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https://atcoder.jp/contests/abc281/tasks/abc281_h | Problem Statement
Takahashi has
A
kinds of level-
1
gems, and
10^{10^{100}}
gems of each of those kinds.
For an integer
n
greater than or equal to
2
, he can put
n
gems that satisfy all of the following conditions into a cauldron to generate a level-
n
gem in return.
No two gems are of the same kind.
Every gem's level is less than
n
.
For every integer
x
greater than or equal to
2
, there is at most one level-
x
gem.
Find the number of kinds of level-
N
gems that Takahashi can obtain, modulo
998244353
.
Here, two level-
2
or higher gems are considered to be of the same kind if and only if they are generated from the same set of gems.
Two sets of gems are distinguished if and only if there is a gem in one of those sets such that the other set does not contain a gem of the same kind.
Any level-
1
gem and any level-
2
or higher gem are of different kinds. | [
{
"input": "3 3\n",
"output": "10\n"
},
{
"input": "1 100\n",
"output": "100\n"
},
{
"input": "200000 1000000000\n",
"output": "797585162\n"
}
] |
https://atcoder.jp/contests/future-contest-2023-final-open/tasks/future_contest_2023_final_a | Problem Statement
A psychic, Takahashi, has discovered a treasure map.
According to the map, there are
50
buried treasures under the ground of an uninhabited island.
The island has a circular shape with a radius of
R=10^9
.
Unfortunately, the map does not indicate the locations of the buried treasures.
Since it is impossible to dig up all the ground, he decided to use his psychic powers to search for the treasures in the following way.
Choose a desired location and stand a wooden rod.
If there is a treasure within a radius of
D=10^6
from the chosen location, the rod will remain standing, and he can find the treasure by digging all the area within the radius
D
.
If there are no treasures within a radius of
D
from the chosen location, the rod will fall in a certain direction according to the rule described below, providing a clue to the location of the treasures.
By repeating this process up to
1000
times, find as many treasures as possible, as quickly as possible.
The law of the falling direction of the rod
Let
q=(qx, qy)
be the coordinates at which the rod stands, then the falling direction
\theta (0\leq \theta<2\pi)
is calculated as follows, using a constant
\sigma
given as an input.
Among the treasures that have not yet been dug up, one is chosen with probability proportional to the inverse of the squared Euclidean distance to
q
.
Let
p=(px,py)
be the coordinates of the chosen treasure, and calculate the direction
\hat{\theta}=\mathrm{atan2}(py-qy,px-qx)
of
p-q
.
Sample a value from Gaussian distribution with mean
\hat{\theta}
and standard deviation
\sigma
and let
\theta
be its remainder divided by
2\pi
. | [] |
https://atcoder.jp/contests/future-contest-2023-final/tasks/future_contest_2023_final_a | Problem Statement
A psychic, Takahashi, has discovered a treasure map.
According to the map, there are
50
buried treasures under the ground of an uninhabited island.
The island has a circular shape with a radius of
R=10^9
.
Unfortunately, the map does not indicate the locations of the buried treasures.
Since it is impossible to dig up all the ground, he decided to use his psychic powers to search for the treasures in the following way.
Choose a desired location and stand a wooden rod.
If there is a treasure within a radius of
D=10^6
from the chosen location, the rod will remain standing, and he can find the treasure by digging all the area within the radius
D
.
If there are no treasures within a radius of
D
from the chosen location, the rod will fall in a certain direction according to the rule described below, providing a clue to the location of the treasures.
By repeating this process up to
1000
times, find as many treasures as possible, as quickly as possible.
The law of the falling direction of the rod
Let
q=(qx, qy)
be the coordinates at which the rod stands, then the falling direction
\theta (0\leq \theta<2\pi)
is calculated as follows, using a constant
\sigma
given as an input.
Among the treasures that have not yet been dug up, one is chosen with probability proportional to the inverse of the squared Euclidean distance to
q
.
Let
p=(px,py)
be the coordinates of the chosen treasure, and calculate the direction
\hat{\theta}=\mathrm{atan2}(py-qy,px-qx)
of
p-q
.
