — the smallest amount of gold and <span class="tex-span"><i>s</i><sub class="lower-index"><i>i</i></sub></span> — the smallest amount of silver coins that should be in the gift to stop robberies on the road. That is, if the gift contains <span class="tex-span"><i>a</i></span> gold and <span class="tex-span"><i>b</i></span> silver coins, then bandits will stop robberies on all the roads that <span class="tex-span"><i>g</i><sub class="lower-index"><i>i</i></sub> ≤ <i>a</i></span> and <span class="tex-span"><i>s</i><sub class="lower-index"><i>i</i></sub> ≤ <i>b</i></span>.</p><p>Unfortunately kingdom treasury doesn't contain neither gold nor silver coins, but there are Olympian tugriks in it. The cost of one gold coin in tugriks is <span class="tex-span"><i>G</i></span>, and the cost of one silver coin in tugriks is <span class="tex-span"><i>S</i></span>. King really wants to send bandits such gift that for any two cities there will exist a safe path between them. Your task is to find the minimal cost in Olympian tugriks of the required gift.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of the input contains two integers <span class="tex-span"><i>N</i></span> and <span class="tex-span"><i>M</i></span> (<span class="tex-span">2 ≤ <i>N</i> ≤ 200</span>, <span class="tex-span">1 ≤ <i>M</i> ≤ 50 000</span>) — the number of cities and the number of roads, respectively. The second line contains two integers <span class="tex-span"><i>G</i></span> and <span class="tex-span"><i>S</i></span> (<span class="tex-span">1 ≤ <i>G</i>, <i>S</i> ≤ 10<sup class="upper-index">9</sup></span>) — the prices of gold and silver coins in tugriks. The following <span class="tex-span"><i>M</i></span> lines contain information about the offer. Each of the records in list is given as four integers <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub>, <i>y</i><sub class="lower-index"><i>i</i></sub>, <i>g</i><sub class="lower-index"><i>i</i></sub>, <i>s</i><sub class="lower-index"><i>i</i></sub></span>, where <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span> are the numbers of cities that the road connects and <span class="tex-span"><i>g</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>s</i><sub class="lower-index"><i>i</i></sub></span> are minimal gold and silver coins requirements for the <span class="tex-span"><i>i</i></span>-th road (<span class="tex-span">1 ≤ <i>x</i><sub class="lower-index"><i>i</i></sub>, <i>y</i><sub class="lower-index"><i>i</i></sub> ≤ <i>N</i></span>, <span class="tex-span">1 ≤ <i>g</i><sub class="lower-index"><i>i</i></sub>, <i>s</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">9</sup></span>). Cities are numbered from <span class="tex-span">1</span> to <span class="tex-span"><i>N</i></span>. It is possible that there are more than one road between a pair of cities. It is possible that a road connects the city with itself.</p></div><div class="output-specification"><div class="section-title">Output</div><p>The output should contain the minimal cost of the gift in Olympian tugriks. If there is no gift that satisfies the given requirements output <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/32b60774ba82efe4c54c149a4e105457250b9e70.png" style="max-width: 100.0%;max-height: 100.0%;"/>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3 3<br/>2 1<br/>1 2 10 15<br/>1 2 4 20<br/>1 3 5 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>30<br/></pre></div></div></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/76">All-Ukrainian School Olympiad in Informatics</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? 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If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="A" data-uuid="ps_9e3fff0154ece47120783511db382ea80131ac40"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">A. Gift</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>The kingdom of Olympia consists of <span class="tex-span"><i>N</i></span> cities and <span class="tex-span"><i>M</i></span> bidirectional roads. Each road connects exactly two cities and two cities can be connected with more than one road. Also it possible that some roads connect city with itself making a loop.</p><p>All roads are constantly plundered with bandits. After a while bandits became bored of wasting time in road robberies, so they suggested the king of Olympia to pay off. According to the offer, bandits want to get a gift consisted of gold and silver coins. Offer also contains a list of restrictions: for each road it is known <span class="tex-span"><i>g</i><sub class="lower-index"><i>i</i></sub></span> — the smallest amount of gold and <span class="tex-span"><i>s</i><sub class="lower-index"><i>i</i></sub></span> — the smallest amount of silver coins that should be in the gift to stop robberies on the road. That is, if the gift contains <span class="tex-span"><i>a</i></span> gold and <span class="tex-span"><i>b</i></span> silver coins, then bandits will stop robberies on all the roads that <span class="tex-span"><i>g</i><sub class="lower-index"><i>i</i></sub> ≤ <i>a</i></span> and <span class="tex-span"><i>s</i><sub class="lower-index"><i>i</i></sub> ≤ <i>b</i></span>.</p><p>Unfortunately kingdom treasury doesn't contain neither gold nor silver coins, but there are Olympian tugriks in it. The cost of one gold coin in tugriks is <span class="tex-span"><i>G</i></span>, and the cost of one silver coin in tugriks is <span class="tex-span"><i>S</i></span>. King really wants to send bandits such gift that for any two cities there will exist a safe path between them. Your task is to find the minimal cost in Olympian tugriks of the required gift.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of the input contains two integers <span class="tex-span"><i>N</i></span> and <span class="tex-span"><i>M</i></span> (<span class="tex-span">2 ≤ <i>N</i> ≤ 200</span>, <span class="tex-span">1 ≤ <i>M</i> ≤ 50 000</span>) — the number of cities and the number of roads, respectively. The second line contains two integers <span class="tex-span"><i>G</i></span> and <span class="tex-span"><i>S</i></span> (<span class="tex-span">1 ≤ <i>G</i>, <i>S</i> ≤ 10<sup class="upper-index">9</sup></span>) — the prices of gold and silver coins in tugriks. The following <span class="tex-span"><i>M</i></span> lines contain information about the offer. Each of the records in list is given as four integers <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub>, <i>y</i><sub class="lower-index"><i>i</i></sub>, <i>g</i><sub class="lower-index"><i>i</i></sub>, <i>s</i><sub class="lower-index"><i>i</i></sub></span>, where <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span> are the numbers of cities that the road connects and <span class="tex-span"><i>g</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>s</i><sub class="lower-index"><i>i</i></sub></span> are minimal gold and silver coins requirements for the <span class="tex-span"><i>i</i></span>-th road (<span class="tex-span">1 ≤ <i>x</i><sub class="lower-index"><i>i</i></sub>, <i>y</i><sub class="lower-index"><i>i</i></sub> ≤ <i>N</i></span>, <span class="tex-span">1 ≤ <i>g</i><sub class="lower-index"><i>i</i></sub>, <i>s</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">9</sup></span>). Cities are numbered from <span class="tex-span">1</span> to <span class="tex-span"><i>N</i></span>. It is possible that there are more than one road between a pair of cities. It is possible that a road connects the city with itself.</p></div><div class="output-specification"><div class="section-title">Output</div><p>The output should contain the minimal cost of the gift in Olympian tugriks. If there is no gift that satisfies the given requirements output <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/32b60774ba82efe4c54c149a4e105457250b9e70.png" style="max-width: 100.0%;max-height: 100.0%;" />.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3 3<br />2 1<br />1 2 10 15<br />1 2 4 20<br />1 3 5 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>30<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=A]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); if (previousStatementText) { if (previousStatementText !== statementText) { $problem.find(".diff-notifier").show(); $problem.find(".diff-notifier-close").click(function() { Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60); 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["Disjoint set union", "Graphs", "Sortings, orderings", "Trees"]
["dsu", "graphs", "sortings", "trees", "*2200"]
https://codeforces.com/blog/entry/1712
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It is easy to see  that there exist two (probably equal) indexes <span class="tex-span"><i>i</i></span> and <span class="tex-span"><i>j</i></span> such that <span class="tex-span"><i>g</i><sub class="lower-index"><i>i</i></sub> = <i>A</i></span> and <span class="tex-span"><i>s</i><sub class="lower-index"><i>j</i></sub> = <i>B</i></span>. It is true, because in the other case we could decrease either <span class="tex-span"><i>A</i></span> or <span class="tex-span"><i>B</i></span> without changing connectivity of the graph.</div><div><br /></div><div>Let <span class="tex-span"><i>R</i>(<i>A</i>, <i>B</i>)</span> be the graph in which for all <span class="tex-span"><i>i</i></span> the following statement holds: <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/f6a7810c1f985efe671bb157563fc069d097fbce.png" style="max-width: 100.0%;max-height: 100.0%;" />.</div><div><br /></div><div>Let <span class="tex-span"><i>T</i>(<i>A</i>)</span> be the weighted graph in which for all edges <span class="tex-span"><i>g</i><sub class="lower-index"><i>i</i></sub> ≤ <i>A</i></span>. For each edge <span class="tex-span"><i>i</i></span> we will assign a weight equal to <span class="tex-span"><i>s</i><sub class="lower-index"><i>i</i></sub></span>. Let's find a spanning tree of this graph, which has the property that its maximal edge is minimal possible. It can be shown that for the fixed <span class="tex-span"><i>A</i></span> the minimal value of <span class="tex-span"><i>B</i></span> for which graph <span class="tex-span"><i>R</i>(<i>A</i>, <i>B</i>)</span> is still connected is equal to the weight of the maximal edge in this spanning tree.</div><div><br /></div><div><i>Claim</i>. Minimal spanning tree of a graph has the property that its maximal edge is minimal possible among all spanning trees.</div><div><i>Proof</i>. Let <span class="tex-span"><i>L</i></span> be the minimal spanning tree of a graph. Suppose there exists a spanning tree <span class="tex-span"><i>P</i></span> in which all edges have smaller weight than the weight of the maximal edge of <span class="tex-span"><i>L</i></span>. We can then remove the maximal edge from <span class="tex-span"><i>L</i></span> and add some edge from <span class="tex-span"><i>P</i></span> to it which will connect the graph back. After that <span class="tex-span"><i>L</i></span> will have strictly smaller weight, which is impossible because it is a minimal spanning tree.</div><div><br /></div><div>Let's sort all edges of the graph in ascending order of <span class="tex-span"><i>g</i><sub class="lower-index"><i>i</i></sub></span>. Then the edges of graph <span class="tex-span"><i>T</i>(<i>A</i>)</span> for the fixed <span class="tex-span"><i>i</i></span> will be all edges with indexes <span class="tex-span"><i>j</i> ≤ <i>i</i></span>.</div><div><br /></div><div>Suppose that for some value of <span class="tex-span"><i>i</i></span> we have already found minimal spanning tree in every connected component of the graph <span class="tex-span"><i>T</i>(<i>g</i><sub class="lower-index"><i>i</i></sub>)</span>. Let's add an edge with index <span class="tex-span"><i>i</i> + 1</span> into it. If it connects two different components, then after this operation they will be merged into one big component and it is obviously that the spanning tree we have in it is the minimal spanning tree. If <span class="tex-span"><i>i</i> + 1</span>-th edge connects two vertices from the same connected component, then it will create exactly one cycle in the graph. We can find the maximal edge in this cycle and remove it from the graph. It can be proven that the remaining tree will be the minimal spanning tree of this connected component.</div><div><br /></div><div>We can perform the search of the maximal edge in a cycle as well as the insertion and removal of the edges in O(N). The total complexity is <span class="tex-span"><i>O</i>(<i>NM</i> + <i>MlogM</i>)</span>.</div></div><div><br /></div><div><div><b>Problem B: Mice (Roman Rizvanov)</b></div><div><br /></div><div>It is easy to see that the number of closest pieces of cheese for each mouse is not greater than 2.</div><div><br /></div><div>Let's find the closest pieces of cheese for each mouse to the left and to the right from it. From two directions we will choose the one which gives us shorter way to cheese or both of them if their lengths are equal. If on the chosen way between the mouse and the cheese stands another mouse, then we should exclude this way from consideration, because another mouse will get to the cheese faster. Now all the directions lead to cheese and for each piece of cheese there is at most one mouse which can potentially eat it from each direction.</div><div><br /></div><div>We will process mice from left to right. If the current mouse can move left and the cheese to the left of it is not chosen by any other mouse or it is chosen by a mouse with the same distance to it, then the current mouse can move to the left and eat this piece of cheese without interfering with other mice. This choice will not affect any choices of the next mice, because only one mouse can go to this piece of cheese from the right (see previous paragraph). Thus, this choice can not decrease the answer. In all other cases the current mouse can not increase the answer by moving left, so it should move to the right if it has such opportunity.</div><div><br /></div><div>The complexity is <span class="tex-span"><i>O</i>(<i>N</i> + <i>M</i>)</span>.</div><div><br /></div><div>This problem can be also solved using dynamic programming.</div></div><div><br /></div><div><b>Problem C: Mutation (Iaroslav Tverdokhlib)</b></div><div><br /></div><div><div>In the editorial we will replace terms &quot;risk&quot;, &quot;genome&quot; and &quot;gene&quot; with &quot;cost&quot;, &quot;string&quot; and &quot;character&quot;, respectively. Let <span class="tex-span"><i>S</i></span> be the starting string.</div><div><br /></div><div>Let <span class="tex-span"><i>M</i></span> be the bitmask of chars which will be removed. Let's iterate over all possible values of <span class="tex-span"><i>M</i></span>. For the fixed <span class="tex-span"><i>M</i></span> we need to find a cost of the string, which remained after removal of <span class="tex-span"><i>M</i></span> and if this cost doesn't exceed <span class="tex-span"><i>T</i></span> we will increase the answer by 1. Naive implementation of this idea has the complexity <span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>K</i></sup><i>N</i>)</span>.</div><div><br /></div><div>We can not get rid of iterating over all <span class="tex-span"><i>M</i></span>, so we will try to optimize a part of the algorithm which finds a cost of the remaining string.</div><div><br /></div><div>Let's take two indexes <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> from the beginning string <span class="tex-span"><i>l</i> &lt; <i>r</i></span>. Let <span class="tex-span"><i>M</i>'</span> be the bitmask of all characters which are located strictly between them. It is obviously that if <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7b04066e365590d0dc24c90dfc15aabd64c75339.png" style="max-width: 100.0%;max-height: 100.0%;" /> or <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/3880b6b45cb2a0ccd5ea51b69f020c9e5a9f7fa1.png" style="max-width: 100.0%;max-height: 100.0%;" /> then <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> can not be neighbours in the remaining string. Hence for the fixed <span class="tex-span"><i>l</i></span> there are not more than <span class="tex-span"><i>K</i></span> possible candidates for <span class="tex-span"><i>r</i></span>, which means that there are <span class="tex-span"><i>O</i>(<i>NK</i>)</span> pairs of such potential neighbours. We will call such pairs &quot;good&quot;.</div><div><br /></div><div>We want to find out what form should have the set <span class="tex-span"><i>M</i></span> that after its removal indexes <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> became adjacent. It is easy to see that the following two conditions should be true:</div><div><br /></div><div>1. <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/07de7c5bc68bc92d118ada183dab5d78f5c631c4.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div>2. <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7fa1a37ebb11a92726d78e30e0ad17ffda729919.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><br /></div><div>Let's iterate over all good pairs of <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> and for each of them we will find the set <span class="tex-span"><i>M</i>'</span>. For each triple <span class="tex-span">(<i>a</i>, <i>b</i>, <i>P</i>)</span> we will store the sum of costs of neighborhood of all pairs <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> for which <span class="tex-span"><i>S</i><sub class="lower-index"><i>l</i></sub> = <i>a</i></span>, <span class="tex-span"><i>S</i><sub class="lower-index"><i>r</i></sub> = <i>b</i></span>, <span class="tex-span"><i>M</i>' = <i>P</i></span>. After that for the fixed <span class="tex-span"><i>M</i></span> we will iterate over all pairs of characters <span class="tex-span">(<i>a</i>, <i>b</i>)</span> and its subsets <span class="tex-span"><i>P</i></span> and add all their costs together. Also we need to add the cost of removal of <span class="tex-span"><i>M</i></span> and the resulting sum will be the cost of the string which will left after removal of <span class="tex-span"><i>M</i></span>. The complexity of such solution is <span class="tex-span"><i>O</i>(3<sup class="upper-index"><i>K</i></sup> * <i>K</i><sup class="upper-index">2</sup> + <i>NK</i>)</span>.</div><div><br /></div><div>We will optimize the previous solution by decreasing a factor near <span class="tex-span">3<sup class="upper-index"><i>K</i></sup></span>. Let's look at the following (incorrect) algorithm:</div><div><br /></div><div>We will iterate over all good pairs <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> and for each of them we will find <span class="tex-span"><i>M</i>'</span>. Let's create an array <span class="tex-span"><i>v</i></span> in which for each mask <span class="tex-span"><i>P</i></span> we will store the sum of costs of neighborhood of all pairs <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> for which <span class="tex-span"><i>M</i>' = <i>P</i></span>. For the fixed <span class="tex-span"><i>M</i></span> we will find a sum of all values from <span class="tex-span"><i>v</i></span> for all submasks of <span class="tex-span"><i>M</i></span>, then add the cost of removal of <span class="tex-span"><i>M</i></span> to it and the resulting sum will be the cost of the remaining string.</div><div><br /></div><div>This algorithm is incorrect, because some costs of neighborhood are added to the total cost, but in fact the respective <span class="tex-span"><i>l</i></span> or <span class="tex-span"><i>r</i></span> are removed. Let's use inclusion-exclusion principle and make the following at the phase of filling array <span class="tex-span"><i>v</i></span>:</div><div><br /></div><div><span class="tex-span"><i>v</i>[<i>M</i>'] +  = <i>cost</i></span></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/b4d392e8baa2755f671b67077d5ad638a2818e1c.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/0939a5ad00766ddcedb4465081c7dc8c63f0dd22.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/872ba326de38444a17ace78f749a43a3e1eff1d1.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><br /></div><div>With such filling of <span class="tex-span"><i>v</i></span> the algorithm described above is correct and the total complexity becomes <span class="tex-span"><i>O</i>(3<sup class="upper-index"><i>K</i></sup> + <i>NK</i>)</span>.</div><div><br /></div><div>This is still not enough for the full solution, but we are almost there. We only need to find a fast way of finding the sum of the values of <span class="tex-span"><i>v</i></span> for all submasks of all masks <span class="tex-span"><i>M</i></span>. We will use the following iterative algorithm for this purpose:</div><div><br /></div><div>Before the first iteration we have an array <span class="tex-span"><i>v</i></span> in which the starting values are stored. After iteration with number <span class="tex-span"><i>i</i></span> in <span class="tex-span"><i>v</i>[<i>mask</i>]</span> we will store the sum of all the values from the original array <span class="tex-span"><i>v</i></span> for all submasks of <span class="tex-span"><i>mask</i></span> for which the first <span class="tex-span"><i>K</i> - <i>i</i></span> bits are equal to the respective bits of <span class="tex-span"><i>mask</i></span>. On iteration with number <span class="tex-span"><i>i</i></span> for all masks in which the <span class="tex-span"><i>i</i></span>-th bit is equal to 1 (bits are numbered from 1) we will perform the following: <span class="tex-span"><i>v</i>[<i>mask</i>] +  = <i>v</i>[<i>mask</i>\{<i>i</i>}]</span>. It is easy to see that after the <span class="tex-span"><i>K</i></span>-th iteration of this algorithm we will have the values we were looking for in array <span class="tex-span"><i>v</i></span>.</div><div><br /></div><div>The complexity is <span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>K</i></sup><i>K</i> + <i>NK</i>)</span>.</div></div><div><br /></div><div><b>Problem D: Plus and XOR (Daniel Neiter)</b></div><div><br /></div><div>Let's take a look at some bit in X, which is equal to 1. If the respective bit in Y is equal to 0, then we can swap these two bits, thus reducing X and increasing Y without changing their sum and xor. We can conclude that if some bit in X is equal to 1 then the respective bit in Y is also equal to 1. Thus, <span class="tex-span"><i>Y</i> = <i>X</i> + <i>B</i></span>. Taking into account that <span class="tex-span"><i>X</i> + <i>Y</i> = <i>X</i> + <i>X</i> + <i>B</i> = <i>A</i>, </span> we can obtain the following formulas for finding <span class="tex-span"><i>X</i></span> and <span class="tex-span"><i>Y</i></span>:</div><div><br /></div><div><span class="tex-span"><i>X</i> = (<i>A</i> - <i>B</i>) / 2</span></div><div><span class="tex-span"><i>Y</i> = <i>X</i> + <i>B</i></span></div><div><div><br /></div><div>One should also notice that if <span class="tex-span"><i>A</i> &lt; <i>B</i></span> or <span class="tex-span"><i>A</i></span> and <span class="tex-span"><i>B</i></span> have different parity, then the answer doesn't exist and we should output -1. If <span class="tex-span"><i>X</i></span> <span class="tex-span"><i>and</i></span> <span class="tex-span">(<i>A</i> - <i>X</i>) ≠ <i>X</i></span> then the answer is also -1.</div></div><div><br /></div><div><b>Problem E: Points (Daniel Neiter)</b></div><div><b><br /></b></div><div>Let's regroup summands and split the sum of squares of distances we are looking for into two sums:</div><div><b><br /></b></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/6e7ca6f50695e36ea199c3704ebb7574c4bfc029.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/b4a6a53d2cb6e9458620cc0b964c69f610df6601.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><br /></div><div>Now we need to rewrite each of these sums in the following way (it will be shown for the first sum):</div><div><br /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/ce7d437559ce56c7602146506aaec7f5b8f5920b.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/14de3bd836c0e823801f884a115983ff447988b5.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><br /></div><div>This formula allows us to find an answer in one pass through the array. The complexity is O(N).</div><div><br /></div><div><div><b>Problem F: Tourist (Ilya Porublyov)</b></div><div><br /></div><div>We can get to the event <span class="tex-span"><i>j</i></span> from the event <span class="tex-span"><i>i</i></span> if the following statements are true:</div><div><br /></div><div><ul><li><span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub> ≤ <i>t</i><sub class="lower-index"><i>j</i></sub></span><br /></li><li><span class="tex-span">|<i>x</i><sub class="lower-index"><i>i</i></sub> - <i>x</i><sub class="lower-index"><i>j</i></sub>| ≤ |<i>t</i><sub class="lower-index"><i>i</i></sub> - <i>t</i><sub class="lower-index"><i>j</i></sub>|· <i>V</i></span><br /></li></ul></div><div>We can represent all the events as points on a plane with coordinates <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i></sub>, <i>t</i><sub class="lower-index"><i>i</i></sub>)</span>. Now we can reformulate the two statements written above in the following way:<br /></div><div><br /></div><div>From the event <span class="tex-span"><i>i</i></span> we can get to the event <span class="tex-span"><i>j</i></span> if the point <span class="tex-span">(<i>x</i><sub class="lower-index"><i>j</i></sub>, <i>t</i><sub class="lower-index"><i>j</i></sub>)</span> lise inside an angle pointed to the top with its vertex in <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i></sub>, <i>t</i><sub class="lower-index"><i>i</i></sub>)</span> and its sides form an angle <span class="tex-span"><i>arctg</i>(<i>V</i>)</span> with vertical axis. Let's make coordinate transformation according to which the point with coordinates <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i></sub>, <i>t</i><sub class="lower-index"><i>i</i></sub>)</span> will transform into the point <span class="tex-span">(<i>p</i><sub class="lower-index"><i>i</i></sub>, <i>q</i><sub class="lower-index"><i>i</i></sub>)</span>, where</div><div><span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub> =  - <i>x</i><sub class="lower-index"><i>i</i></sub> + <i>t</i><sub class="lower-index"><i>i</i></sub> * <i>V</i></span></div><div><span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub> = <i>x</i><sub class="lower-index"><i>i</i></sub> + <i>t</i><sub class="lower-index"><i>i</i></sub> * <i>V</i></span></div><div><br /></div><div>Now we can get to the event <span class="tex-span"><i>j</i></span> from the event <span class="tex-span"><i>i</i></span> if <span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub> ≤ <i>p</i><sub class="lower-index"><i>j</i></sub></span> и <span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub> ≤ <i>q</i><sub class="lower-index"><i>j</i></sub></span>. Let's sort all points in ascending order of <span class="tex-span"><i>p</i></span>. If several points have the same <span class="tex-span"><i>p</i></span> we will sort them by <span class="tex-span"><i>q</i></span>. The second subproblem of our problem can be solved by finding a longest increasing subsequence by <span class="tex-span"><i>q</i></span> in this array. It can be done in <span class="tex-span"><i>O</i>(<i>NlogN</i>)</span>.</div><div><br /></div><div>To solve the first subproblem we can add dummy event with coordinate 0 and time 0 (if it is not present in our set of events yet) and force tourist's start from it.</div><div><br /></div><div>The total complexity if <span class="tex-span"><i>O</i>(<i>NlogN</i>)</span>.</div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/76" class="notice" style="text-decoration: none;">All-Ukrainian School Olympiad in Informatics</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-996-1712").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "996", blogEntryId: "1712", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces" class="tag notice" style="text-decoration: none;">codeforces</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=editorial" class="tag notice" style="text-decoration: none;">editorial</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=uoi2011" class="tag notice" style="text-decoration: none;">uoi2011</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1712"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+30</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1712"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; 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} .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1722"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (22)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="32624" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/wil93" style="position: relative;"> <img src='https://userpic.codeforces.org/14356/avatar/897f1996dfb7343b.jpg'/> </a> <div><a href="/profile/wil93" title="Expert wil93" class="rated-user user-blue">wil93</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/12/2011 23:20">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32624" href="?#comment-32624" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32624" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="14356" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32624"> <div class="moveup"> <div class="ttypography">Thanks very much, I think E's solution is genial. I understood it now, but it would be very difficult for me to come out with a similar thought :)</div> </div> </div> <div class="reply info"> <a class="comment-32624 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32624 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32624"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="33014" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 16:09">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33014" href="?#comment-33014" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="33014" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="33014" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33014"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">Hi,<br /><br />I would like to ask about problem F. Is there a particular reason why you sort by p first before you sort by q? If not, will sorting by q and then by p for tiebreak change the solution? If not, may I know if you can prove so? I can understand how you make the transformation and why the transformation is correct, but I am not convinced that you can get the optimal solution just by sorting and finding the LIS (Do you mean the longest non-decreasing subsequence? From what I understand, I think you first label the vertices according to the time when they appear. If they appear at the same time, then they have the same label.) Can you please give a proof or explanation why it works?<br /><br />Thanks in advance!</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-33014 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33014 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33014"> <li> <div class="comment"> <table class="comment-table" commentId="33025" commentParentId="33014"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/KADR" style="position: relative;"> <img src='https://userpic.codeforces.org/1028/avatar/9089397f80c0fe42.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/KADR" title="Master KADR" class="rated-user user-orange">KADR</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 18:25">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33025" href="?#comment-33025" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-33014" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="33025" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="33025" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1028" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33025"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">If some two events have the same time then it is impossible to visit them both, so we are not interested in their relative order in the sorted array (after performing the transformation).<div><br /></div><div>After the transformation we can get from the point <span class="tex-span">(<i>p</i><sub class="lower-index"><i>i</i></sub>, <i>q</i><sub class="lower-index"><i>i</i></sub>)</span> to the point <span class="tex-span">(<i>p</i><sub class="lower-index"><i>j</i></sub>, <i>q</i><sub class="lower-index"><i>j</i></sub>)</span> iff <span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub> ≤ <i>p</i><sub class="lower-index"><i>j</i></sub></span> and <span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub> ≤ <i>q</i><sub class="lower-index"><i>j</i></sub></span>. After performing the sorting described in the editorial all points reachable from the point <span class="tex-span">(<i>p</i><sub class="lower-index"><i>i</i></sub>, <i>q</i><sub class="lower-index"><i>i</i></sub>)</span> will have greater indexes in the array. This automatically means that the sequence will be non-decreasing by <span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub></span>, so we only need to care about <span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub></span>. The longest non-decreasing sequence by <span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub></span> is the sequence we are looking for.</div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-33025 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33025 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33025"> <li> <div class="comment"> <table class="comment-table" commentId="33026" commentParentId="33025"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 18:27">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33026" href="?#comment-33026" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-33025" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33026" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33026"> <div class="moveup"> <div class="ttypography">Oh, that makes sense now. Thanks!</div> </div> </div> <div class="reply info"> <a class="comment-33026 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33026 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33026"> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="503943" commentParentId="33014"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/AbdAl-mateen" style="position: relative;"> <img src='https://userpic.codeforces.org/694938/avatar/57122394280e75b5.jpg'/> </a> <div><a href="/profile/AbdAl-mateen" title="Newbie AbdAl-mateen" class="rated-user user-gray">AbdAl-mateen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 07:51">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503943" href="?#comment-503943" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-33014" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="503943" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="694938" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503943"> <div class="moveup"> <div class="ttypography"><p>Hi,</p><p><code>Now we can get to the event j from the event i if pi ≤ pj и qi ≤ qj. Let's sort all points in ascending order of p. If several points have the same p we will sort them by q.</code> Can you please explain it for me?</p></div> </div> </div> <div class="reply info"> <a class="comment-503943 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503943 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503943"> <li> <div class="comment"> <table class="comment-table" commentId="503965" commentParentId="503943"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/IlyaCk" style="position: relative;"> <img src='https://userpic.codeforces.org/19187/avatar/40ba7301419542bd.jpg'/> </a> <div><a href="/profile/IlyaCk" title="Expert IlyaCk" class="rated-user user-blue">IlyaCk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 11:02">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503965" href="?#comment-503965" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503943" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="503965" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="19187" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503965"> <div class="moveup"> <div class="ttypography"><p>What do you want to be explained? Why &quot;Now we can get to the event j from the event i if pi ≤ pj и qi ≤ qj.&quot;? Or what &quot;If several points have the same p we will sort them by q.&quot; mean? Or what?</p></div> </div> </div> <div class="reply info"> <a class="comment-503965 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503965 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503965"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="503976" commentParentId="503943"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/IlyaCk" style="position: relative;"> <img src='https://userpic.codeforces.org/19187/avatar/40ba7301419542bd.jpg'/> </a> <div><a href="/profile/IlyaCk" title="Expert IlyaCk" class="rated-user user-blue">IlyaCk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 11:48">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503976" href="?#comment-503976" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503943" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="503976" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="19187" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503976"> <div class="moveup"> <div class="ttypography"><p><a href="https://drive.google.com/file/d/1fwCssJgSTEJ5ic4AzHjhQBQnrypuQkYm/view?usp=sharing">Here</a> is more detailed tutorial. It's in Ukrainian, but you can Google-translate it (result is poor, but some things are still correct) and look at figures and equations.</p><p>I CAN try to reply on more concrete questions, but I don't want to translate the whole text...</p></div> </div> </div> <div class="reply info"> <a class="comment-503976 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503976 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503976"> <li> <div class="comment"> <table class="comment-table" commentId="503980" commentParentId="503976"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/AbdAl-mateen" style="position: relative;"> <img src='https://userpic.codeforces.org/694938/avatar/57122394280e75b5.jpg'/> </a> <div><a href="/profile/AbdAl-mateen" title="Newbie AbdAl-mateen" class="rated-user user-gray">AbdAl-mateen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 13:17">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503980" href="?#comment-503980" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503976" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="503980" revisionCount="4" revision="4"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">4</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="503980" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="694938" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503980"> <div class="moveup"> <div class="ttypography"><p>Well, What are the significances of p, q axes and angle arctg(v)? What do they represent?</p><p>What I understand before, as I mentioned in another comment's reply was as below: to go to j from i: <code>abs(xj - xi) / tj - ti &lt;= v</code> so, </p><p><code>xj + v*tj &gt;= xi + ti*v</code> and <code>-xi + v*ti &gt;= -xj + v*t</code> </p></div> </div> </div> <div class="reply info"> <a class="comment-503980 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503980 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503980"> <li> <div class="comment"> <table class="comment-table" commentId="503987" commentParentId="503980"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/IlyaCk" style="position: relative;"> <img src='https://userpic.codeforces.org/19187/avatar/40ba7301419542bd.jpg'/> </a> <div><a href="/profile/IlyaCk" title="Expert IlyaCk" class="rated-user user-blue">IlyaCk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 15:12">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503987" href="?#comment-503987" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503980" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="503987" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="19187" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503987"> <div class="moveup"> <div class="ttypography"><p>Axis $$$p$$$ is the direction, where the tourist moves (in plane $$$(x,t)$$$), if his speed is ($$${-}v$$$), i.e.maximal by absolute value and directed to left. Its positive ray is the left-bottom border of the area where the tourist can get in time, starting from the origin of the $$$(p,q)$$$ coordiante system. Similarly, $$$q$$$ is the direction, where the tourist moves (in plane $$$(x,t)$$$), if his speed is ($$${+}v$$$), i.e. maximal by absolute value and directed to right; its positive ray is the right-bottom border of the area where the tourist can get in time, starting from the origin of the $$$(p,q)$$$ coordiante system.</p><p>It's not very obvious to look at these axes... But, from other hand, it's not unnatural: we need some effective checking of where the tourist can get in time and where he cannot, so let's try: what, if we'll consider borders of the &quot;reachable-in-time&quot; area as coordinate axes?</p></div> </div> </div> <div class="reply info"> <a class="comment-503987 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503987 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503987"> <li> <div class="comment"> <table class="comment-table" commentId="503991" commentParentId="503987"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/AbdAl-mateen" style="position: relative;"> <img src='https://userpic.codeforces.org/694938/avatar/57122394280e75b5.jpg'/> </a> <div><a href="/profile/AbdAl-mateen" title="Newbie AbdAl-mateen" class="rated-user user-gray">AbdAl-mateen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 16:12">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503991" href="?#comment-503991" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503987" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="503991" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="503991" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="694938" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503991"> <div class="moveup"> <div class="ttypography"><p>I hope this is my last query:</p><p>If tourist needs to go from i to j where xi &gt; xj, that time the velocity is negative. Right? And, the velocity can not be positive and negative at a time,</p><p>But why do we check</p> <pre><code>pi &lt; pj and qi &lt; qj ? </code></pre><p>Why not </p> <pre><code>pi &lt; pj or qi &lt; qj? </code></pre></div> </div> </div> <div class="reply info"> <a class="comment-503991 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503991 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503991"> <li> <div class="comment"> <table class="comment-table" commentId="504027" commentParentId="503991"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/IlyaCk" style="position: relative;"> <img src='https://userpic.codeforces.org/19187/avatar/40ba7301419542bd.jpg'/> </a> <div><a href="/profile/IlyaCk" title="Expert IlyaCk" class="rated-user user-blue">IlyaCk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 22:22">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-504027" href="?#comment-504027" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503991" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="504027" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="19187" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-504027"> <div class="moveup"> <div class="ttypography"><p>The axis directed from bottom to top is $$$t$$$ (time). The tourist cannot travel in time as he wants and/or change time flow direction. All what he can is to choose </p> <ol> <li><p>whether to stay at place with zero velocity (= move in direction of $$$t$$$, which is exactly in the middle between positive direction of $$$p$$$ and positive direction of $$$q$$$);</p></li> <li><p>or to move with velocity ($$$-v$$$), negative and maximal by absolute value, which is exactly positive direction of $$$p$$$;</p></li> <li><p>or to move with velocity ($$$+v$$$), positive and maximal by absolute value, which is exactly positive direction of $$$q$$$;</p></li> <li><p>or to move with velocity $$$0&lt;w&lt;v$$$ (where $$$v$$$ is $$$v$$$ from input data, and $$$w$$$ is actual tourist's velocity), which is in the same quadrant of the $$$(p,q)$$$-system (both $$$p$$$ and $$$q$$$ positive), but $$$q$$$-projection is bigger that $$$p$$$-projection; in other words, $$$0&lt;w&lt;v$$$ corresponds to $$$0&lt;p&lt;q$$$;</p></li> <li><p>or to move with velocity $$$-v&lt;w&lt;0$$$ (where $$$v$$$ is $$$v$$$ from input data, and $$$w$$$ is actual tourist's velocity), which is in the same quadrant of the $$$(p,q)$$$-system (both $$$p$$$ and $$$q$$$ positive), but $$$q$$$-projection is smaller that $$$p$$$-projection; in other words, $$$-v&lt;w&lt;0$$$ corresponds to $$$0&lt;q&lt;p$$$;</p></li> </ol><p>Whereas $$$(q_i &gt; q_j)$$$ (for moving from $$$i$$$ to $$$j$$$) requires either moving with speed $$$w$$$ which is $$$-\infty\leq w &lt; -v$$$, or even moving in reverse direction of time. Similarly, $$$(p_i &gt; p_j)$$$ (for moving from $$$i$$$ to $$$j$$$) requires either moving with speed $$$w$$$ which is $$$v&lt;w\leq\infty$$$, or even moving in reverse direction of time. So, it's required to have <strong>both</strong> $$$(p_i\leq p_j)$$$ <strong>and</strong> $$$(q_i\leq q_j)$$$</p></div> </div> </div> <div class="reply info"> <a class="comment-504027 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-504027 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-504027"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="33574" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/vinhthinhho" style="position: relative;"> <img src='https://userpic.codeforces.org/17649/avatar/4e3c7559e46fc48.jpg'/> </a> <div><a href="/profile/vinhthinhho" title="Candidate Master vinhthinhho" class="rated-user user-violet">vinhthinhho</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/19/2011 11:21">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33574" href="?#comment-33574" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33574" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="17649" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33574"> <div class="moveup"> <div class="ttypography"><p>i dont understand the transformation of (xi,ti), how does it work??? can anyone tell me the answer?</p></div> </div> </div> <div class="reply info"> <a class="comment-33574 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33574 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33574"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="37642" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Master_Chivu" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Master_Chivu" title="Unrated, Master_Chivu" class="rated-user user-black">Master_Chivu</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/11/2011 20:09">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-37642" href="?#comment-37642" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="37642" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="7062" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-37642"> <div class="moveup"> <div class="ttypography">&quot;It is obsiously that if <img align="middle" class="tex-formula" src="/predownloaded/5c/f4/5cf424ac693f1a0c89b939d7a6e6f6ada6700077.png" style="max-width: 100.0%;max-height: 100.0%;" /> or <img align="middle" class="tex-formula" src="/predownloaded/72/41/7241691bc12db2fb46351355cdd678dfea1703d1.png" style="max-width: 100.0%;max-height: 100.0%;" /> then <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> can not be neighbours in the remaining string.&quot;<br />What is &quot;P&quot;?<br />It seems that &quot;P&quot; hasn't been metioned before.<br />I really cannot understand this sentence.<br />And may &quot;absiously&quot; means &quot;abviously&quot;?<br /><br /></div> </div> </div> <div class="reply info"> <a class="comment-37642 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-37642 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-37642"> <li> <div class="comment"> <table class="comment-table" commentId="37653" commentParentId="37642"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/KADR" style="position: relative;"> <img src='https://userpic.codeforces.org/1028/avatar/9089397f80c0fe42.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/KADR" title="Master KADR" class="rated-user user-orange">KADR</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/11/2011 20:25">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-37653" href="?#comment-37653" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-37642" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="37653" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1028" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-37653"> <div class="moveup"> <div class="ttypography">It was a typo. &quot;Obsiously&quot; should be, of course, &quot;obviously&quot;.<div><br /></div><div>Also I occasionally used P instead of M'. It is fixed now, thanks for pointing this out.</div></div> </div> </div> <div class="reply info"> <a class="comment-37653 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-37653 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-37653"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="39030" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Snow_storm" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Snow_storm" title="Expert Snow_storm" class="rated-user user-blue">Snow_storm</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/18/2011 21:22">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-39030" href="?#comment-39030" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="39030" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6824" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-39030"> <div class="moveup"> <div class="ttypography"><p>Problem D is right?</p> <p>I doubts it, for expleam, A=14 and B=4 </p> <p>then X=(14-4)/2=5  Y=5+4=9</p> <p>and A&gt;B and <span class="tex-span"><i>A</i></span> and <span class="tex-span"><i>B</i></span> have some parity and A-X=Y<br /><br />but X^Y=5^9=12  <br />This is my doubts. And I think  (A-B)/2=X&amp;Y .<br />But I don't know the specific X and Y values</p></div> </div> </div> <div class="reply info"> <a class="comment-39030 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-39030 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-39030"> <li> <div class="comment"> <table class="comment-table" commentId="39031" commentParentId="39030"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/KADR" style="position: relative;"> <img src='https://userpic.codeforces.org/1028/avatar/9089397f80c0fe42.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/KADR" title="Master KADR" class="rated-user user-orange">KADR</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/18/2011 21:29">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-39031" href="?#comment-39031" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-39030" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="39031" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1028" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-39031"> <div class="moveup"> <div class="ttypography">Quote from the editorial:<div><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">&quot;If</span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;"><i>X</i></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;"><i>and</i></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;">(<i>A</i> - <i>X</i>) ≠ <i>X</i></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">then the answer is also -1.&quot;</span><br /></div><div>Here X=5 and A-X=9. 5 and 9 = 1, which is not equal to 5. So the answer is -1 here.</div></div> </div> </div> <div class="reply info"> <a class="comment-39031 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-39031 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-39031"> <li> <div class="comment"> <table class="comment-table" commentId="39038" commentParentId="39031"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Snow_storm" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Snow_storm" title="Expert Snow_storm" class="rated-user user-blue">Snow_storm</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/18/2011 21:42">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-39038" href="?#comment-39038" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-39031" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="39038" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6824" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-39038"> <div class="moveup"> <div class="ttypography">I was wrong, <br /><span style="LINE-HEIGHT: 20.0px;FONT-FAMILY: verdana , arial , sans-serif;FONT-SIZE: 12.0px;"><span class="tex-span" style="FONT-FAMILY: &quot;times new roman&quot;;FONT-SIZE: 15.0px;"><i>and is &amp;</i></span></span><br /><br />But I saw many wrong program still through the test,<br /><br />and thank you very much for your patience solutions</div> </div> </div> <div class="reply info"> <a class="comment-39038 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-39038 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-39038"> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="39034" commentParentId="39030"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Snow_storm" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Snow_storm" title="Expert Snow_storm" class="rated-user user-blue">Snow_storm</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/18/2011 21:35">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-39034" href="?#comment-39034" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-39030" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="39034" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6824" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-39034"> <div class="moveup"> <div class="ttypography">I'm sorry, X is smallest, but I'm think if the answer doesn't exist, should add a condition:  X^Y=B</div> </div> </div> <div class="reply info"> <a class="comment-39034 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-39034 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-39034"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="422212" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/stringray" style="position: relative;"> <img src='https://userpic.codeforces.org/575608/avatar/2902babcf56868a2.jpg'/> </a> <div><a href="/profile/stringray" title="Expert stringray" class="rated-user user-blue">stringray</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/27/2018 21:44">6 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-422212" href="?#comment-422212" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="422212" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="575608" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-422212"> <div class="moveup"> <div class="ttypography"><p>Can someone explain the question Gift in this question it is asking for the minimum coins such that every road's gold coin and silver coin constraints are satisfied then if (A,B) is a valid solution then we can make A=infinite and B=infinite so that there will be always a solution also won't A=max(all gi's) and B=max(all si's ) where gi=minimum gold coins for ith road and si=minimum silver coins for ith road (this is what i have understood from the question can anyone tell what's wrong in my understanding )?</p></div> </div> </div> <div class="reply info"> <a class="comment-422212 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-422212 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-422212"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="517643" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Newtech66" style="position: relative;"> <img src='https://userpic.codeforces.org/748716/avatar/ba5b7d94e0bd5415.jpg'/> </a> <div><a href="/profile/Newtech66" title="Expert Newtech66" class="rated-user user-blue">Newtech66</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/10/2019 13:51">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-517643" href="?#comment-517643" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="517643" class="CommentVoteFrame" class="negative-comment-vote" data-commentRating="-10" data-commentUserId="748716" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">-10</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-517643"> <div class="moveup"> <div class="ttypography"><p>Problem D has weak testcases. My solution gets AC despite giving an incorrect answer on the testcase '10 6'.</p></div> </div> </div> <div class="reply info"> <a class="comment-517643 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-517643 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-517643"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="537992" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/memento" style="position: relative;"> <img src='https://userpic.codeforces.org/852933/avatar/950578c1b4afd9dc.jpg'/> </a> <div><a href="/profile/memento" title="Expert memento" class="rated-user user-blue">memento</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Aug/24/2019 21:32">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-537992" href="?#comment-537992" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="537992" class="CommentVoteFrame" data-commentRating="11" data-commentUserId="852933" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+11</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-537992"> <div class="moveup"> <div class="ttypography"><p>Shit. This was 8 years ago.</p></div> </div> </div> <div class="reply info"> <a class="comment-537992 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-537992 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-537992"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="763848" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/vishaaaal" style="position: relative;"> <img src='https://userpic.codeforces.org/1443354/avatar/25a2dd924894eeeb.jpg'/> </a> <div><a href="/profile/vishaaaal" title="Expert vishaaaal" class="rated-user user-blue">vishaaaal</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/20/2021 12:42">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-763848" href="?#comment-763848" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="763848" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1443354" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-763848"> <div class="moveup"> <div class="ttypography"><p>How to solve A without MST??</p> <div class="spoiler"><b class="spoiler-title">Here's my approach</b><div class="spoiler-content" style="display: none;"><p>Let us consider two cities $$$a$$$ and $$$b$$$. We use <em>dfs</em> to calculate the minimum amount of tugriks required for travelling from $$$a$$$ to $$$b$$$. And the answer will be maximum of such value among all pairs of cities.</p><p>The problem is, I think that calculation of this value requires to use Dynamic Programming. Any hints on that??</p></div></div></div> </div> </div> <div class="reply info"> <a class="comment-763848 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-763848 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-763848"> </ul> </div> <br/> <div id="editBox-1722" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In Russian</span> </div> <textarea data-drafts-id="CommentReplyFrame" class="wysiwyg" name="editContent" rows="20" style="width:99%;"></textarea> <div class="error error__content"></div> <div style="text-align:center;"> <input type="button" name="preview" style="padding: 0.25em 1em; 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76B
76
B
en
B. Mice
<div class="problem-statement"><div class="header"><div class="title">B. Mice</div><div class="time-limit"><div class="property-title">time limit per test</div>0.5 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Modern researches has shown that a flock of hungry mice searching for a piece of cheese acts as follows: if there are several pieces of cheese then each mouse chooses the closest one. After that all mice start moving towards the chosen piece of cheese. When a mouse or several mice achieve the destination point and there is still a piece of cheese in it, they eat it and become well-fed. Each mice that reaches this point after that remains hungry. Moving speeds of all mice are equal.</p><p>If there are several ways to choose closest pieces then mice will choose it in a way that would minimize the number of hungry mice. To check this theory scientists decided to conduct an experiment. They located <span class="tex-span"><i>N</i></span> mice and <span class="tex-span"><i>M</i></span> pieces of cheese on a cartesian plane where all mice are located on the line <span class="tex-span"><i>y</i> = <i>Y</i><sub class="lower-index">0</sub></span> and all pieces of cheese — on another line <span class="tex-span"><i>y</i> = <i>Y</i><sub class="lower-index">1</sub></span>. To check the results of the experiment the scientists need a program which simulates the behavior of a flock of hungry mice.</p><p>Write a program that computes the minimal number of mice which will remain hungry, i.e. without cheese.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of the input contains four integer numbers <span class="tex-span"><i>N</i></span> (<span class="tex-span">1 ≤ <i>N</i> ≤ 10<sup class="upper-index">5</sup></span>), <span class="tex-span"><i>M</i></span> (<span class="tex-span">0 ≤ <i>M</i> ≤ 10<sup class="upper-index">5</sup></span>), <span class="tex-span"><i>Y</i><sub class="lower-index">0</sub></span> (<span class="tex-span">0 ≤ <i>Y</i><sub class="lower-index">0</sub> ≤ 10<sup class="upper-index">7</sup></span>), <span class="tex-span"><i>Y</i><sub class="lower-index">1</sub></span> (<span class="tex-span">0 ≤ <i>Y</i><sub class="lower-index">1</sub> ≤ 10<sup class="upper-index">7</sup></span>, <span class="tex-span"><i>Y</i><sub class="lower-index">0</sub> ≠ <i>Y</i><sub class="lower-index">1</sub></span>). The second line contains a strictly increasing sequence of <span class="tex-span"><i>N</i></span> numbers — <span class="tex-span"><i>x</i></span> coordinates of mice. Third line contains a strictly increasing sequence of <span class="tex-span"><i>M</i></span> numbers — <span class="tex-span"><i>x</i></span> coordinates of cheese. All coordinates are integers and do not exceed <span class="tex-span">10<sup class="upper-index">7</sup></span> by absolute value.</p></div><div class="output-specification"><div class="section-title">Output</div><p>The only line of output should contain one number — the minimal number of mice which will remain without cheese.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3 2 0 2<br/>0 1 3<br/>2 5<br/></pre></div><div class="output"><div class="title">Output</div><pre>1<br/></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>All the three mice will choose the first piece of cheese. Second and third mice will eat this piece. The first one will remain hungry, because it was running towards the same piece, but it was late. The second piece of cheese will remain uneaten.</p></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="B" data-uuid="ps_591e6eb458c212c448040b7a18070322185f976e"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">B. Mice</div><div class="time-limit"><div class="property-title">time limit per test</div>0.5 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Modern researches has shown that a flock of hungry mice searching for a piece of cheese acts as follows: if there are several pieces of cheese then each mouse chooses the closest one. After that all mice start moving towards the chosen piece of cheese. When a mouse or several mice achieve the destination point and there is still a piece of cheese in it, they eat it and become well-fed. Each mice that reaches this point after that remains hungry. Moving speeds of all mice are equal.</p><p>If there are several ways to choose closest pieces then mice will choose it in a way that would minimize the number of hungry mice. To check this theory scientists decided to conduct an experiment. They located <span class="tex-span"><i>N</i></span> mice and <span class="tex-span"><i>M</i></span> pieces of cheese on a cartesian plane where all mice are located on the line <span class="tex-span"><i>y</i> = <i>Y</i><sub class="lower-index">0</sub></span> and all pieces of cheese — on another line <span class="tex-span"><i>y</i> = <i>Y</i><sub class="lower-index">1</sub></span>. To check the results of the experiment the scientists need a program which simulates the behavior of a flock of hungry mice.</p><p>Write a program that computes the minimal number of mice which will remain hungry, i.e. without cheese.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of the input contains four integer numbers <span class="tex-span"><i>N</i></span> (<span class="tex-span">1 ≤ <i>N</i> ≤ 10<sup class="upper-index">5</sup></span>), <span class="tex-span"><i>M</i></span> (<span class="tex-span">0 ≤ <i>M</i> ≤ 10<sup class="upper-index">5</sup></span>), <span class="tex-span"><i>Y</i><sub class="lower-index">0</sub></span> (<span class="tex-span">0 ≤ <i>Y</i><sub class="lower-index">0</sub> ≤ 10<sup class="upper-index">7</sup></span>), <span class="tex-span"><i>Y</i><sub class="lower-index">1</sub></span> (<span class="tex-span">0 ≤ <i>Y</i><sub class="lower-index">1</sub> ≤ 10<sup class="upper-index">7</sup></span>, <span class="tex-span"><i>Y</i><sub class="lower-index">0</sub> ≠ <i>Y</i><sub class="lower-index">1</sub></span>). The second line contains a strictly increasing sequence of <span class="tex-span"><i>N</i></span> numbers — <span class="tex-span"><i>x</i></span> coordinates of mice. Third line contains a strictly increasing sequence of <span class="tex-span"><i>M</i></span> numbers — <span class="tex-span"><i>x</i></span> coordinates of cheese. All coordinates are integers and do not exceed <span class="tex-span">10<sup class="upper-index">7</sup></span> by absolute value.</p></div><div class="output-specification"><div class="section-title">Output</div><p>The only line of output should contain one number — the minimal number of mice which will remain without cheese.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3 2 0 2<br />0 1 3<br />2 5<br /></pre></div><div class="output"><div class="title">Output</div><pre>1<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>All the three mice will choose the first piece of cheese. Second and third mice will eat this piece. The first one will remain hungry, because it was running towards the same piece, but it was late. 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["Greedy algorithms", "Two pointers"]
["greedy", "two pointers", "*2100"]
https://codeforces.com/blog/entry/1712
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It is easy to see  that there exist two (probably equal) indexes <span class="tex-span"><i>i</i></span> and <span class="tex-span"><i>j</i></span> such that <span class="tex-span"><i>g</i><sub class="lower-index"><i>i</i></sub> = <i>A</i></span> and <span class="tex-span"><i>s</i><sub class="lower-index"><i>j</i></sub> = <i>B</i></span>. It is true, because in the other case we could decrease either <span class="tex-span"><i>A</i></span> or <span class="tex-span"><i>B</i></span> without changing connectivity of the graph.</div><div><br /></div><div>Let <span class="tex-span"><i>R</i>(<i>A</i>, <i>B</i>)</span> be the graph in which for all <span class="tex-span"><i>i</i></span> the following statement holds: <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/f6a7810c1f985efe671bb157563fc069d097fbce.png" style="max-width: 100.0%;max-height: 100.0%;" />.</div><div><br /></div><div>Let <span class="tex-span"><i>T</i>(<i>A</i>)</span> be the weighted graph in which for all edges <span class="tex-span"><i>g</i><sub class="lower-index"><i>i</i></sub> ≤ <i>A</i></span>. For each edge <span class="tex-span"><i>i</i></span> we will assign a weight equal to <span class="tex-span"><i>s</i><sub class="lower-index"><i>i</i></sub></span>. Let's find a spanning tree of this graph, which has the property that its maximal edge is minimal possible. It can be shown that for the fixed <span class="tex-span"><i>A</i></span> the minimal value of <span class="tex-span"><i>B</i></span> for which graph <span class="tex-span"><i>R</i>(<i>A</i>, <i>B</i>)</span> is still connected is equal to the weight of the maximal edge in this spanning tree.</div><div><br /></div><div><i>Claim</i>. Minimal spanning tree of a graph has the property that its maximal edge is minimal possible among all spanning trees.</div><div><i>Proof</i>. Let <span class="tex-span"><i>L</i></span> be the minimal spanning tree of a graph. Suppose there exists a spanning tree <span class="tex-span"><i>P</i></span> in which all edges have smaller weight than the weight of the maximal edge of <span class="tex-span"><i>L</i></span>. We can then remove the maximal edge from <span class="tex-span"><i>L</i></span> and add some edge from <span class="tex-span"><i>P</i></span> to it which will connect the graph back. After that <span class="tex-span"><i>L</i></span> will have strictly smaller weight, which is impossible because it is a minimal spanning tree.</div><div><br /></div><div>Let's sort all edges of the graph in ascending order of <span class="tex-span"><i>g</i><sub class="lower-index"><i>i</i></sub></span>. Then the edges of graph <span class="tex-span"><i>T</i>(<i>A</i>)</span> for the fixed <span class="tex-span"><i>i</i></span> will be all edges with indexes <span class="tex-span"><i>j</i> ≤ <i>i</i></span>.</div><div><br /></div><div>Suppose that for some value of <span class="tex-span"><i>i</i></span> we have already found minimal spanning tree in every connected component of the graph <span class="tex-span"><i>T</i>(<i>g</i><sub class="lower-index"><i>i</i></sub>)</span>. Let's add an edge with index <span class="tex-span"><i>i</i> + 1</span> into it. If it connects two different components, then after this operation they will be merged into one big component and it is obviously that the spanning tree we have in it is the minimal spanning tree. If <span class="tex-span"><i>i</i> + 1</span>-th edge connects two vertices from the same connected component, then it will create exactly one cycle in the graph. We can find the maximal edge in this cycle and remove it from the graph. It can be proven that the remaining tree will be the minimal spanning tree of this connected component.</div><div><br /></div><div>We can perform the search of the maximal edge in a cycle as well as the insertion and removal of the edges in O(N). The total complexity is <span class="tex-span"><i>O</i>(<i>NM</i> + <i>MlogM</i>)</span>.</div></div><div><br /></div><div><div><b>Problem B: Mice (Roman Rizvanov)</b></div><div><br /></div><div>It is easy to see that the number of closest pieces of cheese for each mouse is not greater than 2.</div><div><br /></div><div>Let's find the closest pieces of cheese for each mouse to the left and to the right from it. From two directions we will choose the one which gives us shorter way to cheese or both of them if their lengths are equal. If on the chosen way between the mouse and the cheese stands another mouse, then we should exclude this way from consideration, because another mouse will get to the cheese faster. Now all the directions lead to cheese and for each piece of cheese there is at most one mouse which can potentially eat it from each direction.</div><div><br /></div><div>We will process mice from left to right. If the current mouse can move left and the cheese to the left of it is not chosen by any other mouse or it is chosen by a mouse with the same distance to it, then the current mouse can move to the left and eat this piece of cheese without interfering with other mice. This choice will not affect any choices of the next mice, because only one mouse can go to this piece of cheese from the right (see previous paragraph). Thus, this choice can not decrease the answer. In all other cases the current mouse can not increase the answer by moving left, so it should move to the right if it has such opportunity.</div><div><br /></div><div>The complexity is <span class="tex-span"><i>O</i>(<i>N</i> + <i>M</i>)</span>.</div><div><br /></div><div>This problem can be also solved using dynamic programming.</div></div><div><br /></div><div><b>Problem C: Mutation (Iaroslav Tverdokhlib)</b></div><div><br /></div><div><div>In the editorial we will replace terms &quot;risk&quot;, &quot;genome&quot; and &quot;gene&quot; with &quot;cost&quot;, &quot;string&quot; and &quot;character&quot;, respectively. Let <span class="tex-span"><i>S</i></span> be the starting string.</div><div><br /></div><div>Let <span class="tex-span"><i>M</i></span> be the bitmask of chars which will be removed. Let's iterate over all possible values of <span class="tex-span"><i>M</i></span>. For the fixed <span class="tex-span"><i>M</i></span> we need to find a cost of the string, which remained after removal of <span class="tex-span"><i>M</i></span> and if this cost doesn't exceed <span class="tex-span"><i>T</i></span> we will increase the answer by 1. Naive implementation of this idea has the complexity <span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>K</i></sup><i>N</i>)</span>.</div><div><br /></div><div>We can not get rid of iterating over all <span class="tex-span"><i>M</i></span>, so we will try to optimize a part of the algorithm which finds a cost of the remaining string.</div><div><br /></div><div>Let's take two indexes <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> from the beginning string <span class="tex-span"><i>l</i> &lt; <i>r</i></span>. Let <span class="tex-span"><i>M</i>'</span> be the bitmask of all characters which are located strictly between them. It is obviously that if <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7b04066e365590d0dc24c90dfc15aabd64c75339.png" style="max-width: 100.0%;max-height: 100.0%;" /> or <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/3880b6b45cb2a0ccd5ea51b69f020c9e5a9f7fa1.png" style="max-width: 100.0%;max-height: 100.0%;" /> then <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> can not be neighbours in the remaining string. Hence for the fixed <span class="tex-span"><i>l</i></span> there are not more than <span class="tex-span"><i>K</i></span> possible candidates for <span class="tex-span"><i>r</i></span>, which means that there are <span class="tex-span"><i>O</i>(<i>NK</i>)</span> pairs of such potential neighbours. We will call such pairs &quot;good&quot;.</div><div><br /></div><div>We want to find out what form should have the set <span class="tex-span"><i>M</i></span> that after its removal indexes <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> became adjacent. It is easy to see that the following two conditions should be true:</div><div><br /></div><div>1. <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/07de7c5bc68bc92d118ada183dab5d78f5c631c4.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div>2. <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7fa1a37ebb11a92726d78e30e0ad17ffda729919.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><br /></div><div>Let's iterate over all good pairs of <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> and for each of them we will find the set <span class="tex-span"><i>M</i>'</span>. For each triple <span class="tex-span">(<i>a</i>, <i>b</i>, <i>P</i>)</span> we will store the sum of costs of neighborhood of all pairs <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> for which <span class="tex-span"><i>S</i><sub class="lower-index"><i>l</i></sub> = <i>a</i></span>, <span class="tex-span"><i>S</i><sub class="lower-index"><i>r</i></sub> = <i>b</i></span>, <span class="tex-span"><i>M</i>' = <i>P</i></span>. After that for the fixed <span class="tex-span"><i>M</i></span> we will iterate over all pairs of characters <span class="tex-span">(<i>a</i>, <i>b</i>)</span> and its subsets <span class="tex-span"><i>P</i></span> and add all their costs together. Also we need to add the cost of removal of <span class="tex-span"><i>M</i></span> and the resulting sum will be the cost of the string which will left after removal of <span class="tex-span"><i>M</i></span>. The complexity of such solution is <span class="tex-span"><i>O</i>(3<sup class="upper-index"><i>K</i></sup> * <i>K</i><sup class="upper-index">2</sup> + <i>NK</i>)</span>.</div><div><br /></div><div>We will optimize the previous solution by decreasing a factor near <span class="tex-span">3<sup class="upper-index"><i>K</i></sup></span>. Let's look at the following (incorrect) algorithm:</div><div><br /></div><div>We will iterate over all good pairs <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> and for each of them we will find <span class="tex-span"><i>M</i>'</span>. Let's create an array <span class="tex-span"><i>v</i></span> in which for each mask <span class="tex-span"><i>P</i></span> we will store the sum of costs of neighborhood of all pairs <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> for which <span class="tex-span"><i>M</i>' = <i>P</i></span>. For the fixed <span class="tex-span"><i>M</i></span> we will find a sum of all values from <span class="tex-span"><i>v</i></span> for all submasks of <span class="tex-span"><i>M</i></span>, then add the cost of removal of <span class="tex-span"><i>M</i></span> to it and the resulting sum will be the cost of the remaining string.</div><div><br /></div><div>This algorithm is incorrect, because some costs of neighborhood are added to the total cost, but in fact the respective <span class="tex-span"><i>l</i></span> or <span class="tex-span"><i>r</i></span> are removed. Let's use inclusion-exclusion principle and make the following at the phase of filling array <span class="tex-span"><i>v</i></span>:</div><div><br /></div><div><span class="tex-span"><i>v</i>[<i>M</i>'] +  = <i>cost</i></span></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/b4d392e8baa2755f671b67077d5ad638a2818e1c.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/0939a5ad00766ddcedb4465081c7dc8c63f0dd22.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/872ba326de38444a17ace78f749a43a3e1eff1d1.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><br /></div><div>With such filling of <span class="tex-span"><i>v</i></span> the algorithm described above is correct and the total complexity becomes <span class="tex-span"><i>O</i>(3<sup class="upper-index"><i>K</i></sup> + <i>NK</i>)</span>.</div><div><br /></div><div>This is still not enough for the full solution, but we are almost there. We only need to find a fast way of finding the sum of the values of <span class="tex-span"><i>v</i></span> for all submasks of all masks <span class="tex-span"><i>M</i></span>. We will use the following iterative algorithm for this purpose:</div><div><br /></div><div>Before the first iteration we have an array <span class="tex-span"><i>v</i></span> in which the starting values are stored. After iteration with number <span class="tex-span"><i>i</i></span> in <span class="tex-span"><i>v</i>[<i>mask</i>]</span> we will store the sum of all the values from the original array <span class="tex-span"><i>v</i></span> for all submasks of <span class="tex-span"><i>mask</i></span> for which the first <span class="tex-span"><i>K</i> - <i>i</i></span> bits are equal to the respective bits of <span class="tex-span"><i>mask</i></span>. On iteration with number <span class="tex-span"><i>i</i></span> for all masks in which the <span class="tex-span"><i>i</i></span>-th bit is equal to 1 (bits are numbered from 1) we will perform the following: <span class="tex-span"><i>v</i>[<i>mask</i>] +  = <i>v</i>[<i>mask</i>\{<i>i</i>}]</span>. It is easy to see that after the <span class="tex-span"><i>K</i></span>-th iteration of this algorithm we will have the values we were looking for in array <span class="tex-span"><i>v</i></span>.</div><div><br /></div><div>The complexity is <span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>K</i></sup><i>K</i> + <i>NK</i>)</span>.</div></div><div><br /></div><div><b>Problem D: Plus and XOR (Daniel Neiter)</b></div><div><br /></div><div>Let's take a look at some bit in X, which is equal to 1. If the respective bit in Y is equal to 0, then we can swap these two bits, thus reducing X and increasing Y without changing their sum and xor. We can conclude that if some bit in X is equal to 1 then the respective bit in Y is also equal to 1. Thus, <span class="tex-span"><i>Y</i> = <i>X</i> + <i>B</i></span>. Taking into account that <span class="tex-span"><i>X</i> + <i>Y</i> = <i>X</i> + <i>X</i> + <i>B</i> = <i>A</i>, </span> we can obtain the following formulas for finding <span class="tex-span"><i>X</i></span> and <span class="tex-span"><i>Y</i></span>:</div><div><br /></div><div><span class="tex-span"><i>X</i> = (<i>A</i> - <i>B</i>) / 2</span></div><div><span class="tex-span"><i>Y</i> = <i>X</i> + <i>B</i></span></div><div><div><br /></div><div>One should also notice that if <span class="tex-span"><i>A</i> &lt; <i>B</i></span> or <span class="tex-span"><i>A</i></span> and <span class="tex-span"><i>B</i></span> have different parity, then the answer doesn't exist and we should output -1. If <span class="tex-span"><i>X</i></span> <span class="tex-span"><i>and</i></span> <span class="tex-span">(<i>A</i> - <i>X</i>) ≠ <i>X</i></span> then the answer is also -1.</div></div><div><br /></div><div><b>Problem E: Points (Daniel Neiter)</b></div><div><b><br /></b></div><div>Let's regroup summands and split the sum of squares of distances we are looking for into two sums:</div><div><b><br /></b></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/6e7ca6f50695e36ea199c3704ebb7574c4bfc029.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/b4a6a53d2cb6e9458620cc0b964c69f610df6601.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><br /></div><div>Now we need to rewrite each of these sums in the following way (it will be shown for the first sum):</div><div><br /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/ce7d437559ce56c7602146506aaec7f5b8f5920b.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/14de3bd836c0e823801f884a115983ff447988b5.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><br /></div><div>This formula allows us to find an answer in one pass through the array. The complexity is O(N).