Sample a value from Gaussian distribution with mean
\hat{\theta}
and standard deviation
\sigma
and let
\theta
be its remainder divided by
2\pi
. | [] |
https://atcoder.jp/contests/agc059/tasks/agc059_a | Problem Statement
Consider a string
t
consisting only of characters
A
,
B
, and
C
.
We can do the following operation with it:
Choose any substring
t[l:r]
and any permutation
(X, Y, Z)
of characters
(
A
,
B
,
C
)
. Here,
t[l:r]
denotes the substring formed by the
l
-th through the
r
-th characters of
t
, where
l
and
r
are of your choice. Then, replace each character
A
,
B
, and
C
in
t[l:r]
by
X
,
Y
, and
Z
, respectively.
For example, for a string
t =
ACBAAC
, we can choose a substring
t[3:6]
and
(X,Y,Z)=(
C
,
B
,
A
)
.
After this operation, the string will become
ACBCCA
.
Alina likes strings in which all characters are the same. She defines the beauty of a string
t
as the minimum number of operations required to make all its characters equal.
You are given a string
S
of length
N
consisting only of characters
A
,
B
, and
C
.
Answer
Q
queries. The
i
-th query is the following:
Given integers
L_i
and
R_i
, find the beauty of the substring
t=S[L_i:R_i]
. | [
{
"input": "6 4\nABCCCA\n3 5\n2 3\n1 3\n1 6\n",
"output": "0\n1\n2\n2\n"
}
] |
https://atcoder.jp/contests/agc059/tasks/agc059_b | Problem Statement
You have
N
balls of colors
C_1, C_2, \ldots, C_N
.
Here, all colors are represented by an integer between
1
and
N
inclusive.
You want to arrange the balls on a circle. After you do that, you will count the number of pairs of colors
(X, Y)
such that
X < Y
and there exist two adjacent balls of colors
X
and
Y
.
Find an arrangement that minimizes the number of such pairs. If there are many such arrangements, find any of them.
For example, for balls of colors
1, 1, 2, 3
, if we arrange them as
1, 1, 2, 3
, we get
3
pairs:
(1, 2), (2, 3), (1, 3)
. If we arrange them as
1, 2, 1, 3
, we get only
2
pairs:
(1, 2), (1, 3)
.
Solve
T
test cases for each input file. | [
{
"input": "3\n3\n1 2 3\n4\n1 2 1 3\n5\n2 2 5 3 3\n",
"output": "1 2 3 \n2 1 3 1 \n3 3 2 5 2 \n"
}
] |
https://atcoder.jp/contests/agc059/tasks/agc059_c | Problem Statement
A teacher has a hidden permutation
P=(P_1,P_2,\ldots,P_N)
of
(1,2,\cdots,N)
.
You are going to determine it.
To do this, you prepared a sequence of pairs of integers
(A_1,B_1),(A_2,B_2),\ldots,(A_{N(N-1)/2},B_{N(N-1)/2})
; this is a permutation of all pairs of the form
(a,b)
(
1 \le a < b \le N
).
Now, you will go over the pairs from the beginning. For a pair
(A_i, B_i)
, you will ask if
P_{A_i}<P_{B_i}
, and the teacher will tell you the answer.
However, you will skip this question if you can already determine the answer to it from previous answers.
Find the number of permutations
P
, for which with your algorithm you will have to ask all
\frac{N(N-1)}{2}
questions, modulo
10^9+7
. | [
{
"input": "2\n1 2\n",
"output": "2\n"
},
{
"input": "4\n1 2\n1 3\n2 3\n2 4\n3 4\n1 4\n",
"output": "4\n"
},
{
"input": "5\n1 2\n2 3\n3 4\n4 5\n1 5\n1 3\n2 4\n3 5\n1 4\n2 5\n",
"output": "0\n"
}
] |
https://atcoder.jp/contests/agc059/tasks/agc059_d | Problem Statement
For an integer array
A=(A_1, A_2, \ldots, A_{N + K-1})
(
1 \leq A_i \leq N+K-1
), let's construct an array
B=(B_1, B_2, \ldots, B_N)
, where
B_i
is the number of distinct elements in
A_i,A_{i+1},\ldots,A_{i+K-1}
.