</div><div><br /></div><div><div><b>Problem F: Tourist (Ilya Porublyov)</b></div><div><br /></div><div>We can get to the event <span class="tex-span"><i>j</i></span> from the event <span class="tex-span"><i>i</i></span> if the following statements are true:</div><div><br /></div><div><ul><li><span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub> ≤ <i>t</i><sub class="lower-index"><i>j</i></sub></span><br /></li><li><span class="tex-span">|<i>x</i><sub class="lower-index"><i>i</i></sub> - <i>x</i><sub class="lower-index"><i>j</i></sub>| ≤ |<i>t</i><sub class="lower-index"><i>i</i></sub> - <i>t</i><sub class="lower-index"><i>j</i></sub>|· <i>V</i></span><br /></li></ul></div><div>We can represent all the events as points on a plane with coordinates <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i></sub>, <i>t</i><sub class="lower-index"><i>i</i></sub>)</span>. Now we can reformulate the two statements written above in the following way:<br /></div><div><br /></div><div>From the event <span class="tex-span"><i>i</i></span> we can get to the event <span class="tex-span"><i>j</i></span> if the point <span class="tex-span">(<i>x</i><sub class="lower-index"><i>j</i></sub>, <i>t</i><sub class="lower-index"><i>j</i></sub>)</span> lise inside an angle pointed to the top with its vertex in <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i></sub>, <i>t</i><sub class="lower-index"><i>i</i></sub>)</span> and its sides form an angle <span class="tex-span"><i>arctg</i>(<i>V</i>)</span> with vertical axis. Let's make coordinate transformation according to which the point with coordinates <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i></sub>, <i>t</i><sub class="lower-index"><i>i</i></sub>)</span> will transform into the point <span class="tex-span">(<i>p</i><sub class="lower-index"><i>i</i></sub>, <i>q</i><sub class="lower-index"><i>i</i></sub>)</span>, where</div><div><span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub> =  - <i>x</i><sub class="lower-index"><i>i</i></sub> + <i>t</i><sub class="lower-index"><i>i</i></sub> * <i>V</i></span></div><div><span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub> = <i>x</i><sub class="lower-index"><i>i</i></sub> + <i>t</i><sub class="lower-index"><i>i</i></sub> * <i>V</i></span></div><div><br /></div><div>Now we can get to the event <span class="tex-span"><i>j</i></span> from the event <span class="tex-span"><i>i</i></span> if <span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub> ≤ <i>p</i><sub class="lower-index"><i>j</i></sub></span> и <span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub> ≤ <i>q</i><sub class="lower-index"><i>j</i></sub></span>. Let's sort all points in ascending order of <span class="tex-span"><i>p</i></span>. If several points have the same <span class="tex-span"><i>p</i></span> we will sort them by <span class="tex-span"><i>q</i></span>. The second subproblem of our problem can be solved by finding a longest increasing subsequence by <span class="tex-span"><i>q</i></span> in this array. It can be done in <span class="tex-span"><i>O</i>(<i>NlogN</i>)</span>.</div><div><br /></div><div>To solve the first subproblem we can add dummy event with coordinate 0 and time 0 (if it is not present in our set of events yet) and force tourist's start from it.</div><div><br /></div><div>The total complexity if <span class="tex-span"><i>O</i>(<i>NlogN</i>)</span>.</div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/76" class="notice" style="text-decoration: none;">All-Ukrainian School Olympiad in Informatics</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-996-1712").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "996", blogEntryId: "1712", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); 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} .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1722"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (22)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="32624" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/wil93" style="position: relative;"> <img src='https://userpic.codeforces.org/14356/avatar/897f1996dfb7343b.jpg'/> </a> <div><a href="/profile/wil93" title="Expert wil93" class="rated-user user-blue">wil93</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/12/2011 23:20">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32624" href="?#comment-32624" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32624" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="14356" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32624"> <div class="moveup"> <div class="ttypography">Thanks very much, I think E's solution is genial. I understood it now, but it would be very difficult for me to come out with a similar thought :)</div> </div> </div> <div class="reply info"> <a class="comment-32624 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32624 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32624"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="33014" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 16:09">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33014" href="?#comment-33014" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="33014" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="33014" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33014"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">Hi,<br /><br />I would like to ask about problem F. Is there a particular reason why you sort by p first before you sort by q? If not, will sorting by q and then by p for tiebreak change the solution? If not, may I know if you can prove so? I can understand how you make the transformation and why the transformation is correct, but I am not convinced that you can get the optimal solution just by sorting and finding the LIS (Do you mean the longest non-decreasing subsequence? From what I understand, I think you first label the vertices according to the time when they appear. If they appear at the same time, then they have the same label.) Can you please give a proof or explanation why it works?<br /><br />Thanks in advance!</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-33014 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33014 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33014"> <li> <div class="comment"> <table class="comment-table" commentId="33025" commentParentId="33014"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/KADR" style="position: relative;"> <img src='https://userpic.codeforces.org/1028/avatar/9089397f80c0fe42.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/KADR" title="Master KADR" class="rated-user user-orange">KADR</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 18:25">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33025" href="?#comment-33025" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-33014" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="33025" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="33025" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1028" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33025"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">If some two events have the same time then it is impossible to visit them both, so we are not interested in their relative order in the sorted array (after performing the transformation).<div><br /></div><div>After the transformation we can get from the point <span class="tex-span">(<i>p</i><sub class="lower-index"><i>i</i></sub>, <i>q</i><sub class="lower-index"><i>i</i></sub>)</span> to the point <span class="tex-span">(<i>p</i><sub class="lower-index"><i>j</i></sub>, <i>q</i><sub class="lower-index"><i>j</i></sub>)</span> iff <span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub> ≤ <i>p</i><sub class="lower-index"><i>j</i></sub></span> and <span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub> ≤ <i>q</i><sub class="lower-index"><i>j</i></sub></span>. After performing the sorting described in the editorial all points reachable from the point <span class="tex-span">(<i>p</i><sub class="lower-index"><i>i</i></sub>, <i>q</i><sub class="lower-index"><i>i</i></sub>)</span> will have greater indexes in the array. This automatically means that the sequence will be non-decreasing by <span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub></span>, so we only need to care about <span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub></span>. The longest non-decreasing sequence by <span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub></span> is the sequence we are looking for.</div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-33025 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33025 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33025"> <li> <div class="comment"> <table class="comment-table" commentId="33026" commentParentId="33025"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 18:27">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33026" href="?#comment-33026" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-33025" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33026" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33026"> <div class="moveup"> <div class="ttypography">Oh, that makes sense now. Thanks!</div> </div> </div> <div class="reply info"> <a class="comment-33026 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33026 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33026"> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="503943" commentParentId="33014"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/AbdAl-mateen" style="position: relative;"> <img src='https://userpic.codeforces.org/694938/avatar/57122394280e75b5.jpg'/> </a> <div><a href="/profile/AbdAl-mateen" title="Newbie AbdAl-mateen" class="rated-user user-gray">AbdAl-mateen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 07:51">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503943" href="?#comment-503943" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-33014" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="503943" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="694938" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503943"> <div class="moveup"> <div class="ttypography"><p>Hi,</p><p><code>Now we can get to the event j from the event i if pi ≤ pj и qi ≤ qj. Let's sort all points in ascending order of p. If several points have the same p we will sort them by q.</code> Can you please explain it for me?</p></div> </div> </div> <div class="reply info"> <a class="comment-503943 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503943 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503943"> <li> <div class="comment"> <table class="comment-table" commentId="503965" commentParentId="503943"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/IlyaCk" style="position: relative;"> <img src='https://userpic.codeforces.org/19187/avatar/40ba7301419542bd.jpg'/> </a> <div><a href="/profile/IlyaCk" title="Expert IlyaCk" class="rated-user user-blue">IlyaCk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 11:02">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503965" href="?#comment-503965" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503943" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="503965" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="19187" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503965"> <div class="moveup"> <div class="ttypography"><p>What do you want to be explained? Why &quot;Now we can get to the event j from the event i if pi ≤ pj и qi ≤ qj.&quot;? Or what &quot;If several points have the same p we will sort them by q.&quot; mean? Or what?</p></div> </div> </div> <div class="reply info"> <a class="comment-503965 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503965 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503965"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="503976" commentParentId="503943"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/IlyaCk" style="position: relative;"> <img src='https://userpic.codeforces.org/19187/avatar/40ba7301419542bd.jpg'/> </a> <div><a href="/profile/IlyaCk" title="Expert IlyaCk" class="rated-user user-blue">IlyaCk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 11:48">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503976" href="?#comment-503976" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503943" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="503976" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="19187" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503976"> <div class="moveup"> <div class="ttypography"><p><a href="https://drive.google.com/file/d/1fwCssJgSTEJ5ic4AzHjhQBQnrypuQkYm/view?usp=sharing">Here</a> is more detailed tutorial. It's in Ukrainian, but you can Google-translate it (result is poor, but some things are still correct) and look at figures and equations.</p><p>I CAN try to reply on more concrete questions, but I don't want to translate the whole text...</p></div> </div> </div> <div class="reply info"> <a class="comment-503976 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503976 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503976"> <li> <div class="comment"> <table class="comment-table" commentId="503980" commentParentId="503976"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/AbdAl-mateen" style="position: relative;"> <img src='https://userpic.codeforces.org/694938/avatar/57122394280e75b5.jpg'/> </a> <div><a href="/profile/AbdAl-mateen" title="Newbie AbdAl-mateen" class="rated-user user-gray">AbdAl-mateen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 13:17">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503980" href="?#comment-503980" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503976" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="503980" revisionCount="4" revision="4"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">4</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="503980" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="694938" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503980"> <div class="moveup"> <div class="ttypography"><p>Well, What are the significances of p, q axes and angle arctg(v)? What do they represent?</p><p>What I understand before, as I mentioned in another comment's reply was as below: to go to j from i: <code>abs(xj - xi) / tj - ti &lt;= v</code> so, </p><p><code>xj + v*tj &gt;= xi + ti*v</code> and <code>-xi + v*ti &gt;= -xj + v*t</code> </p></div> </div> </div> <div class="reply info"> <a class="comment-503980 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503980 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503980"> <li> <div class="comment"> <table class="comment-table" commentId="503987" commentParentId="503980"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/IlyaCk" style="position: relative;"> <img src='https://userpic.codeforces.org/19187/avatar/40ba7301419542bd.jpg'/> </a> <div><a href="/profile/IlyaCk" title="Expert IlyaCk" class="rated-user user-blue">IlyaCk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 15:12">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503987" href="?#comment-503987" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503980" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="503987" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="19187" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503987"> <div class="moveup"> <div class="ttypography"><p>Axis $$$p$$$ is the direction, where the tourist moves (in plane $$$(x,t)$$$), if his speed is ($$${-}v$$$), i.e.maximal by absolute value and directed to left. Its positive ray is the left-bottom border of the area where the tourist can get in time, starting from the origin of the $$$(p,q)$$$ coordiante system. Similarly, $$$q$$$ is the direction, where the tourist moves (in plane $$$(x,t)$$$), if his speed is ($$${+}v$$$), i.e. maximal by absolute value and directed to right; its positive ray is the right-bottom border of the area where the tourist can get in time, starting from the origin of the $$$(p,q)$$$ coordiante system.</p><p>It's not very obvious to look at these axes... But, from other hand, it's not unnatural: we need some effective checking of where the tourist can get in time and where he cannot, so let's try: what, if we'll consider borders of the &quot;reachable-in-time&quot; area as coordinate axes?</p></div> </div> </div> <div class="reply info"> <a class="comment-503987 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503987 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503987"> <li> <div class="comment"> <table class="comment-table" commentId="503991" commentParentId="503987"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/AbdAl-mateen" style="position: relative;"> <img src='https://userpic.codeforces.org/694938/avatar/57122394280e75b5.jpg'/> </a> <div><a href="/profile/AbdAl-mateen" title="Newbie AbdAl-mateen" class="rated-user user-gray">AbdAl-mateen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 16:12">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503991" href="?#comment-503991" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503987" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="503991" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="503991" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="694938" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503991"> <div class="moveup"> <div class="ttypography"><p>I hope this is my last query:</p><p>If tourist needs to go from i to j where xi &gt; xj, that time the velocity is negative. Right? And, the velocity can not be positive and negative at a time,</p><p>But why do we check</p> <pre><code>pi &lt; pj and qi &lt; qj ? </code></pre><p>Why not </p> <pre><code>pi &lt; pj or qi &lt; qj? </code></pre></div> </div> </div> <div class="reply info"> <a class="comment-503991 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503991 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503991"> <li> <div class="comment"> <table class="comment-table" commentId="504027" commentParentId="503991"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/IlyaCk" style="position: relative;"> <img src='https://userpic.codeforces.org/19187/avatar/40ba7301419542bd.jpg'/> </a> <div><a href="/profile/IlyaCk" title="Expert IlyaCk" class="rated-user user-blue">IlyaCk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 22:22">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-504027" href="?#comment-504027" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503991" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="504027" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="19187" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-504027"> <div class="moveup"> <div class="ttypography"><p>The axis directed from bottom to top is $$$t$$$ (time). The tourist cannot travel in time as he wants and/or change time flow direction. All what he can is to choose </p> <ol> <li><p>whether to stay at place with zero velocity (= move in direction of $$$t$$$, which is exactly in the middle between positive direction of $$$p$$$ and positive direction of $$$q$$$);</p></li> <li><p>or to move with velocity ($$$-v$$$), negative and maximal by absolute value, which is exactly positive direction of $$$p$$$;</p></li> <li><p>or to move with velocity ($$$+v$$$), positive and maximal by absolute value, which is exactly positive direction of $$$q$$$;</p></li> <li><p>or to move with velocity $$$0&lt;w&lt;v$$$ (where $$$v$$$ is $$$v$$$ from input data, and $$$w$$$ is actual tourist's velocity), which is in the same quadrant of the $$$(p,q)$$$-system (both $$$p$$$ and $$$q$$$ positive), but $$$q$$$-projection is bigger that $$$p$$$-projection; in other words, $$$0&lt;w&lt;v$$$ corresponds to $$$0&lt;p&lt;q$$$;</p></li> <li><p>or to move with velocity $$$-v&lt;w&lt;0$$$ (where $$$v$$$ is $$$v$$$ from input data, and $$$w$$$ is actual tourist's velocity), which is in the same quadrant of the $$$(p,q)$$$-system (both $$$p$$$ and $$$q$$$ positive), but $$$q$$$-projection is smaller that $$$p$$$-projection; in other words, $$$-v&lt;w&lt;0$$$ corresponds to $$$0&lt;q&lt;p$$$;</p></li> </ol><p>Whereas $$$(q_i &gt; q_j)$$$ (for moving from $$$i$$$ to $$$j$$$) requires either moving with speed $$$w$$$ which is $$$-\infty\leq w &lt; -v$$$, or even moving in reverse direction of time. Similarly, $$$(p_i &gt; p_j)$$$ (for moving from $$$i$$$ to $$$j$$$) requires either moving with speed $$$w$$$ which is $$$v&lt;w\leq\infty$$$, or even moving in reverse direction of time. So, it's required to have <strong>both</strong> $$$(p_i\leq p_j)$$$ <strong>and</strong> $$$(q_i\leq q_j)$$$</p></div> </div> </div> <div class="reply info"> <a class="comment-504027 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-504027 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-504027"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="33574" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/vinhthinhho" style="position: relative;"> <img src='https://userpic.codeforces.org/17649/avatar/4e3c7559e46fc48.jpg'/> </a> <div><a href="/profile/vinhthinhho" title="Candidate Master vinhthinhho" class="rated-user user-violet">vinhthinhho</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/19/2011 11:21">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33574" href="?#comment-33574" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33574" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="17649" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33574"> <div class="moveup"> <div class="ttypography"><p>i dont understand the transformation of (xi,ti), how does it work??? can anyone tell me the answer?</p></div> </div> </div> <div class="reply info"> <a class="comment-33574 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33574 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33574"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="37642" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Master_Chivu" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Master_Chivu" title="Unrated, Master_Chivu" class="rated-user user-black">Master_Chivu</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/11/2011 20:09">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-37642" href="?#comment-37642" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="37642" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="7062" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-37642"> <div class="moveup"> <div class="ttypography">&quot;It is obsiously that if <img align="middle" class="tex-formula" src="/predownloaded/5c/f4/5cf424ac693f1a0c89b939d7a6e6f6ada6700077.png" style="max-width: 100.0%;max-height: 100.0%;" /> or <img align="middle" class="tex-formula" src="/predownloaded/72/41/7241691bc12db2fb46351355cdd678dfea1703d1.png" style="max-width: 100.0%;max-height: 100.0%;" /> then <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> can not be neighbours in the remaining string.&quot;<br />What is &quot;P&quot;?<br />It seems that &quot;P&quot; hasn't been metioned before.<br />I really cannot understand this sentence.<br />And may &quot;absiously&quot; means &quot;abviously&quot;?<br /><br /></div> </div> </div> <div class="reply info"> <a class="comment-37642 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-37642 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-37642"> <li> <div class="comment"> <table class="comment-table" commentId="37653" commentParentId="37642"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/KADR" style="position: relative;"> <img src='https://userpic.codeforces.org/1028/avatar/9089397f80c0fe42.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/KADR" title="Master KADR" class="rated-user user-orange">KADR</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/11/2011 20:25">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-37653" href="?#comment-37653" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-37642" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="37653" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1028" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-37653"> <div class="moveup"> <div class="ttypography">It was a typo. &quot;Obsiously&quot; should be, of course, &quot;obviously&quot;.<div><br /></div><div>Also I occasionally used P instead of M'. It is fixed now, thanks for pointing this out.</div></div> </div> </div> <div class="reply info"> <a class="comment-37653 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-37653 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-37653"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="39030" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Snow_storm" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Snow_storm" title="Expert Snow_storm" class="rated-user user-blue">Snow_storm</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/18/2011 21:22">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-39030" href="?#comment-39030" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="39030" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6824" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-39030"> <div class="moveup"> <div class="ttypography"><p>Problem D is right?</p> <p>I doubts it, for expleam, A=14 and B=4 </p> <p>then X=(14-4)/2=5  Y=5+4=9</p> <p>and A&gt;B and <span class="tex-span"><i>A</i></span> and <span class="tex-span"><i>B</i></span> have some parity and A-X=Y<br /><br />but X^Y=5^9=12  <br />This is my doubts. And I think  (A-B)/2=X&amp;Y .<br />But I don't know the specific X and Y values</p></div> </div> </div> <div class="reply info"> <a class="comment-39030 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-39030 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-39030"> <li> <div class="comment"> <table class="comment-table" commentId="39031" commentParentId="39030"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/KADR" style="position: relative;"> <img src='https://userpic.codeforces.org/1028/avatar/9089397f80c0fe42.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/KADR" title="Master KADR" class="rated-user user-orange">KADR</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/18/2011 21:29">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-39031" href="?#comment-39031" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-39030" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="39031" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1028" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-39031"> <div class="moveup"> <div class="ttypography">Quote from the editorial:<div><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">&quot;If</span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;"><i>X</i></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;"><i>and</i></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;">(<i>A</i> - <i>X</i>) ≠ <i>X</i></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">then the answer is also -1.&quot;</span><br /></div><div>Here X=5 and A-X=9. 5 and 9 = 1, which is not equal to 5. So the answer is -1 here.</div></div> </div> </div> <div class="reply info"> <a class="comment-39031 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-39031 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-39031"> <li> <div class="comment"> <table class="comment-table" commentId="39038" commentParentId="39031"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Snow_storm" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Snow_storm" title="Expert Snow_storm" class="rated-user user-blue">Snow_storm</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/18/2011 21:42">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-39038" href="?#comment-39038" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-39031" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="39038" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6824" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-39038"> <div class="moveup"> <div class="ttypography">I was wrong, <br /><span style="LINE-HEIGHT: 20.0px;FONT-FAMILY: verdana , arial , sans-serif;FONT-SIZE: 12.0px;"><span class="tex-span" style="FONT-FAMILY: &quot;times new roman&quot;;FONT-SIZE: 15.0px;"><i>and is &amp;</i></span></span><br /><br />But I saw many wrong program still through the test,<br /><br />and thank you very much for your patience solutions</div> </div> </div> <div class="reply info"> <a class="comment-39038 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-39038 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-39038"> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="39034" commentParentId="39030"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Snow_storm" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Snow_storm" title="Expert Snow_storm" class="rated-user user-blue">Snow_storm</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/18/2011 21:35">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-39034" href="?#comment-39034" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-39030" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="39034" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6824" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-39034"> <div class="moveup"> <div class="ttypography">I'm sorry, X is smallest, but I'm think if the answer doesn't exist, should add a condition:  X^Y=B</div> </div> </div> <div class="reply info"> <a class="comment-39034 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-39034 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-39034"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="422212" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/stringray" style="position: relative;"> <img src='https://userpic.codeforces.org/575608/avatar/2902babcf56868a2.jpg'/> </a> <div><a href="/profile/stringray" title="Expert stringray" class="rated-user user-blue">stringray</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/27/2018 21:44">6 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-422212" href="?#comment-422212" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="422212" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="575608" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-422212"> <div class="moveup"> <div class="ttypography"><p>Can someone explain the question Gift in this question it is asking for the minimum coins such that every road's gold coin and silver coin constraints are satisfied then if (A,B) is a valid solution then we can make A=infinite and B=infinite so that there will be always a solution also won't A=max(all gi's) and B=max(all si's ) where gi=minimum gold coins for ith road and si=minimum silver coins for ith road (this is what i have understood from the question can anyone tell what's wrong in my understanding )?</p></div> </div> </div> <div class="reply info"> <a class="comment-422212 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-422212 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-422212"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="517643" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Newtech66" style="position: relative;"> <img src='https://userpic.codeforces.org/748716/avatar/ba5b7d94e0bd5415.jpg'/> </a> <div><a href="/profile/Newtech66" title="Expert Newtech66" class="rated-user user-blue">Newtech66</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/10/2019 13:51">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-517643" href="?#comment-517643" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="517643" class="CommentVoteFrame" class="negative-comment-vote" data-commentRating="-10" data-commentUserId="748716" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">-10</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-517643"> <div class="moveup"> <div class="ttypography"><p>Problem D has weak testcases. My solution gets AC despite giving an incorrect answer on the testcase '10 6'.</p></div> </div> </div> <div class="reply info"> <a class="comment-517643 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-517643 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-517643"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="537992" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/memento" style="position: relative;"> <img src='https://userpic.codeforces.org/852933/avatar/950578c1b4afd9dc.jpg'/> </a> <div><a href="/profile/memento" title="Expert memento" class="rated-user user-blue">memento</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Aug/24/2019 21:32">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-537992" href="?#comment-537992" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="537992" class="CommentVoteFrame" data-commentRating="11" data-commentUserId="852933" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+11</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-537992"> <div class="moveup"> <div class="ttypography"><p>Shit. This was 8 years ago.</p></div> </div> </div> <div class="reply info"> <a class="comment-537992 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-537992 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-537992"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="763848" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/vishaaaal" style="position: relative;"> <img src='https://userpic.codeforces.org/1443354/avatar/25a2dd924894eeeb.jpg'/> </a> <div><a href="/profile/vishaaaal" title="Expert vishaaaal" class="rated-user user-blue">vishaaaal</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/20/2021 12:42">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-763848" href="?#comment-763848" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="763848" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1443354" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-763848"> <div class="moveup"> <div class="ttypography"><p>How to solve A without MST??</p> <div class="spoiler"><b class="spoiler-title">Here's my approach</b><div class="spoiler-content" style="display: none;"><p>Let us consider two cities $$$a$$$ and $$$b$$$. We use <em>dfs</em> to calculate the minimum amount of tugriks required for travelling from $$$a$$$ to $$$b$$$. And the answer will be maximum of such value among all pairs of cities.</p><p>The problem is, I think that calculation of this value requires to use Dynamic Programming. Any hints on that??</p></div></div></div> </div> </div> <div class="reply info"> <a class="comment-763848 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-763848 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-763848"> </ul> </div> <br/> <div id="editBox-1722" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In Russian</span> </div> <textarea data-drafts-id="CommentReplyFrame" class="wysiwyg" name="editContent" rows="20" style="width:99%;"></textarea> <div class="error error__content"></div> <div style="text-align:center;"> <input type="button" name="preview" style="padding: 0.25em 1em; 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76C
76
C
en
C. Mutation
<div class="problem-statement"><div class="header"><div class="title">C. Mutation</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Scientists of planet Olympia are conducting an experiment in mutation of primitive organisms. Genome of organism from this planet can be represented as a string of the first <span class="tex-span"><i>K</i></span> capital English letters. For each pair of types of genes they assigned <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i>, <i>j</i></sub></span> — a risk of disease occurence in the organism provided that genes of these types are adjacent in the genome, where <span class="tex-span"><i>i</i></span> — the 1-based index of the first gene and <span class="tex-span"><i>j</i></span> — the index of the second gene. The gene 'A' has index 1, 'B' has index 2 and so on. For example, <span class="tex-span"><i>a</i><sub class="lower-index">3, 2</sub></span> stands for the risk of 'CB' fragment. Risk of disease occurence in the organism is equal to the sum of risks for each pair of adjacent genes in the genome.</p><p>Scientists have already obtained a base organism. Some new organisms can be obtained by mutation of this organism. Mutation involves removal of all genes of some particular types. Such removal increases the total risk of disease occurence additionally. For each type of genes scientists determined <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub></span> — the increasement of the total risk of disease occurence provided by removal of all genes having type with index <span class="tex-span"><i>i</i></span>. For example, <span class="tex-span"><i>t</i><sub class="lower-index">4</sub></span> stands for the value of additional total risk increasement in case of removing all the 'D' genes.</p><p>Scientists want to find a number of different organisms that can be obtained from the given one which have the total risk of disease occurence not greater than <span class="tex-span"><i>T</i></span>. They can use only the process of mutation described above. Two organisms are considered different if strings representing their genomes are different. Genome should contain at least one gene.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of the input contains three integer numbers <span class="tex-span"><i>N</i></span> (<span class="tex-span">1 ≤ <i>N</i> ≤ 200 000</span>) — length of the genome of base organism, <span class="tex-span"><i>K</i></span> (<span class="tex-span">1 ≤ <i>K</i> ≤ 22</span>) — the maximal index of gene type in the genome and <span class="tex-span"><i>T</i></span> (<span class="tex-span">1 ≤ <i>T</i> ≤ 2·10<sup class="upper-index">9</sup></span>) — maximal allowable risk of disease occurence. The second line contains the genome of the given organism. It is a string of the first <span class="tex-span"><i>K</i></span> capital English letters having length <span class="tex-span"><i>N</i></span>.</p><p>The third line contains <span class="tex-span"><i>K</i></span> numbers <span class="tex-span"><i>t</i><sub class="lower-index">1</sub>, <i>t</i><sub class="lower-index">2</sub>, ..., <i>t</i><sub class="lower-index"><i>K</i></sub></span>, where <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub></span> is additional risk value of disease occurence provided by removing of all genes of the <span class="tex-span"><i>i</i></span>-th type.</p><p>The following <span class="tex-span"><i>K</i></span> lines contain the elements of the given matrix <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i>, <i>j</i></sub></span>. The <span class="tex-span"><i>i</i></span>-th line contains <span class="tex-span"><i>K</i></span> numbers. The <span class="tex-span"><i>j</i></span>-th number of the <span class="tex-span"><i>i</i></span>-th line stands for a risk of disease occurence for the pair of genes, first of which corresponds to the <span class="tex-span"><i>i</i></span>-th letter and second of which corresponds to the <span class="tex-span"><i>j</i></span>-th letter. The given matrix is <span class="tex-font-style-bf">not</span> necessarily symmetrical.</p><p>All the numbers in the input are integer, non-negative and all of them except <span class="tex-span"><i>T</i></span> are not greater than <span class="tex-span">10<sup class="upper-index">9</sup></span>. It is guaranteed that the maximal possible risk of organism that can be obtained from the given organism is strictly smaller than <span class="tex-span">2<sup class="upper-index">31</sup></span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Output the number of organisms that can be obtained from the base one and which have the total risk of disease occurence not greater than <span class="tex-span"><i>T</i></span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>5 3 13<br/>BACAC<br/>4 1 2<br/>1 2 3<br/>2 3 4<br/>3 4 10<br/></pre></div><div class="output"><div class="title">Output</div><pre>5<br/></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>Explanation: one can obtain the following organisms (risks are stated in brackets): BACAC (11), ACAC (10), BAA (5), B (6), AA (4).</p></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="C" data-uuid="ps_ca46cbeccd3220c3daccb09de7f3148d27d3ee83"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. Mutation</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Scientists of planet Olympia are conducting an experiment in mutation of primitive organisms. Genome of organism from this planet can be represented as a string of the first <span class="tex-span"><i>K</i></span> capital English letters. For each pair of types of genes they assigned <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i>, <i>j</i></sub></span> — a risk of disease occurence in the organism provided that genes of these types are adjacent in the genome, where <span class="tex-span"><i>i</i></span> — the 1-based index of the first gene and <span class="tex-span"><i>j</i></span> — the index of the second gene. The gene 'A' has index 1, 'B' has index 2 and so on. For example, <span class="tex-span"><i>a</i><sub class="lower-index">3, 2</sub></span> stands for the risk of 'CB' fragment. Risk of disease occurence in the organism is equal to the sum of risks for each pair of adjacent genes in the genome.</p><p>Scientists have already obtained a base organism. Some new organisms can be obtained by mutation of this organism. Mutation involves removal of all genes of some particular types. Such removal increases the total risk of disease occurence additionally. For each type of genes scientists determined <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub></span> — the increasement of the total risk of disease occurence provided by removal of all genes having type with index <span class="tex-span"><i>i</i></span>. For example, <span class="tex-span"><i>t</i><sub class="lower-index">4</sub></span> stands for the value of additional total risk increasement in case of removing all the 'D' genes.</p><p>Scientists want to find a number of different organisms that can be obtained from the given one which have the total risk of disease occurence not greater than <span class="tex-span"><i>T</i></span>. They can use only the process of mutation described above. Two organisms are considered different if strings representing their genomes are different. Genome should contain at least one gene.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of the input contains three integer numbers <span class="tex-span"><i>N</i></span> (<span class="tex-span">1 ≤ <i>N</i> ≤ 200 000</span>) — length of the genome of base organism, <span class="tex-span"><i>K</i></span> (<span class="tex-span">1 ≤ <i>K</i> ≤ 22</span>) — the maximal index of gene type in the genome and <span class="tex-span"><i>T</i></span> (<span class="tex-span">1 ≤ <i>T</i> ≤ 2·10<sup class="upper-index">9</sup></span>) — maximal allowable risk of disease occurence. The second line contains the genome of the given organism. It is a string of the first <span class="tex-span"><i>K</i></span> capital English letters having length <span class="tex-span"><i>N</i></span>.</p><p>The third line contains <span class="tex-span"><i>K</i></span> numbers <span class="tex-span"><i>t</i><sub class="lower-index">1</sub>, <i>t</i><sub class="lower-index">2</sub>, ..., <i>t</i><sub class="lower-index"><i>K</i></sub></span>, where <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub></span> is additional risk value of disease occurence provided by removing of all genes of the <span class="tex-span"><i>i</i></span>-th type.</p><p>The following <span class="tex-span"><i>K</i></span> lines contain the elements of the given matrix <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i>, <i>j</i></sub></span>. The <span class="tex-span"><i>i</i></span>-th line contains <span class="tex-span"><i>K</i></span> numbers. The <span class="tex-span"><i>j</i></span>-th number of the <span class="tex-span"><i>i</i></span>-th line stands for a risk of disease occurence for the pair of genes, first of which corresponds to the <span class="tex-span"><i>i</i></span>-th letter and second of which corresponds to the <span class="tex-span"><i>j</i></span>-th letter. The given matrix is <span class="tex-font-style-bf">not</span> necessarily symmetrical.</p><p>All the numbers in the input are integer, non-negative and all of them except <span class="tex-span"><i>T</i></span> are not greater than <span class="tex-span">10<sup class="upper-index">9</sup></span>. It is guaranteed that the maximal possible risk of organism that can be obtained from the given organism is strictly smaller than <span class="tex-span">2<sup class="upper-index">31</sup></span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Output the number of organisms that can be obtained from the base one and which have the total risk of disease occurence not greater than <span class="tex-span"><i>T</i></span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>5 3 13<br />BACAC<br />4 1 2<br />1 2 3<br />2 3 4<br />3 4 10<br /></pre></div><div class="output"><div class="title">Output</div><pre>5<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>Explanation: one can obtain the following organisms (risks are stated in brackets): BACAC (11), ACAC (10), BAA (5), B (6), AA (4).</p></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=C]"); 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["Bitmasks", "Dynamic programming", "Mathematics including integration, differential equations, etc"]
["bitmasks", "dp", "math", "*2700"]
https://codeforces.com/blog/entry/1712
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It is easy to see  that there exist two (probably equal) indexes <span class="tex-span"><i>i</i></span> and <span class="tex-span"><i>j</i></span> such that <span class="tex-span"><i>g</i><sub class="lower-index"><i>i</i></sub> = <i>A</i></span> and <span class="tex-span"><i>s</i><sub class="lower-index"><i>j</i></sub> = <i>B</i></span>. It is true, because in the other case we could decrease either <span class="tex-span"><i>A</i></span> or <span class="tex-span"><i>B</i></span> without changing connectivity of the graph.</div><div><br /></div><div>Let <span class="tex-span"><i>R</i>(<i>A</i>, <i>B</i>)</span> be the graph in which for all <span class="tex-span"><i>i</i></span> the following statement holds: <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/f6a7810c1f985efe671bb157563fc069d097fbce.png" style="max-width: 100.0%;max-height: 100.0%;" />.</div><div><br /></div><div>Let <span class="tex-span"><i>T</i>(<i>A</i>)</span> be the weighted graph in which for all edges <span class="tex-span"><i>g</i><sub class="lower-index"><i>i</i></sub> ≤ <i>A</i></span>. For each edge <span class="tex-span"><i>i</i></span> we will assign a weight equal to <span class="tex-span"><i>s</i><sub class="lower-index"><i>i</i></sub></span>. Let's find a spanning tree of this graph, which has the property that its maximal edge is minimal possible. It can be shown that for the fixed <span class="tex-span"><i>A</i></span> the minimal value of <span class="tex-span"><i>B</i></span> for which graph <span class="tex-span"><i>R</i>(<i>A</i>, <i>B</i>)</span> is still connected is equal to the weight of the maximal edge in this spanning tree.</div><div><br /></div><div><i>Claim</i>. Minimal spanning tree of a graph has the property that its maximal edge is minimal possible among all spanning trees.</div><div><i>Proof</i>. Let <span class="tex-span"><i>L</i></span> be the minimal spanning tree of a graph. Suppose there exists a spanning tree <span class="tex-span"><i>P</i></span> in which all edges have smaller weight than the weight of the maximal edge of <span class="tex-span"><i>L</i></span>. We can then remove the maximal edge from <span class="tex-span"><i>L</i></span> and add some edge from <span class="tex-span"><i>P</i></span> to it which will connect the graph back. After that <span class="tex-span"><i>L</i></span> will have strictly smaller weight, which is impossible because it is a minimal spanning tree.</div><div><br /></div><div>Let's sort all edges of the graph in ascending order of <span class="tex-span"><i>g</i><sub class="lower-index"><i>i</i></sub></span>. Then the edges of graph <span class="tex-span"><i>T</i>(<i>A</i>)</span> for the fixed <span class="tex-span"><i>i</i></span> will be all edges with indexes <span class="tex-span"><i>j</i> ≤ <i>i</i></span>.</div><div><br /></div><div>Suppose that for some value of <span class="tex-span"><i>i</i></span> we have already found minimal spanning tree in every connected component of the graph <span class="tex-span"><i>T</i>(<i>g</i><sub class="lower-index"><i>i</i></sub>)</span>. Let's add an edge with index <span class="tex-span"><i>i</i> + 1</span> into it. If it connects two different components, then after this operation they will be merged into one big component and it is obviously that the spanning tree we have in it is the minimal spanning tree. If <span class="tex-span"><i>i</i> + 1</span>-th edge connects two vertices from the same connected component, then it will create exactly one cycle in the graph. We can find the maximal edge in this cycle and remove it from the graph. It can be proven that the remaining tree will be the minimal spanning tree of this connected component.</div><div><br /></div><div>We can perform the search of the maximal edge in a cycle as well as the insertion and removal of the edges in O(N). The total complexity is <span class="tex-span"><i>O</i>(<i>NM</i> + <i>MlogM</i>)</span>.</div></div><div><br /></div><div><div><b>Problem B: Mice (Roman Rizvanov)</b></div><div><br /></div><div>It is easy to see that the number of closest pieces of cheese for each mouse is not greater than 2.</div><div><br /></div><div>Let's find the closest pieces of cheese for each mouse to the left and to the right from it. From two directions we will choose the one which gives us shorter way to cheese or both of them if their lengths are equal. If on the chosen way between the mouse and the cheese stands another mouse, then we should exclude this way from consideration, because another mouse will get to the cheese faster. Now all the directions lead to cheese and for each piece of cheese there is at most one mouse which can potentially eat it from each direction.</div><div><br /></div><div>We will process mice from left to right. If the current mouse can move left and the cheese to the left of it is not chosen by any other mouse or it is chosen by a mouse with the same distance to it, then the current mouse can move to the left and eat this piece of cheese without interfering with other mice. This choice will not affect any choices of the next mice, because only one mouse can go to this piece of cheese from the right (see previous paragraph). Thus, this choice can not decrease the answer. In all other cases the current mouse can not increase the answer by moving left, so it should move to the right if it has such opportunity.</div><div><br /></div><div>The complexity is <span class="tex-span"><i>O</i>(<i>N</i> + <i>M</i>)</span>.</div><div><br /></div><div>This problem can be also solved using dynamic programming.</div></div><div><br /></div><div><b>Problem C: Mutation (Iaroslav Tverdokhlib)</b></div><div><br /></div><div><div>In the editorial we will replace terms &quot;risk&quot;, &quot;genome&quot; and &quot;gene&quot; with &quot;cost&quot;, &quot;string&quot; and &quot;character&quot;, respectively. Let <span class="tex-span"><i>S</i></span> be the starting string.</div><div><br /></div><div>Let <span class="tex-span"><i>M</i></span> be the bitmask of chars which will be removed. Let's iterate over all possible values of <span class="tex-span"><i>M</i></span>. For the fixed <span class="tex-span"><i>M</i></span> we need to find a cost of the string, which remained after removal of <span class="tex-span"><i>M</i></span> and if this cost doesn't exceed <span class="tex-span"><i>T</i></span> we will increase the answer by 1. Naive implementation of this idea has the complexity <span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>K</i></sup><i>N</i>)</span>.</div><div><br /></div><div>We can not get rid of iterating over all <span class="tex-span"><i>M</i></span>, so we will try to optimize a part of the algorithm which finds a cost of the remaining string.</div><div><br /></div><div>Let's take two indexes <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> from the beginning string <span class="tex-span"><i>l</i> &lt; <i>r</i></span>. Let <span class="tex-span"><i>M</i>'</span> be the bitmask of all characters which are located strictly between them. It is obviously that if <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7b04066e365590d0dc24c90dfc15aabd64c75339.png" style="max-width: 100.0%;max-height: 100.0%;" /> or <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/3880b6b45cb2a0ccd5ea51b69f020c9e5a9f7fa1.png" style="max-width: 100.0%;max-height: 100.0%;" /> then <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> can not be neighbours in the remaining string. Hence for the fixed <span class="tex-span"><i>l</i></span> there are not more than <span class="tex-span"><i>K</i></span> possible candidates for <span class="tex-span"><i>r</i></span>, which means that there are <span class="tex-span"><i>O</i>(<i>NK</i>)</span> pairs of such potential neighbours. We will call such pairs &quot;good&quot;.</div><div><br /></div><div>We want to find out what form should have the set <span class="tex-span"><i>M</i></span> that after its removal indexes <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> became adjacent. It is easy to see that the following two conditions should be true:</div><div><br /></div><div>1. <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/07de7c5bc68bc92d118ada183dab5d78f5c631c4.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div>2. <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7fa1a37ebb11a92726d78e30e0ad17ffda729919.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><br /></div><div>Let's iterate over all good pairs of <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> and for each of them we will find the set <span class="tex-span"><i>M</i>'</span>. For each triple <span class="tex-span">(<i>a</i>, <i>b</i>, <i>P</i>)</span> we will store the sum of costs of neighborhood of all pairs <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> for which <span class="tex-span"><i>S</i><sub class="lower-index"><i>l</i></sub> = <i>a</i></span>, <span class="tex-span"><i>S</i><sub class="lower-index"><i>r</i></sub> = <i>b</i></span>, <span class="tex-span"><i>M</i>' = <i>P</i></span>. After that for the fixed <span class="tex-span"><i>M</i></span> we will iterate over all pairs of characters <span class="tex-span">(<i>a</i>, <i>b</i>)</span> and its subsets <span class="tex-span"><i>P</i></span> and add all their costs together. Also we need to add the cost of removal of <span class="tex-span"><i>M</i></span> and the resulting sum will be the cost of the string which will left after removal of <span class="tex-span"><i>M</i></span>. The complexity of such solution is <span class="tex-span"><i>O</i>(3<sup class="upper-index"><i>K</i></sup> * <i>K</i><sup class="upper-index">2</sup> + <i>NK</i>)</span>.</div><div><br /></div><div>We will optimize the previous solution by decreasing a factor near <span class="tex-span">3<sup class="upper-index"><i>K</i></sup></span>. Let's look at the following (incorrect) algorithm:</div><div><br /></div><div>We will iterate over all good pairs <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> and for each of them we will find <span class="tex-span"><i>M</i>'</span>. Let's create an array <span class="tex-span"><i>v</i></span> in which for each mask <span class="tex-span"><i>P</i></span> we will store the sum of costs of neighborhood of all pairs <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> for which <span class="tex-span"><i>M</i>' = <i>P</i></span>. For the fixed <span class="tex-span"><i>M</i></span> we will find a sum of all values from <span class="tex-span"><i>v</i></span> for all submasks of <span class="tex-span"><i>M</i></span>, then add the cost of removal of <span class="tex-span"><i>M</i></span> to it and the resulting sum will be the cost of the remaining string.</div><div><br /></div><div>This algorithm is incorrect, because some costs of neighborhood are added to the total cost, but in fact the respective <span class="tex-span"><i>l</i></span> or <span class="tex-span"><i>r</i></span> are removed. Let's use inclusion-exclusion principle and make the following at the phase of filling array <span class="tex-span"><i>v</i></span>:</div><div><br /></div><div><span class="tex-span"><i>v</i>[<i>M</i>'] +  = <i>cost</i></span></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/b4d392e8baa2755f671b67077d5ad638a2818e1c.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/0939a5ad00766ddcedb4465081c7dc8c63f0dd22.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/872ba326de38444a17ace78f749a43a3e1eff1d1.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><br /></div><div>With such filling of <span class="tex-span"><i>v</i></span> the algorithm described above is correct and the total complexity becomes <span class="tex-span"><i>O</i>(3<sup class="upper-index"><i>K</i></sup> + <i>NK</i>)</span>.</div><div><br /></div><div>This is still not enough for the full solution, but we are almost there. We only need to find a fast way of finding the sum of the values of <span class="tex-span"><i>v</i></span> for all submasks of all masks <span class="tex-span"><i>M</i></span>. We will use the following iterative algorithm for this purpose:</div><div><br /></div><div>Before the first iteration we have an array <span class="tex-span"><i>v</i></span> in which the starting values are stored. After iteration with number <span class="tex-span"><i>i</i></span> in <span class="tex-span"><i>v</i>[<i>mask</i>]</span> we will store the sum of all the values from the original array <span class="tex-span"><i>v</i></span> for all submasks of <span class="tex-span"><i>mask</i></span> for which the first <span class="tex-span"><i>K</i> - <i>i</i></span> bits are equal to the respective bits of <span class="tex-span"><i>mask</i></span>. On iteration with number <span class="tex-span"><i>i</i></span> for all masks in which the <span class="tex-span"><i>i</i></span>-th bit is equal to 1 (bits are numbered from 1) we will perform the following: <span class="tex-span"><i>v</i>[<i>mask</i>] +  = <i>v</i>[<i>mask</i>\{<i>i</i>}]</span>. It is easy to see that after the <span class="tex-span"><i>K</i></span>-th iteration of this algorithm we will have the values we were looking for in array <span class="tex-span"><i>v</i></span>.</div><div><br /></div><div>The complexity is <span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>K</i></sup><i>K</i> + <i>NK</i>)</span>.</div></div><div><br /></div><div><b>Problem D: Plus and XOR (Daniel Neiter)</b></div><div><br /></div><div>Let's take a look at some bit in X, which is equal to 1. If the respective bit in Y is equal to 0, then we can swap these two bits, thus reducing X and increasing Y without changing their sum and xor. We can conclude that if some bit in X is equal to 1 then the respective bit in Y is also equal to 1. Thus, <span class="tex-span"><i>Y</i> = <i>X</i> + <i>B</i></span>. Taking into account that <span class="tex-span"><i>X</i> + <i>Y</i> = <i>X</i> + <i>X</i> + <i>B</i> = <i>A</i>, </span> we can obtain the following formulas for finding <span class="tex-span"><i>X</i></span> and <span class="tex-span"><i>Y</i></span>:</div><div><br /></div><div><span class="tex-span"><i>X</i> = (<i>A</i> - <i>B</i>) / 2</span></div><div><span class="tex-span"><i>Y</i> = <i>X</i> + <i>B</i></span></div><div><div><br /></div><div>One should also notice that if <span class="tex-span"><i>A</i> &lt; <i>B</i></span> or <span class="tex-span"><i>A</i></span> and <span class="tex-span"><i>B</i></span> have different parity, then the answer doesn't exist and we should output -1. If <span class="tex-span"><i>X</i></span> <span class="tex-span"><i>and</i></span> <span class="tex-span">(<i>A</i> - <i>X</i>) ≠ <i>X</i></span> then the answer is also -1.</div></div><div><br /></div><div><b>Problem E: Points (Daniel Neiter)</b></div><div><b><br /></b></div><div>Let's regroup summands and split the sum of squares of distances we are looking for into two sums:</div><div><b><br /></b></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/6e7ca6f50695e36ea199c3704ebb7574c4bfc029.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/b4a6a53d2cb6e9458620cc0b964c69f610df6601.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><br /></div><div>Now we need to rewrite each of these sums in the following way (it will be shown for the first sum):</div><div><br /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/ce7d437559ce56c7602146506aaec7f5b8f5920b.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/14de3bd836c0e823801f884a115983ff447988b5.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><br /></div><div>This formula allows us to find an answer in one pass through the array. The complexity is O(N).</div><div><br /></div><div><div><b>Problem F: Tourist (Ilya Porublyov)</b></div><div><br /></div><div>We can get to the event <span class="tex-span"><i>j</i></span> from the event <span class="tex-span"><i>i</i></span> if the following statements are true:</div><div><br /></div><div><ul><li><span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub> ≤ <i>t</i><sub class="lower-index"><i>j</i></sub></span><br /></li><li><span class="tex-span">|<i>x</i><sub class="lower-index"><i>i</i></sub> - <i>x</i><sub class="lower-index"><i>j</i></sub>| ≤ |<i>t</i><sub class="lower-index"><i>i</i></sub> - <i>t</i><sub class="lower-index"><i>j</i></sub>|· <i>V</i></span><br /></li></ul></div><div>We can represent all the events as points on a plane with coordinates <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i></sub>, <i>t</i><sub class="lower-index"><i>i</i></sub>)</span>. Now we can reformulate the two statements written above in the following way:<br /></div><div><br /></div><div>From the event <span class="tex-span"><i>i</i></span> we can get to the event <span class="tex-span"><i>j</i></span> if the point <span class="tex-span">(<i>x</i><sub class="lower-index"><i>j</i></sub>, <i>t</i><sub class="lower-index"><i>j</i></sub>)</span> lise inside an angle pointed to the top with its vertex in <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i></sub>, <i>t</i><sub class="lower-index"><i>i</i></sub>)</span> and its sides form an angle <span class="tex-span"><i>arctg</i>(<i>V</i>)</span> with vertical axis. Let's make coordinate transformation according to which the point with coordinates <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i></sub>, <i>t</i><sub class="lower-index"><i>i</i></sub>)</span> will transform into the point <span class="tex-span">(<i>p</i><sub class="lower-index"><i>i</i></sub>, <i>q</i><sub class="lower-index"><i>i</i></sub>)</span>, where</div><div><span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub> =  - <i>x</i><sub class="lower-index"><i>i</i></sub> + <i>t</i><sub class="lower-index"><i>i</i></sub> * <i>V</i></span></div><div><span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub> = <i>x</i><sub class="lower-index"><i>i</i></sub> + <i>t</i><sub class="lower-index"><i>i</i></sub> * <i>V</i></span></div><div><br /></div><div>Now we can get to the event <span class="tex-span"><i>j</i></span> from the event <span class="tex-span"><i>i</i></span> if <span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub> ≤ <i>p</i><sub class="lower-index"><i>j</i></sub></span> и <span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub> ≤ <i>q</i><sub class="lower-index"><i>j</i></sub></span>. Let's sort all points in ascending order of <span class="tex-span"><i>p</i></span>. If several points have the same <span class="tex-span"><i>p</i></span> we will sort them by <span class="tex-span"><i>q</i></span>. The second subproblem of our problem can be solved by finding a longest increasing subsequence by <span class="tex-span"><i>q</i></span> in this array. It can be done in <span class="tex-span"><i>O</i>(<i>NlogN</i>)</span>.</div><div><br /></div><div>To solve the first subproblem we can add dummy event with coordinate 0 and time 0 (if it is not present in our set of events yet) and force tourist's start from it.</div><div><br /></div><div>The total complexity if <span class="tex-span"><i>O</i>(<i>NlogN</i>)</span>.</div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/76" class="notice" style="text-decoration: none;">All-Ukrainian School Olympiad in Informatics</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-996-1712").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "996", blogEntryId: "1712", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces" class="tag notice" style="text-decoration: none;">codeforces</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=editorial" class="tag notice" style="text-decoration: none;">editorial</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=uoi2011" class="tag notice" style="text-decoration: none;">uoi2011</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1712"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+30</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1712"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; 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} .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1722"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (22)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="32624" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/wil93" style="position: relative;"> <img src='https://userpic.codeforces.org/14356/avatar/897f1996dfb7343b.jpg'/> </a> <div><a href="/profile/wil93" title="Expert wil93" class="rated-user user-blue">wil93</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/12/2011 23:20">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32624" href="?#comment-32624" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32624" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="14356" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32624"> <div class="moveup"> <div class="ttypography">Thanks very much, I think E's solution is genial. I understood it now, but it would be very difficult for me to come out with a similar thought :)</div> </div> </div> <div class="reply info"> <a class="comment-32624 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32624 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32624"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="33014" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 16:09">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33014" href="?#comment-33014" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="33014" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="33014" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33014"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">Hi,<br /><br />I would like to ask about problem F. Is there a particular reason why you sort by p first before you sort by q? If not, will sorting by q and then by p for tiebreak change the solution? If not, may I know if you can prove so? I can understand how you make the transformation and why the transformation is correct, but I am not convinced that you can get the optimal solution just by sorting and finding the LIS (Do you mean the longest non-decreasing subsequence? From what I understand, I think you first label the vertices according to the time when they appear. If they appear at the same time, then they have the same label.) Can you please give a proof or explanation why it works?<br /><br />Thanks in advance!</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-33014 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33014 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33014"> <li> <div class="comment"> <table class="comment-table" commentId="33025" commentParentId="33014"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/KADR" style="position: relative;"> <img src='https://userpic.codeforces.org/1028/avatar/9089397f80c0fe42.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/KADR" title="Master KADR" class="rated-user user-orange">KADR</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 18:25">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33025" href="?#comment-33025" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-33014" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="33025" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="33025" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1028" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33025"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">If some two events have the same time then it is impossible to visit them both, so we are not interested in their relative order in the sorted array (after performing the transformation).<div><br /></div><div>After the transformation we can get from the point <span class="tex-span">(<i>p</i><sub class="lower-index"><i>i</i></sub>, <i>q</i><sub class="lower-index"><i>i</i></sub>)</span> to the point <span class="tex-span">(<i>p</i><sub class="lower-index"><i>j</i></sub>, <i>q</i><sub class="lower-index"><i>j</i></sub>)</span> iff <span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub> ≤ <i>p</i><sub class="lower-index"><i>j</i></sub></span> and <span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub> ≤ <i>q</i><sub class="lower-index"><i>j</i></sub></span>. After performing the sorting described in the editorial all points reachable from the point <span class="tex-span">(<i>p</i><sub class="lower-index"><i>i</i></sub>, <i>q</i><sub class="lower-index"><i>i</i></sub>)</span> will have greater indexes in the array. This automatically means that the sequence will be non-decreasing by <span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub></span>, so we only need to care about <span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub></span>. The longest non-decreasing sequence by <span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub></span> is the sequence we are looking for.</div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-33025 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33025 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33025"> <li> <div class="comment"> <table class="comment-table" commentId="33026" commentParentId="33025"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 18:27">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33026" href="?#comment-33026" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-33025" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33026" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33026"> <div class="moveup"> <div class="ttypography">Oh, that makes sense now. Thanks!</div> </div> </div> <div class="reply info"> <a class="comment-33026 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33026 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33026"> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="503943" commentParentId="33014"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/AbdAl-mateen" style="position: relative;"> <img src='https://userpic.codeforces.org/694938/avatar/57122394280e75b5.jpg'/> </a> <div><a href="/profile/AbdAl-mateen" title="Newbie AbdAl-mateen" class="rated-user user-gray">AbdAl-mateen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 07:51">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503943" href="?#comment-503943" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-33014" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="503943" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="694938" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503943"> <div class="moveup"> <div class="ttypography"><p>Hi,</p><p><code>Now we can get to the event j from the event i if pi ≤ pj и qi ≤ qj. Let's sort all points in ascending order of p. If several points have the same p we will sort them by q.</code> Can you please explain it for me?</p></div> </div> </div> <div class="reply info"> <a class="comment-503943 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503943 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503943"> <li> <div class="comment"> <table class="comment-table" commentId="503965" commentParentId="503943"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/IlyaCk" style="position: relative;"> <img src='https://userpic.codeforces.org/19187/avatar/40ba7301419542bd.jpg'/> </a> <div><a href="/profile/IlyaCk" title="Expert IlyaCk" class="rated-user user-blue">IlyaCk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 11:02">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503965" href="?#comment-503965" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503943" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="503965" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="19187" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503965"> <div class="moveup"> <div class="ttypography"><p>What do you want to be explained? Why &quot;Now we can get to the event j from the event i if pi ≤ pj и qi ≤ qj.&quot;? Or what &quot;If several points have the same p we will sort them by q.&quot; mean? Or what?</p></div> </div> </div> <div class="reply info"> <a class="comment-503965 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503965 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503965"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="503976" commentParentId="503943"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/IlyaCk" style="position: relative;"> <img src='https://userpic.codeforces.org/19187/avatar/40ba7301419542bd.jpg'/> </a> <div><a href="/profile/IlyaCk" title="Expert IlyaCk" class="rated-user user-blue">IlyaCk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 11:48">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503976" href="?#comment-503976" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503943" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="503976" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="19187" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503976"> <div class="moveup"> <div class="ttypography"><p><a href="https://drive.google.com/file/d/1fwCssJgSTEJ5ic4AzHjhQBQnrypuQkYm/view?usp=sharing">Here</a> is more detailed tutorial. It's in Ukrainian, but you can Google-translate it (result is poor, but some things are still correct) and look at figures and equations.</p><p>I CAN try to reply on more concrete questions, but I don't want to translate the whole text...</p></div> </div> </div> <div class="reply info"> <a class="comment-503976 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503976 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503976"> <li> <div class="comment"> <table class="comment-table" commentId="503980" commentParentId="503976"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/AbdAl-mateen" style="position: relative;"> <img src='https://userpic.codeforces.org/694938/avatar/57122394280e75b5.jpg'/> </a> <div><a href="/profile/AbdAl-mateen" title="Newbie AbdAl-mateen" class="rated-user user-gray">AbdAl-mateen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 13:17">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503980" href="?#comment-503980" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503976" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="503980" revisionCount="4" revision="4"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">4</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="503980" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="694938" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503980"> <div class="moveup"> <div class="ttypography"><p>Well, What are the significances of p, q axes and angle arctg(v)? What do they represent?</p><p>What I understand before, as I mentioned in another comment's reply was as below: to go to j from i: <code>abs(xj - xi) / tj - ti &lt;= v</code> so, </p><p><code>xj + v*tj &gt;= xi + ti*v</code> and <code>-xi + v*ti &gt;= -xj + v*t</code> </p></div> </div> </div> <div class="reply info"> <a class="comment-503980 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503980 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503980"> <li> <div class="comment"> <table class="comment-table" commentId="503987" commentParentId="503980"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/IlyaCk" style="position: relative;"> <img src='https://userpic.codeforces.org/19187/avatar/40ba7301419542bd.jpg'/> </a> <div><a href="/profile/IlyaCk" title="Expert IlyaCk" class="rated-user user-blue">IlyaCk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 15:12">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503987" href="?#comment-503987" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503980" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="503987" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="19187" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503987"> <div class="moveup"> <div class="ttypography"><p>Axis $$$p$$$ is the direction, where the tourist moves (in plane $$$(x,t)$$$), if his speed is ($$${-}v$$$), i.e.maximal by absolute value and directed to left. Its positive ray is the left-bottom border of the area where the tourist can get in time, starting from the origin of the $$$(p,q)$$$ coordiante system. Similarly, $$$q$$$ is the direction, where the tourist moves (in plane $$$(x,t)$$$), if his speed is ($$${+}v$$$), i.e. maximal by absolute value and directed to right; its positive ray is the right-bottom border of the area where the tourist can get in time, starting from the origin of the $$$(p,q)$$$ coordiante system.</p><p>It's not very obvious to look at these axes... But, from other hand, it's not unnatural: we need some effective checking of where the tourist can get in time and where he cannot, so let's try: what, if we'll consider borders of the &quot;reachable-in-time&quot; area as coordinate axes?</p></div> </div> </div> <div class="reply info"> <a class="comment-503987 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503987 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503987"> <li> <div class="comment"> <table class="comment-table" commentId="503991" commentParentId="503987"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/AbdAl-mateen" style="position: relative;"> <img src='https://userpic.codeforces.org/694938/avatar/57122394280e75b5.jpg'/> </a> <div><a href="/profile/AbdAl-mateen" title="Newbie AbdAl-mateen" class="rated-user user-gray">AbdAl-mateen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 16:12">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503991" href="?#comment-503991" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503987" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="503991" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="503991" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="694938" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503991"> <div class="moveup"> <div class="ttypography"><p>I hope this is my last query:</p><p>If tourist needs to go from i to j where xi &gt; xj, that time the velocity is negative. Right? And, the velocity can not be positive and negative at a time,</p><p>But why do we check</p> <pre><code>pi &lt; pj and qi &lt; qj ? </code></pre><p>Why not </p> <pre><code>pi &lt; pj or qi &lt; qj? </code></pre></div> </div> </div> <div class="reply info"> <a class="comment-503991 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503991 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503991"> <li> <div class="comment"> <table class="comment-table" commentId="504027" commentParentId="503991"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/IlyaCk" style="position: relative;"> <img src='https://userpic.codeforces.org/19187/avatar/40ba7301419542bd.jpg'/> </a> <div><a href="/profile/IlyaCk" title="Expert IlyaCk" class="rated-user user-blue">IlyaCk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 22:22">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-504027" href="?#comment-504027" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503991" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="504027" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="19187" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-504027"> <div class="moveup"> <div class="ttypography"><p>The axis directed from bottom to top is $$$t$$$ (time). The tourist cannot travel in time as he wants and/or change time flow direction. All what he can is to choose </p> <ol> <li><p>whether to stay at place with zero velocity (= move in direction of $$$t$$$, which is exactly in the middle between positive direction of $$$p$$$ and positive direction of $$$q$$$);</p></li> <li><p>or to move with velocity ($$$-v$$$), negative and maximal by absolute value, which is exactly positive direction of $$$p$$$;</p></li> <li><p>or to move with velocity ($$$+v$$$), positive and maximal by absolute value, which is exactly positive direction of $$$q$$$;</p></li> <li><p>or to move with velocity $$$0&lt;w&lt;v$$$ (where $$$v$$$ is $$$v$$$ from input data, and $$$w$$$ is actual tourist's velocity), which is in the same quadrant of the $$$(p,q)$$$-system (both $$$p$$$ and $$$q$$$ positive), but $$$q$$$-projection is bigger that $$$p$$$-projection; in other words, $$$0&lt;w&lt;v$$$ corresponds to $$$0&lt;p&lt;q$$$;</p></li> <li><p>or to move with velocity $$$-v&lt;w&lt;0$$$ (where $$$v$$$ is $$$v$$$ from input data, and $$$w$$$ is actual tourist's velocity), which is in the same quadrant of the $$$(p,q)$$$-system (both $$$p$$$ and $$$q$$$ positive), but $$$q$$$-projection is smaller that $$$p$$$-projection; in other words, $$$-v&lt;w&lt;0$$$ corresponds to $$$0&lt;q&lt;p$$$;</p></li> </ol><p>Whereas $$$(q_i &gt; q_j)$$$ (for moving from $$$i$$$ to $$$j$$$) requires either moving with speed $$$w$$$ which is $$$-\infty\leq w &lt; -v$$$, or even moving in reverse direction of time. Similarly, $$$(p_i &gt; p_j)$$$ (for moving from $$$i$$$ to $$$j$$$) requires either moving with speed $$$w$$$ which is $$$v&lt;w\leq\infty$$$, or even moving in reverse direction of time. So, it's required to have <strong>both</strong> $$$(p_i\leq p_j)$$$ <strong>and</strong> $$$(q_i\leq q_j)$$$</p></div> </div> </div> <div class="reply info"> <a class="comment-504027 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-504027 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-504027"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="33574" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/vinhthinhho" style="position: relative;"> <img src='https://userpic.codeforces.org/17649/avatar/4e3c7559e46fc48.jpg'/> </a> <div><a href="/profile/vinhthinhho" title="Candidate Master vinhthinhho" class="rated-user user-violet">vinhthinhho</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/19/2011 11:21">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33574" href="?#comment-33574" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33574" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="17649" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33574"> <div class="moveup"> <div class="ttypography"><p>i dont understand the transformation of (xi,ti), how does it work??? can anyone tell me the answer?</p></div> </div> </div> <div class="reply info"> <a class="comment-33574 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33574 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33574"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="37642" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Master_Chivu" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Master_Chivu" title="Unrated, Master_Chivu" class="rated-user user-black">Master_Chivu</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/11/2011 20:09">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-37642" href="?