You are given
B_1, B_2, \ldots, B_N
. Determine if there exists an array
A
which could have produced such an array
B
, and if yes, construct one.
Solve
T
test cases for each input file. | [
{
"input": "3\n3 3\n1 2 1\n4 3\n1 2 2 1\n6 4\n3 3 3 3 3 3\n",
"output": "NO\nYES\n1 1 1 2 2 2 \nYES\n1 2 3 1 2 3 1 2 3 \n"
}
] |
https://atcoder.jp/contests/agc059/tasks/agc059_e | Problem Statement
You have an
N \times N
grid board.
You want to color all cells in
3
colors so that no two adjacent (edge-sharing) cells have the same color.
You have already painted the border of the board. Determine if you can color the rest of the board properly.
More precisely, you are given a string
S
of length
4N-4
consisting of characters
1
,
2
, and
3
. The string denotes the colors of the cells on the border, starting from the cell
(1, 1)
, in clockwise order.
Strictly speaking, the
i
-th character of
S
denotes the color of the cell:
(1, i)
for
1 \le i \le N-1
(i - (N-1), N)
for
N \le i \le 2N-2
(N, 3N - 1 - i)
for
2N-1 \le i \le 3N-3
(4N-2 - i, 1)
for
3N-2 \le i \le 4N-4
.
Here,
(r,c)
denotes the cell in the
r
-th row and the
c
-th column.
It is guaranteed that no two adjacent cells on the border have the same color.
Solve
T
test cases for each input file. | [
{
"input": "4\n3\n12312312\n4\n121212121212\n7\n321312312312121212121321\n7\n321312312312121312121321\n",
"output": "NO\nYES\nNO\nYES\n"
}
] |
https://atcoder.jp/contests/agc059/tasks/agc059_f | Problem Statement
Given
N, pos, val
, find the number of permutations
P=(P_1, P_2, \ldots, P_N)
of
(1,2,\ldots,N)
that satisfy all of the following conditions, modulo
10^9+7
:
LIS(P) + LDS(P) = N+1
P_{pos} = val
Here,
LIS(P)
denotes the length of the longest increasing subsequence of
P
, and
LDS(P)
denotes the length of the longest decreasing subsequence of
P
. | [
{
"input": "3 2 2\n",
"output": "2\n"
},
{
"input": "4 1 1\n",
"output": "6\n"
},
{
"input": "5 2 5\n",
"output": "11\n"
},
{
"input": "2022 69 420\n",
"output": "128873576\n"
}
] |
https://atcoder.jp/contests/abc280/tasks/abc280_a | Problem Statement
There is a grid with
H
rows from top to bottom and
W
columns from left to right. Each square has a piece placed on it or is empty.
The state of the grid is represented by
H
strings
S_1, S_2, \ldots, S_H
, each of length
W
.
If the
j
-th character of
S_i
is
#
, the square at the
i
-th row from the top and
j
-th column from the left has a piece on it;
if the
j
-th character of
S_i
is
.
, the square at the
i
-th row from the top and
j
-th column from the left is empty.
How many squares in the grid have pieces on them? | [
{
"input": "3 5\n#....\n.....\n.##..\n",
"output": "3\n"
},
{
"input": "1 10\n..........\n",
"output": "0\n"
},
{
"input": "6 5\n#.#.#\n....#\n..##.\n####.\n..#..\n#####\n",
"output": "16\n"
}
] |
https://atcoder.jp/contests/abc280/tasks/abc280_b | Problem Statement
You are given an integer
N
and a sequence
S=(S_1,\ldots,S_N)
of length
N
.
Find a sequence
A=(A_1,\ldots,A_N)
of length
N
that satisfies the following condition for all
k=1,\ldots,N
:
A_1+A_2+\ldots+A_k = S_k
.