#comment-37642" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="37642" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="7062" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-37642"> <div class="moveup"> <div class="ttypography">&quot;It is obsiously that if <img align="middle" class="tex-formula" src="/predownloaded/5c/f4/5cf424ac693f1a0c89b939d7a6e6f6ada6700077.png" style="max-width: 100.0%;max-height: 100.0%;" /> or <img align="middle" class="tex-formula" src="/predownloaded/72/41/7241691bc12db2fb46351355cdd678dfea1703d1.png" style="max-width: 100.0%;max-height: 100.0%;" /> then <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> can not be neighbours in the remaining string.&quot;<br />What is &quot;P&quot;?<br />It seems that &quot;P&quot; hasn't been metioned before.<br />I really cannot understand this sentence.<br />And may &quot;absiously&quot; means &quot;abviously&quot;?<br /><br /></div> </div> </div> <div class="reply info"> <a class="comment-37642 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-37642 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-37642"> <li> <div class="comment"> <table class="comment-table" commentId="37653" commentParentId="37642"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/KADR" style="position: relative;"> <img src='https://userpic.codeforces.org/1028/avatar/9089397f80c0fe42.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/KADR" title="Master KADR" class="rated-user user-orange">KADR</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/11/2011 20:25">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-37653" href="?#comment-37653" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-37642" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="37653" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1028" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-37653"> <div class="moveup"> <div class="ttypography">It was a typo. &quot;Obsiously&quot; should be, of course, &quot;obviously&quot;.<div><br /></div><div>Also I occasionally used P instead of M'. It is fixed now, thanks for pointing this out.</div></div> </div> </div> <div class="reply info"> <a class="comment-37653 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-37653 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-37653"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="39030" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Snow_storm" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Snow_storm" title="Expert Snow_storm" class="rated-user user-blue">Snow_storm</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/18/2011 21:22">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-39030" href="?#comment-39030" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="39030" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6824" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-39030"> <div class="moveup"> <div class="ttypography"><p>Problem D is right?</p> <p>I doubts it, for expleam, A=14 and B=4 </p> <p>then X=(14-4)/2=5  Y=5+4=9</p> <p>and A&gt;B and <span class="tex-span"><i>A</i></span> and <span class="tex-span"><i>B</i></span> have some parity and A-X=Y<br /><br />but X^Y=5^9=12  <br />This is my doubts. And I think  (A-B)/2=X&amp;Y .<br />But I don't know the specific X and Y values</p></div> </div> </div> <div class="reply info"> <a class="comment-39030 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-39030 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-39030"> <li> <div class="comment"> <table class="comment-table" commentId="39031" commentParentId="39030"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/KADR" style="position: relative;"> <img src='https://userpic.codeforces.org/1028/avatar/9089397f80c0fe42.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/KADR" title="Master KADR" class="rated-user user-orange">KADR</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/18/2011 21:29">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-39031" href="?#comment-39031" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-39030" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="39031" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1028" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-39031"> <div class="moveup"> <div class="ttypography">Quote from the editorial:<div><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">&quot;If</span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;"><i>X</i></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;"><i>and</i></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;">(<i>A</i> - <i>X</i>) ≠ <i>X</i></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">then the answer is also -1.&quot;</span><br /></div><div>Here X=5 and A-X=9. 5 and 9 = 1, which is not equal to 5. So the answer is -1 here.</div></div> </div> </div> <div class="reply info"> <a class="comment-39031 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-39031 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-39031"> <li> <div class="comment"> <table class="comment-table" commentId="39038" commentParentId="39031"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Snow_storm" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Snow_storm" title="Expert Snow_storm" class="rated-user user-blue">Snow_storm</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/18/2011 21:42">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-39038" href="?#comment-39038" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-39031" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="39038" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6824" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-39038"> <div class="moveup"> <div class="ttypography">I was wrong, <br /><span style="LINE-HEIGHT: 20.0px;FONT-FAMILY: verdana , arial , sans-serif;FONT-SIZE: 12.0px;"><span class="tex-span" style="FONT-FAMILY: &quot;times new roman&quot;;FONT-SIZE: 15.0px;"><i>and is &amp;</i></span></span><br /><br />But I saw many wrong program still through the test,<br /><br />and thank you very much for your patience solutions</div> </div> </div> <div class="reply info"> <a class="comment-39038 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-39038 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-39038"> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="39034" commentParentId="39030"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Snow_storm" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Snow_storm" title="Expert Snow_storm" class="rated-user user-blue">Snow_storm</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/18/2011 21:35">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-39034" href="?#comment-39034" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-39030" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="39034" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6824" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-39034"> <div class="moveup"> <div class="ttypography">I'm sorry, X is smallest, but I'm think if the answer doesn't exist, should add a condition:  X^Y=B</div> </div> </div> <div class="reply info"> <a class="comment-39034 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-39034 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-39034"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="422212" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/stringray" style="position: relative;"> <img src='https://userpic.codeforces.org/575608/avatar/2902babcf56868a2.jpg'/> </a> <div><a href="/profile/stringray" title="Expert stringray" class="rated-user user-blue">stringray</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/27/2018 21:44">6 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-422212" href="?#comment-422212" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="422212" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="575608" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-422212"> <div class="moveup"> <div class="ttypography"><p>Can someone explain the question Gift in this question it is asking for the minimum coins such that every road's gold coin and silver coin constraints are satisfied then if (A,B) is a valid solution then we can make A=infinite and B=infinite so that there will be always a solution also won't A=max(all gi's) and B=max(all si's ) where gi=minimum gold coins for ith road and si=minimum silver coins for ith road (this is what i have understood from the question can anyone tell what's wrong in my understanding )?</p></div> </div> </div> <div class="reply info"> <a class="comment-422212 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-422212 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-422212"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="517643" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Newtech66" style="position: relative;"> <img src='https://userpic.codeforces.org/748716/avatar/ba5b7d94e0bd5415.jpg'/> </a> <div><a href="/profile/Newtech66" title="Expert Newtech66" class="rated-user user-blue">Newtech66</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/10/2019 13:51">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-517643" href="?#comment-517643" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="517643" class="CommentVoteFrame" class="negative-comment-vote" data-commentRating="-10" data-commentUserId="748716" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">-10</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-517643"> <div class="moveup"> <div class="ttypography"><p>Problem D has weak testcases. My solution gets AC despite giving an incorrect answer on the testcase '10 6'.</p></div> </div> </div> <div class="reply info"> <a class="comment-517643 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-517643 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-517643"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="537992" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/memento" style="position: relative;"> <img src='https://userpic.codeforces.org/852933/avatar/950578c1b4afd9dc.jpg'/> </a> <div><a href="/profile/memento" title="Expert memento" class="rated-user user-blue">memento</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Aug/24/2019 21:32">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-537992" href="?#comment-537992" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="537992" class="CommentVoteFrame" data-commentRating="11" data-commentUserId="852933" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+11</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-537992"> <div class="moveup"> <div class="ttypography"><p>Shit. This was 8 years ago.</p></div> </div> </div> <div class="reply info"> <a class="comment-537992 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-537992 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-537992"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="763848" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/vishaaaal" style="position: relative;"> <img src='https://userpic.codeforces.org/1443354/avatar/25a2dd924894eeeb.jpg'/> </a> <div><a href="/profile/vishaaaal" title="Expert vishaaaal" class="rated-user user-blue">vishaaaal</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/20/2021 12:42">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-763848" href="?#comment-763848" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="763848" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1443354" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-763848"> <div class="moveup"> <div class="ttypography"><p>How to solve A without MST??</p> <div class="spoiler"><b class="spoiler-title">Here's my approach</b><div class="spoiler-content" style="display: none;"><p>Let us consider two cities $$$a$$$ and $$$b$$$. We use <em>dfs</em> to calculate the minimum amount of tugriks required for travelling from $$$a$$$ to $$$b$$$. And the answer will be maximum of such value among all pairs of cities.</p><p>The problem is, I think that calculation of this value requires to use Dynamic Programming. Any hints on that??</p></div></div></div> </div> </div> <div class="reply info"> <a class="comment-763848 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-763848 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-763848"> </ul> </div> <br/> <div id="editBox-1722" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In Russian</span> </div> <textarea data-drafts-id="CommentReplyFrame" class="wysiwyg" name="editContent" rows="20" style="width:99%;"></textarea> <div class="error error__content"></div> <div style="text-align:center;"> <input type="button" name="preview" style="padding: 0.25em 1em; 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76D
76
D
en
D. Plus and xor
<div class="problem-statement"><div class="header"><div class="title">D. Plus and xor</div><div class="time-limit"><div class="property-title">time limit per test</div>0.5 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Bitwise exclusive OR (or bitwise addition modulo two) is a binary operation which is equivalent to applying logical exclusive OR to every pair of bits located on the same positions in binary notation of operands. In other words, a binary digit of the result is equal to 1 if and only if bits on the respective positions in the operands are different.</p><p>For example, if <span class="tex-span"><i>X</i> = 109<sub class="lower-index">10</sub> = 1101101<sub class="lower-index">2</sub></span>, <span class="tex-span"><i>Y</i> = 41<sub class="lower-index">10</sub> = 101001<sub class="lower-index">2</sub></span>, then: </p><center> <span class="tex-span"><i>X</i></span> <span class="tex-font-style-tt">xor</span> <span class="tex-span"><i>Y</i>  =  68<sub class="lower-index">10</sub>  =  1000100<sub class="lower-index">2</sub></span>. </center><p>Write a program, which takes two non-negative integers <span class="tex-span"><i>A</i></span> and <span class="tex-span"><i>B</i></span> as an input and finds two non-negative integers <span class="tex-span"><i>X</i></span> and <span class="tex-span"><i>Y</i></span>, which satisfy the following conditions: </p><ul> <li> <span class="tex-span"><i>A</i> = <i>X</i> + <i>Y</i></span> </li><li> <span class="tex-span"><i>B</i>  =  <i>X</i></span> <span class="tex-font-style-tt">xor</span> <span class="tex-span"><i>Y</i></span>, where <span class="tex-font-style-tt">xor</span> is bitwise exclusive or. </li><li> <span class="tex-span"><i>X</i></span> is the smallest number among all numbers for which the first two conditions are true. </li></ul></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains integer number <span class="tex-span"><i>A</i></span> and the second line contains integer number <span class="tex-span"><i>B</i></span> (<span class="tex-span">0 ≤ <i>A</i>, <i>B</i> ≤ 2<sup class="upper-index">64</sup> - 1</span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>The only output line should contain two integer non-negative numbers <span class="tex-span"><i>X</i></span> and <span class="tex-span"><i>Y</i></span>. Print the only number <span class="tex-font-style-tt">-1</span> if there is no answer.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>142<br/>76<br/></pre></div><div class="output"><div class="title">Output</div><pre>33 109<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="D" data-uuid="ps_ae5e73d1bce82b4157a6af0b875e419d720fee96"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">D. Plus and xor</div><div class="time-limit"><div class="property-title">time limit per test</div>0.5 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Bitwise exclusive OR (or bitwise addition modulo two) is a binary operation which is equivalent to applying logical exclusive OR to every pair of bits located on the same positions in binary notation of operands. In other words, a binary digit of the result is equal to 1 if and only if bits on the respective positions in the operands are different.</p><p>For example, if <span class="tex-span"><i>X</i> = 109<sub class="lower-index">10</sub> = 1101101<sub class="lower-index">2</sub></span>, <span class="tex-span"><i>Y</i> = 41<sub class="lower-index">10</sub> = 101001<sub class="lower-index">2</sub></span>, then: </p><center> <span class="tex-span"><i>X</i></span> <span class="tex-font-style-tt">xor</span> <span class="tex-span"><i>Y</i>  =  68<sub class="lower-index">10</sub>  =  1000100<sub class="lower-index">2</sub></span>. </center><p>Write a program, which takes two non-negative integers <span class="tex-span"><i>A</i></span> and <span class="tex-span"><i>B</i></span> as an input and finds two non-negative integers <span class="tex-span"><i>X</i></span> and <span class="tex-span"><i>Y</i></span>, which satisfy the following conditions: </p><ul> <li> <span class="tex-span"><i>A</i> = <i>X</i> + <i>Y</i></span> </li><li> <span class="tex-span"><i>B</i>  =  <i>X</i></span> <span class="tex-font-style-tt">xor</span> <span class="tex-span"><i>Y</i></span>, where <span class="tex-font-style-tt">xor</span> is bitwise exclusive or. </li><li> <span class="tex-span"><i>X</i></span> is the smallest number among all numbers for which the first two conditions are true. </li></ul></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains integer number <span class="tex-span"><i>A</i></span> and the second line contains integer number <span class="tex-span"><i>B</i></span> (<span class="tex-span">0 ≤ <i>A</i>, <i>B</i> ≤ 2<sup class="upper-index">64</sup> - 1</span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>The only output line should contain two integer non-negative numbers <span class="tex-span"><i>X</i></span> and <span class="tex-span"><i>Y</i></span>. Print the only number <span class="tex-font-style-tt">-1</span> if there is no answer.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>142<br />76<br /></pre></div><div class="output"><div class="title">Output</div><pre>33 109<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=D]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); if (previousStatementText) { if (previousStatementText !== statementText) { $problem.find(".diff-notifier").show(); $problem.find(".diff-notifier-close").click(function() { Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60); $problem.find(".diff-notifier").hide(); }); $problem.find("a.view-changes").click(function() { $.post("/data/diff", {action: "getDiff", a: previousStatementText, b: statementText}, function (result) { if (result["success"] === "true") { Codeforces.facebox(".diff-popup", "//codeforces.org/s/73366"); 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["Dynamic programming", "Greedy algorithms", "Mathematics including integration, differential equations, etc"]
["dp", "greedy", "math", "*1700"]
https://codeforces.com/blog/entry/1712
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<a href="/blog/entry/120644">Codeforces Round 899 (Div. 2)</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/Misa-Misa" title="Expert Misa-Misa" class="rated-user user-blue">Misa-Misa</a> &rarr; <a href="/blog/entry/121157">Someone please help me understand this.</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/shivam565" title="Specialist shivam565" class="rated-user user-cyan">shivam565</a> &rarr; <a href="/blog/entry/108348">Total number of subarrays with sum atmost k</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> </ul> </div> <div class="bottom-links"> <table style="width:100%;"> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:right;"> <a href="/recent-actions">Detailed &rarr;</a> </td> </tr> </tbody> </table> </div> </div> </div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li><a href="/profile/KADR">KADR</a></li> <li class="current selectedLava"><a href="/blog/KADR">Blog</a></li> <li><a href="/teams/with/KADR">Teams</a></li> <li><a href="/submissions/KADR">Submissions</a></li> <li><a href="/groups/with/KADR">Groups</a></li> <li><a href="/contests/with/KADR">Contests</a></li> <li><a href="/contests/writer/KADR">Problemsetting</a></li> </ul> </div> <div style="margin-top:0;"> <div> <h3><a href="/blog/KADR" style="text-decoration:none;color:black !important;">KADR's blog</a></h3> </div> <div style="margin-top:2em;"> <div class="has-topic-id topic" topicId="1712"> <div class="title"> <a href="/blog/entry/1712"> All-Ukrainian School Olympiad in Informatics: editorial (A,B,C,D,E,F) </a> </div> <div class="info" style="position:relative;"> By&nbsp;<a href="/profile/KADR" title="Master KADR" class="rated-user user-orange">KADR</a>, <span class="format-humantime" title="Apr/12/2011 21:30">12 years ago</span>, translation, <img style="position: relative;top: 5px;" src="//codeforces.org/s/81027/images/flags/24/gb.png" alt="In English" title="In English"/> <span style="position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;"> <div style="margin-top:0.25em;"> </div> </span> </div> <div class="content"> <div class="ttypography"><div>The editorial is now completed.</div><div><br /></div><div><div><b>Problem A: Gift (Roman Iedemskyi)</b></div><div><br /></div><div>Suppose that the pair <span class="tex-span">(<i>A</i>, <i>B</i>)</span> is an optimal solution, where <span class="tex-span"><i>A</i></span> is the number of gold coins in a gift and <span class="tex-span"><i>B</i></span> is a number of silver coins. It is easy to see  that there exist two (probably equal) indexes <span class="tex-span"><i>i</i></span> and <span class="tex-span"><i>j</i></span> such that <span class="tex-span"><i>g</i><sub class="lower-index"><i>i</i></sub> = <i>A</i></span> and <span class="tex-span"><i>s</i><sub class="lower-index"><i>j</i></sub> = <i>B</i></span>. It is true, because in the other case we could decrease either <span class="tex-span"><i>A</i></span> or <span class="tex-span"><i>B</i></span> without changing connectivity of the graph.</div><div><br /></div><div>Let <span class="tex-span"><i>R</i>(<i>A</i>, <i>B</i>)</span> be the graph in which for all <span class="tex-span"><i>i</i></span> the following statement holds: <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/f6a7810c1f985efe671bb157563fc069d097fbce.png" style="max-width: 100.0%;max-height: 100.0%;" />.</div><div><br /></div><div>Let <span class="tex-span"><i>T</i>(<i>A</i>)</span> be the weighted graph in which for all edges <span class="tex-span"><i>g</i><sub class="lower-index"><i>i</i></sub> ≤ <i>A</i></span>. For each edge <span class="tex-span"><i>i</i></span> we will assign a weight equal to <span class="tex-span"><i>s</i><sub class="lower-index"><i>i</i></sub></span>. Let's find a spanning tree of this graph, which has the property that its maximal edge is minimal possible. It can be shown that for the fixed <span class="tex-span"><i>A</i></span> the minimal value of <span class="tex-span"><i>B</i></span> for which graph <span class="tex-span"><i>R</i>(<i>A</i>, <i>B</i>)</span> is still connected is equal to the weight of the maximal edge in this spanning tree.</div><div><br /></div><div><i>Claim</i>. Minimal spanning tree of a graph has the property that its maximal edge is minimal possible among all spanning trees.</div><div><i>Proof</i>. Let <span class="tex-span"><i>L</i></span> be the minimal spanning tree of a graph. Suppose there exists a spanning tree <span class="tex-span"><i>P</i></span> in which all edges have smaller weight than the weight of the maximal edge of <span class="tex-span"><i>L</i></span>. We can then remove the maximal edge from <span class="tex-span"><i>L</i></span> and add some edge from <span class="tex-span"><i>P</i></span> to it which will connect the graph back. After that <span class="tex-span"><i>L</i></span> will have strictly smaller weight, which is impossible because it is a minimal spanning tree.</div><div><br /></div><div>Let's sort all edges of the graph in ascending order of <span class="tex-span"><i>g</i><sub class="lower-index"><i>i</i></sub></span>. Then the edges of graph <span class="tex-span"><i>T</i>(<i>A</i>)</span> for the fixed <span class="tex-span"><i>i</i></span> will be all edges with indexes <span class="tex-span"><i>j</i> ≤ <i>i</i></span>.</div><div><br /></div><div>Suppose that for some value of <span class="tex-span"><i>i</i></span> we have already found minimal spanning tree in every connected component of the graph <span class="tex-span"><i>T</i>(<i>g</i><sub class="lower-index"><i>i</i></sub>)</span>. Let's add an edge with index <span class="tex-span"><i>i</i> + 1</span> into it. If it connects two different components, then after this operation they will be merged into one big component and it is obviously that the spanning tree we have in it is the minimal spanning tree. If <span class="tex-span"><i>i</i> + 1</span>-th edge connects two vertices from the same connected component, then it will create exactly one cycle in the graph. We can find the maximal edge in this cycle and remove it from the graph. It can be proven that the remaining tree will be the minimal spanning tree of this connected component.</div><div><br /></div><div>We can perform the search of the maximal edge in a cycle as well as the insertion and removal of the edges in O(N). The total complexity is <span class="tex-span"><i>O</i>(<i>NM</i> + <i>MlogM</i>)</span>.</div></div><div><br /></div><div><div><b>Problem B: Mice (Roman Rizvanov)</b></div><div><br /></div><div>It is easy to see that the number of closest pieces of cheese for each mouse is not greater than 2.</div><div><br /></div><div>Let's find the closest pieces of cheese for each mouse to the left and to the right from it. From two directions we will choose the one which gives us shorter way to cheese or both of them if their lengths are equal. If on the chosen way between the mouse and the cheese stands another mouse, then we should exclude this way from consideration, because another mouse will get to the cheese faster. Now all the directions lead to cheese and for each piece of cheese there is at most one mouse which can potentially eat it from each direction.</div><div><br /></div><div>We will process mice from left to right. If the current mouse can move left and the cheese to the left of it is not chosen by any other mouse or it is chosen by a mouse with the same distance to it, then the current mouse can move to the left and eat this piece of cheese without interfering with other mice. This choice will not affect any choices of the next mice, because only one mouse can go to this piece of cheese from the right (see previous paragraph). Thus, this choice can not decrease the answer. In all other cases the current mouse can not increase the answer by moving left, so it should move to the right if it has such opportunity.</div><div><br /></div><div>The complexity is <span class="tex-span"><i>O</i>(<i>N</i> + <i>M</i>)</span>.</div><div><br /></div><div>This problem can be also solved using dynamic programming.</div></div><div><br /></div><div><b>Problem C: Mutation (Iaroslav Tverdokhlib)</b></div><div><br /></div><div><div>In the editorial we will replace terms &quot;risk&quot;, &quot;genome&quot; and &quot;gene&quot; with &quot;cost&quot;, &quot;string&quot; and &quot;character&quot;, respectively. Let <span class="tex-span"><i>S</i></span> be the starting string.</div><div><br /></div><div>Let <span class="tex-span"><i>M</i></span> be the bitmask of chars which will be removed. Let's iterate over all possible values of <span class="tex-span"><i>M</i></span>. For the fixed <span class="tex-span"><i>M</i></span> we need to find a cost of the string, which remained after removal of <span class="tex-span"><i>M</i></span> and if this cost doesn't exceed <span class="tex-span"><i>T</i></span> we will increase the answer by 1. Naive implementation of this idea has the complexity <span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>K</i></sup><i>N</i>)</span>.</div><div><br /></div><div>We can not get rid of iterating over all <span class="tex-span"><i>M</i></span>, so we will try to optimize a part of the algorithm which finds a cost of the remaining string.</div><div><br /></div><div>Let's take two indexes <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> from the beginning string <span class="tex-span"><i>l</i> &lt; <i>r</i></span>. Let <span class="tex-span"><i>M</i>'</span> be the bitmask of all characters which are located strictly between them. It is obviously that if <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7b04066e365590d0dc24c90dfc15aabd64c75339.png" style="max-width: 100.0%;max-height: 100.0%;" /> or <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/3880b6b45cb2a0ccd5ea51b69f020c9e5a9f7fa1.png" style="max-width: 100.0%;max-height: 100.0%;" /> then <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> can not be neighbours in the remaining string. Hence for the fixed <span class="tex-span"><i>l</i></span> there are not more than <span class="tex-span"><i>K</i></span> possible candidates for <span class="tex-span"><i>r</i></span>, which means that there are <span class="tex-span"><i>O</i>(<i>NK</i>)</span> pairs of such potential neighbours. We will call such pairs &quot;good&quot;.</div><div><br /></div><div>We want to find out what form should have the set <span class="tex-span"><i>M</i></span> that after its removal indexes <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> became adjacent. It is easy to see that the following two conditions should be true:</div><div><br /></div><div>1. <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/07de7c5bc68bc92d118ada183dab5d78f5c631c4.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div>2. <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7fa1a37ebb11a92726d78e30e0ad17ffda729919.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><br /></div><div>Let's iterate over all good pairs of <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> and for each of them we will find the set <span class="tex-span"><i>M</i>'</span>. For each triple <span class="tex-span">(<i>a</i>, <i>b</i>, <i>P</i>)</span> we will store the sum of costs of neighborhood of all pairs <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> for which <span class="tex-span"><i>S</i><sub class="lower-index"><i>l</i></sub> = <i>a</i></span>, <span class="tex-span"><i>S</i><sub class="lower-index"><i>r</i></sub> = <i>b</i></span>, <span class="tex-span"><i>M</i>' = <i>P</i></span>. After that for the fixed <span class="tex-span"><i>M</i></span> we will iterate over all pairs of characters <span class="tex-span">(<i>a</i>, <i>b</i>)</span> and its subsets <span class="tex-span"><i>P</i></span> and add all their costs together. Also we need to add the cost of removal of <span class="tex-span"><i>M</i></span> and the resulting sum will be the cost of the string which will left after removal of <span class="tex-span"><i>M</i></span>. The complexity of such solution is <span class="tex-span"><i>O</i>(3<sup class="upper-index"><i>K</i></sup> * <i>K</i><sup class="upper-index">2</sup> + <i>NK</i>)</span>.</div><div><br /></div><div>We will optimize the previous solution by decreasing a factor near <span class="tex-span">3<sup class="upper-index"><i>K</i></sup></span>. Let's look at the following (incorrect) algorithm:</div><div><br /></div><div>We will iterate over all good pairs <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> and for each of them we will find <span class="tex-span"><i>M</i>'</span>. Let's create an array <span class="tex-span"><i>v</i></span> in which for each mask <span class="tex-span"><i>P</i></span> we will store the sum of costs of neighborhood of all pairs <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> for which <span class="tex-span"><i>M</i>' = <i>P</i></span>. For the fixed <span class="tex-span"><i>M</i></span> we will find a sum of all values from <span class="tex-span"><i>v</i></span> for all submasks of <span class="tex-span"><i>M</i></span>, then add the cost of removal of <span class="tex-span"><i>M</i></span> to it and the resulting sum will be the cost of the remaining string.</div><div><br /></div><div>This algorithm is incorrect, because some costs of neighborhood are added to the total cost, but in fact the respective <span class="tex-span"><i>l</i></span> or <span class="tex-span"><i>r</i></span> are removed. Let's use inclusion-exclusion principle and make the following at the phase of filling array <span class="tex-span"><i>v</i></span>:</div><div><br /></div><div><span class="tex-span"><i>v</i>[<i>M</i>'] +  = <i>cost</i></span></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/b4d392e8baa2755f671b67077d5ad638a2818e1c.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/0939a5ad00766ddcedb4465081c7dc8c63f0dd22.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/872ba326de38444a17ace78f749a43a3e1eff1d1.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><br /></div><div>With such filling of <span class="tex-span"><i>v</i></span> the algorithm described above is correct and the total complexity becomes <span class="tex-span"><i>O</i>(3<sup class="upper-index"><i>K</i></sup> + <i>NK</i>)</span>.</div><div><br /></div><div>This is still not enough for the full solution, but we are almost there. We only need to find a fast way of finding the sum of the values of <span class="tex-span"><i>v</i></span> for all submasks of all masks <span class="tex-span"><i>M</i></span>. We will use the following iterative algorithm for this purpose:</div><div><br /></div><div>Before the first iteration we have an array <span class="tex-span"><i>v</i></span> in which the starting values are stored. After iteration with number <span class="tex-span"><i>i</i></span> in <span class="tex-span"><i>v</i>[<i>mask</i>]</span> we will store the sum of all the values from the original array <span class="tex-span"><i>v</i></span> for all submasks of <span class="tex-span"><i>mask</i></span> for which the first <span class="tex-span"><i>K</i> - <i>i</i></span> bits are equal to the respective bits of <span class="tex-span"><i>mask</i></span>. On iteration with number <span class="tex-span"><i>i</i></span> for all masks in which the <span class="tex-span"><i>i</i></span>-th bit is equal to 1 (bits are numbered from 1) we will perform the following: <span class="tex-span"><i>v</i>[<i>mask</i>] +  = <i>v</i>[<i>mask</i>\{<i>i</i>}]</span>. It is easy to see that after the <span class="tex-span"><i>K</i></span>-th iteration of this algorithm we will have the values we were looking for in array <span class="tex-span"><i>v</i></span>.</div><div><br /></div><div>The complexity is <span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>K</i></sup><i>K</i> + <i>NK</i>)</span>.</div></div><div><br /></div><div><b>Problem D: Plus and XOR (Daniel Neiter)</b></div><div><br /></div><div>Let's take a look at some bit in X, which is equal to 1. If the respective bit in Y is equal to 0, then we can swap these two bits, thus reducing X and increasing Y without changing their sum and xor. We can conclude that if some bit in X is equal to 1 then the respective bit in Y is also equal to 1. Thus, <span class="tex-span"><i>Y</i> = <i>X</i> + <i>B</i></span>. Taking into account that <span class="tex-span"><i>X</i> + <i>Y</i> = <i>X</i> + <i>X</i> + <i>B</i> = <i>A</i>, </span> we can obtain the following formulas for finding <span class="tex-span"><i>X</i></span> and <span class="tex-span"><i>Y</i></span>:</div><div><br /></div><div><span class="tex-span"><i>X</i> = (<i>A</i> - <i>B</i>) / 2</span></div><div><span class="tex-span"><i>Y</i> = <i>X</i> + <i>B</i></span></div><div><div><br /></div><div>One should also notice that if <span class="tex-span"><i>A</i> &lt; <i>B</i></span> or <span class="tex-span"><i>A</i></span> and <span class="tex-span"><i>B</i></span> have different parity, then the answer doesn't exist and we should output -1. If <span class="tex-span"><i>X</i></span> <span class="tex-span"><i>and</i></span> <span class="tex-span">(<i>A</i> - <i>X</i>) ≠ <i>X</i></span> then the answer is also -1.</div></div><div><br /></div><div><b>Problem E: Points (Daniel Neiter)</b></div><div><b><br /></b></div><div>Let's regroup summands and split the sum of squares of distances we are looking for into two sums:</div><div><b><br /></b></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/6e7ca6f50695e36ea199c3704ebb7574c4bfc029.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/b4a6a53d2cb6e9458620cc0b964c69f610df6601.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><br /></div><div>Now we need to rewrite each of these sums in the following way (it will be shown for the first sum):</div><div><br /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/ce7d437559ce56c7602146506aaec7f5b8f5920b.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/14de3bd836c0e823801f884a115983ff447988b5.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><br /></div><div>This formula allows us to find an answer in one pass through the array. The complexity is O(N).</div><div><br /></div><div><div><b>Problem F: Tourist (Ilya Porublyov)</b></div><div><br /></div><div>We can get to the event <span class="tex-span"><i>j</i></span> from the event <span class="tex-span"><i>i</i></span> if the following statements are true:</div><div><br /></div><div><ul><li><span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub> ≤ <i>t</i><sub class="lower-index"><i>j</i></sub></span><br /></li><li><span class="tex-span">|<i>x</i><sub class="lower-index"><i>i</i></sub> - <i>x</i><sub class="lower-index"><i>j</i></sub>| ≤ |<i>t</i><sub class="lower-index"><i>i</i></sub> - <i>t</i><sub class="lower-index"><i>j</i></sub>|· <i>V</i></span><br /></li></ul></div><div>We can represent all the events as points on a plane with coordinates <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i></sub>, <i>t</i><sub class="lower-index"><i>i</i></sub>)</span>. Now we can reformulate the two statements written above in the following way:<br /></div><div><br /></div><div>From the event <span class="tex-span"><i>i</i></span> we can get to the event <span class="tex-span"><i>j</i></span> if the point <span class="tex-span">(<i>x</i><sub class="lower-index"><i>j</i></sub>, <i>t</i><sub class="lower-index"><i>j</i></sub>)</span> lise inside an angle pointed to the top with its vertex in <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i></sub>, <i>t</i><sub class="lower-index"><i>i</i></sub>)</span> and its sides form an angle <span class="tex-span"><i>arctg</i>(<i>V</i>)</span> with vertical axis. Let's make coordinate transformation according to which the point with coordinates <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i></sub>, <i>t</i><sub class="lower-index"><i>i</i></sub>)</span> will transform into the point <span class="tex-span">(<i>p</i><sub class="lower-index"><i>i</i></sub>, <i>q</i><sub class="lower-index"><i>i</i></sub>)</span>, where</div><div><span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub> =  - <i>x</i><sub class="lower-index"><i>i</i></sub> + <i>t</i><sub class="lower-index"><i>i</i></sub> * <i>V</i></span></div><div><span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub> = <i>x</i><sub class="lower-index"><i>i</i></sub> + <i>t</i><sub class="lower-index"><i>i</i></sub> * <i>V</i></span></div><div><br /></div><div>Now we can get to the event <span class="tex-span"><i>j</i></span> from the event <span class="tex-span"><i>i</i></span> if <span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub> ≤ <i>p</i><sub class="lower-index"><i>j</i></sub></span> и <span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub> ≤ <i>q</i><sub class="lower-index"><i>j</i></sub></span>. Let's sort all points in ascending order of <span class="tex-span"><i>p</i></span>. If several points have the same <span class="tex-span"><i>p</i></span> we will sort them by <span class="tex-span"><i>q</i></span>. The second subproblem of our problem can be solved by finding a longest increasing subsequence by <span class="tex-span"><i>q</i></span> in this array. It can be done in <span class="tex-span"><i>O</i>(<i>NlogN</i>)</span>.</div><div><br /></div><div>To solve the first subproblem we can add dummy event with coordinate 0 and time 0 (if it is not present in our set of events yet) and force tourist's start from it.</div><div><br /></div><div>The total complexity if <span class="tex-span"><i>O</i>(<i>NlogN</i>)</span>.</div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/76" class="notice" style="text-decoration: none;">All-Ukrainian School Olympiad in Informatics</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-996-1712").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "996", blogEntryId: "1712", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces" class="tag notice" style="text-decoration: none;">codeforces</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=editorial" class="tag notice" style="text-decoration: none;">editorial</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=uoi2011" class="tag notice" style="text-decoration: none;">uoi2011</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1712"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+30</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1712"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; 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} .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1722"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (22)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="32624" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/wil93" style="position: relative;"> <img src='https://userpic.codeforces.org/14356/avatar/897f1996dfb7343b.jpg'/> </a> <div><a href="/profile/wil93" title="Expert wil93" class="rated-user user-blue">wil93</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/12/2011 23:20">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32624" href="?#comment-32624" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32624" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="14356" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32624"> <div class="moveup"> <div class="ttypography">Thanks very much, I think E's solution is genial. I understood it now, but it would be very difficult for me to come out with a similar thought :)</div> </div> </div> <div class="reply info"> <a class="comment-32624 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32624 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32624"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="33014" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 16:09">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33014" href="?#comment-33014" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="33014" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="33014" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33014"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">Hi,<br /><br />I would like to ask about problem F. Is there a particular reason why you sort by p first before you sort by q? If not, will sorting by q and then by p for tiebreak change the solution? If not, may I know if you can prove so? I can understand how you make the transformation and why the transformation is correct, but I am not convinced that you can get the optimal solution just by sorting and finding the LIS (Do you mean the longest non-decreasing subsequence? From what I understand, I think you first label the vertices according to the time when they appear. If they appear at the same time, then they have the same label.) Can you please give a proof or explanation why it works?<br /><br />Thanks in advance!</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-33014 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33014 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33014"> <li> <div class="comment"> <table class="comment-table" commentId="33025" commentParentId="33014"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/KADR" style="position: relative;"> <img src='https://userpic.codeforces.org/1028/avatar/9089397f80c0fe42.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/KADR" title="Master KADR" class="rated-user user-orange">KADR</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 18:25">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33025" href="?#comment-33025" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-33014" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="33025" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="33025" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1028" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33025"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">If some two events have the same time then it is impossible to visit them both, so we are not interested in their relative order in the sorted array (after performing the transformation).<div><br /></div><div>After the transformation we can get from the point <span class="tex-span">(<i>p</i><sub class="lower-index"><i>i</i></sub>, <i>q</i><sub class="lower-index"><i>i</i></sub>)</span> to the point <span class="tex-span">(<i>p</i><sub class="lower-index"><i>j</i></sub>, <i>q</i><sub class="lower-index"><i>j</i></sub>)</span> iff <span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub> ≤ <i>p</i><sub class="lower-index"><i>j</i></sub></span> and <span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub> ≤ <i>q</i><sub class="lower-index"><i>j</i></sub></span>. After performing the sorting described in the editorial all points reachable from the point <span class="tex-span">(<i>p</i><sub class="lower-index"><i>i</i></sub>, <i>q</i><sub class="lower-index"><i>i</i></sub>)</span> will have greater indexes in the array. This automatically means that the sequence will be non-decreasing by <span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub></span>, so we only need to care about <span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub></span>. The longest non-decreasing sequence by <span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub></span> is the sequence we are looking for.</div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-33025 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33025 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33025"> <li> <div class="comment"> <table class="comment-table" commentId="33026" commentParentId="33025"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 18:27">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33026" href="?#comment-33026" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-33025" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33026" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33026"> <div class="moveup"> <div class="ttypography">Oh, that makes sense now. Thanks!</div> </div> </div> <div class="reply info"> <a class="comment-33026 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33026 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33026"> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="503943" commentParentId="33014"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/AbdAl-mateen" style="position: relative;"> <img src='https://userpic.codeforces.org/694938/avatar/57122394280e75b5.jpg'/> </a> <div><a href="/profile/AbdAl-mateen" title="Newbie AbdAl-mateen" class="rated-user user-gray">AbdAl-mateen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 07:51">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503943" href="?#comment-503943" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-33014" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="503943" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="694938" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503943"> <div class="moveup"> <div class="ttypography"><p>Hi,</p><p><code>Now we can get to the event j from the event i if pi ≤ pj и qi ≤ qj. Let's sort all points in ascending order of p. If several points have the same p we will sort them by q.</code> Can you please explain it for me?</p></div> </div> </div> <div class="reply info"> <a class="comment-503943 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503943 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503943"> <li> <div class="comment"> <table class="comment-table" commentId="503965" commentParentId="503943"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/IlyaCk" style="position: relative;"> <img src='https://userpic.codeforces.org/19187/avatar/40ba7301419542bd.jpg'/> </a> <div><a href="/profile/IlyaCk" title="Expert IlyaCk" class="rated-user user-blue">IlyaCk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 11:02">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503965" href="?#comment-503965" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503943" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="503965" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="19187" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503965"> <div class="moveup"> <div class="ttypography"><p>What do you want to be explained? Why &quot;Now we can get to the event j from the event i if pi ≤ pj и qi ≤ qj.&quot;? Or what &quot;If several points have the same p we will sort them by q.&quot; mean? Or what?</p></div> </div> </div> <div class="reply info"> <a class="comment-503965 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503965 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503965"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="503976" commentParentId="503943"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/IlyaCk" style="position: relative;"> <img src='https://userpic.codeforces.org/19187/avatar/40ba7301419542bd.jpg'/> </a> <div><a href="/profile/IlyaCk" title="Expert IlyaCk" class="rated-user user-blue">IlyaCk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 11:48">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503976" href="?#comment-503976" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503943" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="503976" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="19187" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503976"> <div class="moveup"> <div class="ttypography"><p><a href="https://drive.google.com/file/d/1fwCssJgSTEJ5ic4AzHjhQBQnrypuQkYm/view?usp=sharing">Here</a> is more detailed tutorial. It's in Ukrainian, but you can Google-translate it (result is poor, but some things are still correct) and look at figures and equations.</p><p>I CAN try to reply on more concrete questions, but I don't want to translate the whole text...</p></div> </div> </div> <div class="reply info"> <a class="comment-503976 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503976 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503976"> <li> <div class="comment"> <table class="comment-table" commentId="503980" commentParentId="503976"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/AbdAl-mateen" style="position: relative;"> <img src='https://userpic.codeforces.org/694938/avatar/57122394280e75b5.jpg'/> </a> <div><a href="/profile/AbdAl-mateen" title="Newbie AbdAl-mateen" class="rated-user user-gray">AbdAl-mateen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 13:17">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503980" href="?#comment-503980" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503976" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="503980" revisionCount="4" revision="4"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">4</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="503980" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="694938" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503980"> <div class="moveup"> <div class="ttypography"><p>Well, What are the significances of p, q axes and angle arctg(v)? What do they represent?</p><p>What I understand before, as I mentioned in another comment's reply was as below: to go to j from i: <code>abs(xj - xi) / tj - ti &lt;= v</code> so, </p><p><code>xj + v*tj &gt;= xi + ti*v</code> and <code>-xi + v*ti &gt;= -xj + v*t</code> </p></div> </div> </div> <div class="reply info"> <a class="comment-503980 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503980 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503980"> <li> <div class="comment"> <table class="comment-table" commentId="503987" commentParentId="503980"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/IlyaCk" style="position: relative;"> <img src='https://userpic.codeforces.org/19187/avatar/40ba7301419542bd.jpg'/> </a> <div><a href="/profile/IlyaCk" title="Expert IlyaCk" class="rated-user user-blue">IlyaCk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 15:12">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503987" href="?#comment-503987" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503980" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="503987" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="19187" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503987"> <div class="moveup"> <div class="ttypography"><p>Axis $$$p$$$ is the direction, where the tourist moves (in plane $$$(x,t)$$$), if his speed is ($$${-}v$$$), i.e.maximal by absolute value and directed to left. Its positive ray is the left-bottom border of the area where the tourist can get in time, starting from the origin of the $$$(p,q)$$$ coordiante system. Similarly, $$$q$$$ is the direction, where the tourist moves (in plane $$$(x,t)$$$), if his speed is ($$${+}v$$$), i.e. maximal by absolute value and directed to right; its positive ray is the right-bottom border of the area where the tourist can get in time, starting from the origin of the $$$(p,q)$$$ coordiante system.</p><p>It's not very obvious to look at these axes... But, from other hand, it's not unnatural: we need some effective checking of where the tourist can get in time and where he cannot, so let's try: what, if we'll consider borders of the &quot;reachable-in-time&quot; area as coordinate axes?</p></div> </div> </div> <div class="reply info"> <a class="comment-503987 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503987 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503987"> <li> <div class="comment"> <table class="comment-table" commentId="503991" commentParentId="503987"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/AbdAl-mateen" style="position: relative;"> <img src='https://userpic.codeforces.org/694938/avatar/57122394280e75b5.jpg'/> </a> <div><a href="/profile/AbdAl-mateen" title="Newbie AbdAl-mateen" class="rated-user user-gray">AbdAl-mateen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 16:12">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503991" href="?#comment-503991" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503987" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="503991" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="503991" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="694938" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503991"> <div class="moveup"> <div class="ttypography"><p>I hope this is my last query:</p><p>If tourist needs to go from i to j where xi &gt; xj, that time the velocity is negative. Right? And, the velocity can not be positive and negative at a time,</p><p>But why do we check</p> <pre><code>pi &lt; pj and qi &lt; qj ? </code></pre><p>Why not </p> <pre><code>pi &lt; pj or qi &lt; qj? </code></pre></div> </div> </div> <div class="reply info"> <a class="comment-503991 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503991 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503991"> <li> <div class="comment"> <table class="comment-table" commentId="504027" commentParentId="503991"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/IlyaCk" style="position: relative;"> <img src='https://userpic.codeforces.org/19187/avatar/40ba7301419542bd.jpg'/> </a> <div><a href="/profile/IlyaCk" title="Expert IlyaCk" class="rated-user user-blue">IlyaCk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 22:22">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-504027" href="?#comment-504027" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503991" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="504027" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="19187" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-504027"> <div class="moveup"> <div class="ttypography"><p>The axis directed from bottom to top is $$$t$$$ (time). The tourist cannot travel in time as he wants and/or change time flow direction. All what he can is to choose </p> <ol> <li><p>whether to stay at place with zero velocity (= move in direction of $$$t$$$, which is exactly in the middle between positive direction of $$$p$$$ and positive direction of $$$q$$$);</p></li> <li><p>or to move with velocity ($$$-v$$$), negative and maximal by absolute value, which is exactly positive direction of $$$p$$$;</p></li> <li><p>or to move with velocity ($$$+v$$$), positive and maximal by absolute value, which is exactly positive direction of $$$q$$$;</p></li> <li><p>or to move with velocity $$$0&lt;w&lt;v$$$ (where $$$v$$$ is $$$v$$$ from input data, and $$$w$$$ is actual tourist's velocity), which is in the same quadrant of the $$$(p,q)$$$-system (both $$$p$$$ and $$$q$$$ positive), but $$$q$$$-projection is bigger that $$$p$$$-projection; in other words, $$$0&lt;w&lt;v$$$ corresponds to $$$0&lt;p&lt;q$$$;</p></li> <li><p>or to move with velocity $$$-v&lt;w&lt;0$$$ (where $$$v$$$ is $$$v$$$ from input data, and $$$w$$$ is actual tourist's velocity), which is in the same quadrant of the $$$(p,q)$$$-system (both $$$p$$$ and $$$q$$$ positive), but $$$q$$$-projection is smaller that $$$p$$$-projection; in other words, $$$-v&lt;w&lt;0$$$ corresponds to $$$0&lt;q&lt;p$$$;</p></li> </ol><p>Whereas $$$(q_i &gt; q_j)$$$ (for moving from $$$i$$$ to $$$j$$$) requires either moving with speed $$$w$$$ which is $$$-\infty\leq w &lt; -v$$$, or even moving in reverse direction of time. Similarly, $$$(p_i &gt; p_j)$$$ (for moving from $$$i$$$ to $$$j$$$) requires either moving with speed $$$w$$$ which is $$$v&lt;w\leq\infty$$$, or even moving in reverse direction of time. So, it's required to have <strong>both</strong> $$$(p_i\leq p_j)$$$ <strong>and</strong> $$$(q_i\leq q_j)$$$</p></div> </div> </div> <div class="reply info"> <a class="comment-504027 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-504027 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-504027"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="33574" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/vinhthinhho" style="position: relative;"> <img src='https://userpic.codeforces.org/17649/avatar/4e3c7559e46fc48.jpg'/> </a> <div><a href="/profile/vinhthinhho" title="Candidate Master vinhthinhho" class="rated-user user-violet">vinhthinhho</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/19/2011 11:21">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33574" href="?#comment-33574" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33574" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="17649" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33574"> <div class="moveup"> <div class="ttypography"><p>i dont understand the transformation of (xi,ti), how does it work??? can anyone tell me the answer?</p></div> </div> </div> <div class="reply info"> <a class="comment-33574 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33574 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33574"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="37642" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Master_Chivu" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Master_Chivu" title="Unrated, Master_Chivu" class="rated-user user-black">Master_Chivu</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/11/2011 20:09">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-37642" href="?#comment-37642" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="37642" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="7062" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-37642"> <div class="moveup"> <div class="ttypography">&quot;It is obsiously that if <img align="middle" class="tex-formula" src="/predownloaded/5c/f4/5cf424ac693f1a0c89b939d7a6e6f6ada6700077.png" style="max-width: 100.0%;max-height: 100.0%;" /> or <img align="middle" class="tex-formula" src="/predownloaded/72/41/7241691bc12db2fb46351355cdd678dfea1703d1.png" style="max-width: 100.0%;max-height: 100.0%;" /> then <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> can not be neighbours in the remaining string.&quot;<br />What is &quot;P&quot;?<br />It seems that &quot;P&quot; hasn't been metioned before.<br />I really cannot understand this sentence.<br />And may &quot;absiously&quot; means &quot;abviously&quot;?<br /><br /></div> </div> </div> <div class="reply info"> <a class="comment-37642 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-37642 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-37642"> <li> <div class="comment"> <table class="comment-table" commentId="37653" commentParentId="37642"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/KADR" style="position: relative;"> <img src='https://userpic.codeforces.org/1028/avatar/9089397f80c0fe42.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/KADR" title="Master KADR" class="rated-user user-orange">KADR</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/11/2011 20:25">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-37653" href="?#comment-37653" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-37642" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="37653" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1028" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-37653"> <div class="moveup"> <div class="ttypography">It was a typo. &quot;Obsiously&quot; should be, of course, &quot;obviously&quot;.<div><br /></div><div>Also I occasionally used P instead of M'. It is fixed now, thanks for pointing this out.</div></div> </div> </div> <div class="reply info"> <a class="comment-37653 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-37653 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-37653"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="39030" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Snow_storm" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Snow_storm" title="Expert Snow_storm" class="rated-user user-blue">Snow_storm</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/18/2011 21:22">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-39030" href="?#comment-39030" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="39030" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6824" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-39030"> <div class="moveup"> <div class="ttypography"><p>Problem D is right?</p> <p>I doubts it, for expleam, A=14 and B=4 </p> <p>then X=(14-4)/2=5  Y=5+4=9</p> <p>and A&gt;B and <span class="tex-span"><i>A</i></span> and <span class="tex-span"><i>B</i></span> have some parity and A-X=Y<br /><br />but X^Y=5^9=12  <br />This is my doubts. And I think  (A-B)/2=X&amp;Y .<br />But I don't know the specific X and Y values</p></div> </div> </div> <div class="reply info"> <a class="comment-39030 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-39030 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-39030"> <li> <div class="comment"> <table class="comment-table" commentId="39031" commentParentId="39030"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/KADR" style="position: relative;"> <img src='https://userpic.codeforces.org/1028/avatar/9089397f80c0fe42.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/KADR" title="Master KADR" class="rated-user user-orange">KADR</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/18/2011 21:29">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-39031" href="?#comment-39031" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-39030" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="39031" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1028" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-39031"> <div class="moveup"> <div class="ttypography">Quote from the editorial:<div><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">&quot;If</span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;"><i>X</i></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;"><i>and</i></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;">(<i>A</i> - <i>X</i>) ≠ <i>X</i></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">then the answer is also -1.&quot;</span><br /></div><div>Here X=5 and A-X=9. 5 and 9 = 1, which is not equal to 5. So the answer is -1 here.</div></div> </div> </div> <div class="reply info"> <a class="comment-39031 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-39031 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-39031"> <li> <div class="comment"> <table class="comment-table" commentId="39038" commentParentId="39031"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Snow_storm" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Snow_storm" title="Expert Snow_storm" class="rated-user user-blue">Snow_storm</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/18/2011 21:42">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-39038" href="?#comment-39038" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-39031" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="39038" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6824" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-39038"> <div class="moveup"> <div class="ttypography">I was wrong, <br /><span style="LINE-HEIGHT: 20.0px;FONT-FAMILY: verdana , arial , sans-serif;FONT-SIZE: 12.0px;"><span class="tex-span" style="FONT-FAMILY: &quot;times new roman&quot;;FONT-SIZE: 15.0px;"><i>and is &amp;</i></span></span><br /><br />But I saw many wrong program still through the test,<br /><br />and thank you very much for your patience solutions</div> </div> </div> <div class="reply info"> <a class="comment-39038 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-39038 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-39038"> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="39034" commentParentId="39030"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Snow_storm" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Snow_storm" title="Expert Snow_storm" class="rated-user user-blue">Snow_storm</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/18/2011 21:35">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-39034" href="?#comment-39034" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-39030" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="39034" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6824" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-39034"> <div class="moveup"> <div class="ttypography">I'm sorry, X is smallest, but I'm think if the answer doesn't exist, should add a condition:  X^Y=B</div> </div> </div> <div class="reply info"> <a class="comment-39034 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-39034 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-39034"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="422212" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/stringray" style="position: relative;"> <img src='https://userpic.codeforces.org/575608/avatar/2902babcf56868a2.jpg'/> </a> <div><a href="/profile/stringray" title="Expert stringray" class="rated-user user-blue">stringray</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/27/2018 21:44">6 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-422212" href="?#comment-422212" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="422212" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="575608" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-422212"> <div class="moveup"> <div class="ttypography"><p>Can someone explain the question Gift in this question it is asking for the minimum coins such that every road's gold coin and silver coin constraints are satisfied then if (A,B) is a valid solution then we can make A=infinite and B=infinite so that there will be always a solution also won't A=max(all gi's) and B=max(all si's ) where gi=minimum gold coins for ith road and si=minimum silver coins for ith road (this is what i have understood from the question can anyone tell what's wrong in my understanding )?</p></div> </div> </div> <div class="reply info"> <a class="comment-422212 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-422212 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-422212"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="517643" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Newtech66" style="position: relative;"> <img src='https://userpic.codeforces.org/748716/avatar/ba5b7d94e0bd5415.jpg'/> </a> <div><a href="/profile/Newtech66" title="Expert Newtech66" class="rated-user user-blue">Newtech66</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/10/2019 13:51">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-517643" href="?#comment-517643" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="517643" class="CommentVoteFrame" class="negative-comment-vote" data-commentRating="-10" data-commentUserId="748716" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">-10</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-517643"> <div class="moveup"> <div class="ttypography"><p>Problem D has weak testcases. My solution gets AC despite giving an incorrect answer on the testcase '10 6'.</p></div> </div> </div> <div class="reply info"> <a class="comment-517643 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-517643 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-517643"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="537992" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/memento" style="position: relative;"> <img src='https://userpic.codeforces.org/852933/avatar/950578c1b4afd9dc.jpg'/> </a> <div><a href="/profile/memento" title="Expert memento" class="rated-user user-blue">memento</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Aug/24/2019 21:32">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-537992" href="?#comment-537992" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="537992" class="CommentVoteFrame" data-commentRating="11" data-commentUserId="852933" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+11</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-537992"> <div class="moveup"> <div class="ttypography"><p>Shit. This was 8 years ago.</p></div> </div> </div> <div class="reply info"> <a class="comment-537992 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-537992 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-537992"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="763848" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/vishaaaal" style="position: relative;"> <img src='https://userpic.codeforces.org/1443354/avatar/25a2dd924894eeeb.jpg'/> </a> <div><a href="/profile/vishaaaal" title="Expert vishaaaal" class="rated-user user-blue">vishaaaal</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/20/2021 12:42">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-763848" href="?#comment-763848" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="763848" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1443354" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-763848"> <div class="moveup"> <div class="ttypography"><p>How to solve A without MST??</p> <div class="spoiler"><b class="spoiler-title">Here's my approach</b><div class="spoiler-content" style="display: none;"><p>Let us consider two cities $$$a$$$ and $$$b$$$. We use <em>dfs</em> to calculate the minimum amount of tugriks required for travelling from $$$a$$$ to $$$b$$$. And the answer will be maximum of such value among all pairs of cities.</p><p>The problem is, I think that calculation of this value requires to use Dynamic Programming. Any hints on that??</p></div></div></div> </div> </div> <div class="reply info"> <a class="comment-763848 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-763848 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-763848"> </ul> </div> <br/> <div id="editBox-1722" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In Russian</span> </div> <textarea data-drafts-id="CommentReplyFrame" class="wysiwyg" name="editContent" rows="20" style="width:99%;"></textarea> <div class="error error__content"></div> <div style="text-align:center;"> <input type="button" name="preview" style="padding: 0.25em 1em; 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76E
76
E
en
E. Points
<div class="problem-statement"><div class="header"><div class="title">E. Points</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>You are given <span class="tex-span"><i>N</i></span> points on a plane. Write a program which will find the sum of squares of distances between all pairs of points.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of input contains one integer number <span class="tex-span"><i>N</i></span> (<span class="tex-span">1 ≤ <i>N</i> ≤ 100 000</span>) — the number of points. Each of the following <span class="tex-span"><i>N</i></span> lines contain two integer numbers <span class="tex-span"><i>X</i></span> and <span class="tex-span"><i>Y</i></span> (<span class="tex-span"> - 10 000 ≤ <i>X</i>, <i>Y</i> ≤ 10 000</span>) — the coordinates of points. Two or more points may coincide.</p></div><div class="output-specification"><div class="section-title">Output</div><p>The only line of output should contain the required sum of squares of distances between all pairs of points.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>4<br/>1 1<br/>-1 -1<br/>1 -1<br/>-1 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>32<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="E" data-uuid="ps_70daeb659d7612f06a85d74289586ac4b37bfa6b"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">E. Points</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>You are given <span class="tex-span"><i>N</i></span> points on a plane. Write a program which will find the sum of squares of distances between all pairs of points.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of input contains one integer number <span class="tex-span"><i>N</i></span> (<span class="tex-span">1 ≤ <i>N</i> ≤ 100 000</span>) — the number of points. Each of the following <span class="tex-span"><i>N</i></span> lines contain two integer numbers <span class="tex-span"><i>X</i></span> and <span class="tex-span"><i>Y</i></span> (<span class="tex-span"> - 10 000 ≤ <i>X</i>, <i>Y</i> ≤ 10 000</span>) — the coordinates of points. Two or more points may coincide.</p></div><div class="output-specification"><div class="section-title">Output</div><p>The only line of output should contain the required sum of squares of distances between all pairs of points.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>4<br />1 1<br />-1 -1<br />1 -1<br />-1 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>32<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=E]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); if (previousStatementText) { if (previousStatementText !== statementText) { $problem.find(".diff-notifier").show(); $problem.find(".diff-notifier-close").click(function() { Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60); 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["Implementation problems, programming technics, simulation", "Mathematics including integration, differential equations, etc"]
["implementation", "math", "*1700"]
https://codeforces.com/blog/entry/1712