Such a sequence
A
always exists and is unique. | [
{
"input": "3\n3 4 8\n",
"output": "3 1 4\n"
},
{
"input": "10\n314159265 358979323 846264338 -327950288 419716939 -937510582 97494459 230781640 628620899 -862803482\n",
"output": "314159265 44820058 487285015 -1174214626 747667227 -1357227521 1035005041 133287181 397839259 -1491424381\n"
}
] |
https://atcoder.jp/contests/abc280/tasks/abc280_c | Problem Statement
You are given strings
S
and
T
.
S
consists of lowercase English letters, and
T
is obtained by inserting a lowercase English letter into
S
.
Find the position of the inserted character in
T
.
If there are multiple candidates, find any of them. | [
{
"input": "atcoder\natcorder\n",
"output": "5\n"
},
{
"input": "million\nmilllion\n",
"output": "5\n"
},
{
"input": "vvwvw\nvvvwvw\n",
"output": "3\n"
}
] |
https://atcoder.jp/contests/abc280/tasks/abc280_d | Problem Statement
You are given an integer
K
greater than or equal to
2
.
Find the minimum positive integer
N
such that
N!
is a multiple of
K
.
Here,
N!
denotes the factorial of
N
. Under the Constraints of this problem, we can prove that such an
N
always exists. | [
{
"input": "30\n",
"output": "5\n"
},
{
"input": "123456789011\n",
"output": "123456789011\n"
},
{
"input": "280\n",
"output": "7\n"
}
] |
https://atcoder.jp/contests/abc280/tasks/abc280_e | Problem Statement
There is a monster with initial stamina
N
.
Takahashi repeatedly attacks the monster while the monster's stamina remains
1
or greater.
An attack by Takahashi reduces the monster's stamina by
2
with probability
\frac{P}{100}
and by
1
with probability
1-\frac{P}{100}
.
Find the expected value, modulo
998244353
(see Notes), of the number of attacks before the monster's stamina becomes
0
or less. | [
{
"input": "3 10\n",
"output": "229596204\n"
},
{
"input": "5 100\n",
"output": "3\n"
},
{
"input": "280 59\n",
"output": "567484387\n"
}
] |
https://atcoder.jp/contests/abc280/tasks/abc280_f | Problem Statement
There are
N
towns numbered
1,\ldots,N
and
M
roads numbered
1,\ldots,M
.
Road
i
connects towns
A_i
and
B_i
. When you use a road, your
score
changes as follows:
when you move from town
A_i
to town
B_i
using road
i
, your score increases by
C_i
; when you move from town
B_i
to town
A_i
using road
i
, your score decreases by
C_i
.
Your score may become negative.
Answer the following
Q
questions.
If you start traveling from town
X_i
with initial score
0
, find the maximum possible score when you are at town
Y_i
.
Here, if you cannot get from town
X_i
to town
Y_i
, print
nan
instead; if you can have as large a score as you want when you are at town
Y_i
, print
inf
instead. | [
{
"input": "5 5 3\n1 2 1\n1 2 2\n3 4 1\n4 5 1\n3 5 2\n5 3\n1 2\n3 1\n",
"output": "-2\ninf\nnan\n"
},
{
"input": "2 1 1\n1 1 1\n1 1\n",
"output": "inf\n"
},
{
"input": "9 7 5\n3 1 4\n1 5 9\n2 6 5\n3 5 8\n9 7 9\n3 2 3\n8 4 6\n2 6\n4 3\n3 8\n3 2\n7 9\n",
"output": "inf\nnan\nnan\ninf\n-9\n"
}
] |
https://atcoder.jp/contests/abc280/tasks/abc280_g | Problem Statement
We have an infinite hexagonal grid shown below.
A hexagonal cell is represented as
(i,j)
with two integers
i
and
j
.
Cell
(i,j)
is adjacent to the following six cells:
(i-1,j-1)
(i-1,j)
(i,j-1)
(i,j+1)
(i+1,j)
(i+1,j+1)
Let us define the distance between two cells
X
and
Y
by the minimum number of moves required to travel from cell
X
to cell
Y
by repeatedly moving to an adjacent cell.
For example, the distance between cells
(0,0)
and
(1,1)
is
1
, and the distance between cells
(2,1)
and
(-1,-1)
is
3
.
You are given
N
cells
(X_1,Y_1),\ldots,(X_N,Y_N)
.
How many ways are there to choose one or more from these
N
cells so that the distance between any two of the chosen cells is at most
D
?
Find the count modulo
998244353
. | [
{
"input": "3 1\n0 0\n0 1\n1 0\n",
"output": "5\n"
},
{
"input": "9 1\n0 0\n0 1\n0 2\n1 0\n1 1\n1 2\n2 0\n2 1\n2 2\n",
"output": "33\n"
},
{
"input": "5 10000000000\n314159265 358979323\n846264338 -327950288\n-419716939 937510582\n-97494459 -230781640\n628620899 862803482\n",
"output": "31\n"
}
] |
https://atcoder.jp/contests/abc280/tasks/abc280_h | Problem Statement
You are given
N
strings
S_1,S_2,\ldots, S_N
.
Let
M = \displaystyle\sum_{i=1}^N \frac{|S_i|(|S_i|+1)}{2}
.
For a string
S
and integers
L
and
R
, let us denote by
S[L, R]
the substring consisting of the
L
-th through
R
-th characters of
S
.
A sequence of triples of integers
((K_1, L_1, R_1), (K_2, L_2, R_2), \ldots, (K_M, L_M, R_M))
of length
M
satisfies the following conditions:
The
M
elements are pairwise distinct.
For all
1 \leq i \leq M
, it holds that
1 \leq K_i \leq N
and
1 \leq L_i \leq R_i \leq |S_{K_i}|
.
For all
1 \leq i \leq j \leq M
, it holds that
S_{K_i}[L_i, R_i] \leq S_{K_j}[L_j, R_j]
in the lexicographical order.
You are given
Q
integers
x_1,x_2,\ldots, x_Q
between
1
and
M
, inclusive. For each
1 \leq i \leq Q
, find a possible instance of
(K_{x_i}, L_{x_i}, R_{x_i})
. We can prove that there always exists a sequence of triples that satisfies the conditions. If multiple triples satisfy the conditions, print any of them. In addition, among different
x_i
's, the conforming sequence of triples does not have to be common.
What is the lexicographical order?
Two strings
S
and
T
are said to be
S \leq T
in the lexicographical order if and only if one of the following conditions is satisfied:
|S| \leq |T|
and
S = T[1, |S|]
.
There exists
1\leq k\leq \min(|S|, |T|)
such that the
i
-th characters of
S
and
T
are the same for all
1\leq i\leq k-1
, and the
k
-th character of
S
is alphabetically strictly smaller than that of
T
. | [
{
"input": "2\nabab\ncab\n2\n5 14\n",
"output": "1 3 4\n2 1 1\n"
},
{
"input": "3\na\na\nba\n2\n1 2\n",
"output": "1 1 1\n1 1 1\n"
},
{
"input": "10\ngxgpuamkx\nszhkbpphykin\nezplvfja\nmopodotkrj\nrimlvumuar\nnexcfyce\neurgvjyos\ndhvuyfvt\nnrdyluacvra\nggwnpnzij\n6\n74 268 310 380 455 489\n",
"output": "3 1 2\n4 4 5\n4 3 7\n9 6 6\n6 6 6\n2 2 12\n"
}
] |
https://atcoder.jp/contests/past202212-open/tasks/past202212_a | Problem Statement
Takahashi has come to an amusement arcade with
N
yen (Japanese currency) in his pocket.
In the arcade, he can pay
X
yen for
Y
tokens any number of times (possibly zero).
Find the maximum total number of tokens that he can get. | [
{
"input": "12 5 3\n",
"output": "6\n"
},
{
"input": "4 5 3\n",
"output": "0\n"
}
] |
https://atcoder.jp/contests/past202212-open/tasks/past202212_b | Problem Statement
You are given integers
A
and
C
, and non-negative integers
B
and
D
.