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<a href="/blog/entry/120644">Codeforces Round 899 (Div. 2)</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/Misa-Misa" title="Expert Misa-Misa" class="rated-user user-blue">Misa-Misa</a> &rarr; <a href="/blog/entry/121157">Someone please help me understand this.</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/shivam565" title="Specialist shivam565" class="rated-user user-cyan">shivam565</a> &rarr; <a href="/blog/entry/108348">Total number of subarrays with sum atmost k</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> </ul> </div> <div class="bottom-links"> <table style="width:100%;"> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:right;"> <a href="/recent-actions">Detailed &rarr;</a> </td> </tr> </tbody> </table> </div> </div> </div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li><a href="/profile/KADR">KADR</a></li> <li class="current selectedLava"><a href="/blog/KADR">Blog</a></li> <li><a href="/teams/with/KADR">Teams</a></li> <li><a href="/submissions/KADR">Submissions</a></li> <li><a href="/groups/with/KADR">Groups</a></li> <li><a href="/contests/with/KADR">Contests</a></li> <li><a href="/contests/writer/KADR">Problemsetting</a></li> </ul> </div> <div style="margin-top:0;"> <div> <h3><a href="/blog/KADR" style="text-decoration:none;color:black !important;">KADR's blog</a></h3> </div> <div style="margin-top:2em;"> <div class="has-topic-id topic" topicId="1712"> <div class="title"> <a href="/blog/entry/1712"> All-Ukrainian School Olympiad in Informatics: editorial (A,B,C,D,E,F) </a> </div> <div class="info" style="position:relative;"> By&nbsp;<a href="/profile/KADR" title="Master KADR" class="rated-user user-orange">KADR</a>, <span class="format-humantime" title="Apr/12/2011 21:30">12 years ago</span>, translation, <img style="position: relative;top: 5px;" src="//codeforces.org/s/81027/images/flags/24/gb.png" alt="In English" title="In English"/> <span style="position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;"> <div style="margin-top:0.25em;"> </div> </span> </div> <div class="content"> <div class="ttypography"><div>The editorial is now completed.</div><div><br /></div><div><div><b>Problem A: Gift (Roman Iedemskyi)</b></div><div><br /></div><div>Suppose that the pair <span class="tex-span">(<i>A</i>, <i>B</i>)</span> is an optimal solution, where <span class="tex-span"><i>A</i></span> is the number of gold coins in a gift and <span class="tex-span"><i>B</i></span> is a number of silver coins. It is easy to see  that there exist two (probably equal) indexes <span class="tex-span"><i>i</i></span> and <span class="tex-span"><i>j</i></span> such that <span class="tex-span"><i>g</i><sub class="lower-index"><i>i</i></sub> = <i>A</i></span> and <span class="tex-span"><i>s</i><sub class="lower-index"><i>j</i></sub> = <i>B</i></span>. It is true, because in the other case we could decrease either <span class="tex-span"><i>A</i></span> or <span class="tex-span"><i>B</i></span> without changing connectivity of the graph.</div><div><br /></div><div>Let <span class="tex-span"><i>R</i>(<i>A</i>, <i>B</i>)</span> be the graph in which for all <span class="tex-span"><i>i</i></span> the following statement holds: <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/f6a7810c1f985efe671bb157563fc069d097fbce.png" style="max-width: 100.0%;max-height: 100.0%;" />.</div><div><br /></div><div>Let <span class="tex-span"><i>T</i>(<i>A</i>)</span> be the weighted graph in which for all edges <span class="tex-span"><i>g</i><sub class="lower-index"><i>i</i></sub> ≤ <i>A</i></span>. For each edge <span class="tex-span"><i>i</i></span> we will assign a weight equal to <span class="tex-span"><i>s</i><sub class="lower-index"><i>i</i></sub></span>. Let's find a spanning tree of this graph, which has the property that its maximal edge is minimal possible. It can be shown that for the fixed <span class="tex-span"><i>A</i></span> the minimal value of <span class="tex-span"><i>B</i></span> for which graph <span class="tex-span"><i>R</i>(<i>A</i>, <i>B</i>)</span> is still connected is equal to the weight of the maximal edge in this spanning tree.</div><div><br /></div><div><i>Claim</i>. Minimal spanning tree of a graph has the property that its maximal edge is minimal possible among all spanning trees.</div><div><i>Proof</i>. Let <span class="tex-span"><i>L</i></span> be the minimal spanning tree of a graph. Suppose there exists a spanning tree <span class="tex-span"><i>P</i></span> in which all edges have smaller weight than the weight of the maximal edge of <span class="tex-span"><i>L</i></span>. We can then remove the maximal edge from <span class="tex-span"><i>L</i></span> and add some edge from <span class="tex-span"><i>P</i></span> to it which will connect the graph back. After that <span class="tex-span"><i>L</i></span> will have strictly smaller weight, which is impossible because it is a minimal spanning tree.</div><div><br /></div><div>Let's sort all edges of the graph in ascending order of <span class="tex-span"><i>g</i><sub class="lower-index"><i>i</i></sub></span>. Then the edges of graph <span class="tex-span"><i>T</i>(<i>A</i>)</span> for the fixed <span class="tex-span"><i>i</i></span> will be all edges with indexes <span class="tex-span"><i>j</i> ≤ <i>i</i></span>.</div><div><br /></div><div>Suppose that for some value of <span class="tex-span"><i>i</i></span> we have already found minimal spanning tree in every connected component of the graph <span class="tex-span"><i>T</i>(<i>g</i><sub class="lower-index"><i>i</i></sub>)</span>. Let's add an edge with index <span class="tex-span"><i>i</i> + 1</span> into it. If it connects two different components, then after this operation they will be merged into one big component and it is obviously that the spanning tree we have in it is the minimal spanning tree. If <span class="tex-span"><i>i</i> + 1</span>-th edge connects two vertices from the same connected component, then it will create exactly one cycle in the graph. We can find the maximal edge in this cycle and remove it from the graph. It can be proven that the remaining tree will be the minimal spanning tree of this connected component.</div><div><br /></div><div>We can perform the search of the maximal edge in a cycle as well as the insertion and removal of the edges in O(N). The total complexity is <span class="tex-span"><i>O</i>(<i>NM</i> + <i>MlogM</i>)</span>.</div></div><div><br /></div><div><div><b>Problem B: Mice (Roman Rizvanov)</b></div><div><br /></div><div>It is easy to see that the number of closest pieces of cheese for each mouse is not greater than 2.</div><div><br /></div><div>Let's find the closest pieces of cheese for each mouse to the left and to the right from it. From two directions we will choose the one which gives us shorter way to cheese or both of them if their lengths are equal. If on the chosen way between the mouse and the cheese stands another mouse, then we should exclude this way from consideration, because another mouse will get to the cheese faster. Now all the directions lead to cheese and for each piece of cheese there is at most one mouse which can potentially eat it from each direction.</div><div><br /></div><div>We will process mice from left to right. If the current mouse can move left and the cheese to the left of it is not chosen by any other mouse or it is chosen by a mouse with the same distance to it, then the current mouse can move to the left and eat this piece of cheese without interfering with other mice. This choice will not affect any choices of the next mice, because only one mouse can go to this piece of cheese from the right (see previous paragraph). Thus, this choice can not decrease the answer. In all other cases the current mouse can not increase the answer by moving left, so it should move to the right if it has such opportunity.</div><div><br /></div><div>The complexity is <span class="tex-span"><i>O</i>(<i>N</i> + <i>M</i>)</span>.</div><div><br /></div><div>This problem can be also solved using dynamic programming.</div></div><div><br /></div><div><b>Problem C: Mutation (Iaroslav Tverdokhlib)</b></div><div><br /></div><div><div>In the editorial we will replace terms &quot;risk&quot;, &quot;genome&quot; and &quot;gene&quot; with &quot;cost&quot;, &quot;string&quot; and &quot;character&quot;, respectively. Let <span class="tex-span"><i>S</i></span> be the starting string.</div><div><br /></div><div>Let <span class="tex-span"><i>M</i></span> be the bitmask of chars which will be removed. Let's iterate over all possible values of <span class="tex-span"><i>M</i></span>. For the fixed <span class="tex-span"><i>M</i></span> we need to find a cost of the string, which remained after removal of <span class="tex-span"><i>M</i></span> and if this cost doesn't exceed <span class="tex-span"><i>T</i></span> we will increase the answer by 1. Naive implementation of this idea has the complexity <span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>K</i></sup><i>N</i>)</span>.</div><div><br /></div><div>We can not get rid of iterating over all <span class="tex-span"><i>M</i></span>, so we will try to optimize a part of the algorithm which finds a cost of the remaining string.</div><div><br /></div><div>Let's take two indexes <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> from the beginning string <span class="tex-span"><i>l</i> &lt; <i>r</i></span>. Let <span class="tex-span"><i>M</i>'</span> be the bitmask of all characters which are located strictly between them. It is obviously that if <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7b04066e365590d0dc24c90dfc15aabd64c75339.png" style="max-width: 100.0%;max-height: 100.0%;" /> or <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/3880b6b45cb2a0ccd5ea51b69f020c9e5a9f7fa1.png" style="max-width: 100.0%;max-height: 100.0%;" /> then <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> can not be neighbours in the remaining string. Hence for the fixed <span class="tex-span"><i>l</i></span> there are not more than <span class="tex-span"><i>K</i></span> possible candidates for <span class="tex-span"><i>r</i></span>, which means that there are <span class="tex-span"><i>O</i>(<i>NK</i>)</span> pairs of such potential neighbours. We will call such pairs &quot;good&quot;.</div><div><br /></div><div>We want to find out what form should have the set <span class="tex-span"><i>M</i></span> that after its removal indexes <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> became adjacent. It is easy to see that the following two conditions should be true:</div><div><br /></div><div>1. <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/07de7c5bc68bc92d118ada183dab5d78f5c631c4.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div>2. <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7fa1a37ebb11a92726d78e30e0ad17ffda729919.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><br /></div><div>Let's iterate over all good pairs of <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> and for each of them we will find the set <span class="tex-span"><i>M</i>'</span>. For each triple <span class="tex-span">(<i>a</i>, <i>b</i>, <i>P</i>)</span> we will store the sum of costs of neighborhood of all pairs <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> for which <span class="tex-span"><i>S</i><sub class="lower-index"><i>l</i></sub> = <i>a</i></span>, <span class="tex-span"><i>S</i><sub class="lower-index"><i>r</i></sub> = <i>b</i></span>, <span class="tex-span"><i>M</i>' = <i>P</i></span>. After that for the fixed <span class="tex-span"><i>M</i></span> we will iterate over all pairs of characters <span class="tex-span">(<i>a</i>, <i>b</i>)</span> and its subsets <span class="tex-span"><i>P</i></span> and add all their costs together. Also we need to add the cost of removal of <span class="tex-span"><i>M</i></span> and the resulting sum will be the cost of the string which will left after removal of <span class="tex-span"><i>M</i></span>. The complexity of such solution is <span class="tex-span"><i>O</i>(3<sup class="upper-index"><i>K</i></sup> * <i>K</i><sup class="upper-index">2</sup> + <i>NK</i>)</span>.</div><div><br /></div><div>We will optimize the previous solution by decreasing a factor near <span class="tex-span">3<sup class="upper-index"><i>K</i></sup></span>. Let's look at the following (incorrect) algorithm:</div><div><br /></div><div>We will iterate over all good pairs <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> and for each of them we will find <span class="tex-span"><i>M</i>'</span>. Let's create an array <span class="tex-span"><i>v</i></span> in which for each mask <span class="tex-span"><i>P</i></span> we will store the sum of costs of neighborhood of all pairs <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> for which <span class="tex-span"><i>M</i>' = <i>P</i></span>. For the fixed <span class="tex-span"><i>M</i></span> we will find a sum of all values from <span class="tex-span"><i>v</i></span> for all submasks of <span class="tex-span"><i>M</i></span>, then add the cost of removal of <span class="tex-span"><i>M</i></span> to it and the resulting sum will be the cost of the remaining string.</div><div><br /></div><div>This algorithm is incorrect, because some costs of neighborhood are added to the total cost, but in fact the respective <span class="tex-span"><i>l</i></span> or <span class="tex-span"><i>r</i></span> are removed. Let's use inclusion-exclusion principle and make the following at the phase of filling array <span class="tex-span"><i>v</i></span>:</div><div><br /></div><div><span class="tex-span"><i>v</i>[<i>M</i>'] +  = <i>cost</i></span></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/b4d392e8baa2755f671b67077d5ad638a2818e1c.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/0939a5ad00766ddcedb4465081c7dc8c63f0dd22.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/872ba326de38444a17ace78f749a43a3e1eff1d1.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><br /></div><div>With such filling of <span class="tex-span"><i>v</i></span> the algorithm described above is correct and the total complexity becomes <span class="tex-span"><i>O</i>(3<sup class="upper-index"><i>K</i></sup> + <i>NK</i>)</span>.</div><div><br /></div><div>This is still not enough for the full solution, but we are almost there. We only need to find a fast way of finding the sum of the values of <span class="tex-span"><i>v</i></span> for all submasks of all masks <span class="tex-span"><i>M</i></span>. We will use the following iterative algorithm for this purpose:</div><div><br /></div><div>Before the first iteration we have an array <span class="tex-span"><i>v</i></span> in which the starting values are stored. After iteration with number <span class="tex-span"><i>i</i></span> in <span class="tex-span"><i>v</i>[<i>mask</i>]</span> we will store the sum of all the values from the original array <span class="tex-span"><i>v</i></span> for all submasks of <span class="tex-span"><i>mask</i></span> for which the first <span class="tex-span"><i>K</i> - <i>i</i></span> bits are equal to the respective bits of <span class="tex-span"><i>mask</i></span>. On iteration with number <span class="tex-span"><i>i</i></span> for all masks in which the <span class="tex-span"><i>i</i></span>-th bit is equal to 1 (bits are numbered from 1) we will perform the following: <span class="tex-span"><i>v</i>[<i>mask</i>] +  = <i>v</i>[<i>mask</i>\{<i>i</i>}]</span>. It is easy to see that after the <span class="tex-span"><i>K</i></span>-th iteration of this algorithm we will have the values we were looking for in array <span class="tex-span"><i>v</i></span>.</div><div><br /></div><div>The complexity is <span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>K</i></sup><i>K</i> + <i>NK</i>)</span>.</div></div><div><br /></div><div><b>Problem D: Plus and XOR (Daniel Neiter)</b></div><div><br /></div><div>Let's take a look at some bit in X, which is equal to 1. If the respective bit in Y is equal to 0, then we can swap these two bits, thus reducing X and increasing Y without changing their sum and xor. We can conclude that if some bit in X is equal to 1 then the respective bit in Y is also equal to 1. Thus, <span class="tex-span"><i>Y</i> = <i>X</i> + <i>B</i></span>. Taking into account that <span class="tex-span"><i>X</i> + <i>Y</i> = <i>X</i> + <i>X</i> + <i>B</i> = <i>A</i>, </span> we can obtain the following formulas for finding <span class="tex-span"><i>X</i></span> and <span class="tex-span"><i>Y</i></span>:</div><div><br /></div><div><span class="tex-span"><i>X</i> = (<i>A</i> - <i>B</i>) / 2</span></div><div><span class="tex-span"><i>Y</i> = <i>X</i> + <i>B</i></span></div><div><div><br /></div><div>One should also notice that if <span class="tex-span"><i>A</i> &lt; <i>B</i></span> or <span class="tex-span"><i>A</i></span> and <span class="tex-span"><i>B</i></span> have different parity, then the answer doesn't exist and we should output -1. If <span class="tex-span"><i>X</i></span> <span class="tex-span"><i>and</i></span> <span class="tex-span">(<i>A</i> - <i>X</i>) ≠ <i>X</i></span> then the answer is also -1.</div></div><div><br /></div><div><b>Problem E: Points (Daniel Neiter)</b></div><div><b><br /></b></div><div>Let's regroup summands and split the sum of squares of distances we are looking for into two sums:</div><div><b><br /></b></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/6e7ca6f50695e36ea199c3704ebb7574c4bfc029.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/b4a6a53d2cb6e9458620cc0b964c69f610df6601.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><br /></div><div>Now we need to rewrite each of these sums in the following way (it will be shown for the first sum):</div><div><br /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/ce7d437559ce56c7602146506aaec7f5b8f5920b.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/14de3bd836c0e823801f884a115983ff447988b5.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><br /></div><div>This formula allows us to find an answer in one pass through the array. The complexity is O(N).</div><div><br /></div><div><div><b>Problem F: Tourist (Ilya Porublyov)</b></div><div><br /></div><div>We can get to the event <span class="tex-span"><i>j</i></span> from the event <span class="tex-span"><i>i</i></span> if the following statements are true:</div><div><br /></div><div><ul><li><span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub> ≤ <i>t</i><sub class="lower-index"><i>j</i></sub></span><br /></li><li><span class="tex-span">|<i>x</i><sub class="lower-index"><i>i</i></sub> - <i>x</i><sub class="lower-index"><i>j</i></sub>| ≤ |<i>t</i><sub class="lower-index"><i>i</i></sub> - <i>t</i><sub class="lower-index"><i>j</i></sub>|· <i>V</i></span><br /></li></ul></div><div>We can represent all the events as points on a plane with coordinates <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i></sub>, <i>t</i><sub class="lower-index"><i>i</i></sub>)</span>. Now we can reformulate the two statements written above in the following way:<br /></div><div><br /></div><div>From the event <span class="tex-span"><i>i</i></span> we can get to the event <span class="tex-span"><i>j</i></span> if the point <span class="tex-span">(<i>x</i><sub class="lower-index"><i>j</i></sub>, <i>t</i><sub class="lower-index"><i>j</i></sub>)</span> lise inside an angle pointed to the top with its vertex in <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i></sub>, <i>t</i><sub class="lower-index"><i>i</i></sub>)</span> and its sides form an angle <span class="tex-span"><i>arctg</i>(<i>V</i>)</span> with vertical axis. Let's make coordinate transformation according to which the point with coordinates <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i></sub>, <i>t</i><sub class="lower-index"><i>i</i></sub>)</span> will transform into the point <span class="tex-span">(<i>p</i><sub class="lower-index"><i>i</i></sub>, <i>q</i><sub class="lower-index"><i>i</i></sub>)</span>, where</div><div><span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub> =  - <i>x</i><sub class="lower-index"><i>i</i></sub> + <i>t</i><sub class="lower-index"><i>i</i></sub> * <i>V</i></span></div><div><span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub> = <i>x</i><sub class="lower-index"><i>i</i></sub> + <i>t</i><sub class="lower-index"><i>i</i></sub> * <i>V</i></span></div><div><br /></div><div>Now we can get to the event <span class="tex-span"><i>j</i></span> from the event <span class="tex-span"><i>i</i></span> if <span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub> ≤ <i>p</i><sub class="lower-index"><i>j</i></sub></span> и <span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub> ≤ <i>q</i><sub class="lower-index"><i>j</i></sub></span>. Let's sort all points in ascending order of <span class="tex-span"><i>p</i></span>. If several points have the same <span class="tex-span"><i>p</i></span> we will sort them by <span class="tex-span"><i>q</i></span>. The second subproblem of our problem can be solved by finding a longest increasing subsequence by <span class="tex-span"><i>q</i></span> in this array. It can be done in <span class="tex-span"><i>O</i>(<i>NlogN</i>)</span>.</div><div><br /></div><div>To solve the first subproblem we can add dummy event with coordinate 0 and time 0 (if it is not present in our set of events yet) and force tourist's start from it.</div><div><br /></div><div>The total complexity if <span class="tex-span"><i>O</i>(<i>NlogN</i>)</span>.</div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/76" class="notice" style="text-decoration: none;">All-Ukrainian School Olympiad in Informatics</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-996-1712").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "996", blogEntryId: "1712", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces" class="tag notice" style="text-decoration: none;">codeforces</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=editorial" class="tag notice" style="text-decoration: none;">editorial</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=uoi2011" class="tag notice" style="text-decoration: none;">uoi2011</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1712"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+30</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1712"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; 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} .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1722"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (22)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="32624" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/wil93" style="position: relative;"> <img src='https://userpic.codeforces.org/14356/avatar/897f1996dfb7343b.jpg'/> </a> <div><a href="/profile/wil93" title="Expert wil93" class="rated-user user-blue">wil93</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/12/2011 23:20">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32624" href="?#comment-32624" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32624" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="14356" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32624"> <div class="moveup"> <div class="ttypography">Thanks very much, I think E's solution is genial. I understood it now, but it would be very difficult for me to come out with a similar thought :)</div> </div> </div> <div class="reply info"> <a class="comment-32624 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32624 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32624"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="33014" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 16:09">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33014" href="?#comment-33014" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="33014" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="33014" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33014"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">Hi,<br /><br />I would like to ask about problem F. Is there a particular reason why you sort by p first before you sort by q? If not, will sorting by q and then by p for tiebreak change the solution? If not, may I know if you can prove so? I can understand how you make the transformation and why the transformation is correct, but I am not convinced that you can get the optimal solution just by sorting and finding the LIS (Do you mean the longest non-decreasing subsequence? From what I understand, I think you first label the vertices according to the time when they appear. If they appear at the same time, then they have the same label.) Can you please give a proof or explanation why it works?<br /><br />Thanks in advance!</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-33014 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33014 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33014"> <li> <div class="comment"> <table class="comment-table" commentId="33025" commentParentId="33014"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/KADR" style="position: relative;"> <img src='https://userpic.codeforces.org/1028/avatar/9089397f80c0fe42.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/KADR" title="Master KADR" class="rated-user user-orange">KADR</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 18:25">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33025" href="?#comment-33025" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-33014" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="33025" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="33025" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1028" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33025"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">If some two events have the same time then it is impossible to visit them both, so we are not interested in their relative order in the sorted array (after performing the transformation).<div><br /></div><div>After the transformation we can get from the point <span class="tex-span">(<i>p</i><sub class="lower-index"><i>i</i></sub>, <i>q</i><sub class="lower-index"><i>i</i></sub>)</span> to the point <span class="tex-span">(<i>p</i><sub class="lower-index"><i>j</i></sub>, <i>q</i><sub class="lower-index"><i>j</i></sub>)</span> iff <span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub> ≤ <i>p</i><sub class="lower-index"><i>j</i></sub></span> and <span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub> ≤ <i>q</i><sub class="lower-index"><i>j</i></sub></span>. After performing the sorting described in the editorial all points reachable from the point <span class="tex-span">(<i>p</i><sub class="lower-index"><i>i</i></sub>, <i>q</i><sub class="lower-index"><i>i</i></sub>)</span> will have greater indexes in the array. This automatically means that the sequence will be non-decreasing by <span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub></span>, so we only need to care about <span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub></span>. The longest non-decreasing sequence by <span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub></span> is the sequence we are looking for.</div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-33025 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33025 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33025"> <li> <div class="comment"> <table class="comment-table" commentId="33026" commentParentId="33025"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 18:27">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33026" href="?#comment-33026" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-33025" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33026" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33026"> <div class="moveup"> <div class="ttypography">Oh, that makes sense now. Thanks!</div> </div> </div> <div class="reply info"> <a class="comment-33026 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33026 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33026"> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="503943" commentParentId="33014"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/AbdAl-mateen" style="position: relative;"> <img src='https://userpic.codeforces.org/694938/avatar/57122394280e75b5.jpg'/> </a> <div><a href="/profile/AbdAl-mateen" title="Newbie AbdAl-mateen" class="rated-user user-gray">AbdAl-mateen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 07:51">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503943" href="?#comment-503943" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-33014" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="503943" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="694938" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503943"> <div class="moveup"> <div class="ttypography"><p>Hi,</p><p><code>Now we can get to the event j from the event i if pi ≤ pj и qi ≤ qj. Let's sort all points in ascending order of p. If several points have the same p we will sort them by q.</code> Can you please explain it for me?</p></div> </div> </div> <div class="reply info"> <a class="comment-503943 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503943 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503943"> <li> <div class="comment"> <table class="comment-table" commentId="503965" commentParentId="503943"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/IlyaCk" style="position: relative;"> <img src='https://userpic.codeforces.org/19187/avatar/40ba7301419542bd.jpg'/> </a> <div><a href="/profile/IlyaCk" title="Expert IlyaCk" class="rated-user user-blue">IlyaCk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 11:02">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503965" href="?#comment-503965" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503943" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="503965" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="19187" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503965"> <div class="moveup"> <div class="ttypography"><p>What do you want to be explained? Why &quot;Now we can get to the event j from the event i if pi ≤ pj и qi ≤ qj.&quot;? Or what &quot;If several points have the same p we will sort them by q.&quot; mean? Or what?</p></div> </div> </div> <div class="reply info"> <a class="comment-503965 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503965 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503965"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="503976" commentParentId="503943"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/IlyaCk" style="position: relative;"> <img src='https://userpic.codeforces.org/19187/avatar/40ba7301419542bd.jpg'/> </a> <div><a href="/profile/IlyaCk" title="Expert IlyaCk" class="rated-user user-blue">IlyaCk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 11:48">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503976" href="?#comment-503976" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503943" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="503976" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="19187" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503976"> <div class="moveup"> <div class="ttypography"><p><a href="https://drive.google.com/file/d/1fwCssJgSTEJ5ic4AzHjhQBQnrypuQkYm/view?usp=sharing">Here</a> is more detailed tutorial. It's in Ukrainian, but you can Google-translate it (result is poor, but some things are still correct) and look at figures and equations.</p><p>I CAN try to reply on more concrete questions, but I don't want to translate the whole text...</p></div> </div> </div> <div class="reply info"> <a class="comment-503976 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503976 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503976"> <li> <div class="comment"> <table class="comment-table" commentId="503980" commentParentId="503976"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/AbdAl-mateen" style="position: relative;"> <img src='https://userpic.codeforces.org/694938/avatar/57122394280e75b5.jpg'/> </a> <div><a href="/profile/AbdAl-mateen" title="Newbie AbdAl-mateen" class="rated-user user-gray">AbdAl-mateen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 13:17">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503980" href="?#comment-503980" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503976" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="503980" revisionCount="4" revision="4"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">4</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="503980" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="694938" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503980"> <div class="moveup"> <div class="ttypography"><p>Well, What are the significances of p, q axes and angle arctg(v)? What do they represent?</p><p>What I understand before, as I mentioned in another comment's reply was as below: to go to j from i: <code>abs(xj - xi) / tj - ti &lt;= v</code> so, </p><p><code>xj + v*tj &gt;= xi + ti*v</code> and <code>-xi + v*ti &gt;= -xj + v*t</code> </p></div> </div> </div> <div class="reply info"> <a class="comment-503980 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503980 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503980"> <li> <div class="comment"> <table class="comment-table" commentId="503987" commentParentId="503980"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/IlyaCk" style="position: relative;"> <img src='https://userpic.codeforces.org/19187/avatar/40ba7301419542bd.jpg'/> </a> <div><a href="/profile/IlyaCk" title="Expert IlyaCk" class="rated-user user-blue">IlyaCk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 15:12">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503987" href="?#comment-503987" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503980" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="503987" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="19187" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503987"> <div class="moveup"> <div class="ttypography"><p>Axis $$$p$$$ is the direction, where the tourist moves (in plane $$$(x,t)$$$), if his speed is ($$${-}v$$$), i.e.maximal by absolute value and directed to left. Its positive ray is the left-bottom border of the area where the tourist can get in time, starting from the origin of the $$$(p,q)$$$ coordiante system. Similarly, $$$q$$$ is the direction, where the tourist moves (in plane $$$(x,t)$$$), if his speed is ($$${+}v$$$), i.e. maximal by absolute value and directed to right; its positive ray is the right-bottom border of the area where the tourist can get in time, starting from the origin of the $$$(p,q)$$$ coordiante system.</p><p>It's not very obvious to look at these axes... But, from other hand, it's not unnatural: we need some effective checking of where the tourist can get in time and where he cannot, so let's try: what, if we'll consider borders of the &quot;reachable-in-time&quot; area as coordinate axes?</p></div> </div> </div> <div class="reply info"> <a class="comment-503987 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503987 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503987"> <li> <div class="comment"> <table class="comment-table" commentId="503991" commentParentId="503987"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/AbdAl-mateen" style="position: relative;"> <img src='https://userpic.codeforces.org/694938/avatar/57122394280e75b5.jpg'/> </a> <div><a href="/profile/AbdAl-mateen" title="Newbie AbdAl-mateen" class="rated-user user-gray">AbdAl-mateen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 16:12">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503991" href="?#comment-503991" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503987" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="503991" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="503991" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="694938" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503991"> <div class="moveup"> <div class="ttypography"><p>I hope this is my last query:</p><p>If tourist needs to go from i to j where xi &gt; xj, that time the velocity is negative. Right? And, the velocity can not be positive and negative at a time,</p><p>But why do we check</p> <pre><code>pi &lt; pj and qi &lt; qj ? </code></pre><p>Why not </p> <pre><code>pi &lt; pj or qi &lt; qj? </code></pre></div> </div> </div> <div class="reply info"> <a class="comment-503991 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503991 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503991"> <li> <div class="comment"> <table class="comment-table" commentId="504027" commentParentId="503991"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/IlyaCk" style="position: relative;"> <img src='https://userpic.codeforces.org/19187/avatar/40ba7301419542bd.jpg'/> </a> <div><a href="/profile/IlyaCk" title="Expert IlyaCk" class="rated-user user-blue">IlyaCk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 22:22">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-504027" href="?#comment-504027" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503991" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="504027" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="19187" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-504027"> <div class="moveup"> <div class="ttypography"><p>The axis directed from bottom to top is $$$t$$$ (time). The tourist cannot travel in time as he wants and/or change time flow direction. All what he can is to choose </p> <ol> <li><p>whether to stay at place with zero velocity (= move in direction of $$$t$$$, which is exactly in the middle between positive direction of $$$p$$$ and positive direction of $$$q$$$);</p></li> <li><p>or to move with velocity ($$$-v$$$), negative and maximal by absolute value, which is exactly positive direction of $$$p$$$;</p></li> <li><p>or to move with velocity ($$$+v$$$), positive and maximal by absolute value, which is exactly positive direction of $$$q$$$;</p></li> <li><p>or to move with velocity $$$0&lt;w&lt;v$$$ (where $$$v$$$ is $$$v$$$ from input data, and $$$w$$$ is actual tourist's velocity), which is in the same quadrant of the $$$(p,q)$$$-system (both $$$p$$$ and $$$q$$$ positive), but $$$q$$$-projection is bigger that $$$p$$$-projection; in other words, $$$0&lt;w&lt;v$$$ corresponds to $$$0&lt;p&lt;q$$$;</p></li> <li><p>or to move with velocity $$$-v&lt;w&lt;0$$$ (where $$$v$$$ is $$$v$$$ from input data, and $$$w$$$ is actual tourist's velocity), which is in the same quadrant of the $$$(p,q)$$$-system (both $$$p$$$ and $$$q$$$ positive), but $$$q$$$-projection is smaller that $$$p$$$-projection; in other words, $$$-v&lt;w&lt;0$$$ corresponds to $$$0&lt;q&lt;p$$$;</p></li> </ol><p>Whereas $$$(q_i &gt; q_j)$$$ (for moving from $$$i$$$ to $$$j$$$) requires either moving with speed $$$w$$$ which is $$$-\infty\leq w &lt; -v$$$, or even moving in reverse direction of time. Similarly, $$$(p_i &gt; p_j)$$$ (for moving from $$$i$$$ to $$$j$$$) requires either moving with speed $$$w$$$ which is $$$v&lt;w\leq\infty$$$, or even moving in reverse direction of time. So, it's required to have <strong>both</strong> $$$(p_i\leq p_j)$$$ <strong>and</strong> $$$(q_i\leq q_j)$$$</p></div> </div> </div> <div class="reply info"> <a class="comment-504027 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-504027 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-504027"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="33574" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/vinhthinhho" style="position: relative;"> <img src='https://userpic.codeforces.org/17649/avatar/4e3c7559e46fc48.jpg'/> </a> <div><a href="/profile/vinhthinhho" title="Candidate Master vinhthinhho" class="rated-user user-violet">vinhthinhho</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/19/2011 11:21">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33574" href="?#comment-33574" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33574" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="17649" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33574"> <div class="moveup"> <div class="ttypography"><p>i dont understand the transformation of (xi,ti), how does it work??? can anyone tell me the answer?</p></div> </div> </div> <div class="reply info"> <a class="comment-33574 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33574 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33574"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="37642" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Master_Chivu" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Master_Chivu" title="Unrated, Master_Chivu" class="rated-user user-black">Master_Chivu</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/11/2011 20:09">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-37642" href="?#comment-37642" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="37642" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="7062" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-37642"> <div class="moveup"> <div class="ttypography">&quot;It is obsiously that if <img align="middle" class="tex-formula" src="/predownloaded/5c/f4/5cf424ac693f1a0c89b939d7a6e6f6ada6700077.png" style="max-width: 100.0%;max-height: 100.0%;" /> or <img align="middle" class="tex-formula" src="/predownloaded/72/41/7241691bc12db2fb46351355cdd678dfea1703d1.png" style="max-width: 100.0%;max-height: 100.0%;" /> then <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> can not be neighbours in the remaining string.&quot;<br />What is &quot;P&quot;?<br />It seems that &quot;P&quot; hasn't been metioned before.<br />I really cannot understand this sentence.<br />And may &quot;absiously&quot; means &quot;abviously&quot;?<br /><br /></div> </div> </div> <div class="reply info"> <a class="comment-37642 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-37642 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-37642"> <li> <div class="comment"> <table class="comment-table" commentId="37653" commentParentId="37642"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/KADR" style="position: relative;"> <img src='https://userpic.codeforces.org/1028/avatar/9089397f80c0fe42.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/KADR" title="Master KADR" class="rated-user user-orange">KADR</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/11/2011 20:25">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-37653" href="?#comment-37653" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-37642" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="37653" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1028" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-37653"> <div class="moveup"> <div class="ttypography">It was a typo. &quot;Obsiously&quot; should be, of course, &quot;obviously&quot;.<div><br /></div><div>Also I occasionally used P instead of M'. It is fixed now, thanks for pointing this out.</div></div> </div> </div> <div class="reply info"> <a class="comment-37653 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-37653 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-37653"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="39030" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Snow_storm" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Snow_storm" title="Expert Snow_storm" class="rated-user user-blue">Snow_storm</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/18/2011 21:22">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-39030" href="?#comment-39030" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="39030" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6824" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-39030"> <div class="moveup"> <div class="ttypography"><p>Problem D is right?</p> <p>I doubts it, for expleam, A=14 and B=4 </p> <p>then X=(14-4)/2=5  Y=5+4=9</p> <p>and A&gt;B and <span class="tex-span"><i>A</i></span> and <span class="tex-span"><i>B</i></span> have some parity and A-X=Y<br /><br />but X^Y=5^9=12  <br />This is my doubts. And I think  (A-B)/2=X&amp;Y .<br />But I don't know the specific X and Y values</p></div> </div> </div> <div class="reply info"> <a class="comment-39030 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-39030 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-39030"> <li> <div class="comment"> <table class="comment-table" commentId="39031" commentParentId="39030"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/KADR" style="position: relative;"> <img src='https://userpic.codeforces.org/1028/avatar/9089397f80c0fe42.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/KADR" title="Master KADR" class="rated-user user-orange">KADR</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/18/2011 21:29">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-39031" href="?#comment-39031" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-39030" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="39031" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1028" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-39031"> <div class="moveup"> <div class="ttypography">Quote from the editorial:<div><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">&quot;If</span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;"><i>X</i></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;"><i>and</i></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;">(<i>A</i> - <i>X</i>) ≠ <i>X</i></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">then the answer is also -1.&quot;</span><br /></div><div>Here X=5 and A-X=9. 5 and 9 = 1, which is not equal to 5. So the answer is -1 here.</div></div> </div> </div> <div class="reply info"> <a class="comment-39031 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-39031 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-39031"> <li> <div class="comment"> <table class="comment-table" commentId="39038" commentParentId="39031"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Snow_storm" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Snow_storm" title="Expert Snow_storm" class="rated-user user-blue">Snow_storm</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/18/2011 21:42">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-39038" href="?#comment-39038" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-39031" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="39038" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6824" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-39038"> <div class="moveup"> <div class="ttypography">I was wrong, <br /><span style="LINE-HEIGHT: 20.0px;FONT-FAMILY: verdana , arial , sans-serif;FONT-SIZE: 12.0px;"><span class="tex-span" style="FONT-FAMILY: &quot;times new roman&quot;;FONT-SIZE: 15.0px;"><i>and is &amp;</i></span></span><br /><br />But I saw many wrong program still through the test,<br /><br />and thank you very much for your patience solutions</div> </div> </div> <div class="reply info"> <a class="comment-39038 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-39038 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-39038"> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="39034" commentParentId="39030"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Snow_storm" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Snow_storm" title="Expert Snow_storm" class="rated-user user-blue">Snow_storm</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/18/2011 21:35">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-39034" href="?#comment-39034" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-39030" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="39034" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6824" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-39034"> <div class="moveup"> <div class="ttypography">I'm sorry, X is smallest, but I'm think if the answer doesn't exist, should add a condition:  X^Y=B</div> </div> </div> <div class="reply info"> <a class="comment-39034 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-39034 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-39034"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="422212" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/stringray" style="position: relative;"> <img src='https://userpic.codeforces.org/575608/avatar/2902babcf56868a2.jpg'/> </a> <div><a href="/profile/stringray" title="Expert stringray" class="rated-user user-blue">stringray</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/27/2018 21:44">6 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-422212" href="?#comment-422212" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="422212" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="575608" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-422212"> <div class="moveup"> <div class="ttypography"><p>Can someone explain the question Gift in this question it is asking for the minimum coins such that every road's gold coin and silver coin constraints are satisfied then if (A,B) is a valid solution then we can make A=infinite and B=infinite so that there will be always a solution also won't A=max(all gi's) and B=max(all si's ) where gi=minimum gold coins for ith road and si=minimum silver coins for ith road (this is what i have understood from the question can anyone tell what's wrong in my understanding )?</p></div> </div> </div> <div class="reply info"> <a class="comment-422212 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-422212 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-422212"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="517643" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Newtech66" style="position: relative;"> <img src='https://userpic.codeforces.org/748716/avatar/ba5b7d94e0bd5415.jpg'/> </a> <div><a href="/profile/Newtech66" title="Expert Newtech66" class="rated-user user-blue">Newtech66</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/10/2019 13:51">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-517643" href="?#comment-517643" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="517643" class="CommentVoteFrame" class="negative-comment-vote" data-commentRating="-10" data-commentUserId="748716" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">-10</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-517643"> <div class="moveup"> <div class="ttypography"><p>Problem D has weak testcases. My solution gets AC despite giving an incorrect answer on the testcase '10 6'.</p></div> </div> </div> <div class="reply info"> <a class="comment-517643 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-517643 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-517643"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="537992" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/memento" style="position: relative;"> <img src='https://userpic.codeforces.org/852933/avatar/950578c1b4afd9dc.jpg'/> </a> <div><a href="/profile/memento" title="Expert memento" class="rated-user user-blue">memento</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Aug/24/2019 21:32">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-537992" href="?#comment-537992" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="537992" class="CommentVoteFrame" data-commentRating="11" data-commentUserId="852933" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+11</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-537992"> <div class="moveup"> <div class="ttypography"><p>Shit. This was 8 years ago.</p></div> </div> </div> <div class="reply info"> <a class="comment-537992 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-537992 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-537992"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="763848" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/vishaaaal" style="position: relative;"> <img src='https://userpic.codeforces.org/1443354/avatar/25a2dd924894eeeb.jpg'/> </a> <div><a href="/profile/vishaaaal" title="Expert vishaaaal" class="rated-user user-blue">vishaaaal</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/20/2021 12:42">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-763848" href="?#comment-763848" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="763848" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1443354" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-763848"> <div class="moveup"> <div class="ttypography"><p>How to solve A without MST??</p> <div class="spoiler"><b class="spoiler-title">Here's my approach</b><div class="spoiler-content" style="display: none;"><p>Let us consider two cities $$$a$$$ and $$$b$$$. We use <em>dfs</em> to calculate the minimum amount of tugriks required for travelling from $$$a$$$ to $$$b$$$. And the answer will be maximum of such value among all pairs of cities.</p><p>The problem is, I think that calculation of this value requires to use Dynamic Programming. Any hints on that??</p></div></div></div> </div> </div> <div class="reply info"> <a class="comment-763848 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-763848 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-763848"> </ul> </div> <br/> <div id="editBox-1722" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In Russian</span> </div> <textarea data-drafts-id="CommentReplyFrame" class="wysiwyg" name="editContent" rows="20" style="width:99%;"></textarea> <div class="error error__content"></div> <div style="text-align:center;"> <input type="button" name="preview" style="padding: 0.25em 1em; 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76F
76
F
en
F. Tourist
<div class="problem-statement"><div class="header"><div class="title">F. Tourist</div><div class="time-limit"><div class="property-title">time limit per test</div>0.5 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Tourist walks along the <span class="tex-span"><i>X</i></span> axis. He can choose either of two directions and any speed not exceeding <span class="tex-span"><i>V</i></span>. He can also stand without moving anywhere. He knows from newspapers that at time <span class="tex-span"><i>t</i><sub class="lower-index">1</sub></span> in the point with coordinate <span class="tex-span"><i>x</i><sub class="lower-index">1</sub></span> an interesting event will occur, at time <span class="tex-span"><i>t</i><sub class="lower-index">2</sub></span> in the point with coordinate <span class="tex-span"><i>x</i><sub class="lower-index">2</sub></span> — another one, and so on up to (<span class="tex-span"><i>x</i><sub class="lower-index"><i>n</i></sub>, <i>t</i><sub class="lower-index"><i>n</i></sub></span>). Interesting events are short so we can assume they are immediate. Event <span class="tex-span"><i>i</i></span> counts visited if at time <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub></span> tourist was at point with coordinate <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span>.</p><p>Write program tourist that will find maximum number of events tourist if: </p><ul> <li> at the beginning (when time is equal to 0) tourist appears at point 0, </li><li> tourist can choose initial point for himself. </li></ul><p>Yes, you should answer on two similar but different questions.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of input contains single integer number <span class="tex-span"><i>N</i></span> (<span class="tex-span">1 ≤ <i>N</i> ≤ 100000</span>) — number of interesting events. The following <span class="tex-span"><i>N</i></span> lines contain two integers <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub></span> — coordinate and time of the <span class="tex-span"><i>i</i></span>-th event. The last line of the input contains integer <span class="tex-span"><i>V</i></span> — maximum speed of the tourist. All <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> will be within range <span class="tex-span"> - 2·10<sup class="upper-index">8</sup> ≤ <i>x</i><sub class="lower-index"><i>i</i></sub> ≤ 2·10<sup class="upper-index">8</sup></span>, all <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub></span> will be between <span class="tex-span">1</span> and <span class="tex-span">2·10<sup class="upper-index">6</sup></span> inclusive. <span class="tex-span"><i>V</i></span> will be positive and will not exceed 1000. The input may contain events that happen at the same time or in the same place but not in the same place at the same time.</p></div><div class="output-specification"><div class="section-title">Output</div><p>The only line of the output should contain two space-sepatated integers — maximum number of events tourist can visit in he starts moving from point 0 at time 0, and maximum number of events tourist can visit if he chooses the initial point for himself.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br/>-1 1<br/>42 7<br/>40 8<br/>2<br/></pre></div><div class="output"><div class="title">Output</div><pre>1 2<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="F" data-uuid="ps_9e86a95dbdc9837e6870ac4835dbc775e8a54de0"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">F. Tourist</div><div class="time-limit"><div class="property-title">time limit per test</div>0.5 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Tourist walks along the <span class="tex-span"><i>X</i></span> axis. He can choose either of two directions and any speed not exceeding <span class="tex-span"><i>V</i></span>. He can also stand without moving anywhere. He knows from newspapers that at time <span class="tex-span"><i>t</i><sub class="lower-index">1</sub></span> in the point with coordinate <span class="tex-span"><i>x</i><sub class="lower-index">1</sub></span> an interesting event will occur, at time <span class="tex-span"><i>t</i><sub class="lower-index">2</sub></span> in the point with coordinate <span class="tex-span"><i>x</i><sub class="lower-index">2</sub></span> — another one, and so on up to (<span class="tex-span"><i>x</i><sub class="lower-index"><i>n</i></sub>, <i>t</i><sub class="lower-index"><i>n</i></sub></span>). Interesting events are short so we can assume they are immediate. Event <span class="tex-span"><i>i</i></span> counts visited if at time <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub></span> tourist was at point with coordinate <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span>.</p><p>Write program tourist that will find maximum number of events tourist if: </p><ul> <li> at the beginning (when time is equal to 0) tourist appears at point 0, </li><li> tourist can choose initial point for himself. </li></ul><p>Yes, you should answer on two similar but different questions.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of input contains single integer number <span class="tex-span"><i>N</i></span> (<span class="tex-span">1 ≤ <i>N</i> ≤ 100000</span>) — number of interesting events. The following <span class="tex-span"><i>N</i></span> lines contain two integers <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub></span> — coordinate and time of the <span class="tex-span"><i>i</i></span>-th event. The last line of the input contains integer <span class="tex-span"><i>V</i></span> — maximum speed of the tourist. All <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> will be within range <span class="tex-span"> - 2·10<sup class="upper-index">8</sup> ≤ <i>x</i><sub class="lower-index"><i>i</i></sub> ≤ 2·10<sup class="upper-index">8</sup></span>, all <span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub></span> will be between <span class="tex-span">1</span> and <span class="tex-span">2·10<sup class="upper-index">6</sup></span> inclusive. <span class="tex-span"><i>V</i></span> will be positive and will not exceed 1000. The input may contain events that happen at the same time or in the same place but not in the same place at the same time.</p></div><div class="output-specification"><div class="section-title">Output</div><p>The only line of the output should contain two space-sepatated integers — maximum number of events tourist can visit in he starts moving from point 0 at time 0, and maximum number of events tourist can visit if he chooses the initial point for himself.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br />-1 1<br />42 7<br />40 8<br />2<br /></pre></div><div class="output"><div class="title">Output</div><pre>1 2<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=F]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); 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["Binary search", "Heaps, binary search trees, segment trees, hash tables, etc", "Dynamic programming"]
["binary search", "data structures", "dp", "*2300"]
https://codeforces.com/blog/entry/1712
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It is easy to see  that there exist two (probably equal) indexes <span class="tex-span"><i>i</i></span> and <span class="tex-span"><i>j</i></span> such that <span class="tex-span"><i>g</i><sub class="lower-index"><i>i</i></sub> = <i>A</i></span> and <span class="tex-span"><i>s</i><sub class="lower-index"><i>j</i></sub> = <i>B</i></span>. It is true, because in the other case we could decrease either <span class="tex-span"><i>A</i></span> or <span class="tex-span"><i>B</i></span> without changing connectivity of the graph.</div><div><br /></div><div>Let <span class="tex-span"><i>R</i>(<i>A</i>, <i>B</i>)</span> be the graph in which for all <span class="tex-span"><i>i</i></span> the following statement holds: <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/f6a7810c1f985efe671bb157563fc069d097fbce.png" style="max-width: 100.0%;max-height: 100.0%;" />.</div><div><br /></div><div>Let <span class="tex-span"><i>T</i>(<i>A</i>)</span> be the weighted graph in which for all edges <span class="tex-span"><i>g</i><sub class="lower-index"><i>i</i></sub> ≤ <i>A</i></span>. For each edge <span class="tex-span"><i>i</i></span> we will assign a weight equal to <span class="tex-span"><i>s</i><sub class="lower-index"><i>i</i></sub></span>. Let's find a spanning tree of this graph, which has the property that its maximal edge is minimal possible. It can be shown that for the fixed <span class="tex-span"><i>A</i></span> the minimal value of <span class="tex-span"><i>B</i></span> for which graph <span class="tex-span"><i>R</i>(<i>A</i>, <i>B</i>)</span> is still connected is equal to the weight of the maximal edge in this spanning tree.</div><div><br /></div><div><i>Claim</i>. Minimal spanning tree of a graph has the property that its maximal edge is minimal possible among all spanning trees.</div><div><i>Proof</i>. Let <span class="tex-span"><i>L</i></span> be the minimal spanning tree of a graph. Suppose there exists a spanning tree <span class="tex-span"><i>P</i></span> in which all edges have smaller weight than the weight of the maximal edge of <span class="tex-span"><i>L</i></span>. We can then remove the maximal edge from <span class="tex-span"><i>L</i></span> and add some edge from <span class="tex-span"><i>P</i></span> to it which will connect the graph back. After that <span class="tex-span"><i>L</i></span> will have strictly smaller weight, which is impossible because it is a minimal spanning tree.</div><div><br /></div><div>Let's sort all edges of the graph in ascending order of <span class="tex-span"><i>g</i><sub class="lower-index"><i>i</i></sub></span>. Then the edges of graph <span class="tex-span"><i>T</i>(<i>A</i>)</span> for the fixed <span class="tex-span"><i>i</i></span> will be all edges with indexes <span class="tex-span"><i>j</i> ≤ <i>i</i></span>.</div><div><br /></div><div>Suppose that for some value of <span class="tex-span"><i>i</i></span> we have already found minimal spanning tree in every connected component of the graph <span class="tex-span"><i>T</i>(<i>g</i><sub class="lower-index"><i>i</i></sub>)</span>. Let's add an edge with index <span class="tex-span"><i>i</i> + 1</span> into it. If it connects two different components, then after this operation they will be merged into one big component and it is obviously that the spanning tree we have in it is the minimal spanning tree. If <span class="tex-span"><i>i</i> + 1</span>-th edge connects two vertices from the same connected component, then it will create exactly one cycle in the graph. We can find the maximal edge in this cycle and remove it from the graph. It can be proven that the remaining tree will be the minimal spanning tree of this connected component.</div><div><br /></div><div>We can perform the search of the maximal edge in a cycle as well as the insertion and removal of the edges in O(N). The total complexity is <span class="tex-span"><i>O</i>(<i>NM</i> + <i>MlogM</i>)</span>.</div></div><div><br /></div><div><div><b>Problem B: Mice (Roman Rizvanov)</b></div><div><br /></div><div>It is easy to see that the number of closest pieces of cheese for each mouse is not greater than 2.</div><div><br /></div><div>Let's find the closest pieces of cheese for each mouse to the left and to the right from it. From two directions we will choose the one which gives us shorter way to cheese or both of them if their lengths are equal. If on the chosen way between the mouse and the cheese stands another mouse, then we should exclude this way from consideration, because another mouse will get to the cheese faster. Now all the directions lead to cheese and for each piece of cheese there is at most one mouse which can potentially eat it from each direction.</div><div><br /></div><div>We will process mice from left to right. If the current mouse can move left and the cheese to the left of it is not chosen by any other mouse or it is chosen by a mouse with the same distance to it, then the current mouse can move to the left and eat this piece of cheese without interfering with other mice. This choice will not affect any choices of the next mice, because only one mouse can go to this piece of cheese from the right (see previous paragraph). Thus, this choice can not decrease the answer. In all other cases the current mouse can not increase the answer by moving left, so it should move to the right if it has such opportunity.</div><div><br /></div><div>The complexity is <span class="tex-span"><i>O</i>(<i>N</i> + <i>M</i>)</span>.</div><div><br /></div><div>This problem can be also solved using dynamic programming.</div></div><div><br /></div><div><b>Problem C: Mutation (Iaroslav Tverdokhlib)</b></div><div><br /></div><div><div>In the editorial we will replace terms &quot;risk&quot;, &quot;genome&quot; and &quot;gene&quot; with &quot;cost&quot;, &quot;string&quot; and &quot;character&quot;, respectively. Let <span class="tex-span"><i>S</i></span> be the starting string.</div><div><br /></div><div>Let <span class="tex-span"><i>M</i></span> be the bitmask of chars which will be removed. Let's iterate over all possible values of <span class="tex-span"><i>M</i></span>. For the fixed <span class="tex-span"><i>M</i></span> we need to find a cost of the string, which remained after removal of <span class="tex-span"><i>M</i></span> and if this cost doesn't exceed <span class="tex-span"><i>T</i></span> we will increase the answer by 1. Naive implementation of this idea has the complexity <span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>K</i></sup><i>N</i>)</span>.</div><div><br /></div><div>We can not get rid of iterating over all <span class="tex-span"><i>M</i></span>, so we will try to optimize a part of the algorithm which finds a cost of the remaining string.</div><div><br /></div><div>Let's take two indexes <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> from the beginning string <span class="tex-span"><i>l</i> &lt; <i>r</i></span>. Let <span class="tex-span"><i>M</i>'</span> be the bitmask of all characters which are located strictly between them. It is obviously that if <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7b04066e365590d0dc24c90dfc15aabd64c75339.png" style="max-width: 100.0%;max-height: 100.0%;" /> or <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/3880b6b45cb2a0ccd5ea51b69f020c9e5a9f7fa1.png" style="max-width: 100.0%;max-height: 100.0%;" /> then <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> can not be neighbours in the remaining string. Hence for the fixed <span class="tex-span"><i>l</i></span> there are not more than <span class="tex-span"><i>K</i></span> possible candidates for <span class="tex-span"><i>r</i></span>, which means that there are <span class="tex-span"><i>O</i>(<i>NK</i>)</span> pairs of such potential neighbours. We will call such pairs &quot;good&quot;.</div><div><br /></div><div>We want to find out what form should have the set <span class="tex-span"><i>M</i></span> that after its removal indexes <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> became adjacent. It is easy to see that the following two conditions should be true:</div><div><br /></div><div>1. <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/07de7c5bc68bc92d118ada183dab5d78f5c631c4.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div>2. <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7fa1a37ebb11a92726d78e30e0ad17ffda729919.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><br /></div><div>Let's iterate over all good pairs of <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> and for each of them we will find the set <span class="tex-span"><i>M</i>'</span>. For each triple <span class="tex-span">(<i>a</i>, <i>b</i>, <i>P</i>)</span> we will store the sum of costs of neighborhood of all pairs <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> for which <span class="tex-span"><i>S</i><sub class="lower-index"><i>l</i></sub> = <i>a</i></span>, <span class="tex-span"><i>S</i><sub class="lower-index"><i>r</i></sub> = <i>b</i></span>, <span class="tex-span"><i>M</i>' = <i>P</i></span>. After that for the fixed <span class="tex-span"><i>M</i></span> we will iterate over all pairs of characters <span class="tex-span">(<i>a</i>, <i>b</i>)</span> and its subsets <span class="tex-span"><i>P</i></span> and add all their costs together. Also we need to add the cost of removal of <span class="tex-span"><i>M</i></span> and the resulting sum will be the cost of the string which will left after removal of <span class="tex-span"><i>M</i></span>. The complexity of such solution is <span class="tex-span"><i>O</i>(3<sup class="upper-index"><i>K</i></sup> * <i>K</i><sup class="upper-index">2</sup> + <i>NK</i>)</span>.</div><div><br /></div><div>We will optimize the previous solution by decreasing a factor near <span class="tex-span">3<sup class="upper-index"><i>K</i></sup></span>. Let's look at the following (incorrect) algorithm:</div><div><br /></div><div>We will iterate over all good pairs <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> and for each of them we will find <span class="tex-span"><i>M</i>'</span>. Let's create an array <span class="tex-span"><i>v</i></span> in which for each mask <span class="tex-span"><i>P</i></span> we will store the sum of costs of neighborhood of all pairs <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> for which <span class="tex-span"><i>M</i>' = <i>P</i></span>. For the fixed <span class="tex-span"><i>M</i></span> we will find a sum of all values from <span class="tex-span"><i>v</i></span> for all submasks of <span class="tex-span"><i>M</i></span>, then add the cost of removal of <span class="tex-span"><i>M</i></span> to it and the resulting sum will be the cost of the remaining string.</div><div><br /></div><div>This algorithm is incorrect, because some costs of neighborhood are added to the total cost, but in fact the respective <span class="tex-span"><i>l</i></span> or <span class="tex-span"><i>r</i></span> are removed. Let's use inclusion-exclusion principle and make the following at the phase of filling array <span class="tex-span"><i>v</i></span>:</div><div><br /></div><div><span class="tex-span"><i>v</i>[<i>M</i>'] +  = <i>cost</i></span></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/b4d392e8baa2755f671b67077d5ad638a2818e1c.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/0939a5ad00766ddcedb4465081c7dc8c63f0dd22.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/872ba326de38444a17ace78f749a43a3e1eff1d1.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><br /></div><div>With such filling of <span class="tex-span"><i>v</i></span> the algorithm described above is correct and the total complexity becomes <span class="tex-span"><i>O</i>(3<sup class="upper-index"><i>K</i></sup> + <i>NK</i>)</span>.</div><div><br /></div><div>This is still not enough for the full solution, but we are almost there. We only need to find a fast way of finding the sum of the values of <span class="tex-span"><i>v</i></span> for all submasks of all masks <span class="tex-span"><i>M</i></span>. We will use the following iterative algorithm for this purpose:</div><div><br /></div><div>Before the first iteration we have an array <span class="tex-span"><i>v</i></span> in which the starting values are stored. After iteration with number <span class="tex-span"><i>i</i></span> in <span class="tex-span"><i>v</i>[<i>mask</i>]</span> we will store the sum of all the values from the original array <span class="tex-span"><i>v</i></span> for all submasks of <span class="tex-span"><i>mask</i></span> for which the first <span class="tex-span"><i>K</i> - <i>i</i></span> bits are equal to the respective bits of <span class="tex-span"><i>mask</i></span>. On iteration with number <span class="tex-span"><i>i</i></span> for all masks in which the <span class="tex-span"><i>i</i></span>-th bit is equal to 1 (bits are numbered from 1) we will perform the following: <span class="tex-span"><i>v</i>[<i>mask</i>] +  = <i>v</i>[<i>mask</i>\{<i>i</i>}]</span>. It is easy to see that after the <span class="tex-span"><i>K</i></span>-th iteration of this algorithm we will have the values we were looking for in array <span class="tex-span"><i>v</i></span>.</div><div><br /></div><div>The complexity is <span class="tex-span"><i>O</i>(2<sup class="upper-index"><i>K</i></sup><i>K</i> + <i>NK</i>)</span>.</div></div><div><br /></div><div><b>Problem D: Plus and XOR (Daniel Neiter)</b></div><div><br /></div><div>Let's take a look at some bit in X, which is equal to 1. If the respective bit in Y is equal to 0, then we can swap these two bits, thus reducing X and increasing Y without changing their sum and xor. We can conclude that if some bit in X is equal to 1 then the respective bit in Y is also equal to 1. Thus, <span class="tex-span"><i>Y</i> = <i>X</i> + <i>B</i></span>. Taking into account that <span class="tex-span"><i>X</i> + <i>Y</i> = <i>X</i> + <i>X</i> + <i>B</i> = <i>A</i>, </span> we can obtain the following formulas for finding <span class="tex-span"><i>X</i></span> and <span class="tex-span"><i>Y</i></span>:</div><div><br /></div><div><span class="tex-span"><i>X</i> = (<i>A</i> - <i>B</i>) / 2</span></div><div><span class="tex-span"><i>Y</i> = <i>X</i> + <i>B</i></span></div><div><div><br /></div><div>One should also notice that if <span class="tex-span"><i>A</i> &lt; <i>B</i></span> or <span class="tex-span"><i>A</i></span> and <span class="tex-span"><i>B</i></span> have different parity, then the answer doesn't exist and we should output -1. If <span class="tex-span"><i>X</i></span> <span class="tex-span"><i>and</i></span> <span class="tex-span">(<i>A</i> - <i>X</i>) ≠ <i>X</i></span> then the answer is also -1.</div></div><div><br /></div><div><b>Problem E: Points (Daniel Neiter)</b></div><div><b><br /></b></div><div>Let's regroup summands and split the sum of squares of distances we are looking for into two sums:</div><div><b><br /></b></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/6e7ca6f50695e36ea199c3704ebb7574c4bfc029.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/b4a6a53d2cb6e9458620cc0b964c69f610df6601.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><br /></div><div>Now we need to rewrite each of these sums in the following way (it will be shown for the first sum):</div><div><br /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/ce7d437559ce56c7602146506aaec7f5b8f5920b.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/14de3bd836c0e823801f884a115983ff447988b5.png" style="max-width: 100.0%;max-height: 100.0%;" /></div><div><br /></div><div>This formula allows us to find an answer in one pass through the array. The complexity is O(N).</div><div><br /></div><div><div><b>Problem F: Tourist (Ilya Porublyov)</b></div><div><br /></div><div>We can get to the event <span class="tex-span"><i>j</i></span> from the event <span class="tex-span"><i>i</i></span> if the following statements are true:</div><div><br /></div><div><ul><li><span class="tex-span"><i>t</i><sub class="lower-index"><i>i</i></sub> ≤ <i>t</i><sub class="lower-index"><i>j</i></sub></span><br /></li><li><span class="tex-span">|<i>x</i><sub class="lower-index"><i>i</i></sub> - <i>x</i><sub class="lower-index"><i>j</i></sub>| ≤ |<i>t</i><sub class="lower-index"><i>i</i></sub> - <i>t</i><sub class="lower-index"><i>j</i></sub>|· <i>V</i></span><br /></li></ul></div><div>We can represent all the events as points on a plane with coordinates <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i></sub>, <i>t</i><sub class="lower-index"><i>i</i></sub>)</span>. Now we can reformulate the two statements written above in the following way:<br /></div><div><br /></div><div>From the event <span class="tex-span"><i>i</i></span> we can get to the event <span class="tex-span"><i>j</i></span> if the point <span class="tex-span">(<i>x</i><sub class="lower-index"><i>j</i></sub>, <i>t</i><sub class="lower-index"><i>j</i></sub>)</span> lise inside an angle pointed to the top with its vertex in <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i></sub>, <i>t</i><sub class="lower-index"><i>i</i></sub>)</span> and its sides form an angle <span class="tex-span"><i>arctg</i>(<i>V</i>)</span> with vertical axis. Let's make coordinate transformation according to which the point with coordinates <span class="tex-span">(<i>x</i><sub class="lower-index"><i>i</i></sub>, <i>t</i><sub class="lower-index"><i>i</i></sub>)</span> will transform into the point <span class="tex-span">(<i>p</i><sub class="lower-index"><i>i</i></sub>, <i>q</i><sub class="lower-index"><i>i</i></sub>)</span>, where</div><div><span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub> =  - <i>x</i><sub class="lower-index"><i>i</i></sub> + <i>t</i><sub class="lower-index"><i>i</i></sub> * <i>V</i></span></div><div><span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub> = <i>x</i><sub class="lower-index"><i>i</i></sub> + <i>t</i><sub class="lower-index"><i>i</i></sub> * <i>V</i></span></div><div><br /></div><div>Now we can get to the event <span class="tex-span"><i>j</i></span> from the event <span class="tex-span"><i>i</i></span> if <span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub> ≤ <i>p</i><sub class="lower-index"><i>j</i></sub></span> и <span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub> ≤ <i>q</i><sub class="lower-index"><i>j</i></sub></span>. Let's sort all points in ascending order of <span class="tex-span"><i>p</i></span>. If several points have the same <span class="tex-span"><i>p</i></span> we will sort them by <span class="tex-span"><i>q</i></span>. The second subproblem of our problem can be solved by finding a longest increasing subsequence by <span class="tex-span"><i>q</i></span> in this array. It can be done in <span class="tex-span"><i>O</i>(<i>NlogN</i>)</span>.</div><div><br /></div><div>To solve the first subproblem we can add dummy event with coordinate 0 and time 0 (if it is not present in our set of events yet) and force tourist's start from it.</div><div><br /></div><div>The total complexity if <span class="tex-span"><i>O</i>(<i>NlogN</i>)</span>.</div></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/76" class="notice" style="text-decoration: none;">All-Ukrainian School Olympiad in Informatics</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-996-1712").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "996", blogEntryId: "1712", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); }); }, function () {}, "Yes", "No"); }); }); </script> <div style="font-size: 1.1rem;line-height: 11px;"> <img style="vertical-align: middle;" src="//codeforces.org/s/81027/images/blog/tags.png" title="Tags" alt="Tags"/> <span style="padding: 0 0.35em;"> <a href="/search?query=codeforces" class="tag notice" style="text-decoration: none;">codeforces</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=editorial" class="tag notice" style="text-decoration: none;">editorial</a>, </span> <span style="padding: 0 0.35em;"> <a href="/search?query=uoi2011" class="tag notice" style="text-decoration: none;">uoi2011</a> </span> </div> <div class="roundbox meta borderTopRound borderBottomRound" style=""> <div class="left-meta"> <ul> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-up-1712"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/voteup.png" alt="Vote: I like it" title="Vote: I like it" /></a> </li> <li style="line-height: 1.6em;"> <span title="Topic rating" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+30</span> </li> <li style="line-height: 1.6em;"> <a href="#" class="topic-vote-down-1712"><img style="vertical-align:middle;position:relative;top:-0.2em" src="//codeforces.org/s/81027/images/actions/votedown.png" alt="Vote: I do not like it" title="Vote: I do not like it" /></a> </li> </ul> </div> <span style="position: relative; 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} .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1722"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (22)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="32624" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/wil93" style="position: relative;"> <img src='https://userpic.codeforces.org/14356/avatar/897f1996dfb7343b.jpg'/> </a> <div><a href="/profile/wil93" title="Expert wil93" class="rated-user user-blue">wil93</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/12/2011 23:20">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-32624" href="?#comment-32624" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="32624" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="14356" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-32624"> <div class="moveup"> <div class="ttypography">Thanks very much, I think E's solution is genial. I understood it now, but it would be very difficult for me to come out with a similar thought :)</div> </div> </div> <div class="reply info"> <a class="comment-32624 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-32624 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-32624"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="33014" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 16:09">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33014" href="?#comment-33014" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="33014" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="33014" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33014"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">Hi,<br /><br />I would like to ask about problem F. Is there a particular reason why you sort by p first before you sort by q? If not, will sorting by q and then by p for tiebreak change the solution? If not, may I know if you can prove so? I can understand how you make the transformation and why the transformation is correct, but I am not convinced that you can get the optimal solution just by sorting and finding the LIS (Do you mean the longest non-decreasing subsequence? From what I understand, I think you first label the vertices according to the time when they appear. If they appear at the same time, then they have the same label.) Can you please give a proof or explanation why it works?<br /><br />Thanks in advance!</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-33014 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33014 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33014"> <li> <div class="comment"> <table class="comment-table" commentId="33025" commentParentId="33014"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/KADR" style="position: relative;"> <img src='https://userpic.codeforces.org/1028/avatar/9089397f80c0fe42.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/KADR" title="Master KADR" class="rated-user user-orange">KADR</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 18:25">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33025" href="?#comment-33025" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-33014" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="33025" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="33025" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1028" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33025"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">If some two events have the same time then it is impossible to visit them both, so we are not interested in their relative order in the sorted array (after performing the transformation).<div><br /></div><div>After the transformation we can get from the point <span class="tex-span">(<i>p</i><sub class="lower-index"><i>i</i></sub>, <i>q</i><sub class="lower-index"><i>i</i></sub>)</span> to the point <span class="tex-span">(<i>p</i><sub class="lower-index"><i>j</i></sub>, <i>q</i><sub class="lower-index"><i>j</i></sub>)</span> iff <span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub> ≤ <i>p</i><sub class="lower-index"><i>j</i></sub></span> and <span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub> ≤ <i>q</i><sub class="lower-index"><i>j</i></sub></span>. After performing the sorting described in the editorial all points reachable from the point <span class="tex-span">(<i>p</i><sub class="lower-index"><i>i</i></sub>, <i>q</i><sub class="lower-index"><i>i</i></sub>)</span> will have greater indexes in the array. This automatically means that the sequence will be non-decreasing by <span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub></span>, so we only need to care about <span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub></span>. The longest non-decreasing sequence by <span class="tex-span"><i>q</i><sub class="lower-index"><i>i</i></sub></span> is the sequence we are looking for.</div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-33025 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33025 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33025"> <li> <div class="comment"> <table class="comment-table" commentId="33026" commentParentId="33025"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/simp1eton" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/simp1eton" title="Candidate Master simp1eton" class="rated-user user-violet">simp1eton</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/15/2011 18:27">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33026" href="?#comment-33026" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-33025" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33026" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4207" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33026"> <div class="moveup"> <div class="ttypography">Oh, that makes sense now. Thanks!</div> </div> </div> <div class="reply info"> <a class="comment-33026 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33026 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33026"> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="503943" commentParentId="33014"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/AbdAl-mateen" style="position: relative;"> <img src='https://userpic.codeforces.org/694938/avatar/57122394280e75b5.jpg'/> </a> <div><a href="/profile/AbdAl-mateen" title="Newbie AbdAl-mateen" class="rated-user user-gray">AbdAl-mateen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 07:51">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503943" href="?#comment-503943" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-33014" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="503943" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="694938" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503943"> <div class="moveup"> <div class="ttypography"><p>Hi,</p><p><code>Now we can get to the event j from the event i if pi ≤ pj и qi ≤ qj. Let's sort all points in ascending order of p. If several points have the same p we will sort them by q.</code> Can you please explain it for me?</p></div> </div> </div> <div class="reply info"> <a class="comment-503943 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503943 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503943"> <li> <div class="comment"> <table class="comment-table" commentId="503965" commentParentId="503943"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/IlyaCk" style="position: relative;"> <img src='https://userpic.codeforces.org/19187/avatar/40ba7301419542bd.jpg'/> </a> <div><a href="/profile/IlyaCk" title="Expert IlyaCk" class="rated-user user-blue">IlyaCk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 11:02">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503965" href="?#comment-503965" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503943" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="503965" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="19187" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503965"> <div class="moveup"> <div class="ttypography"><p>What do you want to be explained? Why &quot;Now we can get to the event j from the event i if pi ≤ pj и qi ≤ qj.&quot;? Or what &quot;If several points have the same p we will sort them by q.&quot; mean? Or what?</p></div> </div> </div> <div class="reply info"> <a class="comment-503965 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503965 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503965"> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="503976" commentParentId="503943"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/IlyaCk" style="position: relative;"> <img src='https://userpic.codeforces.org/19187/avatar/40ba7301419542bd.jpg'/> </a> <div><a href="/profile/IlyaCk" title="Expert IlyaCk" class="rated-user user-blue">IlyaCk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 11:48">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503976" href="?#comment-503976" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503943" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="503976" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="19187" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503976"> <div class="moveup"> <div class="ttypography"><p><a href="https://drive.google.com/file/d/1fwCssJgSTEJ5ic4AzHjhQBQnrypuQkYm/view?usp=sharing">Here</a> is more detailed tutorial. It's in Ukrainian, but you can Google-translate it (result is poor, but some things are still correct) and look at figures and equations.</p><p>I CAN try to reply on more concrete questions, but I don't want to translate the whole text...