If
\frac{A}{B}<\frac{C}{D}
, print
<
;
if
\frac{A}{B}>\frac{C}{D}
, print
>
;
if
\frac{A}{B}=\frac{C}{D}
, print
=
. | [
{
"input": "1 2 1 3\n",
"output": ">\n"
},
{
"input": "-3 -6 1 2\n",
"output": "=\n"
},
{
"input": "-1 3 1 -4\n",
"output": "<\n"
}
] |
https://atcoder.jp/contests/past202212-open/tasks/past202212_c | Problem Statement
You are given an integer sequence of length
N
:
A = (A_1, \dots, A_N)
.
Find the number of integers
X
that satisfy the following condition.
There are integers
i
,
j
, and
k
such that
A_i \times A_j \times A_k = X
and
1 \leq i \lt j \lt k \leq N
. | [
{
"input": "4\n2 1 3 2\n",
"output": "3\n"
},
{
"input": "10\n3 1 4 1 5 9 2 6 5 3\n",
"output": "37\n"
}
] |
https://atcoder.jp/contests/past202212-open/tasks/past202212_d | Problem Statement
N
players will play a game using cards.
Initially, the first pile contains
M
cards, the second pile contains
0
cards, and each player has
0
cards.
Each card has one of the symbols
+
,
0
, and
-
written on it. The symbol on the
i
-th card from the top of the initial first pile is
S_i
.
In the game, the players take turns doing the following, in this order: player
1
, player
2
,
\ldots
, player
N-1
, player
N
, player
1
, player
2
,
\dots
If the first pile contains
0
cards, end the game. Otherwise, the current player draws the top card from the first pile, and adds it to the player's hand. Then, according to the symbol written on that card, the player does the following.
If
+
is written, add all cards in the second pile to the player's hand.
If
0
is written, do nohing.
If
-
is written, move all cards in the player's hand to the second pile.
Find the number of cards in each player's hand at the end of the game. | [
{
"input": "3 6\n000--+\n",
"output": "0\n0\n6\n"
},
{
"input": "2 6\n++++++\n",
"output": "3\n3\n"
},
{
"input": "7 20\n++-0+-0++-++0-+0-0-0\n",
"output": "6\n3\n0\n4\n0\n2\n0\n"
}
] |
https://atcoder.jp/contests/past202212-open/tasks/past202212_e | Problem Statement
A string consisting of
(
and
)
is said to be a
correct bracket sequence
if it can be made empty by erasing a contiguous occurrence of
()
zero or more times.
For instance,
()
,
(())
, and
(()())()
are correct bracket sequences, while
)(
,
())
, and
(()()))(()
are not.
You are given a string
S
consisting of
(
and
)
. Determine whether
S
is a correct bracket sequence. | [
{
"input": "(())\n",
"output": "Yes\n"
},
{
"input": "())(\n",
"output": "No\n"
},
{
"input": "(\n",
"output": "No\n"
},
{
"input": "((())()()())()()\n",
"output": "Yes\n"
}
] |
https://atcoder.jp/contests/past202212-open/tasks/past202212_f | Problem Statement
Snuke played
N
matches of a
4
-player game, and ranked
1
-st
A
times,
2
-nd
B
times,
3
-rd
C
times, and
4
-th
D
times.
Snuke is happy if the value of his average rank is at most
X
.
At least how many additional matches must be played to make him happy? | [
{
"input": "4\n1 1 1 1\n1.600\n",
"output": "6\n"
},
{
"input": "10\n0 0 0 10\n4.000\n",
"output": "0\n"
}
] |
https://atcoder.jp/contests/past202212-open/tasks/past202212_g | Problem Statement
You are given an integer sequence of length
N
:
A = (A_1, A_2, \ldots, A_N)
.
Print the maximum possible value of
A_l + A_{l+1} + \cdots + A_r
for a pair
(l, r)
such that
1 \leq l \leq r \leq N
. | [
{
"input": "10\n-6 5 -3 3 -1 4 -1 5 -9 2\n",
"output": "12\n"
},
{
"input": "3\n-1 -2 -3\n",
"output": "-1\n"
},
{
"input": "20\n-14 74 -48 38 -51 43 5 37 -39 -29 80 -44 -55 59 17 89 -37 -68 38 -16\n",
"output": "176\n"
}
] |
https://atcoder.jp/contests/past202212-open/tasks/past202212_h | Problem Statement
You are given a positive integer
N
that has
D
digits when written in base
10
.