</p></div> </div> </div> <div class="reply info"> <a class="comment-503976 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503976 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503976"> <li> <div class="comment"> <table class="comment-table" commentId="503980" commentParentId="503976"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/AbdAl-mateen" style="position: relative;"> <img src='https://userpic.codeforces.org/694938/avatar/57122394280e75b5.jpg'/> </a> <div><a href="/profile/AbdAl-mateen" title="Newbie AbdAl-mateen" class="rated-user user-gray">AbdAl-mateen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 13:17">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503980" href="?#comment-503980" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503976" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="503980" revisionCount="4" revision="4"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">4</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="503980" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="694938" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503980"> <div class="moveup"> <div class="ttypography"><p>Well, What are the significances of p, q axes and angle arctg(v)? What do they represent?</p><p>What I understand before, as I mentioned in another comment's reply was as below: to go to j from i: <code>abs(xj - xi) / tj - ti &lt;= v</code> so, </p><p><code>xj + v*tj &gt;= xi + ti*v</code> and <code>-xi + v*ti &gt;= -xj + v*t</code> </p></div> </div> </div> <div class="reply info"> <a class="comment-503980 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503980 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503980"> <li> <div class="comment"> <table class="comment-table" commentId="503987" commentParentId="503980"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/IlyaCk" style="position: relative;"> <img src='https://userpic.codeforces.org/19187/avatar/40ba7301419542bd.jpg'/> </a> <div><a href="/profile/IlyaCk" title="Expert IlyaCk" class="rated-user user-blue">IlyaCk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 15:12">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503987" href="?#comment-503987" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503980" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="503987" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="19187" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503987"> <div class="moveup"> <div class="ttypography"><p>Axis $$$p$$$ is the direction, where the tourist moves (in plane $$$(x,t)$$$), if his speed is ($$${-}v$$$), i.e.maximal by absolute value and directed to left. Its positive ray is the left-bottom border of the area where the tourist can get in time, starting from the origin of the $$$(p,q)$$$ coordiante system. Similarly, $$$q$$$ is the direction, where the tourist moves (in plane $$$(x,t)$$$), if his speed is ($$${+}v$$$), i.e. maximal by absolute value and directed to right; its positive ray is the right-bottom border of the area where the tourist can get in time, starting from the origin of the $$$(p,q)$$$ coordiante system.</p><p>It's not very obvious to look at these axes... But, from other hand, it's not unnatural: we need some effective checking of where the tourist can get in time and where he cannot, so let's try: what, if we'll consider borders of the &quot;reachable-in-time&quot; area as coordinate axes?</p></div> </div> </div> <div class="reply info"> <a class="comment-503987 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503987 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503987"> <li> <div class="comment"> <table class="comment-table" commentId="503991" commentParentId="503987"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/AbdAl-mateen" style="position: relative;"> <img src='https://userpic.codeforces.org/694938/avatar/57122394280e75b5.jpg'/> </a> <div><a href="/profile/AbdAl-mateen" title="Newbie AbdAl-mateen" class="rated-user user-gray">AbdAl-mateen</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 16:12">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-503991" href="?#comment-503991" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503987" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="503991" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="503991" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="694938" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-503991"> <div class="moveup"> <div class="ttypography"><p>I hope this is my last query:</p><p>If tourist needs to go from i to j where xi &gt; xj, that time the velocity is negative. Right? And, the velocity can not be positive and negative at a time,</p><p>But why do we check</p> <pre><code>pi &lt; pj and qi &lt; qj ? </code></pre><p>Why not </p> <pre><code>pi &lt; pj or qi &lt; qj? </code></pre></div> </div> </div> <div class="reply info"> <a class="comment-503991 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-503991 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-503991"> <li> <div class="comment"> <table class="comment-table" commentId="504027" commentParentId="503991"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/IlyaCk" style="position: relative;"> <img src='https://userpic.codeforces.org/19187/avatar/40ba7301419542bd.jpg'/> </a> <div><a href="/profile/IlyaCk" title="Expert IlyaCk" class="rated-user user-blue">IlyaCk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/05/2019 22:22">5 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-504027" href="?#comment-504027" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-503991" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="504027" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="19187" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-504027"> <div class="moveup"> <div class="ttypography"><p>The axis directed from bottom to top is $$$t$$$ (time). The tourist cannot travel in time as he wants and/or change time flow direction. All what he can is to choose </p> <ol> <li><p>whether to stay at place with zero velocity (= move in direction of $$$t$$$, which is exactly in the middle between positive direction of $$$p$$$ and positive direction of $$$q$$$);</p></li> <li><p>or to move with velocity ($$$-v$$$), negative and maximal by absolute value, which is exactly positive direction of $$$p$$$;</p></li> <li><p>or to move with velocity ($$$+v$$$), positive and maximal by absolute value, which is exactly positive direction of $$$q$$$;</p></li> <li><p>or to move with velocity $$$0&lt;w&lt;v$$$ (where $$$v$$$ is $$$v$$$ from input data, and $$$w$$$ is actual tourist's velocity), which is in the same quadrant of the $$$(p,q)$$$-system (both $$$p$$$ and $$$q$$$ positive), but $$$q$$$-projection is bigger that $$$p$$$-projection; in other words, $$$0&lt;w&lt;v$$$ corresponds to $$$0&lt;p&lt;q$$$;</p></li> <li><p>or to move with velocity $$$-v&lt;w&lt;0$$$ (where $$$v$$$ is $$$v$$$ from input data, and $$$w$$$ is actual tourist's velocity), which is in the same quadrant of the $$$(p,q)$$$-system (both $$$p$$$ and $$$q$$$ positive), but $$$q$$$-projection is smaller that $$$p$$$-projection; in other words, $$$-v&lt;w&lt;0$$$ corresponds to $$$0&lt;q&lt;p$$$;</p></li> </ol><p>Whereas $$$(q_i &gt; q_j)$$$ (for moving from $$$i$$$ to $$$j$$$) requires either moving with speed $$$w$$$ which is $$$-\infty\leq w &lt; -v$$$, or even moving in reverse direction of time. Similarly, $$$(p_i &gt; p_j)$$$ (for moving from $$$i$$$ to $$$j$$$) requires either moving with speed $$$w$$$ which is $$$v&lt;w\leq\infty$$$, or even moving in reverse direction of time. So, it's required to have <strong>both</strong> $$$(p_i\leq p_j)$$$ <strong>and</strong> $$$(q_i\leq q_j)$$$</p></div> </div> </div> <div class="reply info"> <a class="comment-504027 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-504027 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-504027"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="33574" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/vinhthinhho" style="position: relative;"> <img src='https://userpic.codeforces.org/17649/avatar/4e3c7559e46fc48.jpg'/> </a> <div><a href="/profile/vinhthinhho" title="Candidate Master vinhthinhho" class="rated-user user-violet">vinhthinhho</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/19/2011 11:21">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33574" href="?#comment-33574" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33574" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="17649" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33574"> <div class="moveup"> <div class="ttypography"><p>i dont understand the transformation of (xi,ti), how does it work??? can anyone tell me the answer?</p></div> </div> </div> <div class="reply info"> <a class="comment-33574 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33574 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33574"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="37642" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Master_Chivu" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Master_Chivu" title="Unrated, Master_Chivu" class="rated-user user-black">Master_Chivu</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/11/2011 20:09">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-37642" href="?#comment-37642" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="37642" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="7062" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-37642"> <div class="moveup"> <div class="ttypography">&quot;It is obsiously that if <img align="middle" class="tex-formula" src="/predownloaded/5c/f4/5cf424ac693f1a0c89b939d7a6e6f6ada6700077.png" style="max-width: 100.0%;max-height: 100.0%;" /> or <img align="middle" class="tex-formula" src="/predownloaded/72/41/7241691bc12db2fb46351355cdd678dfea1703d1.png" style="max-width: 100.0%;max-height: 100.0%;" /> then <span class="tex-span"><i>l</i></span> and <span class="tex-span"><i>r</i></span> can not be neighbours in the remaining string.&quot;<br />What is &quot;P&quot;?<br />It seems that &quot;P&quot; hasn't been metioned before.<br />I really cannot understand this sentence.<br />And may &quot;absiously&quot; means &quot;abviously&quot;?<br /><br /></div> </div> </div> <div class="reply info"> <a class="comment-37642 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-37642 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-37642"> <li> <div class="comment"> <table class="comment-table" commentId="37653" commentParentId="37642"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/KADR" style="position: relative;"> <img src='https://userpic.codeforces.org/1028/avatar/9089397f80c0fe42.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/KADR" title="Master KADR" class="rated-user user-orange">KADR</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/11/2011 20:25">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-37653" href="?#comment-37653" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-37642" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="37653" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1028" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-37653"> <div class="moveup"> <div class="ttypography">It was a typo. &quot;Obsiously&quot; should be, of course, &quot;obviously&quot;.<div><br /></div><div>Also I occasionally used P instead of M'. It is fixed now, thanks for pointing this out.</div></div> </div> </div> <div class="reply info"> <a class="comment-37653 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-37653 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-37653"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="39030" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Snow_storm" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Snow_storm" title="Expert Snow_storm" class="rated-user user-blue">Snow_storm</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/18/2011 21:22">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-39030" href="?#comment-39030" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="39030" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6824" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-39030"> <div class="moveup"> <div class="ttypography"><p>Problem D is right?</p> <p>I doubts it, for expleam, A=14 and B=4 </p> <p>then X=(14-4)/2=5  Y=5+4=9</p> <p>and A&gt;B and <span class="tex-span"><i>A</i></span> and <span class="tex-span"><i>B</i></span> have some parity and A-X=Y<br /><br />but X^Y=5^9=12  <br />This is my doubts. And I think  (A-B)/2=X&amp;Y .<br />But I don't know the specific X and Y values</p></div> </div> </div> <div class="reply info"> <a class="comment-39030 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-39030 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-39030"> <li> <div class="comment"> <table class="comment-table" commentId="39031" commentParentId="39030"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/KADR" style="position: relative;"> <img src='https://userpic.codeforces.org/1028/avatar/9089397f80c0fe42.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/KADR" title="Master KADR" class="rated-user user-orange">KADR</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/18/2011 21:29">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-39031" href="?#comment-39031" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-39030" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="39031" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1028" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-39031"> <div class="moveup"> <div class="ttypography">Quote from the editorial:<div><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">&quot;If</span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;"><i>X</i></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;"><i>and</i></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span class="tex-span" style="font-size: 15.0px;font-family: &quot;times new roman&quot;;">(<i>A</i> - <i>X</i>) ≠ <i>X</i></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;">then the answer is also -1.&quot;</span><br /></div><div>Here X=5 and A-X=9. 5 and 9 = 1, which is not equal to 5. So the answer is -1 here.</div></div> </div> </div> <div class="reply info"> <a class="comment-39031 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-39031 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-39031"> <li> <div class="comment"> <table class="comment-table" commentId="39038" commentParentId="39031"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Snow_storm" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Snow_storm" title="Expert Snow_storm" class="rated-user user-blue">Snow_storm</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/18/2011 21:42">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-39038" href="?#comment-39038" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-39031" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="39038" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6824" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-39038"> <div class="moveup"> <div class="ttypography">I was wrong, <br /><span style="LINE-HEIGHT: 20.0px;FONT-FAMILY: verdana , arial , sans-serif;FONT-SIZE: 12.0px;"><span class="tex-span" style="FONT-FAMILY: &quot;times new roman&quot;;FONT-SIZE: 15.0px;"><i>and is &amp;</i></span></span><br /><br />But I saw many wrong program still through the test,<br /><br />and thank you very much for your patience solutions</div> </div> </div> <div class="reply info"> <a class="comment-39038 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-39038 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-39038"> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="39034" commentParentId="39030"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Snow_storm" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/Snow_storm" title="Expert Snow_storm" class="rated-user user-blue">Snow_storm</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/18/2011 21:35">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-39034" href="?#comment-39034" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-39030" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="39034" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="6824" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-39034"> <div class="moveup"> <div class="ttypography">I'm sorry, X is smallest, but I'm think if the answer doesn't exist, should add a condition:  X^Y=B</div> </div> </div> <div class="reply info"> <a class="comment-39034 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-39034 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-39034"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="422212" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/stringray" style="position: relative;"> <img src='https://userpic.codeforces.org/575608/avatar/2902babcf56868a2.jpg'/> </a> <div><a href="/profile/stringray" title="Expert stringray" class="rated-user user-blue">stringray</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Mar/27/2018 21:44">6 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-422212" href="?#comment-422212" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="422212" class="CommentVoteFrame" data-commentRating="1" data-commentUserId="575608" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+1</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-422212"> <div class="moveup"> <div class="ttypography"><p>Can someone explain the question Gift in this question it is asking for the minimum coins such that every road's gold coin and silver coin constraints are satisfied then if (A,B) is a valid solution then we can make A=infinite and B=infinite so that there will be always a solution also won't A=max(all gi's) and B=max(all si's ) where gi=minimum gold coins for ith road and si=minimum silver coins for ith road (this is what i have understood from the question can anyone tell what's wrong in my understanding )?</p></div> </div> </div> <div class="reply info"> <a class="comment-422212 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-422212 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-422212"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="517643" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/Newtech66" style="position: relative;"> <img src='https://userpic.codeforces.org/748716/avatar/ba5b7d94e0bd5415.jpg'/> </a> <div><a href="/profile/Newtech66" title="Expert Newtech66" class="rated-user user-blue">Newtech66</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Jun/10/2019 13:51">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-517643" href="?#comment-517643" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="517643" class="CommentVoteFrame" class="negative-comment-vote" data-commentRating="-10" data-commentUserId="748716" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">-10</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-517643"> <div class="moveup"> <div class="ttypography"><p>Problem D has weak testcases. My solution gets AC despite giving an incorrect answer on the testcase '10 6'.</p></div> </div> </div> <div class="reply info"> <a class="comment-517643 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-517643 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-517643"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="537992" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/memento" style="position: relative;"> <img src='https://userpic.codeforces.org/852933/avatar/950578c1b4afd9dc.jpg'/> </a> <div><a href="/profile/memento" title="Expert memento" class="rated-user user-blue">memento</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Aug/24/2019 21:32">4 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-537992" href="?#comment-537992" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="537992" class="CommentVoteFrame" data-commentRating="11" data-commentUserId="852933" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+11</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-537992"> <div class="moveup"> <div class="ttypography"><p>Shit. This was 8 years ago.</p></div> </div> </div> <div class="reply info"> <a class="comment-537992 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-537992 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-537992"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="763848" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/vishaaaal" style="position: relative;"> <img src='https://userpic.codeforces.org/1443354/avatar/25a2dd924894eeeb.jpg'/> </a> <div><a href="/profile/vishaaaal" title="Expert vishaaaal" class="rated-user user-blue">vishaaaal</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Feb/20/2021 12:42">3 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-763848" href="?#comment-763848" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="763848" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1443354" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-763848"> <div class="moveup"> <div class="ttypography"><p>How to solve A without MST??</p> <div class="spoiler"><b class="spoiler-title">Here's my approach</b><div class="spoiler-content" style="display: none;"><p>Let us consider two cities $$$a$$$ and $$$b$$$. We use <em>dfs</em> to calculate the minimum amount of tugriks required for travelling from $$$a$$$ to $$$b$$$. And the answer will be maximum of such value among all pairs of cities.</p><p>The problem is, I think that calculation of this value requires to use Dynamic Programming. 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77A
77
A
en
A. Heroes
<div class="problem-statement"><div class="header"><div class="title">A. Heroes</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>The year of 2012 is coming...</p><p>According to an ancient choradrican legend in this very year, in 2012, Diablo and his brothers Mephisto and Baal will escape from hell, and innumerable hordes of demons will enslave the human world. But seven brave heroes have already gathered on the top of a mountain Arreat to protect us mere mortals from the effect of this terrible evil.</p><p>The seven great heroes are: amazon <span class="tex-font-style-tt">Anka</span>, barbarian <span class="tex-font-style-tt">Chapay</span>, sorceress <span class="tex-font-style-tt">Cleo</span>, druid <span class="tex-font-style-tt">Troll</span>, necromancer <span class="tex-font-style-tt">Dracul</span>, paladin <span class="tex-font-style-tt">Snowy</span> and a professional hit girl <span class="tex-font-style-tt">Hexadecimal</span>. Heroes already know how much experience will be given for each of the three megabosses: <span class="tex-span"><i>a</i></span> for Mephisto, <span class="tex-span"><i>b</i></span> for Diablo and <span class="tex-span"><i>c</i></span> for Baal.</p><p>Here's the problem: heroes are as much as seven and megabosses are only three! Then our heroes decided to split into three teams, where each team will go to destroy their own megaboss. Each team member will receive a <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/d9049b74dfcebaef5774f475b1e3ef4ed39cfc63.png" style="max-width: 100.0%;max-height: 100.0%;"/> of experience, rounded down, where <span class="tex-span"><i>x</i></span> will be the amount of experience for the killed megaboss and <span class="tex-span"><i>y</i></span> — the number of people in the team.</p><p>Heroes do not want to hurt each other's feelings, so they want to split into teams so that the difference between the hero who received the maximum number of experience and the hero who received the minimum number of experience were minimal. Since there can be several divisions into teams, then you need to find the one in which <span class="tex-font-style-underline">the total amount of liking in teams</span> were maximum.</p><p>It is known that some heroes like others. But if hero <span class="tex-span"><i>p</i></span> likes hero <span class="tex-span"><i>q</i></span>, this does not mean that the hero <span class="tex-span"><i>q</i></span> likes hero <span class="tex-span"><i>p</i></span>. No hero likes himself.</p><p>The total amount of liking in teams is the amount of ordered pairs <span class="tex-span">(<i>p</i>, <i>q</i>)</span>, such that heroes <span class="tex-span"><i>p</i></span> and <span class="tex-span"><i>q</i></span> are in the same group, and hero <span class="tex-span"><i>p</i></span> likes hero <span class="tex-span"><i>q</i></span> (but it is not important if hero <span class="tex-span"><i>q</i></span> likes hero <span class="tex-span"><i>p</i></span>). In case of heroes <span class="tex-span"><i>p</i></span> and <span class="tex-span"><i>q</i></span> likes each other and they are in the same group, this pair should be counted twice, as <span class="tex-span">(<i>p</i>, <i>q</i>)</span> and <span class="tex-span">(<i>q</i>, <i>p</i>)</span>.</p><p>A team can consist even of a single hero, but it is important that every megaboss was destroyed. All heroes must be involved in the campaign against evil. None of the heroes can be in more than one team.</p><p>It is guaranteed that every hero is able to destroy any megaboss alone.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains a single non-negative integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">0 ≤ <i>n</i> ≤ 42</span>) — amount of liking between the heroes. Next <span class="tex-span"><i>n</i></span> lines describe liking in the form "<span class="tex-font-style-tt">p likes q</span>", meaning that the hero <span class="tex-font-style-tt">p</span> likes the hero <span class="tex-font-style-tt">q</span> (<span class="tex-font-style-tt">p</span> <span class="tex-span"> ≠ </span> <span class="tex-font-style-tt">q</span>). Every liking is described in the input exactly once, no hero likes himself.</p><p>In the last line are given three integers <span class="tex-span"><i>a</i></span>, <span class="tex-span"><i>b</i></span> and <span class="tex-span"><i>c</i></span> (<span class="tex-span">1 ≤ <i>a</i>, <i>b</i>, <i>c</i> ≤ 2·10<sup class="upper-index">9</sup></span>), separated by spaces: the experience for Mephisto, the experience for Diablo and experience for Baal.</p><p>In all the pretests, except for examples from the statement, the following condition is satisfied: <span class="tex-span"><i>a</i> = <i>b</i> = <i>c</i></span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print two integers — the minimal difference in the experience between two heroes who will receive the maximum and minimum number of experience points, and the maximal total amount of liking in teams (the number of friendships between heroes that end up in one team).</p><p><span class="tex-font-style-bf">When calculating the second answer, the team division should satisfy the difference-minimizing contraint. I.e. primary you should minimize the difference in the experience and secondary you should maximize the total amount of liking.</span></p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br/>Troll likes Dracul<br/>Dracul likes Anka<br/>Snowy likes Hexadecimal<br/>210 200 180<br/></pre></div><div class="output"><div class="title">Output</div><pre>30 3<br/></pre></div><div class="input"><div class="title">Input</div><pre>2<br/>Anka likes Chapay<br/>Chapay likes Anka<br/>10000 50 50<br/></pre></div><div class="output"><div class="title">Output</div><pre>1950 2<br/></pre></div></div></div><div class="note"><div class="section-title">Note</div><p><span class="tex-font-style-bf">A note to first example:</span> it the first team should be <span class="tex-font-style-tt">Dracul</span>, <span class="tex-font-style-tt">Troll</span> and <span class="tex-font-style-tt">Anka</span>, in the second one <span class="tex-font-style-tt">Hexadecimal</span> and <span class="tex-font-style-tt">Snowy</span>, and in the third <span class="tex-font-style-tt">Cleo</span> и <span class="tex-font-style-tt">Chapay</span>.</p></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="A" data-uuid="ps_39e4d8b2e6ba07f0b4bbad5cfa45e85e125b2c5f"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">A. Heroes</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>The year of 2012 is coming...</p><p>According to an ancient choradrican legend in this very year, in 2012, Diablo and his brothers Mephisto and Baal will escape from hell, and innumerable hordes of demons will enslave the human world. But seven brave heroes have already gathered on the top of a mountain Arreat to protect us mere mortals from the effect of this terrible evil.</p><p>The seven great heroes are: amazon <span class="tex-font-style-tt">Anka</span>, barbarian <span class="tex-font-style-tt">Chapay</span>, sorceress <span class="tex-font-style-tt">Cleo</span>, druid <span class="tex-font-style-tt">Troll</span>, necromancer <span class="tex-font-style-tt">Dracul</span>, paladin <span class="tex-font-style-tt">Snowy</span> and a professional hit girl <span class="tex-font-style-tt">Hexadecimal</span>. Heroes already know how much experience will be given for each of the three megabosses: <span class="tex-span"><i>a</i></span> for Mephisto, <span class="tex-span"><i>b</i></span> for Diablo and <span class="tex-span"><i>c</i></span> for Baal.</p><p>Here's the problem: heroes are as much as seven and megabosses are only three! Then our heroes decided to split into three teams, where each team will go to destroy their own megaboss. Each team member will receive a <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/d9049b74dfcebaef5774f475b1e3ef4ed39cfc63.png" style="max-width: 100.0%;max-height: 100.0%;" /> of experience, rounded down, where <span class="tex-span"><i>x</i></span> will be the amount of experience for the killed megaboss and <span class="tex-span"><i>y</i></span> — the number of people in the team.</p><p>Heroes do not want to hurt each other's feelings, so they want to split into teams so that the difference between the hero who received the maximum number of experience and the hero who received the minimum number of experience were minimal. Since there can be several divisions into teams, then you need to find the one in which <span class="tex-font-style-underline">the total amount of liking in teams</span> were maximum.</p><p>It is known that some heroes like others. But if hero <span class="tex-span"><i>p</i></span> likes hero <span class="tex-span"><i>q</i></span>, this does not mean that the hero <span class="tex-span"><i>q</i></span> likes hero <span class="tex-span"><i>p</i></span>. No hero likes himself.</p><p>The total amount of liking in teams is the amount of ordered pairs <span class="tex-span">(<i>p</i>, <i>q</i>)</span>, such that heroes <span class="tex-span"><i>p</i></span> and <span class="tex-span"><i>q</i></span> are in the same group, and hero <span class="tex-span"><i>p</i></span> likes hero <span class="tex-span"><i>q</i></span> (but it is not important if hero <span class="tex-span"><i>q</i></span> likes hero <span class="tex-span"><i>p</i></span>). In case of heroes <span class="tex-span"><i>p</i></span> and <span class="tex-span"><i>q</i></span> likes each other and they are in the same group, this pair should be counted twice, as <span class="tex-span">(<i>p</i>, <i>q</i>)</span> and <span class="tex-span">(<i>q</i>, <i>p</i>)</span>.</p><p>A team can consist even of a single hero, but it is important that every megaboss was destroyed. All heroes must be involved in the campaign against evil. None of the heroes can be in more than one team.</p><p>It is guaranteed that every hero is able to destroy any megaboss alone.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains a single non-negative integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">0 ≤ <i>n</i> ≤ 42</span>) — amount of liking between the heroes. Next <span class="tex-span"><i>n</i></span> lines describe liking in the form &quot;<span class="tex-font-style-tt">p likes q</span>&quot;, meaning that the hero <span class="tex-font-style-tt">p</span> likes the hero <span class="tex-font-style-tt">q</span> (<span class="tex-font-style-tt">p</span> <span class="tex-span"> ≠ </span> <span class="tex-font-style-tt">q</span>). Every liking is described in the input exactly once, no hero likes himself.</p><p>In the last line are given three integers <span class="tex-span"><i>a</i></span>, <span class="tex-span"><i>b</i></span> and <span class="tex-span"><i>c</i></span> (<span class="tex-span">1 ≤ <i>a</i>, <i>b</i>, <i>c</i> ≤ 2·10<sup class="upper-index">9</sup></span>), separated by spaces: the experience for Mephisto, the experience for Diablo and experience for Baal.</p><p>In all the pretests, except for examples from the statement, the following condition is satisfied: <span class="tex-span"><i>a</i> = <i>b</i> = <i>c</i></span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print two integers — the minimal difference in the experience between two heroes who will receive the maximum and minimum number of experience points, and the maximal total amount of liking in teams (the number of friendships between heroes that end up in one team).</p><p><span class="tex-font-style-bf">When calculating the second answer, the team division should satisfy the difference-minimizing contraint. I.e. primary you should minimize the difference in the experience and secondary you should maximize the total amount of liking.</span></p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br />Troll likes Dracul<br />Dracul likes Anka<br />Snowy likes Hexadecimal<br />210 200 180<br /></pre></div><div class="output"><div class="title">Output</div><pre>30 3<br /></pre></div><div class="input"><div class="title">Input</div><pre>2<br />Anka likes Chapay<br />Chapay likes Anka<br />10000 50 50<br /></pre></div><div class="output"><div class="title">Output</div><pre>1950 2<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p><span class="tex-font-style-bf">A note to first example:</span> it the first team should be <span class="tex-font-style-tt">Dracul</span>, <span class="tex-font-style-tt">Troll</span> and <span class="tex-font-style-tt">Anka</span>, in the second one <span class="tex-font-style-tt">Hexadecimal</span> and <span class="tex-font-style-tt">Snowy</span>, and in the third <span class="tex-font-style-tt">Cleo</span> и <span class="tex-font-style-tt">Chapay</span>.</p></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=A]"); 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["Brute force", "Implementation problems, programming technics, simulation"]
["brute force", "implementation", "*1400"]
https://codeforces.com/blog/entry/1769
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It's relation of needed events to all. In this case needed events are all pairs (p,q) where p &gt;= 4q</div><div>All events are all possible pairs (p,q) </div><div>How we can count them?</div><div>All possible pairs is Cartasian product. We can draw it like rectangle.</div><div>Its area - number of all possible pairs.</div><div>Also we need to find area of polygon, where p &gt;= 4q.</div><div>For this let's draw line y=4x and needed set of points is above this line.</div><div>Our answer is relation between this area and area of whole rectangle.</div><div>I think finding areas isn't problem.</div><div>There is one case that I draw on second image, when 4b &lt; a</div><div>There are 2 cases - when a=0 and b=0</div><div>When a=0 we have only left part of image, so answer is 0.5</div><div>When b=0 we have vertical line, so answer is 1.0</div><div>Sorry for some mistakes in English.</div><div><br /></div><div><img src="/predownloaded/68/b4/68b4dc0894eaf043f47f55af361b054a23fa4417.png" style="max-width: 100.0%;max-height: 100.0%;" /><img src="/predownloaded/2b/b0/2bb01cca19ab594d6286fbf8a0ad464f9ed81684.png" style="max-width: 100.0%;max-height: 100.0%;" /><br /></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/77" class="notice" style="text-decoration: none;">Codeforces Beta Round 69 (Div. 1 Only)</a> </span> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/80" class="notice" style="text-decoration: none;">Codeforces Beta Round 69 (Div. 2 Only)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-4391-1769").click(function() { var that = this; 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top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33856" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2447" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33856"> <div class="moveup"> <div class="ttypography">GOOD 77B not , <br />Codeforces Beta Round #69 (Div. 1 Only) Problem B<br />Codeforces Beta Round #69 (Div. 2 Only) Problem D<br />this is better :D</div> </div> </div> <div class="reply info"> <a class="comment-33856 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33856 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33856"> <li> <div class="comment"> <table class="comment-table" commentId="33864" commentParentId="33856"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/andryk" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/andryk" title="Pupil andryk" class="rated-user user-green">andryk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/20/2011 00:27">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33864" href="?#comment-33864" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-33856" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33864" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13728" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33864"> <div class="moveup"> <div class="ttypography">Thanks. Title changed )</div> </div> </div> <div class="reply info"> <a class="comment-33864 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33864 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33864"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="33901" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Shuaib" style="position: relative;"> <img src='https://userpic.codeforces.org/2929/avatar/963ad42782c05a17.jpg'/> </a> <div><a href="/profile/Shuaib" title="Expert Shuaib" class="rated-user user-blue">Shuaib</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/20/2011 07:02">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33901" href="?#comment-33901" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33901" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2929" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33901"> <div class="moveup"> <div class="ttypography">Excellent clarification (albeit weak English ;) ). Thanks a tons though.<div><br /></div></div> </div> </div> <div class="reply info"> <a class="comment-33901 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33901 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33901"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="33996" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mkagenius" style="position: relative;"> <img src='https://userpic.codeforces.org/4476/avatar/b4856becb562e36a.jpg'/> </a> <div><a href="/profile/mkagenius" title="Specialist mkagenius" class="rated-user user-cyan">mkagenius</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/20/2011 20:31">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33996" href="?#comment-33996" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33996" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4476" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33996"> <div class="moveup"> <div class="ttypography">I solved it differently.<div>It is really interesting to note , people think so differently yet do the same thing.</div><div>Feynman Rocks!</div></div> </div> </div> <div class="reply info"> <a class="comment-33996 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33996 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33996"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="221011" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/R.A.X" style="position: relative;"> <img src='https://userpic.codeforces.org/122476/avatar/686763c746ac6e7b.jpg'/> </a> <div><a href="/profile/R.A.X" title="Specialist R.A.X" class="rated-user user-cyan">R.A.X</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/06/2015 13:39">9 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-221011" href="?#comment-221011" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="221011" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="122476" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-221011"> <div class="moveup"> <div class="ttypography"><p>can't we solve this problem by following method ? for a given p we can have any q from -b to p/4. Therefore this length can be written as :- f(x) = b + x/4 we can integrate f(x) from 0 to a g(a)-g(0)=b*a-a*a/8 and the total number of ways to choose two numbers will be a*2b so probability is = ( g(a)-g(0) ) / 2ab But this is giving WA <a href="//codeforces.com/contest/77/submission/10611164">code</a></p></div> </div> </div> <div class="reply info"> <a class="comment-221011 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-221011 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-221011"> <li> <div class="comment"> <table class="comment-table" commentId="221052" commentParentId="221011"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/sepehr103" style="position: relative;"> <img src='https://userpic.codeforces.org/143200/avatar/d9c701d045b44793.jpg'/> </a> <div><a href="/profile/sepehr103" title="Expert sepehr103" class="rated-user user-blue">sepehr103</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/06/2015 17:37">9 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-221052" href="?#comment-221052" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-221011" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="221052" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="143200" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-221052"> <div class="moveup"> <div class="ttypography"><p>Yes you can my dear :) if you wait another 4 years, there will be some sort of method named solve, which solves this problem without any code :)</p></div> </div> </div> <div class="reply info"> <a class="comment-221052 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-221052 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-221052"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1779" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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77B
77
B
en
B. Falling Anvils
<div class="problem-statement"><div class="header"><div class="title">B. Falling Anvils</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>For some reason in many American cartoons anvils fall from time to time onto heroes' heads. Of course, safes, wardrobes, cruisers, planes fall sometimes too... But anvils do so most of all.</p><p>Anvils come in different sizes and shapes. Quite often they get the hero stuck deep in the ground. But have you ever thought who throws anvils from the sky? From what height? We are sure that such questions have never troubled you!</p><p>It turns out that throwing an anvil properly is not an easy task at all. Let's describe one of the most popular anvil throwing models.</p><p>Let the height <span class="tex-span"><i>p</i></span> of the potential victim vary in the range <span class="tex-span">[0;<i>a</i>]</span> and the direction of the wind <span class="tex-span"><i>q</i></span> vary in the range <span class="tex-span">[ - <i>b</i>;<i>b</i>]</span>. <span class="tex-span"><i>p</i></span> <span class="tex-font-style-bf">and</span> <span class="tex-span"><i>q</i></span> <span class="tex-font-style-bf">could be any real (floating) numbers.</span> Then we can assume that the anvil will fit the toon's head perfectly only if the following equation has at least one real root: </p><center> <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/9434a010522e7b78f7a8cd60aee1eb14db5ba441.png" style="max-width: 100.0%;max-height: 100.0%;"/> </center><p>Determine the probability with which an aim can be successfully hit by an anvil.</p><p>You can assume that the <span class="tex-span"><i>p</i></span> and <span class="tex-span"><i>q</i></span> coefficients are chosen equiprobably and independently in their ranges.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains integer <span class="tex-span"><i>t</i></span> (<span class="tex-span">1 ≤ <i>t</i> ≤ 10000</span>) — amount of testcases.</p><p>Each of the following <span class="tex-span"><i>t</i></span> lines contain two space-separated integers <span class="tex-span"><i>a</i></span> and <span class="tex-span"><i>b</i></span> (<span class="tex-span">0 ≤ <i>a</i>, <i>b</i> ≤ 10<sup class="upper-index">6</sup></span>).</p><p>Pretests contain all the tests with <span class="tex-span">0 &lt; <i>a</i> &lt; 10, 0 ≤ <i>b</i> &lt; 10</span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span"><i>t</i></span> lines — the probability of a successful anvil hit for each testcase. The absolute or relative error of the answer should not exceed <span class="tex-span">10<sup class="upper-index"> - 6</sup></span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2<br/>4 2<br/>1 2<br/></pre></div><div class="output"><div class="title">Output</div><pre>0.6250000000<br/>0.5312500000<br/></pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="B" data-uuid="ps_6e5437601717e78589346ec27c6d5081b3cd15eb"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">B. Falling Anvils</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>For some reason in many American cartoons anvils fall from time to time onto heroes' heads. Of course, safes, wardrobes, cruisers, planes fall sometimes too... But anvils do so most of all.</p><p>Anvils come in different sizes and shapes. Quite often they get the hero stuck deep in the ground. But have you ever thought who throws anvils from the sky? From what height? We are sure that such questions have never troubled you!</p><p>It turns out that throwing an anvil properly is not an easy task at all. Let's describe one of the most popular anvil throwing models.</p><p>Let the height <span class="tex-span"><i>p</i></span> of the potential victim vary in the range <span class="tex-span">[0;<i>a</i>]</span> and the direction of the wind <span class="tex-span"><i>q</i></span> vary in the range <span class="tex-span">[ - <i>b</i>;<i>b</i>]</span>. <span class="tex-span"><i>p</i></span> <span class="tex-font-style-bf">and</span> <span class="tex-span"><i>q</i></span> <span class="tex-font-style-bf">could be any real (floating) numbers.</span> Then we can assume that the anvil will fit the toon's head perfectly only if the following equation has at least one real root: </p><center> <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/9434a010522e7b78f7a8cd60aee1eb14db5ba441.png" style="max-width: 100.0%;max-height: 100.0%;" /> </center><p>Determine the probability with which an aim can be successfully hit by an anvil.</p><p>You can assume that the <span class="tex-span"><i>p</i></span> and <span class="tex-span"><i>q</i></span> coefficients are chosen equiprobably and independently in their ranges.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains integer <span class="tex-span"><i>t</i></span> (<span class="tex-span">1 ≤ <i>t</i> ≤ 10000</span>) — amount of testcases.</p><p>Each of the following <span class="tex-span"><i>t</i></span> lines contain two space-separated integers <span class="tex-span"><i>a</i></span> and <span class="tex-span"><i>b</i></span> (<span class="tex-span">0 ≤ <i>a</i>, <i>b</i> ≤ 10<sup class="upper-index">6</sup></span>).</p><p>Pretests contain all the tests with <span class="tex-span">0 &lt; <i>a</i> &lt; 10, 0 ≤ <i>b</i> &lt; 10</span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span"><i>t</i></span> lines — the probability of a successful anvil hit for each testcase. The absolute or relative error of the answer should not exceed <span class="tex-span">10<sup class="upper-index"> - 6</sup></span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2<br />4 2<br />1 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>0.6250000000<br />0.5312500000<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=B]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); if (previousStatementText) { if (previousStatementText !== statementText) { $problem.find(".diff-notifier").show(); $problem.find(".diff-notifier-close").click(function() { Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60); $problem.find(".diff-notifier").hide(); 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["Mathematics including integration, differential equations, etc", "Probabilities, expected values, statistics, random variables, etc"]
["math", "probabilities", "*1800"]
https://codeforces.com/blog/entry/1769
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It's relation of needed events to all. In this case needed events are all pairs (p,q) where p &gt;= 4q</div><div>All events are all possible pairs (p,q) </div><div>How we can count them?</div><div>All possible pairs is Cartasian product. We can draw it like rectangle.</div><div>Its area - number of all possible pairs.</div><div>Also we need to find area of polygon, where p &gt;= 4q.</div><div>For this let's draw line y=4x and needed set of points is above this line.</div><div>Our answer is relation between this area and area of whole rectangle.</div><div>I think finding areas isn't problem.</div><div>There is one case that I draw on second image, when 4b &lt; a</div><div>There are 2 cases - when a=0 and b=0</div><div>When a=0 we have only left part of image, so answer is 0.5</div><div>When b=0 we have vertical line, so answer is 1.0</div><div>Sorry for some mistakes in English.</div><div><br /></div><div><img src="/predownloaded/68/b4/68b4dc0894eaf043f47f55af361b054a23fa4417.png" style="max-width: 100.0%;max-height: 100.0%;" /><img src="/predownloaded/2b/b0/2bb01cca19ab594d6286fbf8a0ad464f9ed81684.png" style="max-width: 100.0%;max-height: 100.0%;" /><br /></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/77" class="notice" style="text-decoration: none;">Codeforces Beta Round 69 (Div. 1 Only)</a> </span> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/80" class="notice" style="text-decoration: none;">Codeforces Beta Round 69 (Div. 2 Only)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-4391-1769").click(function() { var that = this; 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margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1779"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (6)</a> </div> <div class="comments-actions-div"> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="33856" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/iman_MC" style="position: relative;"> <img src='https://userpic.codeforces.org/2447/avatar/b2ab3e48d7eb8c6.jpg'/> </a> <div><a href="/profile/iman_MC" title="Pupil iman_MC" class="rated-user user-green">iman_MC</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/20/2011 00:22">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33856" href="?#comment-33856" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33856" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2447" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33856"> <div class="moveup"> <div class="ttypography">GOOD 77B not , <br />Codeforces Beta Round #69 (Div. 1 Only) Problem B<br />Codeforces Beta Round #69 (Div. 2 Only) Problem D<br />this is better :D</div> </div> </div> <div class="reply info"> <a class="comment-33856 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33856 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33856"> <li> <div class="comment"> <table class="comment-table" commentId="33864" commentParentId="33856"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/andryk" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/andryk" title="Pupil andryk" class="rated-user user-green">andryk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/20/2011 00:27">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33864" href="?#comment-33864" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-33856" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33864" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13728" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33864"> <div class="moveup"> <div class="ttypography">Thanks. Title changed )</div> </div> </div> <div class="reply info"> <a class="comment-33864 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33864 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33864"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="33901" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Shuaib" style="position: relative;"> <img src='https://userpic.codeforces.org/2929/avatar/963ad42782c05a17.jpg'/> </a> <div><a href="/profile/Shuaib" title="Expert Shuaib" class="rated-user user-blue">Shuaib</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/20/2011 07:02">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33901" href="?#comment-33901" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33901" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2929" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33901"> <div class="moveup"> <div class="ttypography">Excellent clarification (albeit weak English ;) ). Thanks a tons though.<div><br /></div></div> </div> </div> <div class="reply info"> <a class="comment-33901 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33901 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33901"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="33996" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mkagenius" style="position: relative;"> <img src='https://userpic.codeforces.org/4476/avatar/b4856becb562e36a.jpg'/> </a> <div><a href="/profile/mkagenius" title="Specialist mkagenius" class="rated-user user-cyan">mkagenius</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/20/2011 20:31">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33996" href="?#comment-33996" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33996" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4476" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33996"> <div class="moveup"> <div class="ttypography">I solved it differently.<div>It is really interesting to note , people think so differently yet do the same thing.</div><div>Feynman Rocks!</div></div> </div> </div> <div class="reply info"> <a class="comment-33996 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33996 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33996"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="221011" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/R.A.X" style="position: relative;"> <img src='https://userpic.codeforces.org/122476/avatar/686763c746ac6e7b.jpg'/> </a> <div><a href="/profile/R.A.X" title="Specialist R.A.X" class="rated-user user-cyan">R.A.X</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/06/2015 13:39">9 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-221011" href="?#comment-221011" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="221011" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="122476" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-221011"> <div class="moveup"> <div class="ttypography"><p>can't we solve this problem by following method ? for a given p we can have any q from -b to p/4. Therefore this length can be written as :- f(x) = b + x/4 we can integrate f(x) from 0 to a g(a)-g(0)=b*a-a*a/8 and the total number of ways to choose two numbers will be a*2b so probability is = ( g(a)-g(0) ) / 2ab But this is giving WA <a href="//codeforces.com/contest/77/submission/10611164">code</a></p></div> </div> </div> <div class="reply info"> <a class="comment-221011 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-221011 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-221011"> <li> <div class="comment"> <table class="comment-table" commentId="221052" commentParentId="221011"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/sepehr103" style="position: relative;"> <img src='https://userpic.codeforces.org/143200/avatar/d9c701d045b44793.jpg'/> </a> <div><a href="/profile/sepehr103" title="Expert sepehr103" class="rated-user user-blue">sepehr103</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/06/2015 17:37">9 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-221052" href="?#comment-221052" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-221011" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="221052" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="143200" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-221052"> <div class="moveup"> <div class="ttypography"><p>Yes you can my dear :) if you wait another 4 years, there will be some sort of method named solve, which solves this problem without any code :)</p></div> </div> </div> <div class="reply info"> <a class="comment-221052 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-221052 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-221052"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1779" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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77C
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C
en
C. Beavermuncher-0xFF
<div class="problem-statement"><div class="header"><div class="title">C. Beavermuncher-0xFF</div><div class="time-limit"><div class="property-title">time limit per test</div>3 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p><span class="tex-font-style-it">"Eat a beaver, save a tree!" — That will be the motto of ecologists' urgent meeting in Beaverley Hills.</span></p><p><span class="tex-font-style-it">And the whole point is that the population of beavers on the Earth has reached incredible sizes! Each day their number increases in several times and they don't even realize how much their unhealthy obsession with trees harms the nature and the humankind. The amount of oxygen in the atmosphere has dropped to 17 per cent and, as the best minds of the world think, that is not the end.</span></p><p><span class="tex-font-style-it">In the middle of the 50-s of the previous century a group of soviet scientists succeed in foreseeing the situation with beavers and worked out a secret technology to clean territory. The technology bears a mysterious title "Beavermuncher-0xFF". Now the fate of the planet lies on the fragile shoulders of a small group of people who has dedicated their lives to science.</span></p><p><span class="tex-font-style-it">The prototype is ready, you now need to urgently carry out its experiments in practice.</span> </p><p>You are given a tree, completely occupied by beavers. A tree is a connected undirected graph without cycles. The tree consists of <span class="tex-span"><i>n</i></span> vertices, the <span class="tex-span"><i>i</i></span>-th vertex contains <span class="tex-span"><i>k</i><sub class="lower-index"><i>i</i></sub></span> beavers. </p><p>"Beavermuncher-0xFF" works by the following principle: being at some vertex <span class="tex-span"><i>u</i></span>, it can go to the vertex <span class="tex-span"><i>v</i></span>, if they are connected by an edge, and eat <span class="tex-font-style-bf">exactly one</span> beaver located at the vertex <span class="tex-span"><i>v</i></span>. It is impossible to move to the vertex <span class="tex-span"><i>v</i></span> if there are no beavers left in <span class="tex-span"><i>v</i></span>. "Beavermuncher-0xFF" <span class="tex-font-style-bf">cannot</span> just stand at some vertex and eat beavers in it. "Beavermuncher-0xFF" must move without stops.</p><p>Why does the "Beavermuncher-0xFF" works like this? Because the developers have not provided place for the battery in it and eating beavers is necessary for converting their mass into pure energy.</p><p>It is guaranteed that the beavers will be shocked by what is happening, which is why they will not be able to move from a vertex of the tree to another one. As for the "Beavermuncher-0xFF", it can move along each edge in both directions while conditions described above are fulfilled.</p><p>The root of the tree is located at the vertex <span class="tex-span"><i>s</i></span>. This means that the "Beavermuncher-0xFF" begins its mission at the vertex <span class="tex-span"><i>s</i></span> and it must return there at the end of experiment, because no one is going to take it down from a high place. </p><p>Determine the maximum number of beavers "Beavermuncher-0xFF" can eat and return to the starting vertex.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains integer <span class="tex-span"><i>n</i></span> — the number of vertices in the tree (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup></span>). The second line contains <span class="tex-span"><i>n</i></span> integers <span class="tex-span"><i>k</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>k</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">5</sup></span>) — amounts of beavers on corresponding vertices. Following <span class="tex-span"><i>n</i> - 1</span> lines describe the tree. Each line contains two integers separated by space. These integers represent two vertices connected by an edge. Vertices are numbered from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span>. The last line contains integer <span class="tex-span"><i>s</i></span> — the number of the starting vertex (<span class="tex-span">1 ≤ <i>s</i> ≤ <i>n</i></span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print the maximum number of beavers munched by the "Beavermuncher-0xFF".</p><p>Please, do not use <span class="tex-font-style-tt">%lld</span> specificator to write 64-bit integers in C++. It is preferred to use <span class="tex-font-style-tt">cout</span> (also you may use <span class="tex-font-style-tt">%I64d</span>).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>5<br/>1 3 1 3 2<br/>2 5<br/>3 4<br/>4 5<br/>1 5<br/>4<br/></pre></div><div class="output"><div class="title">Output</div><pre>6<br/></pre></div><div class="input"><div class="title">Input</div><pre>3<br/>2 1 1<br/>3 2<br/>1 2<br/>3<br/></pre></div><div class="output"><div class="title">Output</div><pre>2<br/></pre></div></div></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/77">Codeforces Beta Round 69 (Div. 1 Only)</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? 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If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="C" data-uuid="ps_8e0e767d2c3603dea60ab44402f03bed0b3f89d5"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. Beavermuncher-0xFF</div><div class="time-limit"><div class="property-title">time limit per test</div>3 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p><span class="tex-font-style-it">&quot;Eat a beaver, save a tree!&quot; — That will be the motto of ecologists' urgent meeting in Beaverley Hills.</span></p><p><span class="tex-font-style-it">And the whole point is that the population of beavers on the Earth has reached incredible sizes! Each day their number increases in several times and they don't even realize how much their unhealthy obsession with trees harms the nature and the humankind. The amount of oxygen in the atmosphere has dropped to 17 per cent and, as the best minds of the world think, that is not the end.</span></p><p><span class="tex-font-style-it">In the middle of the 50-s of the previous century a group of soviet scientists succeed in foreseeing the situation with beavers and worked out a secret technology to clean territory. The technology bears a mysterious title &quot;Beavermuncher-0xFF&quot;. Now the fate of the planet lies on the fragile shoulders of a small group of people who has dedicated their lives to science.</span></p><p><span class="tex-font-style-it">The prototype is ready, you now need to urgently carry out its experiments in practice.</span> </p><p>You are given a tree, completely occupied by beavers. A tree is a connected undirected graph without cycles. The tree consists of <span class="tex-span"><i>n</i></span> vertices, the <span class="tex-span"><i>i</i></span>-th vertex contains <span class="tex-span"><i>k</i><sub class="lower-index"><i>i</i></sub></span> beavers. </p><p>&quot;Beavermuncher-0xFF&quot; works by the following principle: being at some vertex <span class="tex-span"><i>u</i></span>, it can go to the vertex <span class="tex-span"><i>v</i></span>, if they are connected by an edge, and eat <span class="tex-font-style-bf">exactly one</span> beaver located at the vertex <span class="tex-span"><i>v</i></span>. It is impossible to move to the vertex <span class="tex-span"><i>v</i></span> if there are no beavers left in <span class="tex-span"><i>v</i></span>. &quot;Beavermuncher-0xFF&quot; <span class="tex-font-style-bf">cannot</span> just stand at some vertex and eat beavers in it. &quot;Beavermuncher-0xFF&quot; must move without stops.</p><p>Why does the &quot;Beavermuncher-0xFF&quot; works like this? Because the developers have not provided place for the battery in it and eating beavers is necessary for converting their mass into pure energy.</p><p>It is guaranteed that the beavers will be shocked by what is happening, which is why they will not be able to move from a vertex of the tree to another one. As for the &quot;Beavermuncher-0xFF&quot;, it can move along each edge in both directions while conditions described above are fulfilled.</p><p>The root of the tree is located at the vertex <span class="tex-span"><i>s</i></span>. This means that the &quot;Beavermuncher-0xFF&quot; begins its mission at the vertex <span class="tex-span"><i>s</i></span> and it must return there at the end of experiment, because no one is going to take it down from a high place. </p><p>Determine the maximum number of beavers &quot;Beavermuncher-0xFF&quot; can eat and return to the starting vertex.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains integer <span class="tex-span"><i>n</i></span> — the number of vertices in the tree (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup></span>). The second line contains <span class="tex-span"><i>n</i></span> integers <span class="tex-span"><i>k</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>k</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">5</sup></span>) — amounts of beavers on corresponding vertices. Following <span class="tex-span"><i>n</i> - 1</span> lines describe the tree. Each line contains two integers separated by space. These integers represent two vertices connected by an edge. Vertices are numbered from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span>. The last line contains integer <span class="tex-span"><i>s</i></span> — the number of the starting vertex (<span class="tex-span">1 ≤ <i>s</i> ≤ <i>n</i></span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print the maximum number of beavers munched by the &quot;Beavermuncher-0xFF&quot;.</p><p>Please, do not use <span class="tex-font-style-tt">%lld</span> specificator to write 64-bit integers in C++. It is preferred to use <span class="tex-font-style-tt">cout</span> (also you may use <span class="tex-font-style-tt">%I64d</span>).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>5<br />1 3 1 3 2<br />2 5<br />3 4<br />4 5<br />1 5<br />4<br /></pre></div><div class="output"><div class="title">Output</div><pre>6<br /></pre></div><div class="input"><div class="title">Input</div><pre>3<br />2 1 1<br />3 2<br />1 2<br />3<br /></pre></div><div class="output"><div class="title">Output</div><pre>2<br /></pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=C]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); if (previousStatementText) { if (previousStatementText !== statementText) { $problem.find(".diff-notifier").show(); 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["Dfs and similar", "Dynamic programming", "Disjoint set union", "Greedy algorithms", "Trees"]
["dfs and similar", "dp", "dsu", "greedy", "trees", "*2100"]
https://codeforces.com/blog/entry/1769
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It's relation of needed events to all. In this case needed events are all pairs (p,q) where p &gt;= 4q</div><div>All events are all possible pairs (p,q) </div><div>How we can count them?</div><div>All possible pairs is Cartasian product. We can draw it like rectangle.</div><div>Its area - number of all possible pairs.</div><div>Also we need to find area of polygon, where p &gt;= 4q.</div><div>For this let's draw line y=4x and needed set of points is above this line.</div><div>Our answer is relation between this area and area of whole rectangle.</div><div>I think finding areas isn't problem.</div><div>There is one case that I draw on second image, when 4b &lt; a</div><div>There are 2 cases - when a=0 and b=0</div><div>When a=0 we have only left part of image, so answer is 0.5</div><div>When b=0 we have vertical line, so answer is 1.0</div><div>Sorry for some mistakes in English.</div><div><br /></div><div><img src="/predownloaded/68/b4/68b4dc0894eaf043f47f55af361b054a23fa4417.png" style="max-width: 100.0%;max-height: 100.0%;" /><img src="/predownloaded/2b/b0/2bb01cca19ab594d6286fbf8a0ad464f9ed81684.png" style="max-width: 100.0%;max-height: 100.0%;" /><br /></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/77" class="notice" style="text-decoration: none;">Codeforces Beta Round 69 (Div. 1 Only)</a> </span> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/80" class="notice" style="text-decoration: none;">Codeforces Beta Round 69 (Div. 2 Only)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-4391-1769").click(function() { var that = this; 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margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1779"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (6)</a> </div> <div class="comments-actions-div"> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="33856" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/iman_MC" style="position: relative;"> <img src='https://userpic.codeforces.org/2447/avatar/b2ab3e48d7eb8c6.jpg'/> </a> <div><a href="/profile/iman_MC" title="Pupil iman_MC" class="rated-user user-green">iman_MC</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/20/2011 00:22">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33856" href="?#comment-33856" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33856" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2447" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33856"> <div class="moveup"> <div class="ttypography">GOOD 77B not , <br />Codeforces Beta Round #69 (Div. 1 Only) Problem B<br />Codeforces Beta Round #69 (Div. 2 Only) Problem D<br />this is better :D</div> </div> </div> <div class="reply info"> <a class="comment-33856 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33856 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33856"> <li> <div class="comment"> <table class="comment-table" commentId="33864" commentParentId="33856"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/andryk" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/andryk" title="Pupil andryk" class="rated-user user-green">andryk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/20/2011 00:27">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33864" href="?#comment-33864" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-33856" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33864" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13728" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33864"> <div class="moveup"> <div class="ttypography">Thanks. Title changed )</div> </div> </div> <div class="reply info"> <a class="comment-33864 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33864 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33864"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="33901" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Shuaib" style="position: relative;"> <img src='https://userpic.codeforces.org/2929/avatar/963ad42782c05a17.jpg'/> </a> <div><a href="/profile/Shuaib" title="Expert Shuaib" class="rated-user user-blue">Shuaib</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/20/2011 07:02">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33901" href="?#comment-33901" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33901" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2929" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33901"> <div class="moveup"> <div class="ttypography">Excellent clarification (albeit weak English ;) ). Thanks a tons though.<div><br /></div></div> </div> </div> <div class="reply info"> <a class="comment-33901 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33901 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33901"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="33996" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mkagenius" style="position: relative;"> <img src='https://userpic.codeforces.org/4476/avatar/b4856becb562e36a.jpg'/> </a> <div><a href="/profile/mkagenius" title="Specialist mkagenius" class="rated-user user-cyan">mkagenius</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/20/2011 20:31">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33996" href="?#comment-33996" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33996" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4476" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33996"> <div class="moveup"> <div class="ttypography">I solved it differently.<div>It is really interesting to note , people think so differently yet do the same thing.</div><div>Feynman Rocks!</div></div> </div> </div> <div class="reply info"> <a class="comment-33996 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33996 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33996"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="221011" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/R.A.X" style="position: relative;"> <img src='https://userpic.codeforces.org/122476/avatar/686763c746ac6e7b.jpg'/> </a> <div><a href="/profile/R.A.X" title="Specialist R.A.X" class="rated-user user-cyan">R.A.X</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/06/2015 13:39">9 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-221011" href="?#comment-221011" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="221011" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="122476" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-221011"> <div class="moveup"> <div class="ttypography"><p>can't we solve this problem by following method ? for a given p we can have any q from -b to p/4. Therefore this length can be written as :- f(x) = b + x/4 we can integrate f(x) from 0 to a g(a)-g(0)=b*a-a*a/8 and the total number of ways to choose two numbers will be a*2b so probability is = ( g(a)-g(0) ) / 2ab But this is giving WA <a href="//codeforces.com/contest/77/submission/10611164">code</a></p></div> </div> </div> <div class="reply info"> <a class="comment-221011 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-221011 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-221011"> <li> <div class="comment"> <table class="comment-table" commentId="221052" commentParentId="221011"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/sepehr103" style="position: relative;"> <img src='https://userpic.codeforces.org/143200/avatar/d9c701d045b44793.jpg'/> </a> <div><a href="/profile/sepehr103" title="Expert sepehr103" class="rated-user user-blue">sepehr103</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/06/2015 17:37">9 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-221052" href="?#comment-221052" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-221011" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="221052" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="143200" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-221052"> <div class="moveup"> <div class="ttypography"><p>Yes you can my dear :) if you wait another 4 years, there will be some sort of method named solve, which solves this problem without any code :)</p></div> </div> </div> <div class="reply info"> <a class="comment-221052 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-221052 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-221052"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1779" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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77D
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en
D. Domino Carpet
<div class="problem-statement"><div class="header"><div class="title">D. Domino Carpet</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p><span class="tex-font-style-it">...Mike the TV greets you again!</span> </p><p><span class="tex-font-style-it">Tired of the monotonous furniture? Sick of gray routine? Dreaming about dizzying changes in your humble abode? We have something to offer you!</span> </p><p><span class="tex-font-style-it">This domino carpet for only $99.99 will change your life! You can lay it on the floor, hang it on the wall or even on the ceiling! Among other things ...</span> </p><p>Having watched the commercial, virus Hexadecimal also wanted to get a Domino Carpet and wanted badly to be photographed in front of it. But of course, a virus will never consent to buying a licensed Carpet! So she ordered a truck of dominoes and decided to make such a Carpet herself. </p><p>The original Domino Carpet is a field of squares <span class="tex-span"><i>n</i> × <i>m</i></span> in size. Each square is half of a domino, and can be rotated either vertically or horizontally, independently from its neighbors. Vertically rotated domino halves look like this: </p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/dc948fb9935610f2edcaa94edaf504f4f95af644.png" style="max-width: 100.0%;max-height: 100.0%;"/> </center> <p>And horizontally rotated halves look like this: </p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/6d5cf56290803c55abdec640fa97b6ceb82374ed.png" style="max-width: 100.0%;max-height: 100.0%;"/> </center><p>Notice, that some halves looks the same in both rotations, but other halves differ.</p><p>Dominoes bought by Hexadecimal are represented by uncuttable chips <span class="tex-span">1 × 2</span> in size, which can be laid either vertically or horizontally. If the chip is laid vertically, then both of it's halves should be laid vertically orientated; if the chip is laid horizontally, then both of it's halves should be laid horizontally.</p><p>The samples of valid and invalid dominoes laid vertically and horizontally are: </p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/8fa8d68db3606f6415610de9abeb091c7231d052.png" style="max-width: 100.0%;max-height: 100.0%;"/> </center> <p>Virus Hexadecimal assembles her own Domino Carpet so that the following conditions are satisfied:</p><ul> <li> each carpet square is covered by a domino chip, i.e. there are no empty squares; </li><li> all domino chips lie entirely within the carpet and don't overlap with each other; </li><li> if there is a horizontal domino chip with its left half in column <span class="tex-span"><i>j</i></span> then there are no horizontal domino chips with their left halves in columns <span class="tex-span"><i>j</i> - 1</span> or <span class="tex-span"><i>j</i> + 1</span>. </li></ul><p>Before starting to assemble her own Domino Carpet, the virus wants to know the number of ways to achieve the intended purpose modulo <span class="tex-span">10<sup class="upper-index">9</sup> + 7</span>.</p><p>You can assume that the virus has an infinitely large number of dominoes of each type.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>m</i></span>, separated by a space — the size of the Domino Carpet (<span class="tex-span">1 ≤ <i>n</i>, <i>m</i> ≤ 250</span>). Next <span class="tex-span">4<i>n</i> + 1</span> lines contain <span class="tex-span">4<i>m</i> + 1</span> symbols. </p><p>Each square of the Domino Carpet, which is a domino half, is described by a <span class="tex-span">3 × 3</span> square. Symbol <span class="tex-font-style-tt">'O'</span> in this square indicates the presence of a point, symbol <span class="tex-font-style-tt">'.'</span> — its absence. </p><p>Each <span class="tex-span">3 × 3</span> square is delineated from adjacent squares by symbols <span class="tex-font-style-tt">'#'</span> as shown in the examples. </p><p>It is guaranteed that every box describes the correct half of a domino. </p><p>In all pretests the Domino Carpets have the size of <span class="tex-span">2 × 2</span> and <span class="tex-span">4 × 4</span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single number, the number of ways to assemble the Domino Carpet modulo <span class="tex-span">10<sup class="upper-index">9</sup> + 7</span>, using only standard dominoes of size <span class="tex-span">1 × 2</span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3 4<br/>#################<br/>#O..#...#O.O#...#<br/>#.O.#.O.#.O.#...#<br/>#..O#...#O.O#...#<br/>#################<br/>#O.O#OOO#O.O#...#<br/>#.O.#...#...#.O.#<br/>#O.O#OOO#O.O#...#<br/>#################<br/>#O.O#...#O.O#...#<br/>#...#...#...#.O.#<br/>#O.O#...#O.O#...#<br/>#################<br/></pre></div><div class="output"><div class="title">Output</div><pre>3</pre></div><div class="input"><div class="title">Input</div><pre>2 2<br/>#########<br/>#O.O#O.O#<br/>#.O.#...#<br/>#O.O#O.O#<br/>#########<br/>#...#O.O#<br/>#...#...#<br/>#...#O.O#<br/>#########<br/></pre></div><div class="output"><div class="title">Output</div><pre>2</pre></div><div class="input"><div class="title">Input</div><pre>2 2<br/>#########<br/>#..O#O..#<br/>#...#...#<br/>#O..#..O#<br/>#########<br/>#O..#..O#<br/>#...#...#<br/>#..O#O..#<br/>#########<br/></pre></div><div class="output"><div class="title">Output</div><pre>0</pre></div></div></div><div class="note"><div class="section-title">Note</div><p><span class="tex-font-style-bf">A note to the first example:</span> all correct ways to make Domino Carpet are represented below:</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/b96abcb2ea9a01c1e90dc1f2e7d56330b3ce0765.png" style="max-width: 100.0%;max-height: 100.0%;"/> </center><p>And this way is incorrect:</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/9357443c252ff7e9673f82f5a07af65082e20eb0.png" style="max-width: 100.0%;max-height: 100.0%;"/> </center></div></div>
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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict. </div> </div> <div class="roundbox sidebox borderTopRound " style=""> <table class="rtable "> <tbody> <tr> <th class="left" style="width:100%;"><a style="color: black" href="/contest/77">Codeforces Beta Round 69 (Div. 1 Only)</a></th> </tr> <tr> <td class="left bottom" colspan="1"><span class="contest-state-phase">Finished</span></td> </tr> </tbody> </table> </div> <div class="roundbox sidebox borderTopRound " style=""> <div class="caption titled">&rarr; Practice? <div class="top-links"> </div> </div> <div> <div style="margin:1em;font-size:0.8em;"> Want to solve the contest problems after the official contest ends? 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="D" data-uuid="ps_d9a222985855af7c17577a53d5f5bba9559b5612"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">D. Domino Carpet</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p><span class="tex-font-style-it">...Mike the TV greets you again!</span> </p><p><span class="tex-font-style-it">Tired of the monotonous furniture? Sick of gray routine? Dreaming about dizzying changes in your humble abode? We have something to offer you!</span> </p><p><span class="tex-font-style-it">This domino carpet for only $99.99 will change your life! You can lay it on the floor, hang it on the wall or even on the ceiling! Among other things ...</span> </p><p>Having watched the commercial, virus Hexadecimal also wanted to get a Domino Carpet and wanted badly to be photographed in front of it. But of course, a virus will never consent to buying a licensed Carpet! So she ordered a truck of dominoes and decided to make such a Carpet herself. </p><p>The original Domino Carpet is a field of squares <span class="tex-span"><i>n</i> × <i>m</i></span> in size. Each square is half of a domino, and can be rotated either vertically or horizontally, independently from its neighbors. Vertically rotated domino halves look like this: </p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/dc948fb9935610f2edcaa94edaf504f4f95af644.png" style="max-width: 100.0%;max-height: 100.0%;" /> </center> <p>And horizontally rotated halves look like this: </p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/6d5cf56290803c55abdec640fa97b6ceb82374ed.png" style="max-width: 100.0%;max-height: 100.0%;" /> </center><p>Notice, that some halves looks the same in both rotations, but other halves differ.</p><p>Dominoes bought by Hexadecimal are represented by uncuttable chips <span class="tex-span">1 × 2</span> in size, which can be laid either vertically or horizontally. If the chip is laid vertically, then both of it's halves should be laid vertically orientated; if the chip is laid horizontally, then both of it's halves should be laid horizontally.</p><p>The samples of valid and invalid dominoes laid vertically and horizontally are: </p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/8fa8d68db3606f6415610de9abeb091c7231d052.png" style="max-width: 100.0%;max-height: 100.0%;" /> </center> <p>Virus Hexadecimal assembles her own Domino Carpet so that the following conditions are satisfied:</p><ul> <li> each carpet square is covered by a domino chip, i.e. there are no empty squares; </li><li> all domino chips lie entirely within the carpet and don't overlap with each other; </li><li> if there is a horizontal domino chip with its left half in column <span class="tex-span"><i>j</i></span> then there are no horizontal domino chips with their left halves in columns <span class="tex-span"><i>j</i> - 1</span> or <span class="tex-span"><i>j</i> + 1</span>. </li></ul><p>Before starting to assemble her own Domino Carpet, the virus wants to know the number of ways to achieve the intended purpose modulo <span class="tex-span">10<sup class="upper-index">9</sup> + 7</span>.</p><p>You can assume that the virus has an infinitely large number of dominoes of each type.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>m</i></span>, separated by a space — the size of the Domino Carpet (<span class="tex-span">1 ≤ <i>n</i>, <i>m</i> ≤ 250</span>). Next <span class="tex-span">4<i>n</i> + 1</span> lines contain <span class="tex-span">4<i>m</i> + 1</span> symbols. </p><p>Each square of the Domino Carpet, which is a domino half, is described by a <span class="tex-span">3 × 3</span> square. Symbol <span class="tex-font-style-tt">'O'</span> in this square indicates the presence of a point, symbol <span class="tex-font-style-tt">'.'</span> — its absence. </p><p>Each <span class="tex-span">3 × 3</span> square is delineated from adjacent squares by symbols <span class="tex-font-style-tt">'#'</span> as shown in the examples. </p><p>It is guaranteed that every box describes the correct half of a domino. </p><p>In all pretests the Domino Carpets have the size of <span class="tex-span">2 × 2</span> and <span class="tex-span">4 × 4</span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single number, the number of ways to assemble the Domino Carpet modulo <span class="tex-span">10<sup class="upper-index">9</sup> + 7</span>, using only standard dominoes of size <span class="tex-span">1 × 2</span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3 4<br />#################<br />#O..#...#O.O#...#<br />#.O.#.O.#.O.#...#<br />#..O#...#O.O#...#<br />#################<br />#O.O#OOO#O.O#...#<br />#.O.#...#...#.O.#<br />#O.O#OOO#O.O#...#<br />#################<br />#O.O#...#O.O#...#<br />#...#...#...#.O.#<br />#O.O#...#O.O#...#<br />#################<br /></pre></div><div class="output"><div class="title">Output</div><pre>3</pre></div><div class="input"><div class="title">Input</div><pre>2 2<br />#########<br />#O.O#O.O#<br />#.O.#...#<br />#O.O#O.O#<br />#########<br />#...#O.O#<br />#...#...#<br />#...#O.O#<br />#########<br /></pre></div><div class="output"><div class="title">Output</div><pre>2</pre></div><div class="input"><div class="title">Input</div><pre>2 2<br />#########<br />#..O#O..#<br />#...#...#<br />#O..#..O#<br />#########<br />#O..#..O#<br />#...#...#<br />#..O#O..#<br />#########<br /></pre></div><div class="output"><div class="title">Output</div><pre>0</pre></div></div></div><div class="note"><div class="section-title">Note</div><p><span class="tex-font-style-bf">A note to the first example:</span> all correct ways to make Domino Carpet are represented below:</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/b96abcb2ea9a01c1e90dc1f2e7d56330b3ce0765.png" style="max-width: 100.0%;max-height: 100.0%;" /> </center><p>And this way is incorrect:</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/9357443c252ff7e9673f82f5a07af65082e20eb0.png" style="max-width: 100.0%;max-height: 100.0%;" /> </center></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=D]"); 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["Dynamic programming", "Implementation problems, programming technics, simulation"]
["dp", "implementation", "*2300"]
https://codeforces.com/blog/entry/1769
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It's relation of needed events to all. In this case needed events are all pairs (p,q) where p &gt;= 4q</div><div>All events are all possible pairs (p,q) </div><div>How we can count them?</div><div>All possible pairs is Cartasian product. We can draw it like rectangle.</div><div>Its area - number of all possible pairs.</div><div>Also we need to find area of polygon, where p &gt;= 4q.</div><div>For this let's draw line y=4x and needed set of points is above this line.</div><div>Our answer is relation between this area and area of whole rectangle.</div><div>I think finding areas isn't problem.</div><div>There is one case that I draw on second image, when 4b &lt; a</div><div>There are 2 cases - when a=0 and b=0</div><div>When a=0 we have only left part of image, so answer is 0.5</div><div>When b=0 we have vertical line, so answer is 1.0</div><div>Sorry for some mistakes in English.</div><div><br /></div><div><img src="/predownloaded/68/b4/68b4dc0894eaf043f47f55af361b054a23fa4417.png" style="max-width: 100.0%;max-height: 100.0%;" /><img src="/predownloaded/2b/b0/2bb01cca19ab594d6286fbf8a0ad464f9ed81684.png" style="max-width: 100.0%;max-height: 100.0%;" /><br /></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/77" class="notice" style="text-decoration: none;">Codeforces Beta Round 69 (Div. 1 Only)</a> </span> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/80" class="notice" style="text-decoration: none;">Codeforces Beta Round 69 (Div. 2 Only)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-4391-1769").click(function() { var that = this; 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margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1779"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (6)</a> </div> <div class="comments-actions-div"> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="33856" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/iman_MC" style="position: relative;"> <img src='https://userpic.codeforces.org/2447/avatar/b2ab3e48d7eb8c6.jpg'/> </a> <div><a href="/profile/iman_MC" title="Pupil iman_MC" class="rated-user user-green">iman_MC</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/20/2011 00:22">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33856" href="?#comment-33856" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33856" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2447" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33856"> <div class="moveup"> <div class="ttypography">GOOD 77B not , <br />Codeforces Beta Round #69 (Div. 1 Only) Problem B<br />Codeforces Beta Round #69 (Div. 2 Only) Problem D<br />this is better :D</div> </div> </div> <div class="reply info"> <a class="comment-33856 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33856 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33856"> <li> <div class="comment"> <table class="comment-table" commentId="33864" commentParentId="33856"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/andryk" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/andryk" title="Pupil andryk" class="rated-user user-green">andryk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/20/2011 00:27">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33864" href="?#comment-33864" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-33856" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33864" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13728" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33864"> <div class="moveup"> <div class="ttypography">Thanks. Title changed )</div> </div> </div> <div class="reply info"> <a class="comment-33864 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33864 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33864"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="33901" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Shuaib" style="position: relative;"> <img src='https://userpic.codeforces.org/2929/avatar/963ad42782c05a17.jpg'/> </a> <div><a href="/profile/Shuaib" title="Expert Shuaib" class="rated-user user-blue">Shuaib</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/20/2011 07:02">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33901" href="?#comment-33901" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33901" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2929" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33901"> <div class="moveup"> <div class="ttypography">Excellent clarification (albeit weak English ;) ). Thanks a tons though.<div><br /></div></div> </div> </div> <div class="reply info"> <a class="comment-33901 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33901 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33901"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="33996" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mkagenius" style="position: relative;"> <img src='https://userpic.codeforces.org/4476/avatar/b4856becb562e36a.jpg'/> </a> <div><a href="/profile/mkagenius" title="Specialist mkagenius" class="rated-user user-cyan">mkagenius</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/20/2011 20:31">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33996" href="?#comment-33996" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33996" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4476" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33996"> <div class="moveup"> <div class="ttypography">I solved it differently.<div>It is really interesting to note , people think so differently yet do the same thing.</div><div>Feynman Rocks!</div></div> </div> </div> <div class="reply info"> <a class="comment-33996 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33996 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33996"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="221011" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/R.A.X" style="position: relative;"> <img src='https://userpic.codeforces.org/122476/avatar/686763c746ac6e7b.jpg'/> </a> <div><a href="/profile/R.A.X" title="Specialist R.A.X" class="rated-user user-cyan">R.A.X</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/06/2015 13:39">9 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-221011" href="?#comment-221011" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="221011" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="122476" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-221011"> <div class="moveup"> <div class="ttypography"><p>can't we solve this problem by following method ? for a given p we can have any q from -b to p/4. Therefore this length can be written as :- f(x) = b + x/4 we can integrate f(x) from 0 to a g(a)-g(0)=b*a-a*a/8 and the total number of ways to choose two numbers will be a*2b so probability is = ( g(a)-g(0) ) / 2ab But this is giving WA <a href="//codeforces.com/contest/77/submission/10611164">code</a></p></div> </div> </div> <div class="reply info"> <a class="comment-221011 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-221011 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-221011"> <li> <div class="comment"> <table class="comment-table" commentId="221052" commentParentId="221011"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/sepehr103" style="position: relative;"> <img src='https://userpic.codeforces.org/143200/avatar/d9c701d045b44793.jpg'/> </a> <div><a href="/profile/sepehr103" title="Expert sepehr103" class="rated-user user-blue">sepehr103</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/06/2015 17:37">9 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-221052" href="?#comment-221052" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-221011" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="221052" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="143200" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-221052"> <div class="moveup"> <div class="ttypography"><p>Yes you can my dear :) if you wait another 4 years, there will be some sort of method named solve, which solves this problem without any code :)</p></div> </div> </div> <div class="reply info"> <a class="comment-221052 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-221052 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-221052"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1779" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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77E
77
E
en
E. Martian Food
<div class="problem-statement"><div class="header"><div class="title">E. Martian Food</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Have you ever tasted Martian food? Well, you should.</p><p>Their signature dish is served on a completely black plate with the radius of <span class="tex-span"><i>R</i></span>, flat as a pancake.</p><p>First, they put a perfectly circular portion of the Golden Honduras on the plate. It has the radius of <span class="tex-span"><i>r</i></span> and is located as close to the edge of the plate as possible staying entirely within the plate. I. e. Golden Honduras touches the edge of the plate from the inside. It is believed that the proximity of the portion of the Golden Honduras to the edge of a plate demonstrates the neatness and exactness of the Martians.</p><p>Then a perfectly round portion of Pink Guadeloupe is put on the plate. The Guadeloupe should not overlap with Honduras, should not go beyond the border of the plate, but should have the maximum radius. I. e. Pink Guadeloupe should touch the edge of the plate from the inside, and touch Golden Honduras from the outside. For it is the size of the Rose Guadeloupe that shows the generosity and the hospitality of the Martians.</p><p>Further, the first portion (of the same perfectly round shape) of Green Bull Terrier is put on the plate. It should come in contact with Honduras and Guadeloupe, should not go beyond the border of the plate and should have maximum radius.</p><p>Each of the following portions of the Green Bull Terrier must necessarily touch the Golden Honduras, the previous portion of the Green Bull Terrier and touch the edge of a plate, but should not go beyond the border.</p><p>To determine whether a stranger is worthy to touch the food, the Martians ask him to find the radius of the <span class="tex-span"><i>k</i></span>-th portion of the Green Bull Terrier knowing the radii of a plate and a portion of the Golden Honduras. And are you worthy?</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains integer <span class="tex-span"><i>t</i></span> (<span class="tex-span">1 ≤ <i>t</i> ≤ 10<sup class="upper-index">4</sup></span>) — amount of testcases.</p><p>Each of the following <span class="tex-span"><i>t</i></span> lines contain three positive integers: the radii of the plate and a portion of the Golden Honduras <span class="tex-span"><i>R</i></span> and <span class="tex-span"><i>r</i></span> (<span class="tex-span">1 ≤ <i>r</i> &lt; <i>R</i> ≤ 10<sup class="upper-index">4</sup></span>) and the number <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>k</i> ≤ 10<sup class="upper-index">4</sup></span>).</p><p>In the pretests <span class="tex-span">1 ≤ <i>k</i> ≤ 2</span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span"><i>t</i></span> lines — the radius of the <span class="tex-span"><i>k</i></span>-th portion of the Green Bull Terrier for each test. The absolute or relative error of the answer should not exceed <span class="tex-span">10<sup class="upper-index"> - 6</sup></span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2<br/>4 3 1<br/>4 2 2<br/></pre></div><div class="output"><div class="title">Output</div><pre>0.9230769231<br/>0.6666666667<br/></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>Dish from the first sample looks like this:</p><p><img class="tex-graphics" src="https://espresso.codeforces.com/e15f6caf257ceae8305cd82507b96dfac1b579ee.png" style="max-width: 100.0%;max-height: 100.0%;"/></p><p>Dish from the second sample looks like this:</p><p><img class="tex-graphics" src="https://espresso.codeforces.com/625a74ccb42332c9df05a22f8e17f81f086476d5.png" style="max-width: 100.0%;max-height: 100.0%;"/></p></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="E" data-uuid="ps_8a13e3a0397b957e013bdc99665a0c73da8ec4ed"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">E. Martian Food</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Have you ever tasted Martian food? Well, you should.</p><p>Their signature dish is served on a completely black plate with the radius of <span class="tex-span"><i>R</i></span>, flat as a pancake.</p><p>First, they put a perfectly circular portion of the Golden Honduras on the plate. It has the radius of <span class="tex-span"><i>r</i></span> and is located as close to the edge of the plate as possible staying entirely within the plate. I. e. Golden Honduras touches the edge of the plate from the inside. It is believed that the proximity of the portion of the Golden Honduras to the edge of a plate demonstrates the neatness and exactness of the Martians.</p><p>Then a perfectly round portion of Pink Guadeloupe is put on the plate. The Guadeloupe should not overlap with Honduras, should not go beyond the border of the plate, but should have the maximum radius. I. e. Pink Guadeloupe should touch the edge of the plate from the inside, and touch Golden Honduras from the outside. For it is the size of the Rose Guadeloupe that shows the generosity and the hospitality of the Martians.</p><p>Further, the first portion (of the same perfectly round shape) of Green Bull Terrier is put on the plate. It should come in contact with Honduras and Guadeloupe, should not go beyond the border of the plate and should have maximum radius.</p><p>Each of the following portions of the Green Bull Terrier must necessarily touch the Golden Honduras, the previous portion of the Green Bull Terrier and touch the edge of a plate, but should not go beyond the border.</p><p>To determine whether a stranger is worthy to touch the food, the Martians ask him to find the radius of the <span class="tex-span"><i>k</i></span>-th portion of the Green Bull Terrier knowing the radii of a plate and a portion of the Golden Honduras. And are you worthy?</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains integer <span class="tex-span"><i>t</i></span> (<span class="tex-span">1 ≤ <i>t</i> ≤ 10<sup class="upper-index">4</sup></span>) — amount of testcases.</p><p>Each of the following <span class="tex-span"><i>t</i></span> lines contain three positive integers: the radii of the plate and a portion of the Golden Honduras <span class="tex-span"><i>R</i></span> and <span class="tex-span"><i>r</i></span> (<span class="tex-span">1 ≤ <i>r</i> &lt; <i>R</i> ≤ 10<sup class="upper-index">4</sup></span>) and the number <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>k</i> ≤ 10<sup class="upper-index">4</sup></span>).</p><p>In the pretests <span class="tex-span">1 ≤ <i>k</i> ≤ 2</span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span"><i>t</i></span> lines — the radius of the <span class="tex-span"><i>k</i></span>-th portion of the Green Bull Terrier for each test. The absolute or relative error of the answer should not exceed <span class="tex-span">10<sup class="upper-index"> - 6</sup></span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2<br />4 3 1<br />4 2 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>0.9230769231<br />0.6666666667<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>Dish from the first sample looks like this:</p><p><img class="tex-graphics" src="https://espresso.codeforces.com/e15f6caf257ceae8305cd82507b96dfac1b579ee.png" style="max-width: 100.0%;max-height: 100.0%;" /></p><p>Dish from the second sample looks like this:</p><p><img class="tex-graphics" src="https://espresso.codeforces.com/625a74ccb42332c9df05a22f8e17f81f086476d5.png" style="max-width: 100.0%;max-height: 100.0%;" /></p></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=E]"); 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["Geometry, computational geometry"]
["geometry", "*2800"]
https://codeforces.com/blog/entry/1769
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It's relation of needed events to all. In this case needed events are all pairs (p,q) where p &gt;= 4q</div><div>All events are all possible pairs (p,q) </div><div>How we can count them?</div><div>All possible pairs is Cartasian product. We can draw it like rectangle.</div><div>Its area - number of all possible pairs.</div><div>Also we need to find area of polygon, where p &gt;= 4q.</div><div>For this let's draw line y=4x and needed set of points is above this line.</div><div>Our answer is relation between this area and area of whole rectangle.</div><div>I think finding areas isn't problem.</div><div>There is one case that I draw on second image, when 4b &lt; a</div><div>There are 2 cases - when a=0 and b=0</div><div>When a=0 we have only left part of image, so answer is 0.5</div><div>When b=0 we have vertical line, so answer is 1.0</div><div>Sorry for some mistakes in English.</div><div><br /></div><div><img src="/predownloaded/68/b4/68b4dc0894eaf043f47f55af361b054a23fa4417.png" style="max-width: 100.0%;max-height: 100.0%;" /><img src="/predownloaded/2b/b0/2bb01cca19ab594d6286fbf8a0ad464f9ed81684.png" style="max-width: 100.0%;max-height: 100.0%;" /><br /></div></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/77" class="notice" style="text-decoration: none;">Codeforces Beta Round 69 (Div. 1 Only)</a> </span> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/80" class="notice" style="text-decoration: none;">Codeforces Beta Round 69 (Div. 2 Only)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-4391-1769").click(function() { var that = this; 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top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33856" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2447" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33856"> <div class="moveup"> <div class="ttypography">GOOD 77B not , <br />Codeforces Beta Round #69 (Div. 1 Only) Problem B<br />Codeforces Beta Round #69 (Div. 2 Only) Problem D<br />this is better :D</div> </div> </div> <div class="reply info"> <a class="comment-33856 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33856 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33856"> <li> <div class="comment"> <table class="comment-table" commentId="33864" commentParentId="33856"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/andryk" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/andryk" title="Pupil andryk" class="rated-user user-green">andryk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/20/2011 00:27">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33864" href="?#comment-33864" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-33856" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33864" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="13728" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33864"> <div class="moveup"> <div class="ttypography">Thanks. Title changed )</div> </div> </div> <div class="reply info"> <a class="comment-33864 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33864 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33864"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="33901" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/Shuaib" style="position: relative;"> <img src='https://userpic.codeforces.org/2929/avatar/963ad42782c05a17.jpg'/> </a> <div><a href="/profile/Shuaib" title="Expert Shuaib" class="rated-user user-blue">Shuaib</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/20/2011 07:02">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33901" href="?#comment-33901" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33901" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="2929" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33901"> <div class="moveup"> <div class="ttypography">Excellent clarification (albeit weak English ;) ). Thanks a tons though.<div><br /></div></div> </div> </div> <div class="reply info"> <a class="comment-33901 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33901 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33901"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="33996" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/mkagenius" style="position: relative;"> <img src='https://userpic.codeforces.org/4476/avatar/b4856becb562e36a.jpg'/> </a> <div><a href="/profile/mkagenius" title="Specialist mkagenius" class="rated-user user-cyan">mkagenius</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/20/2011 20:31">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-33996" href="?#comment-33996" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="33996" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="4476" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-33996"> <div class="moveup"> <div class="ttypography">I solved it differently.<div>It is really interesting to note , people think so differently yet do the same thing.</div><div>Feynman Rocks!</div></div> </div> </div> <div class="reply info"> <a class="comment-33996 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-33996 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-33996"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="221011" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/R.A.X" style="position: relative;"> <img src='https://userpic.codeforces.org/122476/avatar/686763c746ac6e7b.jpg'/> </a> <div><a href="/profile/R.A.X" title="Specialist R.A.X" class="rated-user user-cyan">R.A.X</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/06/2015 13:39">9 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-221011" href="?#comment-221011" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="221011" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="122476" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-221011"> <div class="moveup"> <div class="ttypography"><p>can't we solve this problem by following method ? for a given p we can have any q from -b to p/4. Therefore this length can be written as :- f(x) = b + x/4 we can integrate f(x) from 0 to a g(a)-g(0)=b*a-a*a/8 and the total number of ways to choose two numbers will be a*2b so probability is = ( g(a)-g(0) ) / 2ab But this is giving WA <a href="//codeforces.com/contest/77/submission/10611164">code</a></p></div> </div> </div> <div class="reply info"> <a class="comment-221011 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-221011 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-221011"> <li> <div class="comment"> <table class="comment-table" commentId="221052" commentParentId="221011"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/sepehr103" style="position: relative;"> <img src='https://userpic.codeforces.org/143200/avatar/d9c701d045b44793.jpg'/> </a> <div><a href="/profile/sepehr103" title="Expert sepehr103" class="rated-user user-blue">sepehr103</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/06/2015 17:37">9 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-221052" href="?#comment-221052" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-221011" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="221052" class="CommentVoteFrame" data-commentRating="8" data-commentUserId="143200" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+8</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-221052"> <div class="moveup"> <div class="ttypography"><p>Yes you can my dear :) if you wait another 4 years, there will be some sort of method named solve, which solves this problem without any code :)</p></div> </div> </div> <div class="reply info"> <a class="comment-221052 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-221052 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-221052"> </ul> </div> </li> </ul> </div> <br/> <div id="editBox-1779" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; 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78A
78
A
en
A. Haiku
<div class="problem-statement"><div class="header"><div class="title">A. Haiku</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Haiku is a genre of Japanese traditional poetry.</p><p>A haiku poem consists of 17 syllables split into three phrases, containing 5, 7 and 5 syllables correspondingly (the first phrase should contain exactly 5 syllables, the second phrase should contain exactly 7 syllables, and the third phrase should contain exactly 5 syllables). A haiku masterpiece contains a description of a moment in those three phrases. Every word is important in a small poem, which is why haiku are rich with symbols. Each word has a special meaning, a special role. The main principle of haiku is to say much using a few words.</p><p>To simplify the matter, in the given problem we will consider that the number of syllable in the phrase is equal to the number of vowel letters there. Only the following letters are regarded as vowel letters: "<span class="tex-font-style-tt">a</span>", "<span class="tex-font-style-tt">e</span>", "<span class="tex-font-style-tt">i</span>", "<span class="tex-font-style-tt">o</span>" and "<span class="tex-font-style-tt">u</span>".</p><p>Three phases from a certain poem are given. Determine whether it is haiku or not.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The input data consists of three lines. The length of each line is between <span class="tex-span">1</span> and <span class="tex-span">100</span>, inclusive. The <span class="tex-span"><i>i</i></span>-th line contains the <span class="tex-span"><i>i</i></span>-th phrase of the poem. Each phrase consists of one or more words, which are separated by one or more spaces. A word is a non-empty sequence of lowercase Latin letters. Leading and/or trailing spaces in phrases are allowed. Every phrase has at least one non-space character. See the example for clarification.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print "<span class="tex-font-style-tt">YES</span>" (without the quotes) if the poem is a haiku. Otherwise, print "<span class="tex-font-style-tt">NO</span>" (also without the quotes).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>on codeforces <br/>beta round is running<br/> a rustling of keys <br/></pre></div><div class="output"><div class="title">Output</div><pre>YES</pre></div><div class="input"><div class="title">Input</div><pre>how many gallons<br/>of edo s rain did you drink<br/> cuckoo<br/></pre></div><div class="output"><div class="title">Output</div><pre>NO</pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="A" data-uuid="ps_9e9fe846e921b4b34a99dfb93e583011008bb5c4"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">A. Haiku</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Haiku is a genre of Japanese traditional poetry.</p><p>A haiku poem consists of 17 syllables split into three phrases, containing 5, 7 and 5 syllables correspondingly (the first phrase should contain exactly 5 syllables, the second phrase should contain exactly 7 syllables, and the third phrase should contain exactly 5 syllables). A haiku masterpiece contains a description of a moment in those three phrases. Every word is important in a small poem, which is why haiku are rich with symbols. Each word has a special meaning, a special role. The main principle of haiku is to say much using a few words.</p><p>To simplify the matter, in the given problem we will consider that the number of syllable in the phrase is equal to the number of vowel letters there. Only the following letters are regarded as vowel letters: &quot;<span class="tex-font-style-tt">a</span>&quot;, &quot;<span class="tex-font-style-tt">e</span>&quot;, &quot;<span class="tex-font-style-tt">i</span>&quot;, &quot;<span class="tex-font-style-tt">o</span>&quot; and &quot;<span class="tex-font-style-tt">u</span>&quot;.</p><p>Three phases from a certain poem are given. Determine whether it is haiku or not.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The input data consists of three lines. The length of each line is between <span class="tex-span">1</span> and <span class="tex-span">100</span>, inclusive. The <span class="tex-span"><i>i</i></span>-th line contains the <span class="tex-span"><i>i</i></span>-th phrase of the poem. Each phrase consists of one or more words, which are separated by one or more spaces. A word is a non-empty sequence of lowercase Latin letters. Leading and/or trailing spaces in phrases are allowed. Every phrase has at least one non-space character. See the example for clarification.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print &quot;<span class="tex-font-style-tt">YES</span>&quot; (without the quotes) if the poem is a haiku. 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["Implementation problems, programming technics, simulation", "Prefix- and Z-functions, suffix structures, Knuth\u2013Morris\u2013Pratt algorithm, etc"]
["implementation", "strings", "*800"]
https://codeforces.com/blog/entry/1812
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<a href="/blog/entry/120644">Codeforces Round 899 (Div. 2)</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/Misa-Misa" title="Expert Misa-Misa" class="rated-user user-blue">Misa-Misa</a> &rarr; <a href="/blog/entry/121157">Someone please help me understand this.</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> <li><div style="font-size:0.9em;padding:0.5em 0;"> <a href="/profile/shivam565" title="Specialist shivam565" class="rated-user user-cyan">shivam565</a> &rarr; <a href="/blog/entry/108348">Total number of subarrays with sum atmost k</a> &nbsp;&nbsp;<img alt="New comment(s)" title="New comment(s)" src="//codeforces.org/s/81027/images/icons/comment-12x12.png" style="vertical-align:middle;"/> </div> </li> </ul> </div> <div class="bottom-links"> <table style="width:100%;"> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:right;"> <a href="/recent-actions">Detailed &rarr;</a> </td> </tr> </tbody> </table> </div> </div> </div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li><a href="/profile/Ripatti">Ripatti</a></li> <li class="current selectedLava"><a href="/blog/Ripatti">Blog</a></li> <li><a href="/teams/with/Ripatti">Teams</a></li> <li><a href="/submissions/Ripatti">Submissions</a></li> <li><a href="/groups/with/Ripatti">Groups</a></li> <li><a href="/contests/with/Ripatti">Contests</a></li> <li><a href="/contests/writer/Ripatti">Problemsetting</a></li> </ul> </div> <div style="margin-top:0;"> <div> <h3><a href="/blog/Ripatti" style="text-decoration:none;color:black !important;">Ripatti's blog</a></h3> </div> <div style="margin-top:2em;"> <div class="has-topic-id topic" topicId="1812"> <div class="title"> <a href="/blog/entry/1812"> Solutions for Codeforces Beta Round #70 (Div. 2) </a> </div> <div class="info" style="position:relative;"> By&nbsp;<a href="/profile/Ripatti" title="Master Ripatti" class="rated-user user-orange">Ripatti</a>, <span class="format-humantime" title="Apr/27/2011 21:34">12 years ago</span>, translation, <img style="position: relative;top: 5px;" src="//codeforces.org/s/81027/images/flags/24/gb.png" alt="In English" title="In English"/> <span style="position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;"> <div style="margin-top:0.25em;"> </div> </span> </div> <div class="content"> <div class="ttypography"><p><b>A.</b> You should count a number of vowels for every of three phrases. Next, you should compare this numbers with numbers 5, 7 and 5. If all is <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">matched, answer is YES, otherwise answer is NO.</span></span><br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Ripatti" title="Майор Ripatti">Ripatti</a>.<br /> <br /><br /><b>B.</b> At first, you can <span class="tex-span">[<i>n</i> / 7]</span> times output string &quot;ROYGBIV&quot; (<span class="tex-span">[]</span> is a rounding down). After than you can output &quot;&quot;, &quot;G&quot;, &quot;GB&quot;, &quot;YGB&quot;, &quot;YGBI&quot;, &quot;OYGBI&quot; or &quot;OYGBIV&quot; according to remainder of division <span class="tex-span"><i>n</i></span> by 7. A resulting string will satisfy problem's <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">requirement</span></span>s.<br /><br />You can also build answer in other way.<br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Ripatti" title="Майор Ripatti">Ripatti</a>.<br /><br /><br /><b>C.</b> If <span class="tex-span"><i>n</i></span> is even, Marsel wins - he just <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">symmetrically</span></span> repeats moves of Timur.<br /><br />Now <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">consider</span></span> a case of odd <span class="tex-span"><i>n</i></span>. If Timur cannot move - he is losing automatically. If he can do a move, he always can split one log into few parts that this parts cannot be splitted again. It can be done if we have find minimal <span class="tex-span"><i>t</i></span> that <span class="tex-span"><i>k</i> ≤ <i>t</i> &lt; <i>m</i></span> and <span class="tex-span"><i>t</i>|<i>m</i></span>. Next we split log into parts with length <span class="tex-span"><i>t</i></span>. Thereafter Timur <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">symmetrically</span></span> repeats moves of Marsel and wins.<br /><br />For checking that Timur could move or not, you can iterate over all divisors of <span class="tex-span"><i>m</i></span>. If there is exists some divisor <span class="tex-span"><i>t</i></span> that <span class="tex-span"><i>k</i> ≤ <i>t</i> &lt; <i>m</i></span>, Timar can do a move. Chech of all divisors can be done in <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/57a7a3f5b8d1b2dbfe8e5c99d75603ca680ed752.png" style="max-width: 100.0%;max-height: 100.0%;" /> time.<br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Lepetrandr" title="Майор Lepetrandr">Lepetrandr</a>.<br /><br /><br /><b>D.</b> It should be solved like a classical problem &quot;count the  number of square cells 1x1 lying inside the circle&quot;. Firstly, lets find the highest hexagon that lies inside the circle. Then we move to the right and up from this hexagon, and then go down until we find hexagon lying inside the circle. Repeat this process until you reach the rightmost part of the circle.<br /><br />Thus we can count number of hexagons in each column, answer is sum of this numbers. Total number of operations is <span class="tex-span"><i>O</i>(<i>n</i>)</span>.<br /><br />Few words about implementation. Coordinates of every considered point looks like <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5f82590fa40eaa083356a550a808418b9148fa88.png" style="max-width: 100.0%;max-height: 100.0%;" />. That's why distance between this points and (0,0) should be calculated using integers only. For example, criteria &quot;point <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5f82590fa40eaa083356a550a808418b9148fa88.png" style="max-width: 100.0%;max-height: 100.0%;" /> lies inside circle of radius <span class="tex-span"><i>R</i></span>&quot; looks like <span class="tex-span"><i>x</i><sup class="upper-index">2</sup> + 3<i>y</i><sup class="upper-index">2</sup> ≤ 4<i>R</i><sup class="upper-index">2</sup></span>.<br /><br />Also you can solve this problem in <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/4b2fa1e3d3d43bd9f28ff6c3140f816dc0e0621a.png" style="max-width: 100.0%;max-height: 100.0%;" />. For every column of hexagons you can find number of hexagons inside circle by using binary search.<br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Ripatti" title="Майор Ripatti">Ripatti</a>.<br /><br /><br /><b>E.</b> Firstly, let's calculate the following value:<br />dp[t][x0][y0][x][y] == true iff scientist from block (x0,y0) can reach block (x,y) in time t, considering toxic coolant.<br /><br />Secondly, let's consider a graph consisting of 4 parts:<br />1 - source (one vertex)<br />2 - first fraction (nxn vertices)<br />3 - second fraction (nxn vertices)<br />4 - sink (one vertex)<br />Each vertex of each fraction is for one block. Build edge from source to each vertex of the first fraction with capability as number of scientists in corresponding block. Build edge from each vertex of the second fraction to sink with capability as number of rescue capsules in corresponding block. Build edge from vertex (x0,y0) of the first fraction  to vertex (x,y) of the second fraction iff dp[T][x0][y0][x][y]==true for at least one T. Capability of this edges is infinity.<br /><br />As one can see, value of maxflow in this graph is answer for the problem.<br /><br />Complexity of this solution is <span class="tex-span"><i>O</i>(<i>tn</i><sup class="upper-index">4</sup> + <i>kn</i><sup class="upper-index">6</sup>)</span>, where <span class="tex-span"><i>k</i></span> is maximum possible number of scientists in each block(in this problem <span class="tex-span"><i>k</i> = 9</span>).<br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Ripatti" title="Майор Ripatti">Ripatti</a>.</p></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/78" class="notice" style="text-decoration: none;">Codeforces Beta Round 70 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-440-1812").click(function() { var that = this; 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line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/Ripatti"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/Ripatti"> Ripatti </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Apr/27/2011 21:34">12 years ago</span> </li> <li> <a href="/blog/entry/1812#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1812#comments"> 16 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1822"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (15)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="34769" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/lijunle" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/lijunle" title="Expert lijunle" class="rated-user user-blue">lijunle</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/27/2011 22:19">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34769" href="?#comment-34769" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34769" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3498" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34769"> <div class="moveup"> <div class="ttypography">where is the english version?</div> </div> </div> <div class="reply info"> <a class="comment-34769 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34769 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34769"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="34798" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/philolo1" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/philolo1" title="Expert philolo1" class="rated-user user-blue">philolo1</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/27/2011 23:50">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34798" href="?#comment-34798" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34798" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34798" class="CommentVoteFrame" data-commentRating="14" data-commentUserId="5296" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+14</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34798"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">For problem B it is also possible to use a randomiszed algorithm<br /><br />do<br />{<br />    randomsolution=randomCalc();<br /><br />}while(!isValid(randomsolution));</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34798 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34798 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34798"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="34824" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/khanhptnk" style="position: relative;"> <img src='https://userpic.codeforces.org/825/avatar/782b10196222b19a.jpg'/> </a> <div><a href="/profile/khanhptnk" title="Pupil khanhptnk" class="rated-user user-green">khanhptnk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 06:16">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34824" href="?#comment-34824" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34824" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="825" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34824"> <div class="moveup"> <div class="ttypography">Please fix typing e</div> </div> </div> <div class="reply info"> <a class="comment-34824 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34824 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34824"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="34825" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/CosmoRied" style="position: relative;"> <img src='https://userpic.codeforces.org/1587/avatar/81ab1025994d02ad.jpg'/> </a> <div><a href="/profile/CosmoRied" title="Newbie CosmoRied" class="rated-user user-gray">CosmoRied</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 06:25">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34825" href="?#comment-34825" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34825" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1587" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34825"> <div class="moveup"> <div class="ttypography"><div>Please elaborate on problem D, i found that counting hexagons easy initially, but as N gets bigger, my answer fails. I think I misunderstood the question even after reading it several times... For example, I don't completely understand this clarification: <span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> Then we move to the right and up from this hexagon, and then go down until we find hexagon lying inside the circle. Repeat this process until you reach the rightmost part of the circle.</span><br /></div></div> </div> </div> <div class="reply info"> <a class="comment-34825 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34825 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34825"> <li> <div class="comment"> <table class="comment-table" commentId="34842" commentParentId="34825"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/-dp-" style="position: relative;"> <img src='https://userpic.codeforces.org/11821/avatar/a4cdea736f51eae5.jpg'/> </a> <div><a href="/profile/-dp-" title="Expert -dp-" class="rated-user user-blue">-dp-</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 14:12">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34842" href="?#comment-34842" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34825" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34842" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34842" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="11821" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34842"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><img src="/predownloaded/8d/73/8d735c490afae2da710bde22bc2230729f8c22ee.png" style="max-width: 100.0%;max-height: 100.0%;" /><br /></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34842 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34842 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34842"> <li> <div class="comment"> <table class="comment-table" commentId="34846" commentParentId="34842"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 15:26">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34846" href="?#comment-34846" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34842" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34846" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34846" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34846"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">I have TLE on Java with this solution. Does it actually fits to time?</div><div class="from-renderer"><img src="/predownloaded/0c/3d/0c3d1187036bc67e800887cf7eea5c3275f9f91e.png" style="max-width: 100.0%;max-height: 100.0%;" /><br /></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34846 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34846 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34846"> <li> <div class="comment"> <table class="comment-table" commentId="34848" commentParentId="34846"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/CosmoRied" style="position: relative;"> <img src='https://userpic.codeforces.org/1587/avatar/81ab1025994d02ad.jpg'/> </a> <div><a href="/profile/CosmoRied" title="Newbie CosmoRied" class="rated-user user-gray">CosmoRied</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 16:15">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34848" href="?#comment-34848" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34846" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34848" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34848" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1587" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34848"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"></div></div> </div> </div> <div class="reply info"> <a class="comment-34848 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34848 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34848"> <li> <div class="comment"> <table class="comment-table" commentId="34849" commentParentId="34848"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/CosmoRied" style="position: relative;"> <img src='https://userpic.codeforces.org/1587/avatar/81ab1025994d02ad.jpg'/> </a> <div><a href="/profile/CosmoRied" title="Newbie CosmoRied" class="rated-user user-gray">CosmoRied</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 16:24">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34849" href="?#comment-34849" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34848" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34849" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1587" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34849"> <div class="moveup"> <div class="ttypography">? Why didn't it post? Can you tell me how to get (x, y) co-ordinate as the board is hexagonal? </div> </div> </div> <div class="reply info"> <a class="comment-34849 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34849 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34849"> <li> <div class="comment"> <table class="comment-table" commentId="34853" commentParentId="34849"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:13">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34853" href="?#comment-34853" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34849" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34853" revisionCount="3" revision="3"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">3</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34853" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34853"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><div><br /></div></div> </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34853 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34853 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34853"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="34854" commentParentId="34846"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/-dp-" style="position: relative;"> <img src='https://userpic.codeforces.org/11821/avatar/a4cdea736f51eae5.jpg'/> </a> <div><a href="/profile/-dp-" title="Expert -dp-" class="rated-user user-blue">-dp-</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:16">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34854" href="?#comment-34854" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34846" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34854" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34854" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="11821" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34854"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">I think you didn't get the main idea. I've updated my picture, hope it's more clear now. We do not need to check white hexagons, only red and green ones. So, total number of hexagons we need to check is O(R). This solution easily fits to time even on Python, and on C++ it works 60ms.</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34854 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34854 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34854"> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="34855" commentParentId="34842"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:22">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34855" href="?#comment-34855" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34842" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34855" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34855"> <div class="moveup"> <div class="ttypography">Thanks for editing. But what next? We got some hexagons, but still can not say how many hexagons <b>inside</b> this quarter of circle. Just border hexagons. What I missunderstood?</div> </div> </div> <div class="reply info"> <a class="comment-34855 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34855 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34855"> <li> <div class="comment"> <table class="comment-table" commentId="34856" commentParentId="34855"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/riadwaw" style="position: relative;"> <img src='https://userpic.codeforces.org/8452/avatar/7b374574b05a50df.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/riadwaw" title="International Master riadwaw" class="rated-user user-orange">riadwaw</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:32">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34856" href="?#comment-34856" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34855" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34856" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="8452" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34856"> <div class="moveup"> <div class="ttypography">We  choose highest hexagon in every column.<div>So, we can calculate it's count</div><div>(all from highest downto - highest)in every column<br /></div></div> </div> </div> <div class="reply info"> <a class="comment-34856 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34856 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34856"> <li> <div class="comment"> <table class="comment-table" commentId="34857" commentParentId="34856"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:33">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34857" href="?#comment-34857" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34856" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34857" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34857"> <div class="moveup"> <div class="ttypography">oh. so easy. Thanks! :)</div> </div> </div> <div class="reply info"> <a class="comment-34857 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34857 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34857"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="34847" commentParentId="34825"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 15:39">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34847" href="?#comment-34847" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34825" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34847" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34847"> <div class="moveup"> <div class="ttypography">try to check precision.<div>You can write smthng like </div><div><div>double d1 =  Math.sqrt(x1 * x1 + y1 * y1);</div><div>if (d1 &gt; R &amp;&amp;  d1 - R &gt; 1e-6) return false;</div></div></div> </div> </div> <div class="reply info"> <a class="comment-34847 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34847 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34847"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="133979" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/fastholf" style="position: relative;"> <img src='https://userpic.codeforces.org/15935/avatar/c2afbb3d3535dfac.jpg'/> </a> <div><a href="/profile/fastholf" title="Expert fastholf" class="rated-user user-blue">fastholf</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/19/2013 13:22">10 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-133979" href="?#comment-133979" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="133979" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="15935" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-133979"> <div class="moveup"> <div class="ttypography"><p>For task B</p> <pre><code>res[0] = 'R'; res[1] = 'O'; res[2] = 'Y'; res[3] = 'G'; res[4] = 'B'; res[5] = 'I'; res[6] = 'V'; int n; cin &gt;&gt; n; for (int i = 7; i &lt; n; ++i) { res[i] = res[i - 4]; } </code></pre><p>works as well.</p></div> </div> </div> <div class="reply info"> <a class="comment-133979 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-133979 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-133979"> </ul> </div> <br/> <div id="editBox-1822" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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78B
78
B
en
B. Easter Eggs
<div class="problem-statement"><div class="header"><div class="title">B. Easter Eggs</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>The Easter Rabbit laid <span class="tex-span"><i>n</i></span> eggs in a circle and is about to paint them. </p><p>Each egg should be painted one color out of 7: red, orange, yellow, green, blue, indigo or violet. Also, the following conditions should be satisfied:</p><ul> <li> Each of the seven colors should be used to paint at least one egg. </li><li> Any four eggs <span class="tex-font-style-bf">lying sequentially</span> should be painted different colors. </li></ul><p>Help the Easter Rabbit paint the eggs in the required manner. We know that it is always possible.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The only line contains an integer <span class="tex-span"><i>n</i></span> — the amount of eggs (<span class="tex-span">7 ≤ <i>n</i> ≤ 100</span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print one line consisting of <span class="tex-span"><i>n</i></span> characters. The <span class="tex-span"><i>i</i></span>-th character should describe the color of the <span class="tex-span"><i>i</i></span>-th egg in the order they lie in the circle. The colors should be represented as follows: "<span class="tex-font-style-tt">R</span>" stands for red, "<span class="tex-font-style-tt">O</span>" stands for orange, "<span class="tex-font-style-tt">Y</span>" stands for yellow, "<span class="tex-font-style-tt">G</span>" stands for green, "<span class="tex-font-style-tt">B</span>" stands for blue, "<span class="tex-font-style-tt">I</span>" stands for indigo, "<span class="tex-font-style-tt">V</span>" stands for violet.</p><p>If there are several answers, print any of them.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>8<br/></pre></div><div class="output"><div class="title">Output</div><pre>ROYGRBIV<br/></pre></div><div class="input"><div class="title">Input</div><pre>13<br/></pre></div><div class="output"><div class="title">Output</div><pre>ROYGBIVGBIVYG<br/></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>The way the eggs will be painted in the first sample is shown on the picture: </p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/32fa33fe3fe2d501ac2b4aee881df9a52a892868.png" style="max-width: 100.0%;max-height: 100.0%;"/> </center></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="B" data-uuid="ps_fa9d42e6c016c3ea40052ea5974d3479850cf615"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">B. Easter Eggs</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>The Easter Rabbit laid <span class="tex-span"><i>n</i></span> eggs in a circle and is about to paint them. </p><p>Each egg should be painted one color out of 7: red, orange, yellow, green, blue, indigo or violet. Also, the following conditions should be satisfied:</p><ul> <li> Each of the seven colors should be used to paint at least one egg. </li><li> Any four eggs <span class="tex-font-style-bf">lying sequentially</span> should be painted different colors. </li></ul><p>Help the Easter Rabbit paint the eggs in the required manner. We know that it is always possible.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The only line contains an integer <span class="tex-span"><i>n</i></span> — the amount of eggs (<span class="tex-span">7 ≤ <i>n</i> ≤ 100</span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print one line consisting of <span class="tex-span"><i>n</i></span> characters. The <span class="tex-span"><i>i</i></span>-th character should describe the color of the <span class="tex-span"><i>i</i></span>-th egg in the order they lie in the circle. The colors should be represented as follows: &quot;<span class="tex-font-style-tt">R</span>&quot; stands for red, &quot;<span class="tex-font-style-tt">O</span>&quot; stands for orange, &quot;<span class="tex-font-style-tt">Y</span>&quot; stands for yellow, &quot;<span class="tex-font-style-tt">G</span>&quot; stands for green, &quot;<span class="tex-font-style-tt">B</span>&quot; stands for blue, &quot;<span class="tex-font-style-tt">I</span>&quot; stands for indigo, &quot;<span class="tex-font-style-tt">V</span>&quot; stands for violet.</p><p>If there are several answers, print any of them.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>8<br /></pre></div><div class="output"><div class="title">Output</div><pre>ROYGRBIV<br /></pre></div><div class="input"><div class="title">Input</div><pre>13<br /></pre></div><div class="output"><div class="title">Output</div><pre>ROYGBIVGBIVYG<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>The way the eggs will be painted in the first sample is shown on the picture: </p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/32fa33fe3fe2d501ac2b4aee881df9a52a892868.png" style="max-width: 100.0%;max-height: 100.0%;" /> </center></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=B]"); 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["Constructive algorithms", "Implementation problems, programming technics, simulation"]
["constructive algorithms", "implementation", "*1200"]
https://codeforces.com/blog/entry/1812
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Next, you should compare this numbers with numbers 5, 7 and 5. If all is <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">matched, answer is YES, otherwise answer is NO.</span></span><br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Ripatti" title="Майор Ripatti">Ripatti</a>.<br /> <br /><br /><b>B.</b> At first, you can <span class="tex-span">[<i>n</i> / 7]</span> times output string &quot;ROYGBIV&quot; (<span class="tex-span">[]</span> is a rounding down). After than you can output &quot;&quot;, &quot;G&quot;, &quot;GB&quot;, &quot;YGB&quot;, &quot;YGBI&quot;, &quot;OYGBI&quot; or &quot;OYGBIV&quot; according to remainder of division <span class="tex-span"><i>n</i></span> by 7. A resulting string will satisfy problem's <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">requirement</span></span>s.<br /><br />You can also build answer in other way.<br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Ripatti" title="Майор Ripatti">Ripatti</a>.<br /><br /><br /><b>C.</b> If <span class="tex-span"><i>n</i></span> is even, Marsel wins - he just <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">symmetrically</span></span> repeats moves of Timur.<br /><br />Now <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">consider</span></span> a case of odd <span class="tex-span"><i>n</i></span>. If Timur cannot move - he is losing automatically. If he can do a move, he always can split one log into few parts that this parts cannot be splitted again. It can be done if we have find minimal <span class="tex-span"><i>t</i></span> that <span class="tex-span"><i>k</i> ≤ <i>t</i> &lt; <i>m</i></span> and <span class="tex-span"><i>t</i>|<i>m</i></span>. Next we split log into parts with length <span class="tex-span"><i>t</i></span>. Thereafter Timur <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">symmetrically</span></span> repeats moves of Marsel and wins.<br /><br />For checking that Timur could move or not, you can iterate over all divisors of <span class="tex-span"><i>m</i></span>. If there is exists some divisor <span class="tex-span"><i>t</i></span> that <span class="tex-span"><i>k</i> ≤ <i>t</i> &lt; <i>m</i></span>, Timar can do a move. Chech of all divisors can be done in <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/57a7a3f5b8d1b2dbfe8e5c99d75603ca680ed752.png" style="max-width: 100.0%;max-height: 100.0%;" /> time.<br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Lepetrandr" title="Майор Lepetrandr">Lepetrandr</a>.<br /><br /><br /><b>D.</b> It should be solved like a classical problem &quot;count the  number of square cells 1x1 lying inside the circle&quot;. Firstly, lets find the highest hexagon that lies inside the circle. Then we move to the right and up from this hexagon, and then go down until we find hexagon lying inside the circle. Repeat this process until you reach the rightmost part of the circle.<br /><br />Thus we can count number of hexagons in each column, answer is sum of this numbers. Total number of operations is <span class="tex-span"><i>O</i>(<i>n</i>)</span>.<br /><br />Few words about implementation. Coordinates of every considered point looks like <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5f82590fa40eaa083356a550a808418b9148fa88.png" style="max-width: 100.0%;max-height: 100.0%;" />. That's why distance between this points and (0,0) should be calculated using integers only. For example, criteria &quot;point <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5f82590fa40eaa083356a550a808418b9148fa88.png" style="max-width: 100.0%;max-height: 100.0%;" /> lies inside circle of radius <span class="tex-span"><i>R</i></span>&quot; looks like <span class="tex-span"><i>x</i><sup class="upper-index">2</sup> + 3<i>y</i><sup class="upper-index">2</sup> ≤ 4<i>R</i><sup class="upper-index">2</sup></span>.<br /><br />Also you can solve this problem in <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/4b2fa1e3d3d43bd9f28ff6c3140f816dc0e0621a.png" style="max-width: 100.0%;max-height: 100.0%;" />. For every column of hexagons you can find number of hexagons inside circle by using binary search.<br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Ripatti" title="Майор Ripatti">Ripatti</a>.<br /><br /><br /><b>E.</b> Firstly, let's calculate the following value:<br />dp[t][x0][y0][x][y] == true iff scientist from block (x0,y0) can reach block (x,y) in time t, considering toxic coolant.<br /><br />Secondly, let's consider a graph consisting of 4 parts:<br />1 - source (one vertex)<br />2 - first fraction (nxn vertices)<br />3 - second fraction (nxn vertices)<br />4 - sink (one vertex)<br />Each vertex of each fraction is for one block. Build edge from source to each vertex of the first fraction with capability as number of scientists in corresponding block. Build edge from each vertex of the second fraction to sink with capability as number of rescue capsules in corresponding block. Build edge from vertex (x0,y0) of the first fraction  to vertex (x,y) of the second fraction iff dp[T][x0][y0][x][y]==true for at least one T. Capability of this edges is infinity.<br /><br />As one can see, value of maxflow in this graph is answer for the problem.<br /><br />Complexity of this solution is <span class="tex-span"><i>O</i>(<i>tn</i><sup class="upper-index">4</sup> + <i>kn</i><sup class="upper-index">6</sup>)</span>, where <span class="tex-span"><i>k</i></span> is maximum possible number of scientists in each block(in this problem <span class="tex-span"><i>k</i> = 9</span>).<br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Ripatti" title="Майор Ripatti">Ripatti</a>.</p></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/78" class="notice" style="text-decoration: none;">Codeforces Beta Round 70 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-440-1812").click(function() { var that = this; 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line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/Ripatti"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/Ripatti"> Ripatti </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Apr/27/2011 21:34">12 years ago</span> </li> <li> <a href="/blog/entry/1812#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1812#comments"> 16 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1822"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (15)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="34769" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/lijunle" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/lijunle" title="Expert lijunle" class="rated-user user-blue">lijunle</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/27/2011 22:19">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34769" href="?#comment-34769" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34769" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3498" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34769"> <div class="moveup"> <div class="ttypography">where is the english version?</div> </div> </div> <div class="reply info"> <a class="comment-34769 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34769 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34769"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="34798" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/philolo1" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/philolo1" title="Expert philolo1" class="rated-user user-blue">philolo1</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/27/2011 23:50">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34798" href="?#comment-34798" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34798" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34798" class="CommentVoteFrame" data-commentRating="14" data-commentUserId="5296" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+14</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34798"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">For problem B it is also possible to use a randomiszed algorithm<br /><br />do<br />{<br />    randomsolution=randomCalc();<br /><br />}while(!isValid(randomsolution));</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34798 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34798 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34798"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="34824" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/khanhptnk" style="position: relative;"> <img src='https://userpic.codeforces.org/825/avatar/782b10196222b19a.jpg'/> </a> <div><a href="/profile/khanhptnk" title="Pupil khanhptnk" class="rated-user user-green">khanhptnk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 06:16">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34824" href="?#comment-34824" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34824" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="825" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34824"> <div class="moveup"> <div class="ttypography">Please fix typing e</div> </div> </div> <div class="reply info"> <a class="comment-34824 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34824 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34824"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="34825" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/CosmoRied" style="position: relative;"> <img src='https://userpic.codeforces.org/1587/avatar/81ab1025994d02ad.jpg'/> </a> <div><a href="/profile/CosmoRied" title="Newbie CosmoRied" class="rated-user user-gray">CosmoRied</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 06:25">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34825" href="?#comment-34825" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34825" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1587" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34825"> <div class="moveup"> <div class="ttypography"><div>Please elaborate on problem D, i found that counting hexagons easy initially, but as N gets bigger, my answer fails. I think I misunderstood the question even after reading it several times... For example, I don't completely understand this clarification: <span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> Then we move to the right and up from this hexagon, and then go down until we find hexagon lying inside the circle. Repeat this process until you reach the rightmost part of the circle.</span><br /></div></div> </div> </div> <div class="reply info"> <a class="comment-34825 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34825 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34825"> <li> <div class="comment"> <table class="comment-table" commentId="34842" commentParentId="34825"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/-dp-" style="position: relative;"> <img src='https://userpic.codeforces.org/11821/avatar/a4cdea736f51eae5.jpg'/> </a> <div><a href="/profile/-dp-" title="Expert -dp-" class="rated-user user-blue">-dp-</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 14:12">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34842" href="?#comment-34842" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34825" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34842" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34842" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="11821" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34842"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><img src="/predownloaded/8d/73/8d735c490afae2da710bde22bc2230729f8c22ee.png" style="max-width: 100.0%;max-height: 100.0%;" /><br /></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34842 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34842 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34842"> <li> <div class="comment"> <table class="comment-table" commentId="34846" commentParentId="34842"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 15:26">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34846" href="?#comment-34846" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34842" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34846" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34846" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34846"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">I have TLE on Java with this solution. Does it actually fits to time?</div><div class="from-renderer"><img src="/predownloaded/0c/3d/0c3d1187036bc67e800887cf7eea5c3275f9f91e.png" style="max-width: 100.0%;max-height: 100.0%;" /><br /></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34846 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34846 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34846"> <li> <div class="comment"> <table class="comment-table" commentId="34848" commentParentId="34846"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/CosmoRied" style="position: relative;"> <img src='https://userpic.codeforces.org/1587/avatar/81ab1025994d02ad.jpg'/> </a> <div><a href="/profile/CosmoRied" title="Newbie CosmoRied" class="rated-user user-gray">CosmoRied</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 16:15">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34848" href="?#comment-34848" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34846" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34848" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34848" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1587" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34848"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"></div></div> </div> </div> <div class="reply info"> <a class="comment-34848 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34848 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34848"> <li> <div class="comment"> <table class="comment-table" commentId="34849" commentParentId="34848"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/CosmoRied" style="position: relative;"> <img src='https://userpic.codeforces.org/1587/avatar/81ab1025994d02ad.jpg'/> </a> <div><a href="/profile/CosmoRied" title="Newbie CosmoRied" class="rated-user user-gray">CosmoRied</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 16:24">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34849" href="?#comment-34849" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34848" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34849" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1587" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34849"> <div class="moveup"> <div class="ttypography">? Why didn't it post? Can you tell me how to get (x, y) co-ordinate as the board is hexagonal? </div> </div> </div> <div class="reply info"> <a class="comment-34849 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34849 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34849"> <li> <div class="comment"> <table class="comment-table" commentId="34853" commentParentId="34849"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:13">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34853" href="?#comment-34853" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34849" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34853" revisionCount="3" revision="3"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">3</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34853" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34853"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><div><br /></div></div> </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34853 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34853 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34853"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="34854" commentParentId="34846"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/-dp-" style="position: relative;"> <img src='https://userpic.codeforces.org/11821/avatar/a4cdea736f51eae5.jpg'/> </a> <div><a href="/profile/-dp-" title="Expert -dp-" class="rated-user user-blue">-dp-</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:16">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34854" href="?#comment-34854" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34846" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34854" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34854" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="11821" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34854"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">I think you didn't get the main idea. I've updated my picture, hope it's more clear now. We do not need to check white hexagons, only red and green ones. So, total number of hexagons we need to check is O(R). This solution easily fits to time even on Python, and on C++ it works 60ms.</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34854 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34854 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34854"> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="34855" commentParentId="34842"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:22">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34855" href="?#comment-34855" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34842" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34855" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34855"> <div class="moveup"> <div class="ttypography">Thanks for editing. But what next? We got some hexagons, but still can not say how many hexagons <b>inside</b> this quarter of circle. Just border hexagons. What I missunderstood?</div> </div> </div> <div class="reply info"> <a class="comment-34855 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34855 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34855"> <li> <div class="comment"> <table class="comment-table" commentId="34856" commentParentId="34855"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/riadwaw" style="position: relative;"> <img src='https://userpic.codeforces.org/8452/avatar/7b374574b05a50df.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/riadwaw" title="International Master riadwaw" class="rated-user user-orange">riadwaw</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:32">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34856" href="?#comment-34856" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34855" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34856" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="8452" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34856"> <div class="moveup"> <div class="ttypography">We  choose highest hexagon in every column.<div>So, we can calculate it's count</div><div>(all from highest downto - highest)in every column<br /></div></div> </div> </div> <div class="reply info"> <a class="comment-34856 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34856 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34856"> <li> <div class="comment"> <table class="comment-table" commentId="34857" commentParentId="34856"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:33">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34857" href="?#comment-34857" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34856" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34857" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34857"> <div class="moveup"> <div class="ttypography">oh. so easy. Thanks! :)</div> </div> </div> <div class="reply info"> <a class="comment-34857 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34857 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34857"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="34847" commentParentId="34825"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 15:39">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34847" href="?#comment-34847" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34825" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34847" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34847"> <div class="moveup"> <div class="ttypography">try to check precision.<div>You can write smthng like </div><div><div>double d1 =  Math.sqrt(x1 * x1 + y1 * y1);</div><div>if (d1 &gt; R &amp;&amp;  d1 - R &gt; 1e-6) return false;</div></div></div> </div> </div> <div class="reply info"> <a class="comment-34847 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34847 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34847"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="133979" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/fastholf" style="position: relative;"> <img src='https://userpic.codeforces.org/15935/avatar/c2afbb3d3535dfac.jpg'/> </a> <div><a href="/profile/fastholf" title="Expert fastholf" class="rated-user user-blue">fastholf</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/19/2013 13:22">10 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-133979" href="?#comment-133979" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="133979" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="15935" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-133979"> <div class="moveup"> <div class="ttypography"><p>For task B</p> <pre><code>res[0] = 'R'; res[1] = 'O'; res[2] = 'Y'; res[3] = 'G'; res[4] = 'B'; res[5] = 'I'; res[6] = 'V'; int n; cin &gt;&gt; n; for (int i = 7; i &lt; n; ++i) { res[i] = res[i - 4]; } </code></pre><p>works as well.</p></div> </div> </div> <div class="reply info"> <a class="comment-133979 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-133979 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-133979"> </ul> </div> <br/> <div id="editBox-1822" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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78C
78
C
en
C. Beaver Game
<div class="problem-statement"><div class="header"><div class="title">C. Beaver Game</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Two beavers, Timur and Marsel, play the following game.</p><p>There are <span class="tex-span"><i>n</i></span> logs, each of exactly <span class="tex-span"><i>m</i></span> meters in length. The beavers move in turns. For each move a beaver chooses a log and gnaws it into some number (more than one) of <span class="tex-font-style-bf">equal</span> parts, the length of each one is expressed by an integer and is no less than <span class="tex-span"><i>k</i></span> meters. Each resulting part is also a log which can be gnawed in future by any beaver. The beaver that can't make a move loses. Thus, the other beaver wins.</p><p>Timur makes the first move. The players play in the optimal way. Determine the winner.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains three integers <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>m</i></span>, <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>n</i>, <i>m</i>, <i>k</i> ≤ 10<sup class="upper-index">9</sup></span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print "<span class="tex-font-style-tt">Timur</span>", if Timur wins, or "<span class="tex-font-style-tt">Marsel</span>", if Marsel wins. You should print everything without the quotes. </p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>1 15 4<br/></pre></div><div class="output"><div class="title">Output</div><pre>Timur</pre></div><div class="input"><div class="title">Input</div><pre>4 9 5<br/></pre></div><div class="output"><div class="title">Output</div><pre>Marsel</pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first sample the beavers only have one log, of <span class="tex-span">15</span> meters in length. Timur moves first. The only move he can do is to split the log into <span class="tex-span">3</span> parts each <span class="tex-span">5</span> meters in length. Then Marsel moves but he can't split any of the resulting logs, as <span class="tex-span"><i>k</i> = 4</span>. Thus, the winner is Timur.</p><p>In the second example the beavers have <span class="tex-span">4</span> logs <span class="tex-span">9</span> meters in length. Timur can't split any of them, so that the resulting parts possessed the length of not less than <span class="tex-span">5</span> meters, that's why he loses instantly.</p></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="C" data-uuid="ps_911e40b9b20423daadcd4c3d9e937dd3d19f2cd0"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. Beaver Game</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Two beavers, Timur and Marsel, play the following game.</p><p>There are <span class="tex-span"><i>n</i></span> logs, each of exactly <span class="tex-span"><i>m</i></span> meters in length. The beavers move in turns. For each move a beaver chooses a log and gnaws it into some number (more than one) of <span class="tex-font-style-bf">equal</span> parts, the length of each one is expressed by an integer and is no less than <span class="tex-span"><i>k</i></span> meters. Each resulting part is also a log which can be gnawed in future by any beaver. The beaver that can't make a move loses. Thus, the other beaver wins.</p><p>Timur makes the first move. The players play in the optimal way. Determine the winner.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains three integers <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>m</i></span>, <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>n</i>, <i>m</i>, <i>k</i> ≤ 10<sup class="upper-index">9</sup></span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print &quot;<span class="tex-font-style-tt">Timur</span>&quot;, if Timur wins, or &quot;<span class="tex-font-style-tt">Marsel</span>&quot;, if Marsel wins. You should print everything without the quotes. </p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>1 15 4<br /></pre></div><div class="output"><div class="title">Output</div><pre>Timur</pre></div><div class="input"><div class="title">Input</div><pre>4 9 5<br /></pre></div><div class="output"><div class="title">Output</div><pre>Marsel</pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first sample the beavers only have one log, of <span class="tex-span">15</span> meters in length. Timur moves first. The only move he can do is to split the log into <span class="tex-span">3</span> parts each <span class="tex-span">5</span> meters in length. Then Marsel moves but he can't split any of the resulting logs, as <span class="tex-span"><i>k</i> = 4</span>. Thus, the winner is Timur.</p><p>In the second example the beavers have <span class="tex-span">4</span> logs <span class="tex-span">9</span> meters in length. 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["Dynamic programming", "Games, Sprague\u2013Grundy theorem", "Number theory: Euler function, GCD, divisibility, etc"]
["dp", "games", "number theory", "*2000"]
https://codeforces.com/blog/entry/1812
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Next, you should compare this numbers with numbers 5, 7 and 5. If all is <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">matched, answer is YES, otherwise answer is NO.</span></span><br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Ripatti" title="Майор Ripatti">Ripatti</a>.<br /> <br /><br /><b>B.</b> At first, you can <span class="tex-span">[<i>n</i> / 7]</span> times output string &quot;ROYGBIV&quot; (<span class="tex-span">[]</span> is a rounding down). After than you can output &quot;&quot;, &quot;G&quot;, &quot;GB&quot;, &quot;YGB&quot;, &quot;YGBI&quot;, &quot;OYGBI&quot; or &quot;OYGBIV&quot; according to remainder of division <span class="tex-span"><i>n</i></span> by 7. A resulting string will satisfy problem's <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">requirement</span></span>s.<br /><br />You can also build answer in other way.<br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Ripatti" title="Майор Ripatti">Ripatti</a>.<br /><br /><br /><b>C.</b> If <span class="tex-span"><i>n</i></span> is even, Marsel wins - he just <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">symmetrically</span></span> repeats moves of Timur.<br /><br />Now <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">consider</span></span> a case of odd <span class="tex-span"><i>n</i></span>. If Timur cannot move - he is losing automatically. If he can do a move, he always can split one log into few parts that this parts cannot be splitted again. It can be done if we have find minimal <span class="tex-span"><i>t</i></span> that <span class="tex-span"><i>k</i> ≤ <i>t</i> &lt; <i>m</i></span> and <span class="tex-span"><i>t</i>|<i>m</i></span>. Next we split log into parts with length <span class="tex-span"><i>t</i></span>. Thereafter Timur <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">symmetrically</span></span> repeats moves of Marsel and wins.<br /><br />For checking that Timur could move or not, you can iterate over all divisors of <span class="tex-span"><i>m</i></span>. If there is exists some divisor <span class="tex-span"><i>t</i></span> that <span class="tex-span"><i>k</i> ≤ <i>t</i> &lt; <i>m</i></span>, Timar can do a move. Chech of all divisors can be done in <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/57a7a3f5b8d1b2dbfe8e5c99d75603ca680ed752.png" style="max-width: 100.0%;max-height: 100.0%;" /> time.<br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Lepetrandr" title="Майор Lepetrandr">Lepetrandr</a>.<br /><br /><br /><b>D.</b> It should be solved like a classical problem &quot;count the  number of square cells 1x1 lying inside the circle&quot;. Firstly, lets find the highest hexagon that lies inside the circle. Then we move to the right and up from this hexagon, and then go down until we find hexagon lying inside the circle. Repeat this process until you reach the rightmost part of the circle.<br /><br />Thus we can count number of hexagons in each column, answer is sum of this numbers. Total number of operations is <span class="tex-span"><i>O</i>(<i>n</i>)</span>.<br /><br />Few words about implementation. Coordinates of every considered point looks like <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5f82590fa40eaa083356a550a808418b9148fa88.png" style="max-width: 100.0%;max-height: 100.0%;" />. That's why distance between this points and (0,0) should be calculated using integers only. For example, criteria &quot;point <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5f82590fa40eaa083356a550a808418b9148fa88.png" style="max-width: 100.0%;max-height: 100.0%;" /> lies inside circle of radius <span class="tex-span"><i>R</i></span>&quot; looks like <span class="tex-span"><i>x</i><sup class="upper-index">2</sup> + 3<i>y</i><sup class="upper-index">2</sup> ≤ 4<i>R</i><sup class="upper-index">2</sup></span>.<br /><br />Also you can solve this problem in <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/4b2fa1e3d3d43bd9f28ff6c3140f816dc0e0621a.png" style="max-width: 100.0%;max-height: 100.0%;" />. For every column of hexagons you can find number of hexagons inside circle by using binary search.<br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Ripatti" title="Майор Ripatti">Ripatti</a>.<br /><br /><br /><b>E.</b> Firstly, let's calculate the following value:<br />dp[t][x0][y0][x][y] == true iff scientist from block (x0,y0) can reach block (x,y) in time t, considering toxic coolant.<br /><br />Secondly, let's consider a graph consisting of 4 parts:<br />1 - source (one vertex)<br />2 - first fraction (nxn vertices)<br />3 - second fraction (nxn vertices)<br />4 - sink (one vertex)<br />Each vertex of each fraction is for one block. Build edge from source to each vertex of the first fraction with capability as number of scientists in corresponding block. Build edge from each vertex of the second fraction to sink with capability as number of rescue capsules in corresponding block. Build edge from vertex (x0,y0) of the first fraction  to vertex (x,y) of the second fraction iff dp[T][x0][y0][x][y]==true for at least one T. Capability of this edges is infinity.<br /><br />As one can see, value of maxflow in this graph is answer for the problem.<br /><br />Complexity of this solution is <span class="tex-span"><i>O</i>(<i>tn</i><sup class="upper-index">4</sup> + <i>kn</i><sup class="upper-index">6</sup>)</span>, where <span class="tex-span"><i>k</i></span> is maximum possible number of scientists in each block(in this problem <span class="tex-span"><i>k</i> = 9</span>).<br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Ripatti" title="Майор Ripatti">Ripatti</a>.</p></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/78" class="notice" style="text-decoration: none;">Codeforces Beta Round 70 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-440-1812").click(function() { var that = this; 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line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/Ripatti"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/Ripatti"> Ripatti </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Apr/27/2011 21:34">12 years ago</span> </li> <li> <a href="/blog/entry/1812#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1812#comments"> 16 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1822"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (15)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="34769" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/lijunle" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/lijunle" title="Expert lijunle" class="rated-user user-blue">lijunle</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/27/2011 22:19">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34769" href="?#comment-34769" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34769" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3498" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34769"> <div class="moveup"> <div class="ttypography">where is the english version?</div> </div> </div> <div class="reply info"> <a class="comment-34769 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34769 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34769"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="34798" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/philolo1" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/philolo1" title="Expert philolo1" class="rated-user user-blue">philolo1</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/27/2011 23:50">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34798" href="?#comment-34798" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34798" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34798" class="CommentVoteFrame" data-commentRating="14" data-commentUserId="5296" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+14</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34798"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">For problem B it is also possible to use a randomiszed algorithm<br /><br />do<br />{<br />    randomsolution=randomCalc();<br /><br />}while(!isValid(randomsolution));</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34798 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34798 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34798"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="34824" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/khanhptnk" style="position: relative;"> <img src='https://userpic.codeforces.org/825/avatar/782b10196222b19a.jpg'/> </a> <div><a href="/profile/khanhptnk" title="Pupil khanhptnk" class="rated-user user-green">khanhptnk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 06:16">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34824" href="?#comment-34824" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34824" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="825" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34824"> <div class="moveup"> <div class="ttypography">Please fix typing e</div> </div> </div> <div class="reply info"> <a class="comment-34824 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34824 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34824"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="34825" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/CosmoRied" style="position: relative;"> <img src='https://userpic.codeforces.org/1587/avatar/81ab1025994d02ad.jpg'/> </a> <div><a href="/profile/CosmoRied" title="Newbie CosmoRied" class="rated-user user-gray">CosmoRied</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 06:25">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34825" href="?#comment-34825" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34825" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1587" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34825"> <div class="moveup"> <div class="ttypography"><div>Please elaborate on problem D, i found that counting hexagons easy initially, but as N gets bigger, my answer fails. I think I misunderstood the question even after reading it several times... For example, I don't completely understand this clarification: <span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> Then we move to the right and up from this hexagon, and then go down until we find hexagon lying inside the circle. Repeat this process until you reach the rightmost part of the circle.</span><br /></div></div> </div> </div> <div class="reply info"> <a class="comment-34825 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34825 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34825"> <li> <div class="comment"> <table class="comment-table" commentId="34842" commentParentId="34825"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/-dp-" style="position: relative;"> <img src='https://userpic.codeforces.org/11821/avatar/a4cdea736f51eae5.jpg'/> </a> <div><a href="/profile/-dp-" title="Expert -dp-" class="rated-user user-blue">-dp-</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 14:12">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34842" href="?#comment-34842" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34825" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34842" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34842" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="11821" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34842"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><img src="/predownloaded/8d/73/8d735c490afae2da710bde22bc2230729f8c22ee.png" style="max-width: 100.0%;max-height: 100.0%;" /><br /></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34842 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34842 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34842"> <li> <div class="comment"> <table class="comment-table" commentId="34846" commentParentId="34842"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 15:26">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34846" href="?#comment-34846" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34842" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34846" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34846" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34846"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">I have TLE on Java with this solution. Does it actually fits to time?</div><div class="from-renderer"><img src="/predownloaded/0c/3d/0c3d1187036bc67e800887cf7eea5c3275f9f91e.png" style="max-width: 100.0%;max-height: 100.0%;" /><br /></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34846 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34846 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34846"> <li> <div class="comment"> <table class="comment-table" commentId="34848" commentParentId="34846"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/CosmoRied" style="position: relative;"> <img src='https://userpic.codeforces.org/1587/avatar/81ab1025994d02ad.jpg'/> </a> <div><a href="/profile/CosmoRied" title="Newbie CosmoRied" class="rated-user user-gray">CosmoRied</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 16:15">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34848" href="?#comment-34848" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34846" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34848" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34848" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1587" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34848"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"></div></div> </div> </div> <div class="reply info"> <a class="comment-34848 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34848 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34848"> <li> <div class="comment"> <table class="comment-table" commentId="34849" commentParentId="34848"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/CosmoRied" style="position: relative;"> <img src='https://userpic.codeforces.org/1587/avatar/81ab1025994d02ad.jpg'/> </a> <div><a href="/profile/CosmoRied" title="Newbie CosmoRied" class="rated-user user-gray">CosmoRied</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 16:24">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34849" href="?#comment-34849" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34848" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34849" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1587" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34849"> <div class="moveup"> <div class="ttypography">? Why didn't it post? Can you tell me how to get (x, y) co-ordinate as the board is hexagonal? </div> </div> </div> <div class="reply info"> <a class="comment-34849 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34849 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34849"> <li> <div class="comment"> <table class="comment-table" commentId="34853" commentParentId="34849"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:13">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34853" href="?#comment-34853" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34849" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34853" revisionCount="3" revision="3"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">3</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34853" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34853"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><div><br /></div></div> </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34853 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34853 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34853"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="34854" commentParentId="34846"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/-dp-" style="position: relative;"> <img src='https://userpic.codeforces.org/11821/avatar/a4cdea736f51eae5.jpg'/> </a> <div><a href="/profile/-dp-" title="Expert -dp-" class="rated-user user-blue">-dp-</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:16">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34854" href="?#comment-34854" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34846" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34854" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34854" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="11821" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34854"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">I think you didn't get the main idea. I've updated my picture, hope it's more clear now. We do not need to check white hexagons, only red and green ones. So, total number of hexagons we need to check is O(R). This solution easily fits to time even on Python, and on C++ it works 60ms.</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34854 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34854 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34854"> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="34855" commentParentId="34842"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:22">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34855" href="?#comment-34855" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34842" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34855" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34855"> <div class="moveup"> <div class="ttypography">Thanks for editing. But what next? We got some hexagons, but still can not say how many hexagons <b>inside</b> this quarter of circle. Just border hexagons. What I missunderstood?</div> </div> </div> <div class="reply info"> <a class="comment-34855 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34855 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34855"> <li> <div class="comment"> <table class="comment-table" commentId="34856" commentParentId="34855"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/riadwaw" style="position: relative;"> <img src='https://userpic.codeforces.org/8452/avatar/7b374574b05a50df.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/riadwaw" title="International Master riadwaw" class="rated-user user-orange">riadwaw</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:32">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34856" href="?#comment-34856" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34855" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34856" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="8452" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34856"> <div class="moveup"> <div class="ttypography">We  choose highest hexagon in every column.<div>So, we can calculate it's count</div><div>(all from highest downto - highest)in every column<br /></div></div> </div> </div> <div class="reply info"> <a class="comment-34856 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34856 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34856"> <li> <div class="comment"> <table class="comment-table" commentId="34857" commentParentId="34856"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:33">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34857" href="?#comment-34857" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34856" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34857" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34857"> <div class="moveup"> <div class="ttypography">oh. so easy. Thanks! :)</div> </div> </div> <div class="reply info"> <a class="comment-34857 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34857 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34857"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="34847" commentParentId="34825"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 15:39">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34847" href="?#comment-34847" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34825" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34847" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34847"> <div class="moveup"> <div class="ttypography">try to check precision.<div>You can write smthng like </div><div><div>double d1 =  Math.sqrt(x1 * x1 + y1 * y1);</div><div>if (d1 &gt; R &amp;&amp;  d1 - R &gt; 1e-6) return false;</div></div></div> </div> </div> <div class="reply info"> <a class="comment-34847 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34847 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34847"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="133979" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/fastholf" style="position: relative;"> <img src='https://userpic.codeforces.org/15935/avatar/c2afbb3d3535dfac.jpg'/> </a> <div><a href="/profile/fastholf" title="Expert fastholf" class="rated-user user-blue">fastholf</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/19/2013 13:22">10 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-133979" href="?#comment-133979" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="133979" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="15935" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-133979"> <div class="moveup"> <div class="ttypography"><p>For task B</p> <pre><code>res[0] = 'R'; res[1] = 'O'; res[2] = 'Y'; res[3] = 'G'; res[4] = 'B'; res[5] = 'I'; res[6] = 'V'; int n; cin &gt;&gt; n; for (int i = 7; i &lt; n; ++i) { res[i] = res[i - 4]; } </code></pre><p>works as well.</p></div> </div> </div> <div class="reply info"> <a class="comment-133979 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-133979 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-133979"> </ul> </div> <br/> <div id="editBox-1822" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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78D
78
D
en
D. Archer's Shot
<div class="problem-statement"><div class="header"><div class="title">D. Archer's Shot</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>A breakthrough among computer games, "Civilization XIII", is striking in its scale and elaborate details. Let's take a closer look at one of them.</p><p>The playing area in the game is split into congruent cells that are regular hexagons. The side of each cell is equal to 1. Each unit occupies exactly one cell of the playing field. The field can be considered infinite. </p><p>Let's take a look at the battle unit called an "Archer". Each archer has a parameter "shot range". It's a positive integer that determines the radius of the circle in which the archer can hit a target. The center of the circle coincides with the center of the cell in which the archer stays. A cell is considered to be under the archer’s fire if and only if all points of this cell, including border points are located inside the circle or on its border.</p><p>The picture below shows the borders for shot ranges equal to <span class="tex-span">3</span>, <span class="tex-span">4</span> and <span class="tex-span">5</span>. The archer is depicted as <span class="tex-span"><i>A</i></span>. </p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/357492d6c820da466bc70e64bbe7cc977eb72b68.png" style="max-width: 100.0%;max-height: 100.0%;"/> </center><p>Find the number of cells that are under fire for some archer.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first and only line of input contains a single positive integer <span class="tex-span"><i>k</i></span> — the archer's shot range (<span class="tex-span">1 ≤ <i>k</i> ≤ 10<sup class="upper-index">6</sup></span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print the single number, the number of cells that are under fire.</p><p>Please do not use the <span class="tex-font-style-tt">%lld</span> specificator to read or write 64-bit integers in C++. It is preferred to use the <span class="tex-font-style-tt">cout</span> stream (also you may use the <span class="tex-font-style-tt">%I64d</span> specificator).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br/></pre></div><div class="output"><div class="title">Output</div><pre>7</pre></div><div class="input"><div class="title">Input</div><pre>4<br/></pre></div><div class="output"><div class="title">Output</div><pre>13</pre></div><div class="input"><div class="title">Input</div><pre>5<br/></pre></div><div class="output"><div class="title">Output</div><pre>19</pre></div></div></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="D" data-uuid="ps_1d66a8e0e18da8dad82d6a40e446c442f8395f4f"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">D. Archer's Shot</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>A breakthrough among computer games, &quot;Civilization XIII&quot;, is striking in its scale and elaborate details. Let's take a closer look at one of them.</p><p>The playing area in the game is split into congruent cells that are regular hexagons. The side of each cell is equal to 1. Each unit occupies exactly one cell of the playing field. The field can be considered infinite. </p><p>Let's take a look at the battle unit called an &quot;Archer&quot;. Each archer has a parameter &quot;shot range&quot;. It's a positive integer that determines the radius of the circle in which the archer can hit a target. The center of the circle coincides with the center of the cell in which the archer stays. A cell is considered to be under the archer’s fire if and only if all points of this cell, including border points are located inside the circle or on its border.</p><p>The picture below shows the borders for shot ranges equal to <span class="tex-span">3</span>, <span class="tex-span">4</span> and <span class="tex-span">5</span>. The archer is depicted as <span class="tex-span"><i>A</i></span>. </p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/357492d6c820da466bc70e64bbe7cc977eb72b68.png" style="max-width: 100.0%;max-height: 100.0%;" /> </center><p>Find the number of cells that are under fire for some archer.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first and only line of input contains a single positive integer <span class="tex-span"><i>k</i></span> — the archer's shot range (<span class="tex-span">1 ≤ <i>k</i> ≤ 10<sup class="upper-index">6</sup></span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print the single number, the number of cells that are under fire.</p><p>Please do not use the <span class="tex-font-style-tt">%lld</span> specificator to read or write 64-bit integers in C++. It is preferred to use the <span class="tex-font-style-tt">cout</span> stream (also you may use the <span class="tex-font-style-tt">%I64d</span> specificator).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br /></pre></div><div class="output"><div class="title">Output</div><pre>7</pre></div><div class="input"><div class="title">Input</div><pre>4<br /></pre></div><div class="output"><div class="title">Output</div><pre>13</pre></div><div class="input"><div class="title">Input</div><pre>5<br /></pre></div><div class="output"><div class="title">Output</div><pre>19</pre></div></div></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=D]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); 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["Binary search", "Geometry, computational geometry", "Mathematics including integration, differential equations, etc", "Two pointers"]
["binary search", "geometry", "math", "two pointers", "*2300"]
https://codeforces.com/blog/entry/1812
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Next, you should compare this numbers with numbers 5, 7 and 5. If all is <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">matched, answer is YES, otherwise answer is NO.</span></span><br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Ripatti" title="Майор Ripatti">Ripatti</a>.<br /> <br /><br /><b>B.</b> At first, you can <span class="tex-span">[<i>n</i> / 7]</span> times output string &quot;ROYGBIV&quot; (<span class="tex-span">[]</span> is a rounding down). After than you can output &quot;&quot;, &quot;G&quot;, &quot;GB&quot;, &quot;YGB&quot;, &quot;YGBI&quot;, &quot;OYGBI&quot; or &quot;OYGBIV&quot; according to remainder of division <span class="tex-span"><i>n</i></span> by 7. A resulting string will satisfy problem's <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">requirement</span></span>s.<br /><br />You can also build answer in other way.<br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Ripatti" title="Майор Ripatti">Ripatti</a>.<br /><br /><br /><b>C.</b> If <span class="tex-span"><i>n</i></span> is even, Marsel wins - he just <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">symmetrically</span></span> repeats moves of Timur.<br /><br />Now <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">consider</span></span> a case of odd <span class="tex-span"><i>n</i></span>. If Timur cannot move - he is losing automatically. If he can do a move, he always can split one log into few parts that this parts cannot be splitted again. It can be done if we have find minimal <span class="tex-span"><i>t</i></span> that <span class="tex-span"><i>k</i> ≤ <i>t</i> &lt; <i>m</i></span> and <span class="tex-span"><i>t</i>|<i>m</i></span>. Next we split log into parts with length <span class="tex-span"><i>t</i></span>. Thereafter Timur <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">symmetrically</span></span> repeats moves of Marsel and wins.<br /><br />For checking that Timur could move or not, you can iterate over all divisors of <span class="tex-span"><i>m</i></span>. If there is exists some divisor <span class="tex-span"><i>t</i></span> that <span class="tex-span"><i>k</i> ≤ <i>t</i> &lt; <i>m</i></span>, Timar can do a move. Chech of all divisors can be done in <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/57a7a3f5b8d1b2dbfe8e5c99d75603ca680ed752.png" style="max-width: 100.0%;max-height: 100.0%;" /> time.<br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Lepetrandr" title="Майор Lepetrandr">Lepetrandr</a>.<br /><br /><br /><b>D.</b> It should be solved like a classical problem &quot;count the  number of square cells 1x1 lying inside the circle&quot;. Firstly, lets find the highest hexagon that lies inside the circle. Then we move to the right and up from this hexagon, and then go down until we find hexagon lying inside the circle. Repeat this process until you reach the rightmost part of the circle.<br /><br />Thus we can count number of hexagons in each column, answer is sum of this numbers. Total number of operations is <span class="tex-span"><i>O</i>(<i>n</i>)</span>.<br /><br />Few words about implementation. Coordinates of every considered point looks like <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5f82590fa40eaa083356a550a808418b9148fa88.png" style="max-width: 100.0%;max-height: 100.0%;" />. That's why distance between this points and (0,0) should be calculated using integers only. For example, criteria &quot;point <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5f82590fa40eaa083356a550a808418b9148fa88.png" style="max-width: 100.0%;max-height: 100.0%;" /> lies inside circle of radius <span class="tex-span"><i>R</i></span>&quot; looks like <span class="tex-span"><i>x</i><sup class="upper-index">2</sup> + 3<i>y</i><sup class="upper-index">2</sup> ≤ 4<i>R</i><sup class="upper-index">2</sup></span>.<br /><br />Also you can solve this problem in <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/4b2fa1e3d3d43bd9f28ff6c3140f816dc0e0621a.png" style="max-width: 100.0%;max-height: 100.0%;" />. For every column of hexagons you can find number of hexagons inside circle by using binary search.<br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Ripatti" title="Майор Ripatti">Ripatti</a>.<br /><br /><br /><b>E.</b> Firstly, let's calculate the following value:<br />dp[t][x0][y0][x][y] == true iff scientist from block (x0,y0) can reach block (x,y) in time t, considering toxic coolant.<br /><br />Secondly, let's consider a graph consisting of 4 parts:<br />1 - source (one vertex)<br />2 - first fraction (nxn vertices)<br />3 - second fraction (nxn vertices)<br />4 - sink (one vertex)<br />Each vertex of each fraction is for one block. Build edge from source to each vertex of the first fraction with capability as number of scientists in corresponding block. Build edge from each vertex of the second fraction to sink with capability as number of rescue capsules in corresponding block. Build edge from vertex (x0,y0) of the first fraction  to vertex (x,y) of the second fraction iff dp[T][x0][y0][x][y]==true for at least one T. Capability of this edges is infinity.<br /><br />As one can see, value of maxflow in this graph is answer for the problem.<br /><br />Complexity of this solution is <span class="tex-span"><i>O</i>(<i>tn</i><sup class="upper-index">4</sup> + <i>kn</i><sup class="upper-index">6</sup>)</span>, where <span class="tex-span"><i>k</i></span> is maximum possible number of scientists in each block(in this problem <span class="tex-span"><i>k</i> = 9</span>).<br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Ripatti" title="Майор Ripatti">Ripatti</a>.</p></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/78" class="notice" style="text-decoration: none;">Codeforces Beta Round 70 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-440-1812").click(function() { var that = this; 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line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/Ripatti"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/Ripatti"> Ripatti </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Apr/27/2011 21:34">12 years ago</span> </li> <li> <a href="/blog/entry/1812#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1812#comments"> 16 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1822"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (15)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="34769" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/lijunle" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/lijunle" title="Expert lijunle" class="rated-user user-blue">lijunle</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/27/2011 22:19">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34769" href="?#comment-34769" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34769" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3498" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34769"> <div class="moveup"> <div class="ttypography">where is the english version?</div> </div> </div> <div class="reply info"> <a class="comment-34769 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34769 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34769"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="34798" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/philolo1" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/philolo1" title="Expert philolo1" class="rated-user user-blue">philolo1</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/27/2011 23:50">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34798" href="?#comment-34798" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34798" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34798" class="CommentVoteFrame" data-commentRating="14" data-commentUserId="5296" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+14</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34798"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">For problem B it is also possible to use a randomiszed algorithm<br /><br />do<br />{<br />    randomsolution=randomCalc();<br /><br />}while(!isValid(randomsolution));</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34798 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34798 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34798"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="34824" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/khanhptnk" style="position: relative;"> <img src='https://userpic.codeforces.org/825/avatar/782b10196222b19a.jpg'/> </a> <div><a href="/profile/khanhptnk" title="Pupil khanhptnk" class="rated-user user-green">khanhptnk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 06:16">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34824" href="?#comment-34824" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34824" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="825" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34824"> <div class="moveup"> <div class="ttypography">Please fix typing e</div> </div> </div> <div class="reply info"> <a class="comment-34824 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34824 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34824"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="34825" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/CosmoRied" style="position: relative;"> <img src='https://userpic.codeforces.org/1587/avatar/81ab1025994d02ad.jpg'/> </a> <div><a href="/profile/CosmoRied" title="Newbie CosmoRied" class="rated-user user-gray">CosmoRied</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 06:25">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34825" href="?#comment-34825" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34825" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1587" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34825"> <div class="moveup"> <div class="ttypography"><div>Please elaborate on problem D, i found that counting hexagons easy initially, but as N gets bigger, my answer fails. I think I misunderstood the question even after reading it several times... For example, I don't completely understand this clarification: <span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> Then we move to the right and up from this hexagon, and then go down until we find hexagon lying inside the circle. Repeat this process until you reach the rightmost part of the circle.</span><br /></div></div> </div> </div> <div class="reply info"> <a class="comment-34825 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34825 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34825"> <li> <div class="comment"> <table class="comment-table" commentId="34842" commentParentId="34825"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/-dp-" style="position: relative;"> <img src='https://userpic.codeforces.org/11821/avatar/a4cdea736f51eae5.jpg'/> </a> <div><a href="/profile/-dp-" title="Expert -dp-" class="rated-user user-blue">-dp-</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 14:12">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34842" href="?#comment-34842" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34825" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34842" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34842" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="11821" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34842"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><img src="/predownloaded/8d/73/8d735c490afae2da710bde22bc2230729f8c22ee.png" style="max-width: 100.0%;max-height: 100.0%;" /><br /></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34842 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34842 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34842"> <li> <div class="comment"> <table class="comment-table" commentId="34846" commentParentId="34842"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 15:26">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34846" href="?#comment-34846" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34842" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34846" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34846" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34846"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">I have TLE on Java with this solution. Does it actually fits to time?</div><div class="from-renderer"><img src="/predownloaded/0c/3d/0c3d1187036bc67e800887cf7eea5c3275f9f91e.png" style="max-width: 100.0%;max-height: 100.0%;" /><br /></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34846 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34846 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34846"> <li> <div class="comment"> <table class="comment-table" commentId="34848" commentParentId="34846"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/CosmoRied" style="position: relative;"> <img src='https://userpic.codeforces.org/1587/avatar/81ab1025994d02ad.jpg'/> </a> <div><a href="/profile/CosmoRied" title="Newbie CosmoRied" class="rated-user user-gray">CosmoRied</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 16:15">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34848" href="?#comment-34848" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34846" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34848" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34848" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1587" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34848"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"></div></div> </div> </div> <div class="reply info"> <a class="comment-34848 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34848 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34848"> <li> <div class="comment"> <table class="comment-table" commentId="34849" commentParentId="34848"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/CosmoRied" style="position: relative;"> <img src='https://userpic.codeforces.org/1587/avatar/81ab1025994d02ad.jpg'/> </a> <div><a href="/profile/CosmoRied" title="Newbie CosmoRied" class="rated-user user-gray">CosmoRied</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 16:24">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34849" href="?#comment-34849" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34848" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34849" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1587" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34849"> <div class="moveup"> <div class="ttypography">? Why didn't it post? Can you tell me how to get (x, y) co-ordinate as the board is hexagonal? </div> </div> </div> <div class="reply info"> <a class="comment-34849 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34849 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34849"> <li> <div class="comment"> <table class="comment-table" commentId="34853" commentParentId="34849"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:13">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34853" href="?#comment-34853" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34849" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34853" revisionCount="3" revision="3"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">3</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34853" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34853"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><div><br /></div></div> </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34853 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34853 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34853"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="34854" commentParentId="34846"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/-dp-" style="position: relative;"> <img src='https://userpic.codeforces.org/11821/avatar/a4cdea736f51eae5.jpg'/> </a> <div><a href="/profile/-dp-" title="Expert -dp-" class="rated-user user-blue">-dp-</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:16">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34854" href="?#comment-34854" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34846" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34854" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34854" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="11821" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34854"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">I think you didn't get the main idea. I've updated my picture, hope it's more clear now. We do not need to check white hexagons, only red and green ones. So, total number of hexagons we need to check is O(R). This solution easily fits to time even on Python, and on C++ it works 60ms.</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34854 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34854 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34854"> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="34855" commentParentId="34842"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:22">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34855" href="?#comment-34855" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34842" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34855" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34855"> <div class="moveup"> <div class="ttypography">Thanks for editing. But what next? We got some hexagons, but still can not say how many hexagons <b>inside</b> this quarter of circle. Just border hexagons. What I missunderstood?</div> </div> </div> <div class="reply info"> <a class="comment-34855 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34855 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34855"> <li> <div class="comment"> <table class="comment-table" commentId="34856" commentParentId="34855"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/riadwaw" style="position: relative;"> <img src='https://userpic.codeforces.org/8452/avatar/7b374574b05a50df.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/riadwaw" title="International Master riadwaw" class="rated-user user-orange">riadwaw</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:32">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34856" href="?#comment-34856" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34855" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34856" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="8452" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34856"> <div class="moveup"> <div class="ttypography">We  choose highest hexagon in every column.<div>So, we can calculate it's count</div><div>(all from highest downto - highest)in every column<br /></div></div> </div> </div> <div class="reply info"> <a class="comment-34856 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34856 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34856"> <li> <div class="comment"> <table class="comment-table" commentId="34857" commentParentId="34856"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:33">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34857" href="?#comment-34857" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34856" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34857" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34857"> <div class="moveup"> <div class="ttypography">oh. so easy. Thanks! :)</div> </div> </div> <div class="reply info"> <a class="comment-34857 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34857 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34857"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="34847" commentParentId="34825"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 15:39">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34847" href="?#comment-34847" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34825" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34847" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34847"> <div class="moveup"> <div class="ttypography">try to check precision.<div>You can write smthng like </div><div><div>double d1 =  Math.sqrt(x1 * x1 + y1 * y1);</div><div>if (d1 &gt; R &amp;&amp;  d1 - R &gt; 1e-6) return false;</div></div></div> </div> </div> <div class="reply info"> <a class="comment-34847 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34847 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34847"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="133979" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/fastholf" style="position: relative;"> <img src='https://userpic.codeforces.org/15935/avatar/c2afbb3d3535dfac.jpg'/> </a> <div><a href="/profile/fastholf" title="Expert fastholf" class="rated-user user-blue">fastholf</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/19/2013 13:22">10 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-133979" href="?#comment-133979" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="133979" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="15935" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-133979"> <div class="moveup"> <div class="ttypography"><p>For task B</p> <pre><code>res[0] = 'R'; res[1] = 'O'; res[2] = 'Y'; res[3] = 'G'; res[4] = 'B'; res[5] = 'I'; res[6] = 'V'; int n; cin &gt;&gt; n; for (int i = 7; i &lt; n; ++i) { res[i] = res[i - 4]; } </code></pre><p>works as well.</p></div> </div> </div> <div class="reply info"> <a class="comment-133979 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-133979 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-133979"> </ul> </div> <br/> <div id="editBox-1822" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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78E
78
E
en
E. Evacuation
<div class="problem-statement"><div class="header"><div class="title">E. Evacuation</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>They've screwed something up yet again... In one nuclear reactor of a research station an uncontrolled reaction is in progress and explosion which will destroy the whole station will happen soon.</p><p>The station is represented by a square <span class="tex-span"><i>n</i> × <i>n</i></span> divided into <span class="tex-span">1 × 1</span> blocks. Each block is either a reactor or a laboratory. There can be several reactors and exactly one of them will explode soon. The reactors can be considered impassable blocks, but one can move through laboratories. Between any two laboratories, which are in adjacent blocks, there is a corridor. Blocks are considered adjacent if they have a common edge.</p><p>In each laboratory there is some number of scientists and some number of rescue capsules. Once the scientist climbs into a capsule, he is considered to be saved. Each capsule has room for not more than one scientist.</p><p>The reactor, which is about to explode, is damaged and a toxic coolant trickles from it into the neighboring blocks. The block, which contains the reactor, is considered infected. Every minute the coolant spreads over the laboratories through corridors. If at some moment one of the blocks is infected, then the next minute all the neighboring laboratories also become infected. Once a lab is infected, all the scientists there that are not in rescue capsules die. The coolant does not spread through reactor blocks.</p><p>There are exactly <span class="tex-span"><i>t</i></span> minutes to the explosion. Any scientist in a minute can move down the corridor to the next lab, if it is not infected. On any corridor an unlimited number of scientists can simultaneously move in both directions. It is believed that the scientists inside a lab moves without consuming time. Moreover, any scientist could get into the rescue capsule instantly. It is also believed that any scientist at any given moment always has the time to perform their actions (move from the given laboratory into the next one, or climb into the rescue capsule) before the laboratory will be infected.</p><p>Find the maximum number of scientists who will be able to escape.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>t</i></span> (<span class="tex-span">2 ≤ <i>n</i> ≤ 10</span>, <span class="tex-span">1 ≤ <i>t</i> ≤ 60</span>). Each of the next <span class="tex-span"><i>n</i></span> lines contains <span class="tex-span"><i>n</i></span> characters. These lines describe the scientists' locations. Then exactly one empty line follows. Each of the next <span class="tex-span"><i>n</i></span> more lines contains <span class="tex-span"><i>n</i></span> characters. These lines describe the rescue capsules' locations.</p><p>In the description of the scientists' and the rescue capsules' locations the character "<span class="tex-font-style-tt">Y</span>" stands for a properly functioning reactor, "<span class="tex-font-style-tt">Z</span>" stands for the malfunctioning reactor. The reactors' positions in both descriptions coincide. There is exactly one malfunctioning reactor on the station. The digits "<span class="tex-font-style-tt">0</span>" - "<span class="tex-font-style-tt">9</span>" stand for the laboratories. In the description of the scientists' locations those numbers stand for the number of scientists in the corresponding laboratories. In the rescue capsules' descriptions they stand for the number of such capsules in each laboratory.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single number — the maximum number of scientists who will manage to save themselves.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3 3<br/>1YZ<br/>1YY<br/>100<br/><br/>0YZ<br/>0YY<br/>003<br/></pre></div><div class="output"><div class="title">Output</div><pre>2</pre></div><div class="input"><div class="title">Input</div><pre>4 4<br/>Y110<br/>1Y1Z<br/>1Y0Y<br/>0100<br/><br/>Y001<br/>0Y0Z<br/>0Y0Y<br/>0005<br/></pre></div><div class="output"><div class="title">Output</div><pre>3</pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the second sample the events could take place as follows: </p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/c29057a40dc0748af4c671a35415c2ff5fde2be5.png" style="max-width: 100.0%;max-height: 100.0%;"/> </center></div></div>
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If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. Never use someone else's code, read the tutorials or communicate with other person during a virtual contest. </div> <div style="text-align:center;margin:1em;"> <form action="/contest/78/virtual" method="get"> <input type="submit" name="submit" value="Start virtual contest" style="padding:0 0.5em;"> </form> </div> </div> <script> $(function () { $(".ContestVirtualFrame .sidebar-caption-icon").click(function() { $(this).toggleClass("la-angle-down la-angle-right"); const $target = $(this).parent().next(); $target.toggle(); const dataPageUrl = $target.attr("data-page-url"); const collapsed = $(this).hasClass("la-angle-right"); const params = { action: "setCollapsed", sidebarFrameSimpleClassName: "ContestVirtualFrame", collapsed }; $.each($target[0].attributes, function(i, a) { const name = a.name; if (name.startsWith("data-extra-key-")) { const key = a.value; const keyIndex = parseInt(name.substring("data-extra-key-".length)); const value = $target.attr("data-extra-value-" + keyIndex); params[key] = value; 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="E" data-uuid="ps_eada482429bd4436ef9d6682dce3ad33f2961d47"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">E. Evacuation</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>They've screwed something up yet again... In one nuclear reactor of a research station an uncontrolled reaction is in progress and explosion which will destroy the whole station will happen soon.</p><p>The station is represented by a square <span class="tex-span"><i>n</i> × <i>n</i></span> divided into <span class="tex-span">1 × 1</span> blocks. Each block is either a reactor or a laboratory. There can be several reactors and exactly one of them will explode soon. The reactors can be considered impassable blocks, but one can move through laboratories. Between any two laboratories, which are in adjacent blocks, there is a corridor. Blocks are considered adjacent if they have a common edge.</p><p>In each laboratory there is some number of scientists and some number of rescue capsules. Once the scientist climbs into a capsule, he is considered to be saved. Each capsule has room for not more than one scientist.</p><p>The reactor, which is about to explode, is damaged and a toxic coolant trickles from it into the neighboring blocks. The block, which contains the reactor, is considered infected. Every minute the coolant spreads over the laboratories through corridors. If at some moment one of the blocks is infected, then the next minute all the neighboring laboratories also become infected. Once a lab is infected, all the scientists there that are not in rescue capsules die. The coolant does not spread through reactor blocks.</p><p>There are exactly <span class="tex-span"><i>t</i></span> minutes to the explosion. Any scientist in a minute can move down the corridor to the next lab, if it is not infected. On any corridor an unlimited number of scientists can simultaneously move in both directions. It is believed that the scientists inside a lab moves without consuming time. Moreover, any scientist could get into the rescue capsule instantly. It is also believed that any scientist at any given moment always has the time to perform their actions (move from the given laboratory into the next one, or climb into the rescue capsule) before the laboratory will be infected.</p><p>Find the maximum number of scientists who will be able to escape.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>t</i></span> (<span class="tex-span">2 ≤ <i>n</i> ≤ 10</span>, <span class="tex-span">1 ≤ <i>t</i> ≤ 60</span>). Each of the next <span class="tex-span"><i>n</i></span> lines contains <span class="tex-span"><i>n</i></span> characters. These lines describe the scientists' locations. Then exactly one empty line follows. Each of the next <span class="tex-span"><i>n</i></span> more lines contains <span class="tex-span"><i>n</i></span> characters. These lines describe the rescue capsules' locations.</p><p>In the description of the scientists' and the rescue capsules' locations the character &quot;<span class="tex-font-style-tt">Y</span>&quot; stands for a properly functioning reactor, &quot;<span class="tex-font-style-tt">Z</span>&quot; stands for the malfunctioning reactor. The reactors' positions in both descriptions coincide. There is exactly one malfunctioning reactor on the station. The digits &quot;<span class="tex-font-style-tt">0</span>&quot; - &quot;<span class="tex-font-style-tt">9</span>&quot; stand for the laboratories. In the description of the scientists' locations those numbers stand for the number of scientists in the corresponding laboratories. In the rescue capsules' descriptions they stand for the number of such capsules in each laboratory.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single number — the maximum number of scientists who will manage to save themselves.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3 3<br />1YZ<br />1YY<br />100<br /><br />0YZ<br />0YY<br />003<br /></pre></div><div class="output"><div class="title">Output</div><pre>2</pre></div><div class="input"><div class="title">Input</div><pre>4 4<br />Y110<br />1Y1Z<br />1Y0Y<br />0100<br /><br />Y001<br />0Y0Z<br />0Y0Y<br />0005<br /></pre></div><div class="output"><div class="title">Output</div><pre>3</pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the second sample the events could take place as follows: </p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/c29057a40dc0748af4c671a35415c2ff5fde2be5.png" style="max-width: 100.0%;max-height: 100.0%;" /> </center></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=E]"); 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["Graph network flows", "Graphs", "Shortest paths on weighted and unweighted graphs"]
["flows", "graphs", "shortest paths", "*2300"]
https://codeforces.com/blog/entry/1812
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Next, you should compare this numbers with numbers 5, 7 and 5. If all is <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">matched, answer is YES, otherwise answer is NO.</span></span><br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Ripatti" title="Майор Ripatti">Ripatti</a>.<br /> <br /><br /><b>B.</b> At first, you can <span class="tex-span">[<i>n</i> / 7]</span> times output string &quot;ROYGBIV&quot; (<span class="tex-span">[]</span> is a rounding down). After than you can output &quot;&quot;, &quot;G&quot;, &quot;GB&quot;, &quot;YGB&quot;, &quot;YGBI&quot;, &quot;OYGBI&quot; or &quot;OYGBIV&quot; according to remainder of division <span class="tex-span"><i>n</i></span> by 7. A resulting string will satisfy problem's <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">requirement</span></span>s.<br /><br />You can also build answer in other way.<br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Ripatti" title="Майор Ripatti">Ripatti</a>.<br /><br /><br /><b>C.</b> If <span class="tex-span"><i>n</i></span> is even, Marsel wins - he just <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">symmetrically</span></span> repeats moves of Timur.<br /><br />Now <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">consider</span></span> a case of odd <span class="tex-span"><i>n</i></span>. If Timur cannot move - he is losing automatically. If he can do a move, he always can split one log into few parts that this parts cannot be splitted again. It can be done if we have find minimal <span class="tex-span"><i>t</i></span> that <span class="tex-span"><i>k</i> ≤ <i>t</i> &lt; <i>m</i></span> and <span class="tex-span"><i>t</i>|<i>m</i></span>. Next we split log into parts with length <span class="tex-span"><i>t</i></span>. Thereafter Timur <span lang="en"><span title="Нажмите, чтобы увидеть альтернативный перевод">symmetrically</span></span> repeats moves of Marsel and wins.<br /><br />For checking that Timur could move or not, you can iterate over all divisors of <span class="tex-span"><i>m</i></span>. If there is exists some divisor <span class="tex-span"><i>t</i></span> that <span class="tex-span"><i>k</i> ≤ <i>t</i> &lt; <i>m</i></span>, Timar can do a move. Chech of all divisors can be done in <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/57a7a3f5b8d1b2dbfe8e5c99d75603ca680ed752.png" style="max-width: 100.0%;max-height: 100.0%;" /> time.<br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Lepetrandr" title="Майор Lepetrandr">Lepetrandr</a>.<br /><br /><br /><b>D.</b> It should be solved like a classical problem &quot;count the  number of square cells 1x1 lying inside the circle&quot;. Firstly, lets find the highest hexagon that lies inside the circle. Then we move to the right and up from this hexagon, and then go down until we find hexagon lying inside the circle. Repeat this process until you reach the rightmost part of the circle.<br /><br />Thus we can count number of hexagons in each column, answer is sum of this numbers. Total number of operations is <span class="tex-span"><i>O</i>(<i>n</i>)</span>.<br /><br />Few words about implementation. Coordinates of every considered point looks like <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5f82590fa40eaa083356a550a808418b9148fa88.png" style="max-width: 100.0%;max-height: 100.0%;" />. That's why distance between this points and (0,0) should be calculated using integers only. For example, criteria &quot;point <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5f82590fa40eaa083356a550a808418b9148fa88.png" style="max-width: 100.0%;max-height: 100.0%;" /> lies inside circle of radius <span class="tex-span"><i>R</i></span>&quot; looks like <span class="tex-span"><i>x</i><sup class="upper-index">2</sup> + 3<i>y</i><sup class="upper-index">2</sup> ≤ 4<i>R</i><sup class="upper-index">2</sup></span>.<br /><br />Also you can solve this problem in <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/4b2fa1e3d3d43bd9f28ff6c3140f816dc0e0621a.png" style="max-width: 100.0%;max-height: 100.0%;" />. For every column of hexagons you can find number of hexagons inside circle by using binary search.<br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Ripatti" title="Майор Ripatti">Ripatti</a>.<br /><br /><br /><b>E.</b> Firstly, let's calculate the following value:<br />dp[t][x0][y0][x][y] == true iff scientist from block (x0,y0) can reach block (x,y) in time t, considering toxic coolant.<br /><br />Secondly, let's consider a graph consisting of 4 parts:<br />1 - source (one vertex)<br />2 - first fraction (nxn vertices)<br />3 - second fraction (nxn vertices)<br />4 - sink (one vertex)<br />Each vertex of each fraction is for one block. Build edge from source to each vertex of the first fraction with capability as number of scientists in corresponding block. Build edge from each vertex of the second fraction to sink with capability as number of rescue capsules in corresponding block. Build edge from vertex (x0,y0) of the first fraction  to vertex (x,y) of the second fraction iff dp[T][x0][y0][x][y]==true for at least one T. Capability of this edges is infinity.<br /><br />As one can see, value of maxflow in this graph is answer for the problem.<br /><br />Complexity of this solution is <span class="tex-span"><i>O</i>(<i>tn</i><sup class="upper-index">4</sup> + <i>kn</i><sup class="upper-index">6</sup>)</span>, where <span class="tex-span"><i>k</i></span> is maximum possible number of scientists in each block(in this problem <span class="tex-span"><i>k</i> = 9</span>).<br /><br />Author of problem is <a class="rated-user user-orange" href="../../../profile/Ripatti" title="Майор Ripatti">Ripatti</a>.</p></div> </div> <div style="font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;"> <img src="//codeforces.org/s/81027/images/icons/paperclip-16x16.png" style="vertical-align: middle;"/> <span style="padding: 0 0.35em;">Tutorial of <a href="/contest/78" class="notice" style="text-decoration: none;">Codeforces Beta Round 70 (Div. 2)</a> </span> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-440-1812").click(function() { var that = this; 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line-height: 1.65em; top: 0.75rem; left: 0.8em;"> </span> <div class="right-meta"> <ul> <li> <a href="/profile/Ripatti"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/user_16x16.png" alt="Author" title="Author" /></a> <a href="/profile/Ripatti"> Ripatti </a> </li> <li> <img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/date_16x16.png" alt="Publication date" title="Publication date" /> <span class="format-humantime" title="Apr/27/2011 21:34">12 years ago</span> </li> <li> <a href="/blog/entry/1812#comments"><img style="vertical-align:middle;position:relative;top:-1px" src="//codeforces.org/s/81027/images/blog/comments_16x16.png" alt="Comments" title="Comments" /></a> <a href="/blog/entry/1812#comments"> 16 </a> </li> </ul> </div> <br style="clear:both;"/> </div> <style type="text/css"> .comments .title { float: left; } .comments .comments-actions-div { float: right; margin-top: 3rem; margin-right: 0.5em; } .comments .comments-actions-div .separator { margin: 0 1rem; } .comments label.show-archived { } .comments label.show-archived, .comments label.show-archived * { font-size: 1.4rem !important; color: black !important; /*position: relative !important;*/ /*bottom: 0.4rem !important;*/ } .comments label.show-archived input { height: 1.4rem !important; width: 1.4rem !important; position: relative; top: 0.25rem; } .new-root-comment { font-size: 1.4rem !important; } </style> <div class="comments" commentableId="1822"> <div style="display: flow-root"> <div class="title"> <img src="//codeforces.org/s/81027/images/icons/comments-48x48.png" alt="Comments" title="Comments" style="position:relative;top:0.6em;"/> <a name="comments">Comments (15)</a> </div> <div class="comments-actions-div"> <label class="show-archived"> <input type="checkbox" class="show-archived-checkbox" /> Show archived </label> <span class="separator">|</span> <a href="#" class="new-root-comment" >Write comment?</a> </div> </div> <div class="comment"> <table class="comment-table" commentId="34769" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/lijunle" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/lijunle" title="Expert lijunle" class="rated-user user-blue">lijunle</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/27/2011 22:19">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34769" href="?#comment-34769" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34769" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="3498" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34769"> <div class="moveup"> <div class="ttypography">where is the english version?</div> </div> </div> <div class="reply info"> <a class="comment-34769 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34769 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34769"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="34798" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/philolo1" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/philolo1" title="Expert philolo1" class="rated-user user-blue">philolo1</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/27/2011 23:50">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34798" href="?#comment-34798" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34798" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34798" class="CommentVoteFrame" data-commentRating="14" data-commentUserId="5296" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+14</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34798"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">For problem B it is also possible to use a randomiszed algorithm<br /><br />do<br />{<br />    randomsolution=randomCalc();<br /><br />}while(!isValid(randomsolution));</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34798 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34798 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34798"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="34824" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/khanhptnk" style="position: relative;"> <img src='https://userpic.codeforces.org/825/avatar/782b10196222b19a.jpg'/> </a> <div><a href="/profile/khanhptnk" title="Pupil khanhptnk" class="rated-user user-green">khanhptnk</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 06:16">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34824" href="?#comment-34824" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34824" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="825" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34824"> <div class="moveup"> <div class="ttypography">Please fix typing e</div> </div> </div> <div class="reply info"> <a class="comment-34824 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34824 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34824"> </ul> </div> <div class="comment"> <table class="comment-table" commentId="34825" commentParentId="-1"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/CosmoRied" style="position: relative;"> <img src='https://userpic.codeforces.org/1587/avatar/81ab1025994d02ad.jpg'/> </a> <div><a href="/profile/CosmoRied" title="Newbie CosmoRied" class="rated-user user-gray">CosmoRied</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 06:25">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34825" href="?#comment-34825" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34825" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1587" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34825"> <div class="moveup"> <div class="ttypography"><div>Please elaborate on problem D, i found that counting hexagons easy initially, but as N gets bigger, my answer fails. I think I misunderstood the question even after reading it several times... For example, I don't completely understand this clarification: <span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> Then we move to the right and up from this hexagon, and then go down until we find hexagon lying inside the circle. Repeat this process until you reach the rightmost part of the circle.</span><br /></div></div> </div> </div> <div class="reply info"> <a class="comment-34825 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34825 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34825"> <li> <div class="comment"> <table class="comment-table" commentId="34842" commentParentId="34825"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/-dp-" style="position: relative;"> <img src='https://userpic.codeforces.org/11821/avatar/a4cdea736f51eae5.jpg'/> </a> <div><a href="/profile/-dp-" title="Expert -dp-" class="rated-user user-blue">-dp-</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 14:12">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34842" href="?#comment-34842" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34825" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34842" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34842" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="11821" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34842"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><img src="/predownloaded/8d/73/8d735c490afae2da710bde22bc2230729f8c22ee.png" style="max-width: 100.0%;max-height: 100.0%;" /><br /></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34842 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34842 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34842"> <li> <div class="comment"> <table class="comment-table" commentId="34846" commentParentId="34842"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 15:26">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34846" href="?#comment-34846" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34842" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34846" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34846" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34846"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">I have TLE on Java with this solution. Does it actually fits to time?</div><div class="from-renderer"><img src="/predownloaded/0c/3d/0c3d1187036bc67e800887cf7eea5c3275f9f91e.png" style="max-width: 100.0%;max-height: 100.0%;" /><br /></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34846 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34846 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34846"> <li> <div class="comment"> <table class="comment-table" commentId="34848" commentParentId="34846"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/CosmoRied" style="position: relative;"> <img src='https://userpic.codeforces.org/1587/avatar/81ab1025994d02ad.jpg'/> </a> <div><a href="/profile/CosmoRied" title="Newbie CosmoRied" class="rated-user user-gray">CosmoRied</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 16:15">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34848" href="?#comment-34848" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34846" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34848" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34848" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1587" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34848"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"></div></div> </div> </div> <div class="reply info"> <a class="comment-34848 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34848 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34848"> <li> <div class="comment"> <table class="comment-table" commentId="34849" commentParentId="34848"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/CosmoRied" style="position: relative;"> <img src='https://userpic.codeforces.org/1587/avatar/81ab1025994d02ad.jpg'/> </a> <div><a href="/profile/CosmoRied" title="Newbie CosmoRied" class="rated-user user-gray">CosmoRied</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 16:24">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34849" href="?#comment-34849" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34848" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34849" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="1587" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34849"> <div class="moveup"> <div class="ttypography">? Why didn't it post? Can you tell me how to get (x, y) co-ordinate as the board is hexagonal? </div> </div> </div> <div class="reply info"> <a class="comment-34849 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34849 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34849"> <li> <div class="comment"> <table class="comment-table" commentId="34853" commentParentId="34849"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:13">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34853" href="?#comment-34853" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34849" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34853" revisionCount="3" revision="3"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">3</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34853" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34853"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><div class="from-renderer"><div><br /></div></div> </div></div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34853 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34853 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34853"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="34854" commentParentId="34846"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/-dp-" style="position: relative;"> <img src='https://userpic.codeforces.org/11821/avatar/a4cdea736f51eae5.jpg'/> </a> <div><a href="/profile/-dp-" title="Expert -dp-" class="rated-user user-blue">-dp-</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:16">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34854" href="?#comment-34854" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34846" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> <span style="" commentId="34854" revisionCount="2" revision="2"> <a href="#" style="text-decoration:none;font-size:1.4rem;color:#bebebe;" class="leftRevision">&larr;</a> Rev. <span class="revision">2</span> <a href="#" style="text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;" class="rightRevision">&rarr;</a> </span> &nbsp; <span commentid="34854" class="CommentVoteFrame" data-commentRating="3" data-commentUserId="11821" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:green;font-weight:bold;">+3</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34854"> <div class="moveup"> <div class="ttypography"><div class="from-renderer"><div class="from-renderer">I think you didn't get the main idea. I've updated my picture, hope it's more clear now. We do not need to check white hexagons, only red and green ones. So, total number of hexagons we need to check is O(R). This solution easily fits to time even on Python, and on C++ it works 60ms.</div> </div></div> </div> </div> <div class="reply info"> <a class="comment-34854 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34854 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34854"> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="34855" commentParentId="34842"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:22">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34855" href="?#comment-34855" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34842" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34855" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34855"> <div class="moveup"> <div class="ttypography">Thanks for editing. But what next? We got some hexagons, but still can not say how many hexagons <b>inside</b> this quarter of circle. Just border hexagons. What I missunderstood?</div> </div> </div> <div class="reply info"> <a class="comment-34855 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34855 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34855"> <li> <div class="comment"> <table class="comment-table" commentId="34856" commentParentId="34855"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/riadwaw" style="position: relative;"> <img src='https://userpic.codeforces.org/8452/avatar/7b374574b05a50df.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a> <div><a href="/profile/riadwaw" title="International Master riadwaw" class="rated-user user-orange">riadwaw</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:32">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34856" href="?#comment-34856" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34855" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34856" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="8452" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34856"> <div class="moveup"> <div class="ttypography">We  choose highest hexagon in every column.<div>So, we can calculate it's count</div><div>(all from highest downto - highest)in every column<br /></div></div> </div> </div> <div class="reply info"> <a class="comment-34856 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34856 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34856"> <li> <div class="comment"> <table class="comment-table" commentId="34857" commentParentId="34856"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 17:33">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34857" href="?#comment-34857" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34856" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34857" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34857"> <div class="moveup"> <div class="ttypography">oh. so easy. Thanks! :)</div> </div> </div> <div class="reply info"> <a class="comment-34857 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34857 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34857"> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> </ul> </div> </li> <li> <div class="comment"> <table class="comment-table" commentId="34847" commentParentId="34825"> <tr> <td class="left"> <div class="avatar"> <a href="/profile/denys.astanin" style="position: relative;"> <img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a> <div><a href="/profile/denys.astanin" title="Specialist denys.astanin" class="rated-user user-cyan">denys.astanin</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="Apr/28/2011 15:39">12 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-34847" href="?#comment-34847" style="font-size:1.2em;">#</a></span> <span class="item"><a title="Parent comment" href="#comment-34825" style="font-size:1.2em;">^</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="34847" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="12829" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-34847"> <div class="moveup"> <div class="ttypography">try to check precision.<div>You can write smthng like </div><div><div>double d1 =  Math.sqrt(x1 * x1 + y1 * y1);</div><div>if (d1 &gt; R &amp;&amp;  d1 - R &gt; 1e-6) return false;</div></div></div> </div> </div> <div class="reply info"> <a class="comment-34847 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-34847 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-34847"> </ul> </div> </li> </ul> </div> <div class="comment"> <table class="comment-table" commentId="133979" commentParentId="-1"> <tr> <td class="left"> <div style="position: absolute; left: 0;" class="comment-indent-holder"> <div class="comment-no-indent"> <span>&raquo;</span> </div> </div> <div class="avatar"> <a href="/profile/fastholf" style="position: relative;"> <img src='https://userpic.codeforces.org/15935/avatar/c2afbb3d3535dfac.jpg'/> </a> <div><a href="/profile/fastholf" title="Expert fastholf" class="rated-user user-blue">fastholf</a></div> </div> </td> <td class="right"> <div class="info"> <span class="item"><span class="format-humantime" title="May/19/2013 13:22">10 years ago</span>,</span> <span class="item"><a title="Link to comment" name="comment-133979" href="?#comment-133979" style="font-size:1.2em;">#</a></span> <span class="item">|</span> <span style="position: relative; top: 2px;"> </span> <div style="position:absolute;right:0;top:0;"> &nbsp; <span commentid="133979" class="CommentVoteFrame" data-commentRating="0" data-commentUserId="15935" style="position:relative;" > <a href="#" class="vote-for-comment" voteDirection="1" dd="x"><img style="position:relative;top:3px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-voteup-blue.png" alt="Vote: I like it" title="Vote: I like it"/></a> <span class="commentRating"><span style="color:gray;font-weight:bold;">0</span></span> <a href="#" class="vote-for-comment" voteDirection="-1" dd="y"><img style="position:relative;top:2px;opacity:0.35;" src="//codeforces.org/s/81027/images/actions/comment-votedown-blue.png" alt="Vote: I do not like it" title="Vote: I do not like it"/></a> </span> </div> </div> <div class="comment-content comment-content-133979"> <div class="moveup"> <div class="ttypography"><p>For task B</p> <pre><code>res[0] = 'R'; res[1] = 'O'; res[2] = 'Y'; res[3] = 'G'; res[4] = 'B'; res[5] = 'I'; res[6] = 'V'; int n; cin &gt;&gt; n; for (int i = 7; i &lt; n; ++i) { res[i] = res[i - 4]; } </code></pre><p>works as well.</p></div> </div> </div> <div class="reply info"> <a class="comment-133979 en false" href="#" style="text-decoration: none;"><span class="arrow">&rarr;</span></a> <a class="comment-133979 en false" href="#">Reply</a> </div> </td> </tr> </table> <ul class="comment-children comment-133979"> </ul> </div> <br/> <div id="editBox-1822" style="width:50em;display:none;"> <div class="previewBody" style="border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;">&nbsp;</div> <div style="width: 1px">&nbsp;</div> <div class="commentLocale" style="position: relative; top: 0.5em;left:4px;display: none;"> <input type="radio" name="locale" value="en"><span style="font-size: 1.2rem;position: relative; bottom: 3px;">In English</span> <input style="margin-left:1em" type="radio" name="locale" value="ru"><span style="font-size: 1.2rem;position: relative; 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79A
79
A
en
A. Bus Game
<div class="problem-statement"><div class="header"><div class="title">A. Bus Game</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>After Fox Ciel won an onsite round of a programming contest, she took a bus to return to her castle. The fee of the bus was 220 yen. She met Rabbit Hanako in the bus. They decided to play the following game because they got bored in the bus.</p><ul> <li> Initially, there is a pile that contains <span class="tex-span"><i>x</i></span> 100-yen coins and <span class="tex-span"><i>y</i></span> 10-yen coins. </li><li> They take turns alternatively. Ciel takes the first turn. </li><li> In each turn, they must take exactly 220 yen from the pile. In Ciel's turn, if there are multiple ways to take 220 yen, she will choose the way that contains the maximal number of 100-yen coins. In Hanako's turn, if there are multiple ways to take 220 yen, she will choose the way that contains the maximal number of 10-yen coins. </li><li> If Ciel or Hanako can't take exactly 220 yen from the pile, she loses. </li></ul><p> </p><p>Determine the winner of the game.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>x</i></span> (<span class="tex-span">0 ≤ <i>x</i> ≤ 10<sup class="upper-index">6</sup></span>) and <span class="tex-span"><i>y</i></span> (<span class="tex-span">0 ≤ <i>y</i> ≤ 10<sup class="upper-index">6</sup></span>), separated by a single space.</p></div><div class="output-specification"><div class="section-title">Output</div><p>If Ciel wins, print "<span class="tex-font-style-tt">Ciel</span>". Otherwise, print "<span class="tex-font-style-tt">Hanako</span>".</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2 2<br/></pre></div><div class="output"><div class="title">Output</div><pre>Ciel<br/></pre></div><div class="input"><div class="title">Input</div><pre>3 22<br/></pre></div><div class="output"><div class="title">Output</div><pre>Hanako<br/></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first turn (Ciel's turn), she will choose 2 100-yen coins and 2 10-yen coins. In the second turn (Hanako's turn), she will choose 1 100-yen coin and 12 10-yen coins. In the third turn (Ciel's turn), she can't pay exactly 220 yen, so Ciel will lose.</p></div></div>
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If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. 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if (!pre) { s = s.replace(/\s+/g, " "); } if (s.length > 0) { result.push(s); } } if (pre && node.tagName === "BR") { result.push("\n"); } node.childNodes.forEach(function (child) { result.push(nodeToText(child, node.tagName === "PRE").join("")); }); if (node.tagName === "DIV" || node.tagName === "P" || node.tagName === "PRE" || node.tagName === "UL" || node.tagName === "LI" ) { result.push("\n"); } if (node.tagName === "NOBR") { result.push(CLOSING_SPACE); } return result; } const isSpecial = function (c) { return c === ',' || c === '.' || c === ';' || c === ')' || c === ' '; } const convertStatementToText = function(statmentNode) { const text = nodeToText(statmentNode, false).join("").replace(/ +/g, " ").replace(/\n\n+/g, "\n\n"); let result = []; for (let i = 0; i < text.length; i++) { const c = text.charAt(i); if (c === OPENING_SPACE) { if (!((i > 0 && text.charAt(i - 1) === '(') || (result.length > 0 && result[result.length - 1] === ' '))) { result.push('+'); } } else if (c === CLOSING_SPACE) { if (!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) { result.push('-'); } } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="A" data-uuid="ps_b37a272e881829ff6b771dc9c0beee894974ce4f"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">A. Bus Game</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>After Fox Ciel won an onsite round of a programming contest, she took a bus to return to her castle. The fee of the bus was 220 yen. She met Rabbit Hanako in the bus. They decided to play the following game because they got bored in the bus.</p><ul> <li> Initially, there is a pile that contains <span class="tex-span"><i>x</i></span> 100-yen coins and <span class="tex-span"><i>y</i></span> 10-yen coins. </li><li> They take turns alternatively. Ciel takes the first turn. </li><li> In each turn, they must take exactly 220 yen from the pile. In Ciel's turn, if there are multiple ways to take 220 yen, she will choose the way that contains the maximal number of 100-yen coins. In Hanako's turn, if there are multiple ways to take 220 yen, she will choose the way that contains the maximal number of 10-yen coins. </li><li> If Ciel or Hanako can't take exactly 220 yen from the pile, she loses. </li></ul><p> </p><p>Determine the winner of the game.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>x</i></span> (<span class="tex-span">0 ≤ <i>x</i> ≤ 10<sup class="upper-index">6</sup></span>) and <span class="tex-span"><i>y</i></span> (<span class="tex-span">0 ≤ <i>y</i> ≤ 10<sup class="upper-index">6</sup></span>), separated by a single space.</p></div><div class="output-specification"><div class="section-title">Output</div><p>If Ciel wins, print &quot;<span class="tex-font-style-tt">Ciel</span>&quot;. Otherwise, print &quot;<span class="tex-font-style-tt">Hanako</span>&quot;.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>Ciel<br /></pre></div><div class="input"><div class="title">Input</div><pre>3 22<br /></pre></div><div class="output"><div class="title">Output</div><pre>Hanako<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first turn (Ciel's turn), she will choose 2 100-yen coins and 2 10-yen coins. In the second turn (Hanako's turn), she will choose 1 100-yen coin and 12 10-yen coins. 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["Greedy algorithms"]
["greedy", "*1200"]
https://codeforces.com/blog/entry/1848
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Игра в автобусе (автор - <span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-weight: normal;"></span></span><span style="font-weight: normal;font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 13.0px;"><a class="rated-user user-red" href="//www.codeforces.com/profile/rng_58" style="font-family: arial;text-decoration: none;font-weight: bold;color: rgb(0,0,204);" title="Colonel rng_58">rng_58</a>)</span></h2>В этой задаче прекрасно работает симуляция &quot;в лоб&quot; - нам прямым текстом сказано, как ходят игроки. Лиса Кейл играет по следующей стратегии: если есть хотя бы две монеты по 100 йен и две монеты по 10 йен, она берёт их. Иначе, если есть хотя бы одна монета по 100 йен и 12 монет по 10 - она забирает их. В противном случае она берет 22 монеты по 10 йен. Если ей это не удаётся - выигрывает Ханако. Кролик поступает точно также, но в обратном порядке. Сложность решения - <i>O(x+y)</i>.<br /><br /><h2>Задача B. Разноцветное поле (автор - <span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-weight: normal;"></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-weight: normal;"><span style="border-collapse: collapse;font-size: 13.0px;line-height: normal;"><a class="rated-user user-red" href="//www.codeforces.com/profile/ir5" style="font-family: arial;text-decoration: none;font-weight: bold;color: rgb(0,0,204);" title="Colonel ir5">ir5</a></span></span></span>)</h2>Решение, использующее массив <i>NxM</i> получает TL/ML, и, разумеется, мы не можем решать задачу &quot;в лоб&quot;. Так как и запросов, и безжизненных клеток не более 1000, нам достаточно научиться отвечать на каждый запрос за время <i>O(K)</i>.<br />Пусть <i>(a, b)</i> - клетка из очередного запроса. Является ли она безжизненной, или нет - решит один цикл <i>for</i> по входным данным.<br />Итак, мы знаем, что на этой клетке что-то растёт. Пусть <i>I</i> - суммарное число клеток перед <i>(a, b)</i>, а <i>J</i> - количество безжизненных клеток перед <i>(a, b)</i>. Тогда ответ определяется значением <i>(I-J) mod 3</i> (где <i>0</i> =&gt; &quot;<i>Carrots</i>&quot;, <i>1</i> =&gt; &quot;<i>Kiwis</i>&quot;, <i>2</i> =&gt; &quot;<i>Grapes</i>&quot;). Путем несложной математики можно понять, что I=(a-1)M+(b-1) (первое слагаемое - это количество клеток в предыдущих строках, а второе - количество предыдущих клеток в текущей строке), а величину <i>J</i> можно опять же подсчитать циклом <i>for</i> за <i>O(K)</i>.<br />Получаем решение за <i>O(TK)</i>, где <i>T</i> - количество запросов.<br /><br /><h2>Задача C. Скучные строки (автор - <span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-weight: normal;"></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-weight: normal;"><span style="border-collapse: collapse;font-size: 13.0px;line-height: normal;"><a class="rated-user user-red" href="//www.codeforces.com/profile/ir5" style="font-family: arial;text-decoration: none;font-weight: bold;color: rgb(0,0,204);" title="Colonel ir5">ir5</a>)</span></span></span></h2>Мы можем представить каждую подстроку в <i>s</i>, совпадающую с какой-либо скучной строкой, как &quot;запрещённый отрезок&quot;. Таких кандидатов в плохие отрезки для каждой из <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> порядка <i>O(n)</i>, поэтому мы можем подсчитать их все за <span class="tex-span"><i>O</i>(|<i>s</i>|· <i>n</i>· |<i>b</i><sub class="lower-index"><i>i</i></sub>|)</span> (да, тут не требуется никаких специальных алгоритмов, например, КМП).<br />Теперь мы можем переписать задачу по-другому: дано не более <span class="tex-span">10<sup class="upper-index">6</sup></span> запрещенных отрезков, найти отрезок, который не содержит полностью ни один из запрещённых. <br /><br />Давайте подсчитаем величину <i>right[i]</i> - минимальная правая граница среди запрещенных интервалов с левой границей в <i>i</i>. Если таких интервалов нет, положим <i>right[i]=|s|</i>.<br /><br />Теперь давайте переберём начало ответа, начиная с <i>|s|</i> и до <i>0</i>. Вначале ответ - пустая строка. Пусть ответ для предыдщего начала - подстрока с <i>i+1</i> до <i>j</i>. Тогда, если <i>right[i]&gt;j</i>, то мы можем спокойно приписать один символ слева и ответ увеличивается на 1 - подстрока с <i>i</i> до <i>j</i>. Если же <i>right[i]&lt;=j,</i> то ответ не может быть дальше, чем до <i>right[i]-1</i>, в противном случае мы полностью покроем &quot;плохой отрезок&quot;. Таким образом, мы пробежимся по всем возможным началам ответов за <i>O(|s|)</i>.<br /><br />Итого время работы - <span class="tex-span"><i>O</i>(|<i>s</i>|· <i>n</i>· |<i>b</i><sub class="lower-index"><i>i</i></sub>|)</span>.<br /><br /><div align="center"><h2>Задача D. Кодовый замок (автор - <span style="font-weight: normal;font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"></span><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 13.0px;"><a class="rated-user user-red" href="//www.codeforces.com/profile/rng_58" style="font-family: arial;text-decoration: none;font-weight: bold;color: rgb(0,0,204);" title="Colonel rng_58">rng_58</a>)</span></h2><div align="left">Давайте слегка переформулируем состояние замка: определим массив <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> следующим образом: <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub> = 0</span>, если панели <span class="tex-span"><i>i</i></span> и <span class="tex-span"><i>i</i> + 1</span> находятся в одинаковом состоянии и <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub> = 1</span> в противном случае. Положим, что панели <span class="tex-span">0</span> и <span class="tex-span"><i>n</i> + 1</span> выключены (OFF). Если Кейл изменяет состояние панелей на отрезке с <i>x</i> до <i>x+a-1</i> (включительно), то в массиве <i>b</i> изменяются значения <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i></sub></span> и <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i> + <i>a</i></sub></span>:<br /><img src="https://irulop.cc/adsl/Deditorial.png" style="max-width: 100.0%;max-height: 100.0%;" /><br /><b>Задача D'</b>.<br />У Вас есть массив <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span>. Не более 20 (<i>=2k</i>) элементов - единички. За каждый ход Вы можете изменить значения в <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i></sub></span> и <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i> + <i>a</i></sub></span>, где <span class="tex-span"><i>a</i></span> - элемент <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> и <span class="tex-span">0 ≤ <i>x</i> ≤ <i>n</i> - <i>a</i></span>. Определите минимальное количество ходов, требуемое для обнуления массива (мы просто &quot;перевернули&quot; порядок действий).<br /><br />Понятно, что порядок ходов не важен. Также понятно, что если массив еще не обнулён, то есть такой индекс <span class="tex-span"><i>x</i></span>, что <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i></sub> = 1</span>, и нам придётся походить, задев этот индекс, хотя бы один раз. Давайте следаем этот ход первым. Далее применим аналогичное рассуждение и получим, что на каждом ходу хотя бы одно из двух чисел <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i></sub></span> и <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i> + <i>a</i></sub></span> - единица. <br /><br /><b>Задача D''.</b><br />Теперь давайте построим граф с вершинами от <i>0</i> до<i> n+1</i>. Ребро между двумя вершинами <span class="tex-span"><i>v</i><sub class="lower-index">1</sub></span> и <span class="tex-span"><i>v</i><sub class="lower-index">2</sub></span> будет в том, и только том случае, если <span class="tex-span">|<i>v</i><sub class="lower-index">1</sub> - <i>v</i><sub class="lower-index">2</sub>|</span> - элемент массива <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> (то есть, мы можем сделать ход <span class="tex-span"><i>b</i><sub class="lower-index"><i>v</i><sub class="lower-index">1</sub></sub></span> и <span class="tex-span"><i>b</i><sub class="lower-index"><i>v</i><sub class="lower-index">2</sub></sub></span>. Также изначально есть не более 20 фишек (стоят в позициях изначальных единиц в массиве <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span>). За один ход мы можем подвинуть фишку по какому-либо ребру. Если две фишки оказываются в одной вершине, они исчезают. Определить минимальное количество ходов, необходимое для избавления от всех фишек.<br /><br />Для начала предподсчитаем попарные расстояния между всеми фишками. Это можно сделать, 20 раз запустив BFS. А далее имеем динамику по подмножествам: <i>d[S]</i> (где <i>S</i> - подмножество фишек) - минимальное количество шагов, чтобы убрать все фишки из <i>S</i>. Если <i>S</i> пусто, <i>d[S=0]</i>=0. Если <i><span class="tex-span"><i>S</i> = {<i>s</i><sub class="lower-index">0</sub>, <i>s</i><sub class="lower-index">1</sub>, ..., <i>s</i><sub class="lower-index"><i>m</i> - 1</sub>}</span></i> непусто, то мы выбирае фишки, которая исчезнет вместе с нулевой, и делаем переход: <span class="tex-span"><i>d</i>[<i>S</i>] = <i>min</i>(<i>d</i>[<i>S</i>\{<i>s</i><sub class="lower-index">0</sub>, <i>s</i><sub class="lower-index"><i>i</i></sub>}] + <i>dist</i>(<i>s</i><sub class="lower-index">0</sub>, <i>s</i><sub class="lower-index"><i>i</i></sub>))</span>, где <span class="tex-span">1 ≤ <i>i</i> ≤ <i>m</i> - 1</span>.<br /><br />Итоговая сложность решения - <span class="tex-span"><i>O</i>(<i>knl</i> + <i>k</i>· 2<sup class="upper-index">2<i>k</i></sup>)</span>.<br /><br /></div></div></div> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-1484-1848").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "1484", blogEntryId: "1848", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); 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79B
79
B
en
B. Colorful Field
<div class="problem-statement"><div class="header"><div class="title">B. Colorful Field</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Fox Ciel saw a large field while she was on a bus. The field was a <span class="tex-span"><i>n</i> × <i>m</i></span> rectangle divided into <span class="tex-span">1 × 1</span> cells. Some cells were wasteland, and other each cell contained crop plants: either carrots or kiwis or grapes. </p><p>After seeing the field carefully, Ciel found that the crop plants of each cell were planted in following procedure:</p><ul> <li> Assume that the rows are numbered <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span> from top to bottom and the columns are numbered <span class="tex-span">1</span> to <span class="tex-span"><i>m</i></span> from left to right, and a cell in row <span class="tex-span"><i>i</i></span> and column <span class="tex-span"><i>j</i></span> is represented as <span class="tex-span">(<i>i</i>, <i>j</i>)</span>. </li><li> First, each field is either cultivated or waste. Crop plants will be planted in the cultivated cells in the order of <span class="tex-span">(1, 1) → ... → (1, <i>m</i>) → (2, 1) → ... → (2, <i>m</i>) → ... → (<i>n</i>, 1) → ... → (<i>n</i>, <i>m</i>)</span>. Waste cells will be ignored. </li><li> Crop plants (either carrots or kiwis or grapes) will be planted in each cell one after another cyclically. Carrots will be planted in the first cell, then kiwis in the second one, grapes in the third one, carrots in the forth one, kiwis in the fifth one, and so on. </li></ul><p>The following figure will show you the example of this procedure. Here, a white square represents a cultivated cell, and a black square represents a waste cell.</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/cc18980b9ec1718d966c039f7bc7ad3858b1bca3.png" style="max-width: 100.0%;max-height: 100.0%;"/> </center><p>Now she is wondering how to determine the crop plants in some certain cells. </p></div><div class="input-specification"><div class="section-title">Input</div><p>In the first line there are four positive integers <span class="tex-span"><i>n</i>, <i>m</i>, <i>k</i>, <i>t</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 4·10<sup class="upper-index">4</sup>, 1 ≤ <i>m</i> ≤ 4·10<sup class="upper-index">4</sup>, 1 ≤ <i>k</i> ≤ 10<sup class="upper-index">3</sup>, 1 ≤ <i>t</i> ≤ 10<sup class="upper-index">3</sup></span>), each of which represents the height of the field, the width of the field, the number of waste cells and the number of queries that ask the kind of crop plants in a certain cell.</p><p>Following each <span class="tex-span"><i>k</i></span> lines contains two integers <span class="tex-span"><i>a</i>, <i>b</i></span> (<span class="tex-span">1 ≤ <i>a</i> ≤ <i>n</i>, 1 ≤ <i>b</i> ≤ <i>m</i></span>), which denotes a cell <span class="tex-span">(<i>a</i>, <i>b</i>)</span> is waste. It is guaranteed that the same cell will not appear twice in this section.</p><p>Following each <span class="tex-span"><i>t</i></span> lines contains two integers <span class="tex-span"><i>i</i>, <i>j</i></span> (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>n</i>, 1 ≤ <i>j</i> ≤ <i>m</i></span>), which is a query that asks you the kind of crop plants of a cell <span class="tex-span">(<i>i</i>, <i>j</i>)</span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>For each query, if the cell is waste, print <span class="tex-font-style-tt">Waste</span>. Otherwise, print the name of crop plants in the cell: either <span class="tex-font-style-tt">Carrots</span> or <span class="tex-font-style-tt">Kiwis</span> or <span class="tex-font-style-tt">Grapes</span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>4 5 5 6<br/>4 3<br/>1 3<br/>3 3<br/>2 5<br/>3 2<br/>1 3<br/>1 4<br/>2 3<br/>2 4<br/>1 1<br/>1 1<br/></pre></div><div class="output"><div class="title">Output</div><pre>Waste<br/>Grapes<br/>Carrots<br/>Kiwis<br/>Carrots<br/>Carrots<br/></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>The sample corresponds to the figure in the statement.</p></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="B" data-uuid="ps_cfd602251026ce7651b9f3b2ebf7ef0e9204cb94"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">B. Colorful Field</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Fox Ciel saw a large field while she was on a bus. The field was a <span class="tex-span"><i>n</i> × <i>m</i></span> rectangle divided into <span class="tex-span">1 × 1</span> cells. Some cells were wasteland, and other each cell contained crop plants: either carrots or kiwis or grapes. </p><p>After seeing the field carefully, Ciel found that the crop plants of each cell were planted in following procedure:</p><ul> <li> Assume that the rows are numbered <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span> from top to bottom and the columns are numbered <span class="tex-span">1</span> to <span class="tex-span"><i>m</i></span> from left to right, and a cell in row <span class="tex-span"><i>i</i></span> and column <span class="tex-span"><i>j</i></span> is represented as <span class="tex-span">(<i>i</i>, <i>j</i>)</span>. </li><li> First, each field is either cultivated or waste. Crop plants will be planted in the cultivated cells in the order of <span class="tex-span">(1, 1) → ... → (1, <i>m</i>) → (2, 1) → ... → (2, <i>m</i>) → ... → (<i>n</i>, 1) → ... → (<i>n</i>, <i>m</i>)</span>. Waste cells will be ignored. </li><li> Crop plants (either carrots or kiwis or grapes) will be planted in each cell one after another cyclically. Carrots will be planted in the first cell, then kiwis in the second one, grapes in the third one, carrots in the forth one, kiwis in the fifth one, and so on. </li></ul><p>The following figure will show you the example of this procedure. Here, a white square represents a cultivated cell, and a black square represents a waste cell.</p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/cc18980b9ec1718d966c039f7bc7ad3858b1bca3.png" style="max-width: 100.0%;max-height: 100.0%;" /> </center><p>Now she is wondering how to determine the crop plants in some certain cells. </p></div><div class="input-specification"><div class="section-title">Input</div><p>In the first line there are four positive integers <span class="tex-span"><i>n</i>, <i>m</i>, <i>k</i>, <i>t</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 4·10<sup class="upper-index">4</sup>, 1 ≤ <i>m</i> ≤ 4·10<sup class="upper-index">4</sup>, 1 ≤ <i>k</i> ≤ 10<sup class="upper-index">3</sup>, 1 ≤ <i>t</i> ≤ 10<sup class="upper-index">3</sup></span>), each of which represents the height of the field, the width of the field, the number of waste cells and the number of queries that ask the kind of crop plants in a certain cell.</p><p>Following each <span class="tex-span"><i>k</i></span> lines contains two integers <span class="tex-span"><i>a</i>, <i>b</i></span> (<span class="tex-span">1 ≤ <i>a</i> ≤ <i>n</i>, 1 ≤ <i>b</i> ≤ <i>m</i></span>), which denotes a cell <span class="tex-span">(<i>a</i>, <i>b</i>)</span> is waste. It is guaranteed that the same cell will not appear twice in this section.</p><p>Following each <span class="tex-span"><i>t</i></span> lines contains two integers <span class="tex-span"><i>i</i>, <i>j</i></span> (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>n</i>, 1 ≤ <i>j</i> ≤ <i>m</i></span>), which is a query that asks you the kind of crop plants of a cell <span class="tex-span">(<i>i</i>, <i>j</i>)</span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>For each query, if the cell is waste, print <span class="tex-font-style-tt">Waste</span>. Otherwise, print the name of crop plants in the cell: either <span class="tex-font-style-tt">Carrots</span> or <span class="tex-font-style-tt">Kiwis</span> or <span class="tex-font-style-tt">Grapes</span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>4 5 5 6<br />4 3<br />1 3<br />3 3<br />2 5<br />3 2<br />1 3<br />1 4<br />2 3<br />2 4<br />1 1<br />1 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>Waste<br />Grapes<br />Carrots<br />Kiwis<br />Carrots<br />Carrots<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>The sample corresponds to the figure in the statement.</p></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=B]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); 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["Implementation problems, programming technics, simulation", "Sortings, orderings"]
["implementation", "sortings", "*1400"]
https://codeforces.com/blog/entry/1848
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Игра в автобусе (автор - <span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-weight: normal;"></span></span><span style="font-weight: normal;font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 13.0px;"><a class="rated-user user-red" href="//www.codeforces.com/profile/rng_58" style="font-family: arial;text-decoration: none;font-weight: bold;color: rgb(0,0,204);" title="Colonel rng_58">rng_58</a>)</span></h2>В этой задаче прекрасно работает симуляция &quot;в лоб&quot; - нам прямым текстом сказано, как ходят игроки. Лиса Кейл играет по следующей стратегии: если есть хотя бы две монеты по 100 йен и две монеты по 10 йен, она берёт их. Иначе, если есть хотя бы одна монета по 100 йен и 12 монет по 10 - она забирает их. В противном случае она берет 22 монеты по 10 йен. Если ей это не удаётся - выигрывает Ханако. Кролик поступает точно также, но в обратном порядке. Сложность решения - <i>O(x+y)</i>.<br /><br /><h2>Задача B. Разноцветное поле (автор - <span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-weight: normal;"></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-weight: normal;"><span style="border-collapse: collapse;font-size: 13.0px;line-height: normal;"><a class="rated-user user-red" href="//www.codeforces.com/profile/ir5" style="font-family: arial;text-decoration: none;font-weight: bold;color: rgb(0,0,204);" title="Colonel ir5">ir5</a></span></span></span>)</h2>Решение, использующее массив <i>NxM</i> получает TL/ML, и, разумеется, мы не можем решать задачу &quot;в лоб&quot;. Так как и запросов, и безжизненных клеток не более 1000, нам достаточно научиться отвечать на каждый запрос за время <i>O(K)</i>.<br />Пусть <i>(a, b)</i> - клетка из очередного запроса. Является ли она безжизненной, или нет - решит один цикл <i>for</i> по входным данным.<br />Итак, мы знаем, что на этой клетке что-то растёт. Пусть <i>I</i> - суммарное число клеток перед <i>(a, b)</i>, а <i>J</i> - количество безжизненных клеток перед <i>(a, b)</i>. Тогда ответ определяется значением <i>(I-J) mod 3</i> (где <i>0</i> =&gt; &quot;<i>Carrots</i>&quot;, <i>1</i> =&gt; &quot;<i>Kiwis</i>&quot;, <i>2</i> =&gt; &quot;<i>Grapes</i>&quot;). Путем несложной математики можно понять, что I=(a-1)M+(b-1) (первое слагаемое - это количество клеток в предыдущих строках, а второе - количество предыдущих клеток в текущей строке), а величину <i>J</i> можно опять же подсчитать циклом <i>for</i> за <i>O(K)</i>.<br />Получаем решение за <i>O(TK)</i>, где <i>T</i> - количество запросов.<br /><br /><h2>Задача C. Скучные строки (автор - <span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-weight: normal;"></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-weight: normal;"><span style="border-collapse: collapse;font-size: 13.0px;line-height: normal;"><a class="rated-user user-red" href="//www.codeforces.com/profile/ir5" style="font-family: arial;text-decoration: none;font-weight: bold;color: rgb(0,0,204);" title="Colonel ir5">ir5</a>)</span></span></span></h2>Мы можем представить каждую подстроку в <i>s</i>, совпадающую с какой-либо скучной строкой, как &quot;запрещённый отрезок&quot;. Таких кандидатов в плохие отрезки для каждой из <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> порядка <i>O(n)</i>, поэтому мы можем подсчитать их все за <span class="tex-span"><i>O</i>(|<i>s</i>|· <i>n</i>· |<i>b</i><sub class="lower-index"><i>i</i></sub>|)</span> (да, тут не требуется никаких специальных алгоритмов, например, КМП).<br />Теперь мы можем переписать задачу по-другому: дано не более <span class="tex-span">10<sup class="upper-index">6</sup></span> запрещенных отрезков, найти отрезок, который не содержит полностью ни один из запрещённых. <br /><br />Давайте подсчитаем величину <i>right[i]</i> - минимальная правая граница среди запрещенных интервалов с левой границей в <i>i</i>. Если таких интервалов нет, положим <i>right[i]=|s|</i>.<br /><br />Теперь давайте переберём начало ответа, начиная с <i>|s|</i> и до <i>0</i>. Вначале ответ - пустая строка. Пусть ответ для предыдщего начала - подстрока с <i>i+1</i> до <i>j</i>. Тогда, если <i>right[i]&gt;j</i>, то мы можем спокойно приписать один символ слева и ответ увеличивается на 1 - подстрока с <i>i</i> до <i>j</i>. Если же <i>right[i]&lt;=j,</i> то ответ не может быть дальше, чем до <i>right[i]-1</i>, в противном случае мы полностью покроем &quot;плохой отрезок&quot;. Таким образом, мы пробежимся по всем возможным началам ответов за <i>O(|s|)</i>.<br /><br />Итого время работы - <span class="tex-span"><i>O</i>(|<i>s</i>|· <i>n</i>· |<i>b</i><sub class="lower-index"><i>i</i></sub>|)</span>.<br /><br /><div align="center"><h2>Задача D. Кодовый замок (автор - <span style="font-weight: normal;font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"></span><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 13.0px;"><a class="rated-user user-red" href="//www.codeforces.com/profile/rng_58" style="font-family: arial;text-decoration: none;font-weight: bold;color: rgb(0,0,204);" title="Colonel rng_58">rng_58</a>)</span></h2><div align="left">Давайте слегка переформулируем состояние замка: определим массив <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> следующим образом: <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub> = 0</span>, если панели <span class="tex-span"><i>i</i></span> и <span class="tex-span"><i>i</i> + 1</span> находятся в одинаковом состоянии и <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub> = 1</span> в противном случае. Положим, что панели <span class="tex-span">0</span> и <span class="tex-span"><i>n</i> + 1</span> выключены (OFF). Если Кейл изменяет состояние панелей на отрезке с <i>x</i> до <i>x+a-1</i> (включительно), то в массиве <i>b</i> изменяются значения <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i></sub></span> и <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i> + <i>a</i></sub></span>:<br /><img src="https://irulop.cc/adsl/Deditorial.png" style="max-width: 100.0%;max-height: 100.0%;" /><br /><b>Задача D'</b>.<br />У Вас есть массив <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span>. Не более 20 (<i>=2k</i>) элементов - единички. За каждый ход Вы можете изменить значения в <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i></sub></span> и <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i> + <i>a</i></sub></span>, где <span class="tex-span"><i>a</i></span> - элемент <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> и <span class="tex-span">0 ≤ <i>x</i> ≤ <i>n</i> - <i>a</i></span>. Определите минимальное количество ходов, требуемое для обнуления массива (мы просто &quot;перевернули&quot; порядок действий).<br /><br />Понятно, что порядок ходов не важен. Также понятно, что если массив еще не обнулён, то есть такой индекс <span class="tex-span"><i>x</i></span>, что <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i></sub> = 1</span>, и нам придётся походить, задев этот индекс, хотя бы один раз. Давайте следаем этот ход первым. Далее применим аналогичное рассуждение и получим, что на каждом ходу хотя бы одно из двух чисел <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i></sub></span> и <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i> + <i>a</i></sub></span> - единица. <br /><br /><b>Задача D''.</b><br />Теперь давайте построим граф с вершинами от <i>0</i> до<i> n+1</i>. Ребро между двумя вершинами <span class="tex-span"><i>v</i><sub class="lower-index">1</sub></span> и <span class="tex-span"><i>v</i><sub class="lower-index">2</sub></span> будет в том, и только том случае, если <span class="tex-span">|<i>v</i><sub class="lower-index">1</sub> - <i>v</i><sub class="lower-index">2</sub>|</span> - элемент массива <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> (то есть, мы можем сделать ход <span class="tex-span"><i>b</i><sub class="lower-index"><i>v</i><sub class="lower-index">1</sub></sub></span> и <span class="tex-span"><i>b</i><sub class="lower-index"><i>v</i><sub class="lower-index">2</sub></sub></span>. Также изначально есть не более 20 фишек (стоят в позициях изначальных единиц в массиве <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span>). За один ход мы можем подвинуть фишку по какому-либо ребру. Если две фишки оказываются в одной вершине, они исчезают. Определить минимальное количество ходов, необходимое для избавления от всех фишек.<br /><br />Для начала предподсчитаем попарные расстояния между всеми фишками. Это можно сделать, 20 раз запустив BFS. А далее имеем динамику по подмножествам: <i>d[S]</i> (где <i>S</i> - подмножество фишек) - минимальное количество шагов, чтобы убрать все фишки из <i>S</i>. Если <i>S</i> пусто, <i>d[S=0]</i>=0. Если <i><span class="tex-span"><i>S</i> = {<i>s</i><sub class="lower-index">0</sub>, <i>s</i><sub class="lower-index">1</sub>, ..., <i>s</i><sub class="lower-index"><i>m</i> - 1</sub>}</span></i> непусто, то мы выбирае фишки, которая исчезнет вместе с нулевой, и делаем переход: <span class="tex-span"><i>d</i>[<i>S</i>] = <i>min</i>(<i>d</i>[<i>S</i>\{<i>s</i><sub class="lower-index">0</sub>, <i>s</i><sub class="lower-index"><i>i</i></sub>}] + <i>dist</i>(<i>s</i><sub class="lower-index">0</sub>, <i>s</i><sub class="lower-index"><i>i</i></sub>))</span>, где <span class="tex-span">1 ≤ <i>i</i> ≤ <i>m</i> - 1</span>.<br /><br />Итоговая сложность решения - <span class="tex-span"><i>O</i>(<i>knl</i> + <i>k</i>· 2<sup class="upper-index">2<i>k</i></sup>)</span>.<br /><br /></div></div></div> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-1484-1848").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "1484", blogEntryId: "1848", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); 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79C
79
C
en
C. Beaver
<div class="problem-statement"><div class="header"><div class="title">C. Beaver</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>After Fox Ciel got off a bus, she found that the bus she was on was a wrong bus and she lost her way in a strange town. However, she fortunately met her friend Beaver Taro and asked which way to go to her castle. Taro's response to her was a string <span class="tex-span"><i>s</i></span>, and she tried to remember the string <span class="tex-span"><i>s</i></span> correctly.</p><p>However, Ciel feels <span class="tex-span"><i>n</i></span> strings <span class="tex-span"><i>b</i><sub class="lower-index">1</sub>, <i>b</i><sub class="lower-index">2</sub>, ... , <i>b</i><sub class="lower-index"><i>n</i></sub></span> are really boring, and unfortunately she dislikes to remember a string that contains a boring substring. To make the thing worse, what she can remember is only the contiguous substring of <span class="tex-span"><i>s</i></span>.</p><p>Determine the longest contiguous substring of <span class="tex-span"><i>s</i></span> that does not contain any boring string, so that she can remember the longest part of Taro's response.</p></div><div class="input-specification"><div class="section-title">Input</div><p>In the first line there is a string <span class="tex-span"><i>s</i></span>. The length of <span class="tex-span"><i>s</i></span> will be between <span class="tex-span">1</span> and <span class="tex-span">10<sup class="upper-index">5</sup></span>, inclusive.</p><p>In the second line there is a single integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10</span>). Next <span class="tex-span"><i>n</i></span> lines, there is a string <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>n</i></span>). Each length of <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> will be between <span class="tex-span">1</span> and <span class="tex-span">10</span>, inclusive.</p><p>Each character of the given strings will be either a English alphabet (both lowercase and uppercase) or a underscore (<span class="tex-font-style-tt">'_'</span>) or a digit. Assume that these strings are case-sensitive.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Output in the first line two space-separated integers <span class="tex-span"><i>len</i></span> and <span class="tex-span"><i>pos</i></span>: the length of the longest contiguous substring of <span class="tex-span"><i>s</i></span> that does not contain any <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span>, and the first position of the substring (0-indexed). The position <span class="tex-span"><i>pos</i></span> must be between <span class="tex-span">0</span> and <span class="tex-span">|<i>s</i>| - <i>len</i></span> inclusive, where <span class="tex-span">|<i>s</i>|</span> is the length of string <span class="tex-span"><i>s</i></span>.</p><p>If there are several solutions, output any.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>Go_straight_along_this_street<br/>5<br/>str<br/>long<br/>tree<br/>biginteger<br/>ellipse<br/></pre></div><div class="output"><div class="title">Output</div><pre>12 4<br/></pre></div><div class="input"><div class="title">Input</div><pre>IhaveNoIdea<br/>9<br/>I<br/>h<br/>a<br/>v<br/>e<br/>N<br/>o<br/>I<br/>d<br/></pre></div><div class="output"><div class="title">Output</div><pre>0 0<br/></pre></div><div class="input"><div class="title">Input</div><pre>unagioisii<br/>2<br/>ioi<br/>unagi<br/></pre></div><div class="output"><div class="title">Output</div><pre>5 5<br/></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first sample, the solution is <span class="tex-font-style-tt">traight_alon</span>.</p><p>In the second sample, the solution is an empty string, so the output can be «<span class="tex-font-style-tt">0 0</span>», «<span class="tex-font-style-tt">0 1</span>», «<span class="tex-font-style-tt">0 2</span>», and so on.</p><p>In the third sample, the solution is either <span class="tex-font-style-tt">nagio</span> or <span class="tex-font-style-tt">oisii</span>.</p></div></div>
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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="C" data-uuid="ps_688fab291cde9d4a247ac8798ad3d7cf5b0893bb"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. Beaver</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>After Fox Ciel got off a bus, she found that the bus she was on was a wrong bus and she lost her way in a strange town. However, she fortunately met her friend Beaver Taro and asked which way to go to her castle. Taro's response to her was a string <span class="tex-span"><i>s</i></span>, and she tried to remember the string <span class="tex-span"><i>s</i></span> correctly.</p><p>However, Ciel feels <span class="tex-span"><i>n</i></span> strings <span class="tex-span"><i>b</i><sub class="lower-index">1</sub>, <i>b</i><sub class="lower-index">2</sub>, ... , <i>b</i><sub class="lower-index"><i>n</i></sub></span> are really boring, and unfortunately she dislikes to remember a string that contains a boring substring. To make the thing worse, what she can remember is only the contiguous substring of <span class="tex-span"><i>s</i></span>.</p><p>Determine the longest contiguous substring of <span class="tex-span"><i>s</i></span> that does not contain any boring string, so that she can remember the longest part of Taro's response.</p></div><div class="input-specification"><div class="section-title">Input</div><p>In the first line there is a string <span class="tex-span"><i>s</i></span>. The length of <span class="tex-span"><i>s</i></span> will be between <span class="tex-span">1</span> and <span class="tex-span">10<sup class="upper-index">5</sup></span>, inclusive.</p><p>In the second line there is a single integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10</span>). Next <span class="tex-span"><i>n</i></span> lines, there is a string <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>n</i></span>). Each length of <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> will be between <span class="tex-span">1</span> and <span class="tex-span">10</span>, inclusive.</p><p>Each character of the given strings will be either a English alphabet (both lowercase and uppercase) or a underscore (<span class="tex-font-style-tt">'_'</span>) or a digit. Assume that these strings are case-sensitive.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Output in the first line two space-separated integers <span class="tex-span"><i>len</i></span> and <span class="tex-span"><i>pos</i></span>: the length of the longest contiguous substring of <span class="tex-span"><i>s</i></span> that does not contain any <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span>, and the first position of the substring (0-indexed). The position <span class="tex-span"><i>pos</i></span> must be between <span class="tex-span">0</span> and <span class="tex-span">|<i>s</i>| - <i>len</i></span> inclusive, where <span class="tex-span">|<i>s</i>|</span> is the length of string <span class="tex-span"><i>s</i></span>.</p><p>If there are several solutions, output any.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>Go_straight_along_this_street<br />5<br />str<br />long<br />tree<br />biginteger<br />ellipse<br /></pre></div><div class="output"><div class="title">Output</div><pre>12 4<br /></pre></div><div class="input"><div class="title">Input</div><pre>IhaveNoIdea<br />9<br />I<br />h<br />a<br />v<br />e<br />N<br />o<br />I<br />d<br /></pre></div><div class="output"><div class="title">Output</div><pre>0 0<br /></pre></div><div class="input"><div class="title">Input</div><pre>unagioisii<br />2<br />ioi<br />unagi<br /></pre></div><div class="output"><div class="title">Output</div><pre>5 5<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first sample, the solution is <span class="tex-font-style-tt">traight_alon</span>.</p><p>In the second sample, the solution is an empty string, so the output can be «<span class="tex-font-style-tt">0 0</span>», «<span class="tex-font-style-tt">0 1</span>», «<span class="tex-font-style-tt">0 2</span>», and so on.</p><p>In the third sample, the solution is either <span class="tex-font-style-tt">nagio</span> or <span class="tex-font-style-tt">oisii</span>.</p></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=C]"); 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["Heaps, binary search trees, segment trees, hash tables, etc", "Dynamic programming", "Greedy algorithms", "Hashing, hashtables", "Prefix- and Z-functions, suffix structures, Knuth\u2013Morris\u2013Pratt algorithm, etc", "Two pointers"]
["data structures", "dp", "greedy", "hashing", "strings", "two pointers", "*1800"]
https://codeforces.com/blog/entry/1848
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Игра в автобусе (автор - <span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-weight: normal;"></span></span><span style="font-weight: normal;font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 13.0px;"><a class="rated-user user-red" href="//www.codeforces.com/profile/rng_58" style="font-family: arial;text-decoration: none;font-weight: bold;color: rgb(0,0,204);" title="Colonel rng_58">rng_58</a>)</span></h2>В этой задаче прекрасно работает симуляция &quot;в лоб&quot; - нам прямым текстом сказано, как ходят игроки. Лиса Кейл играет по следующей стратегии: если есть хотя бы две монеты по 100 йен и две монеты по 10 йен, она берёт их. Иначе, если есть хотя бы одна монета по 100 йен и 12 монет по 10 - она забирает их. В противном случае она берет 22 монеты по 10 йен. Если ей это не удаётся - выигрывает Ханако. Кролик поступает точно также, но в обратном порядке. Сложность решения - <i>O(x+y)</i>.<br /><br /><h2>Задача B. Разноцветное поле (автор - <span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-weight: normal;"></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-weight: normal;"><span style="border-collapse: collapse;font-size: 13.0px;line-height: normal;"><a class="rated-user user-red" href="//www.codeforces.com/profile/ir5" style="font-family: arial;text-decoration: none;font-weight: bold;color: rgb(0,0,204);" title="Colonel ir5">ir5</a></span></span></span>)</h2>Решение, использующее массив <i>NxM</i> получает TL/ML, и, разумеется, мы не можем решать задачу &quot;в лоб&quot;. Так как и запросов, и безжизненных клеток не более 1000, нам достаточно научиться отвечать на каждый запрос за время <i>O(K)</i>.<br />Пусть <i>(a, b)</i> - клетка из очередного запроса. Является ли она безжизненной, или нет - решит один цикл <i>for</i> по входным данным.<br />Итак, мы знаем, что на этой клетке что-то растёт. Пусть <i>I</i> - суммарное число клеток перед <i>(a, b)</i>, а <i>J</i> - количество безжизненных клеток перед <i>(a, b)</i>. Тогда ответ определяется значением <i>(I-J) mod 3</i> (где <i>0</i> =&gt; &quot;<i>Carrots</i>&quot;, <i>1</i> =&gt; &quot;<i>Kiwis</i>&quot;, <i>2</i> =&gt; &quot;<i>Grapes</i>&quot;). Путем несложной математики можно понять, что I=(a-1)M+(b-1) (первое слагаемое - это количество клеток в предыдущих строках, а второе - количество предыдущих клеток в текущей строке), а величину <i>J</i> можно опять же подсчитать циклом <i>for</i> за <i>O(K)</i>.<br />Получаем решение за <i>O(TK)</i>, где <i>T</i> - количество запросов.<br /><br /><h2>Задача C. Скучные строки (автор - <span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-weight: normal;"></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-weight: normal;"><span style="border-collapse: collapse;font-size: 13.0px;line-height: normal;"><a class="rated-user user-red" href="//www.codeforces.com/profile/ir5" style="font-family: arial;text-decoration: none;font-weight: bold;color: rgb(0,0,204);" title="Colonel ir5">ir5</a>)</span></span></span></h2>Мы можем представить каждую подстроку в <i>s</i>, совпадающую с какой-либо скучной строкой, как &quot;запрещённый отрезок&quot;. Таких кандидатов в плохие отрезки для каждой из <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> порядка <i>O(n)</i>, поэтому мы можем подсчитать их все за <span class="tex-span"><i>O</i>(|<i>s</i>|· <i>n</i>· |<i>b</i><sub class="lower-index"><i>i</i></sub>|)</span> (да, тут не требуется никаких специальных алгоритмов, например, КМП).<br />Теперь мы можем переписать задачу по-другому: дано не более <span class="tex-span">10<sup class="upper-index">6</sup></span> запрещенных отрезков, найти отрезок, который не содержит полностью ни один из запрещённых. <br /><br />Давайте подсчитаем величину <i>right[i]</i> - минимальная правая граница среди запрещенных интервалов с левой границей в <i>i</i>. Если таких интервалов нет, положим <i>right[i]=|s|</i>.<br /><br />Теперь давайте переберём начало ответа, начиная с <i>|s|</i> и до <i>0</i>. Вначале ответ - пустая строка. Пусть ответ для предыдщего начала - подстрока с <i>i+1</i> до <i>j</i>. Тогда, если <i>right[i]&gt;j</i>, то мы можем спокойно приписать один символ слева и ответ увеличивается на 1 - подстрока с <i>i</i> до <i>j</i>. Если же <i>right[i]&lt;=j,</i> то ответ не может быть дальше, чем до <i>right[i]-1</i>, в противном случае мы полностью покроем &quot;плохой отрезок&quot;. Таким образом, мы пробежимся по всем возможным началам ответов за <i>O(|s|)</i>.<br /><br />Итого время работы - <span class="tex-span"><i>O</i>(|<i>s</i>|· <i>n</i>· |<i>b</i><sub class="lower-index"><i>i</i></sub>|)</span>.<br /><br /><div align="center"><h2>Задача D. Кодовый замок (автор - <span style="font-weight: normal;font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"></span><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 13.0px;"><a class="rated-user user-red" href="//www.codeforces.com/profile/rng_58" style="font-family: arial;text-decoration: none;font-weight: bold;color: rgb(0,0,204);" title="Colonel rng_58">rng_58</a>)</span></h2><div align="left">Давайте слегка переформулируем состояние замка: определим массив <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> следующим образом: <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub> = 0</span>, если панели <span class="tex-span"><i>i</i></span> и <span class="tex-span"><i>i</i> + 1</span> находятся в одинаковом состоянии и <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub> = 1</span> в противном случае. Положим, что панели <span class="tex-span">0</span> и <span class="tex-span"><i>n</i> + 1</span> выключены (OFF). Если Кейл изменяет состояние панелей на отрезке с <i>x</i> до <i>x+a-1</i> (включительно), то в массиве <i>b</i> изменяются значения <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i></sub></span> и <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i> + <i>a</i></sub></span>:<br /><img src="https://irulop.cc/adsl/Deditorial.png" style="max-width: 100.0%;max-height: 100.0%;" /><br /><b>Задача D'</b>.<br />У Вас есть массив <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span>. Не более 20 (<i>=2k</i>) элементов - единички. За каждый ход Вы можете изменить значения в <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i></sub></span> и <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i> + <i>a</i></sub></span>, где <span class="tex-span"><i>a</i></span> - элемент <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> и <span class="tex-span">0 ≤ <i>x</i> ≤ <i>n</i> - <i>a</i></span>. Определите минимальное количество ходов, требуемое для обнуления массива (мы просто &quot;перевернули&quot; порядок действий).<br /><br />Понятно, что порядок ходов не важен. Также понятно, что если массив еще не обнулён, то есть такой индекс <span class="tex-span"><i>x</i></span>, что <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i></sub> = 1</span>, и нам придётся походить, задев этот индекс, хотя бы один раз. Давайте следаем этот ход первым. Далее применим аналогичное рассуждение и получим, что на каждом ходу хотя бы одно из двух чисел <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i></sub></span> и <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i> + <i>a</i></sub></span> - единица. <br /><br /><b>Задача D''.</b><br />Теперь давайте построим граф с вершинами от <i>0</i> до<i> n+1</i>. Ребро между двумя вершинами <span class="tex-span"><i>v</i><sub class="lower-index">1</sub></span> и <span class="tex-span"><i>v</i><sub class="lower-index">2</sub></span> будет в том, и только том случае, если <span class="tex-span">|<i>v</i><sub class="lower-index">1</sub> - <i>v</i><sub class="lower-index">2</sub>|</span> - элемент массива <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> (то есть, мы можем сделать ход <span class="tex-span"><i>b</i><sub class="lower-index"><i>v</i><sub class="lower-index">1</sub></sub></span> и <span class="tex-span"><i>b</i><sub class="lower-index"><i>v</i><sub class="lower-index">2</sub></sub></span>. Также изначально есть не более 20 фишек (стоят в позициях изначальных единиц в массиве <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span>). За один ход мы можем подвинуть фишку по какому-либо ребру. Если две фишки оказываются в одной вершине, они исчезают. Определить минимальное количество ходов, необходимое для избавления от всех фишек.<br /><br />Для начала предподсчитаем попарные расстояния между всеми фишками. Это можно сделать, 20 раз запустив BFS. А далее имеем динамику по подмножествам: <i>d[S]</i> (где <i>S</i> - подмножество фишек) - минимальное количество шагов, чтобы убрать все фишки из <i>S</i>. Если <i>S</i> пусто, <i>d[S=0]</i>=0. Если <i><span class="tex-span"><i>S</i> = {<i>s</i><sub class="lower-index">0</sub>, <i>s</i><sub class="lower-index">1</sub>, ..., <i>s</i><sub class="lower-index"><i>m</i> - 1</sub>}</span></i> непусто, то мы выбирае фишки, которая исчезнет вместе с нулевой, и делаем переход: <span class="tex-span"><i>d</i>[<i>S</i>] = <i>min</i>(<i>d</i>[<i>S</i>\{<i>s</i><sub class="lower-index">0</sub>, <i>s</i><sub class="lower-index"><i>i</i></sub>}] + <i>dist</i>(<i>s</i><sub class="lower-index">0</sub>, <i>s</i><sub class="lower-index"><i>i</i></sub>))</span>, где <span class="tex-span">1 ≤ <i>i</i> ≤ <i>m</i> - 1</span>.<br /><br />Итоговая сложность решения - <span class="tex-span"><i>O</i>(<i>knl</i> + <i>k</i>· 2<sup class="upper-index">2<i>k</i></sup>)</span>.<br /><br /></div></div></div> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-1484-1848").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "1484", blogEntryId: "1848", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); 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79D
79
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en
D. Password
<div class="problem-statement"><div class="header"><div class="title">D. Password</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Finally Fox Ciel arrived in front of her castle!</p><p>She have to type a password to enter her castle. An input device attached to her castle is a bit unusual.</p><p>The input device is a <span class="tex-span">1 × <i>n</i></span> rectangle divided into <span class="tex-span"><i>n</i></span> square panels. They are numbered <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span> from left to right. Each panel has a state either ON or OFF. Initially all panels are in the OFF state. She can enter her castle if and only if <span class="tex-span"><i>x</i><sub class="lower-index">1</sub></span>-th, <span class="tex-span"><i>x</i><sub class="lower-index">2</sub></span>-th, <span class="tex-span">...</span>, <span class="tex-span"><i>x</i><sub class="lower-index"><i>k</i></sub></span>-th panels are in the ON state and other panels are in the OFF state.</p><p>She is given an array <span class="tex-span"><i>a</i><sub class="lower-index">1</sub></span>, <span class="tex-span">...</span>, <span class="tex-span"><i>a</i><sub class="lower-index"><i>l</i></sub></span>. In each move, she can perform the following operation: choose an index <span class="tex-span"><i>i</i></span> (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>l</i></span>), choose consecutive <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> panels, and flip the states of those panels (i.e. ON<span class="tex-span"> → </span>OFF, OFF<span class="tex-span"> → </span>ON).</p><p>Unfortunately she forgets how to type the password with only above operations. Determine the minimal number of operations required to enter her castle.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains three integers <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>k</i></span> and <span class="tex-span"><i>l</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10000, 1 ≤ <i>k</i> ≤ 10, 1 ≤ <i>l</i> ≤ 100</span>), separated by single spaces.</p><p>The second line contains <span class="tex-span"><i>k</i></span> integers <span class="tex-span"><i>x</i><sub class="lower-index">1</sub></span>, ..., <span class="tex-span"><i>x</i><sub class="lower-index"><i>k</i></sub></span> (<span class="tex-span">1 ≤ <i>x</i><sub class="lower-index">1</sub> &lt; <i>x</i><sub class="lower-index">2</sub> &lt; ... &lt; <i>x</i><sub class="lower-index"><i>k</i></sub> ≤ <i>n</i></span>), separated by single spaces.</p><p>The third line contains <span class="tex-span"><i>l</i></span> integers <span class="tex-span"><i>a</i><sub class="lower-index">1</sub></span>, ..., <span class="tex-span"><i>a</i><sub class="lower-index"><i>l</i></sub></span> (<span class="tex-span">1 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ <i>n</i></span>), separated by single spaces. It is possible that some elements of the array <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> are equal value.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print the minimal number of moves required to type the password. If it's impossible, print <span class="tex-font-style-tt">-1</span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>10 8 2<br/>1 2 3 5 6 7 8 9<br/>3 5<br/></pre></div><div class="output"><div class="title">Output</div><pre>2<br/></pre></div><div class="input"><div class="title">Input</div><pre>3 2 1<br/>1 2<br/>3<br/></pre></div><div class="output"><div class="title">Output</div><pre>-1<br/></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>One possible way to type the password in the first example is following: In the first move, choose 1st, 2nd, 3rd panels and flip those panels. In the second move, choose 5th, 6th, 7th, 8th, 9th panels and flip those panels.</p></div></div>
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} </style> <div class="roundbox sidebox sidebar-menu borderTopRound " style=""> <div class="caption titled">&rarr; Contest materials <div class="top-links"> </div> </div> <ul> <li> <span> <a href="/blog/entry/1828" title="Codeforces Beta Round #71" target="_blank">Announcement</a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="266:267" resourceName="Announcement" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1848" title="Codeforces Beta Round #71 - разбор (перевод A-D)" target="_blank">Tutorial #1 <span class="resource-locale">(ru)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="855" resourceName="Codeforces Beta Round #71 - разбор (перевод A-D)" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> <li> <span> <a href="/blog/entry/1839" title="Codeforces Beta Round #71 Editorial" target="_blank">Tutorial #2 <span class="resource-locale">(en)</span></a> </span> <span style="float: right;"> <img class="delete-resource-link" resourceIds="854" resourceName="Codeforces Beta Round #71 Editorial" resourceManual="true" src="//codeforces.org/s/73366/images/icons/close-10x10.png" style="position: relative;bottom: -1px;left: 1px;cursor: pointer;"/> </span> <div style="clear: both;"></div> </li> </ul> </div></div> <div id="pageContent" class="content-with-sidebar"> <div class="second-level-menu"> <ul class="second-level-menu-list"> <li class="current selectedLava"><a href="/contest/79">Problems</a></li> <li><a href="/contest/79/submit">Submit Code</a></li> <li><a href="/contest/79/my">My Submissions</a></li> <li><a href="/contest/79/status">Status</a></li> <li><a href="/contest/79/hacks">Hacks</a></li> <li><a href="/contest/79/room/1">Room</a></li> <li><a href="/contest/79/standings">Standings</a></li> <li><a href="/contest/79/customtest">Custom Invocation</a></li> </ul> </div> <style> #facebox .content:has(.diff-popup) { width: 90vw; 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} } else { result.push(c); } } return result.join("").split("\n").map(value => value.trim()).join("\n"); }; </script> <div class="diff-popup"> </div> <div class="problemindexholder" problemindex="D" data-uuid="ps_2aa603d7046881874bd06e02486b88f2596efe6f"> <div style="display: none; margin:1em 0;text-align: center; position: relative;" class="alert alert-info diff-notifier"> <div>The problem statement has recently been changed. <a class="view-changes" href="#">View the changes.</a></div> <span class="diff-notifier-close" style="position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;">&times;</span> </div> <div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">D. Password</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Finally Fox Ciel arrived in front of her castle!</p><p>She have to type a password to enter her castle. An input device attached to her castle is a bit unusual.</p><p>The input device is a <span class="tex-span">1 × <i>n</i></span> rectangle divided into <span class="tex-span"><i>n</i></span> square panels. They are numbered <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span> from left to right. Each panel has a state either ON or OFF. Initially all panels are in the OFF state. She can enter her castle if and only if <span class="tex-span"><i>x</i><sub class="lower-index">1</sub></span>-th, <span class="tex-span"><i>x</i><sub class="lower-index">2</sub></span>-th, <span class="tex-span">...</span>, <span class="tex-span"><i>x</i><sub class="lower-index"><i>k</i></sub></span>-th panels are in the ON state and other panels are in the OFF state.</p><p>She is given an array <span class="tex-span"><i>a</i><sub class="lower-index">1</sub></span>, <span class="tex-span">...</span>, <span class="tex-span"><i>a</i><sub class="lower-index"><i>l</i></sub></span>. In each move, she can perform the following operation: choose an index <span class="tex-span"><i>i</i></span> (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>l</i></span>), choose consecutive <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> panels, and flip the states of those panels (i.e. ON<span class="tex-span"> → </span>OFF, OFF<span class="tex-span"> → </span>ON).</p><p>Unfortunately she forgets how to type the password with only above operations. Determine the minimal number of operations required to enter her castle.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains three integers <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>k</i></span> and <span class="tex-span"><i>l</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10000, 1 ≤ <i>k</i> ≤ 10, 1 ≤ <i>l</i> ≤ 100</span>), separated by single spaces.</p><p>The second line contains <span class="tex-span"><i>k</i></span> integers <span class="tex-span"><i>x</i><sub class="lower-index">1</sub></span>, ..., <span class="tex-span"><i>x</i><sub class="lower-index"><i>k</i></sub></span> (<span class="tex-span">1 ≤ <i>x</i><sub class="lower-index">1</sub> &lt; <i>x</i><sub class="lower-index">2</sub> &lt; ... &lt; <i>x</i><sub class="lower-index"><i>k</i></sub> ≤ <i>n</i></span>), separated by single spaces.</p><p>The third line contains <span class="tex-span"><i>l</i></span> integers <span class="tex-span"><i>a</i><sub class="lower-index">1</sub></span>, ..., <span class="tex-span"><i>a</i><sub class="lower-index"><i>l</i></sub></span> (<span class="tex-span">1 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ <i>n</i></span>), separated by single spaces. It is possible that some elements of the array <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> are equal value.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print the minimal number of moves required to type the password. If it's impossible, print <span class="tex-font-style-tt">-1</span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>10 8 2<br />1 2 3 5 6 7 8 9<br />3 5<br /></pre></div><div class="output"><div class="title">Output</div><pre>2<br /></pre></div><div class="input"><div class="title">Input</div><pre>3 2 1<br />1 2<br />3<br /></pre></div><div class="output"><div class="title">Output</div><pre>-1<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>One possible way to type the password in the first example is following: In the first move, choose 1st, 2nd, 3rd panels and flip those panels. In the second move, choose 5th, 6th, 7th, 8th, 9th panels and flip those panels.</p></div></div></div> </div> <script> $(function () { Codeforces.addMathJaxListener(function () { let $problem = $("div[problemindex=D]"); let uuid = $problem.attr("data-uuid"); let statementText = convertStatementToText($problem.find(".ttypography").get(0)); let previousStatementText = Codeforces.getFromStorage(uuid); if (previousStatementText) { if (previousStatementText !== statementText) { $problem.find(".diff-notifier").show(); $problem.find(".diff-notifier-close").click(function() { Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60); $problem.find(".diff-notifier").hide(); }); $problem.find("a.view-changes").click(function() { $.post("/data/diff", {action: "getDiff", a: previousStatementText, b: statementText}, function (result) { if (result["success"] === "true") { Codeforces.facebox(".diff-popup", "//codeforces.org/s/73366"); $("#facebox .diff-popup").html(result["diff"]); } }, "json"); }); 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["Bitmasks", "Dynamic programming", "Shortest paths on weighted and unweighted graphs"]
["bitmasks", "dp", "shortest paths", "*2800"]
https://codeforces.com/blog/entry/1848
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Игра в автобусе (автор - <span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-weight: normal;"></span></span><span style="font-weight: normal;font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"> </span><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 13.0px;"><a class="rated-user user-red" href="//www.codeforces.com/profile/rng_58" style="font-family: arial;text-decoration: none;font-weight: bold;color: rgb(0,0,204);" title="Colonel rng_58">rng_58</a>)</span></h2>В этой задаче прекрасно работает симуляция &quot;в лоб&quot; - нам прямым текстом сказано, как ходят игроки. Лиса Кейл играет по следующей стратегии: если есть хотя бы две монеты по 100 йен и две монеты по 10 йен, она берёт их. Иначе, если есть хотя бы одна монета по 100 йен и 12 монет по 10 - она забирает их. В противном случае она берет 22 монеты по 10 йен. Если ей это не удаётся - выигрывает Ханако. Кролик поступает точно также, но в обратном порядке. Сложность решения - <i>O(x+y)</i>.<br /><br /><h2>Задача B. Разноцветное поле (автор - <span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-weight: normal;"></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-weight: normal;"><span style="border-collapse: collapse;font-size: 13.0px;line-height: normal;"><a class="rated-user user-red" href="//www.codeforces.com/profile/ir5" style="font-family: arial;text-decoration: none;font-weight: bold;color: rgb(0,0,204);" title="Colonel ir5">ir5</a></span></span></span>)</h2>Решение, использующее массив <i>NxM</i> получает TL/ML, и, разумеется, мы не можем решать задачу &quot;в лоб&quot;. Так как и запросов, и безжизненных клеток не более 1000, нам достаточно научиться отвечать на каждый запрос за время <i>O(K)</i>.<br />Пусть <i>(a, b)</i> - клетка из очередного запроса. Является ли она безжизненной, или нет - решит один цикл <i>for</i> по входным данным.<br />Итак, мы знаем, что на этой клетке что-то растёт. Пусть <i>I</i> - суммарное число клеток перед <i>(a, b)</i>, а <i>J</i> - количество безжизненных клеток перед <i>(a, b)</i>. Тогда ответ определяется значением <i>(I-J) mod 3</i> (где <i>0</i> =&gt; &quot;<i>Carrots</i>&quot;, <i>1</i> =&gt; &quot;<i>Kiwis</i>&quot;, <i>2</i> =&gt; &quot;<i>Grapes</i>&quot;). Путем несложной математики можно понять, что I=(a-1)M+(b-1) (первое слагаемое - это количество клеток в предыдущих строках, а второе - количество предыдущих клеток в текущей строке), а величину <i>J</i> можно опять же подсчитать циклом <i>for</i> за <i>O(K)</i>.<br />Получаем решение за <i>O(TK)</i>, где <i>T</i> - количество запросов.<br /><br /><h2>Задача C. Скучные строки (автор - <span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-weight: normal;"></span></span><span style="font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"><span style="font-weight: normal;"><span style="border-collapse: collapse;font-size: 13.0px;line-height: normal;"><a class="rated-user user-red" href="//www.codeforces.com/profile/ir5" style="font-family: arial;text-decoration: none;font-weight: bold;color: rgb(0,0,204);" title="Colonel ir5">ir5</a>)</span></span></span></h2>Мы можем представить каждую подстроку в <i>s</i>, совпадающую с какой-либо скучной строкой, как &quot;запрещённый отрезок&quot;. Таких кандидатов в плохие отрезки для каждой из <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> порядка <i>O(n)</i>, поэтому мы можем подсчитать их все за <span class="tex-span"><i>O</i>(|<i>s</i>|· <i>n</i>· |<i>b</i><sub class="lower-index"><i>i</i></sub>|)</span> (да, тут не требуется никаких специальных алгоритмов, например, КМП).<br />Теперь мы можем переписать задачу по-другому: дано не более <span class="tex-span">10<sup class="upper-index">6</sup></span> запрещенных отрезков, найти отрезок, который не содержит полностью ни один из запрещённых. <br /><br />Давайте подсчитаем величину <i>right[i]</i> - минимальная правая граница среди запрещенных интервалов с левой границей в <i>i</i>. Если таких интервалов нет, положим <i>right[i]=|s|</i>.<br /><br />Теперь давайте переберём начало ответа, начиная с <i>|s|</i> и до <i>0</i>. Вначале ответ - пустая строка. Пусть ответ для предыдщего начала - подстрока с <i>i+1</i> до <i>j</i>. Тогда, если <i>right[i]&gt;j</i>, то мы можем спокойно приписать один символ слева и ответ увеличивается на 1 - подстрока с <i>i</i> до <i>j</i>. Если же <i>right[i]&lt;=j,</i> то ответ не может быть дальше, чем до <i>right[i]-1</i>, в противном случае мы полностью покроем &quot;плохой отрезок&quot;. Таким образом, мы пробежимся по всем возможным началам ответов за <i>O(|s|)</i>.<br /><br />Итого время работы - <span class="tex-span"><i>O</i>(|<i>s</i>|· <i>n</i>· |<i>b</i><sub class="lower-index"><i>i</i></sub>|)</span>.<br /><br /><div align="center"><h2>Задача D. Кодовый замок (автор - <span style="font-weight: normal;font-family: verdana , arial , sans-serif;font-size: 12.0px;line-height: 20.0px;"></span><span style="border-collapse: collapse;font-family: verdana , arial , sans-serif;font-size: 13.0px;"><a class="rated-user user-red" href="//www.codeforces.com/profile/rng_58" style="font-family: arial;text-decoration: none;font-weight: bold;color: rgb(0,0,204);" title="Colonel rng_58">rng_58</a>)</span></h2><div align="left">Давайте слегка переформулируем состояние замка: определим массив <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> следующим образом: <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub> = 0</span>, если панели <span class="tex-span"><i>i</i></span> и <span class="tex-span"><i>i</i> + 1</span> находятся в одинаковом состоянии и <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub> = 1</span> в противном случае. Положим, что панели <span class="tex-span">0</span> и <span class="tex-span"><i>n</i> + 1</span> выключены (OFF). Если Кейл изменяет состояние панелей на отрезке с <i>x</i> до <i>x+a-1</i> (включительно), то в массиве <i>b</i> изменяются значения <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i></sub></span> и <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i> + <i>a</i></sub></span>:<br /><img src="https://irulop.cc/adsl/Deditorial.png" style="max-width: 100.0%;max-height: 100.0%;" /><br /><b>Задача D'</b>.<br />У Вас есть массив <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span>. Не более 20 (<i>=2k</i>) элементов - единички. За каждый ход Вы можете изменить значения в <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i></sub></span> и <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i> + <i>a</i></sub></span>, где <span class="tex-span"><i>a</i></span> - элемент <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> и <span class="tex-span">0 ≤ <i>x</i> ≤ <i>n</i> - <i>a</i></span>. Определите минимальное количество ходов, требуемое для обнуления массива (мы просто &quot;перевернули&quot; порядок действий).<br /><br />Понятно, что порядок ходов не важен. Также понятно, что если массив еще не обнулён, то есть такой индекс <span class="tex-span"><i>x</i></span>, что <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i></sub> = 1</span>, и нам придётся походить, задев этот индекс, хотя бы один раз. Давайте следаем этот ход первым. Далее применим аналогичное рассуждение и получим, что на каждом ходу хотя бы одно из двух чисел <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i></sub></span> и <span class="tex-span"><i>b</i><sub class="lower-index"><i>x</i> + <i>a</i></sub></span> - единица. <br /><br /><b>Задача D''.</b><br />Теперь давайте построим граф с вершинами от <i>0</i> до<i> n+1</i>. Ребро между двумя вершинами <span class="tex-span"><i>v</i><sub class="lower-index">1</sub></span> и <span class="tex-span"><i>v</i><sub class="lower-index">2</sub></span> будет в том, и только том случае, если <span class="tex-span">|<i>v</i><sub class="lower-index">1</sub> - <i>v</i><sub class="lower-index">2</sub>|</span> - элемент массива <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> (то есть, мы можем сделать ход <span class="tex-span"><i>b</i><sub class="lower-index"><i>v</i><sub class="lower-index">1</sub></sub></span> и <span class="tex-span"><i>b</i><sub class="lower-index"><i>v</i><sub class="lower-index">2</sub></sub></span>. Также изначально есть не более 20 фишек (стоят в позициях изначальных единиц в массиве <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span>). За один ход мы можем подвинуть фишку по какому-либо ребру. Если две фишки оказываются в одной вершине, они исчезают. Определить минимальное количество ходов, необходимое для избавления от всех фишек.<br /><br />Для начала предподсчитаем попарные расстояния между всеми фишками. Это можно сделать, 20 раз запустив BFS. А далее имеем динамику по подмножествам: <i>d[S]</i> (где <i>S</i> - подмножество фишек) - минимальное количество шагов, чтобы убрать все фишки из <i>S</i>. Если <i>S</i> пусто, <i>d[S=0]</i>=0. Если <i><span class="tex-span"><i>S</i> = {<i>s</i><sub class="lower-index">0</sub>, <i>s</i><sub class="lower-index">1</sub>, ..., <i>s</i><sub class="lower-index"><i>m</i> - 1</sub>}</span></i> непусто, то мы выбирае фишки, которая исчезнет вместе с нулевой, и делаем переход: <span class="tex-span"><i>d</i>[<i>S</i>] = <i>min</i>(<i>d</i>[<i>S</i>\{<i>s</i><sub class="lower-index">0</sub>, <i>s</i><sub class="lower-index"><i>i</i></sub>}] + <i>dist</i>(<i>s</i><sub class="lower-index">0</sub>, <i>s</i><sub class="lower-index"><i>i</i></sub>))</span>, где <span class="tex-span">1 ≤ <i>i</i> ≤ <i>m</i> - 1</span>.<br /><br />Итоговая сложность решения - <span class="tex-span"><i>O</i>(<i>knl</i> + <i>k</i>· 2<sup class="upper-index">2<i>k</i></sup>)</span>.<br /><br /></div></div></div> </div> <script type="text/javascript"> $(document).ready(function () { $(".delete-resource-link-1484-1848").click(function() { var that = this; Codeforces.confirm("Are you sure you want to detach a contest?", function () { $.post("/data/blogAndContest", { action: "detachBlogFromContest", blogId: "1484", blogEntryId: "1848", contestId: $(that).attr("data-contestId"), resourceIds: $(that).attr("data-resourceIds") }, function(json) { Codeforces.reloadAndShowMessageOrShowError(json, "Contest detached"); 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