For
1\leq k\leq D
, let
A_k
be the
k
-th digit from the top when
N
is written in base
10
.
Find the value
\displaystyle\sum_{i=1}^{D-1}\sum_{j=i+1}^D \lvert A_i-A_j \rvert
. | [
{
"input": "3\n287\n",
"output": "12\n"
},
{
"input": "2\n11\n",
"output": "0\n"
},
{
"input": "20\n12345678901234567890\n",
"output": "660\n"
}
] |
https://atcoder.jp/contests/past202212-open/tasks/past202212_i | Problem Statement
There are
N
people numbered
1
to
N
.
You are given
N
pieces of information, each in this form: person
A_i
is taller than person
B_i
. Determine whether they are consistent. | [
{
"input": "3 3\n1 2\n2 3\n3 1\n",
"output": "No\n"
},
{
"input": "4 9\n1 3\n1 3\n1 3\n1 3\n2 4\n1 4\n3 4\n2 3\n1 2\n",
"output": "Yes\n"
},
{
"input": "3 3\n1 2\n2 1\n1 3\n",
"output": "No\n"
},
{
"input": "100 0\n",
"output": "Yes\n"
}
] |
https://atcoder.jp/contests/past202212-open/tasks/past202212_j | Problem Statement
You are given points
S(x_{\mathrm{s}}, y_{\mathrm{s}})
and
T(x_{\mathrm{t}}, y_{\mathrm{t}})
in the
xy
-plane.
You are also given
N
four-tuples
(P_i, Q_i, R_i, W_i)(1 \leq i \leq N)
.
Consider the following procedure.
First, choose an arbitrary (directed) curve
C
from point
S(x_{\mathrm{s}}, y_{\mathrm{s}})
to
T(x_{\mathrm{t}}, y_{\mathrm{t}})
Next, choose arbitrary
K
distinct
integers
A_1, A_2, \ldots, A_K
between
1
and
N
.
Then, for each
i = 1, 2, \ldots, K
, do the following:
If the curve
C
has one or more common points with the line
P_{A_i} x + Q_{A_i} y = R_{A_i}
, you pay
W_{A_i}
yen (the currency in Japan).
Print the minimum possible amount of money you pay in total in the procedure above. | [
{
"input": "4 3\n-2 0 2 0\n2 1 2 7\n0 1 10 10\n1 0 -1 3\n-1 1 0 5\n",
"output": "8\n"
},
{
"input": "2 2\n0 0 0 0\n1 2 3 4\n2 4 6 8\n",
"output": "0\n"
},
{
"input": "20 17\n-6 -77 40 99\n-14 74 -48 27\n-51 43 5 89\n-39 -29 80 75\n-55 59 17 39\n-37 -68 38 62\n14 31 43 49\n49 -7 -65 13\n-40 -45 36 32\n-54 -43 99 77\n-94 57 -22 12\n-85 67 -46 72\n95 68 55 67\n-56 51 -38 22\n32 -19 65 46\n76 66 -53 8\n35 -78 -41 30\n-51 -85 24 64\n45 -53 82 12\n39 19 -52 86\n-11 -67 -33 100\n",
"output": "694\n"
}
] |
https://atcoder.jp/contests/past202212-open/tasks/past202212_k | Problem Statement
Takahashi wants an integer, so he goes to an integer shop.
The integer shop sells every integer between
1
and
10^9
, inclusive. The integer
n
is sold for
A \times n + B \times d(n)
yen (the currency in Japan), where
d(n)
denotes the sum of digits in the decimal notation of
n
.
Takahashi has
X
yen. Find the maximum integer he can buy. | [
{
"input": "3 4 50\n",
"output": "12\n"
},
{
"input": "199 211 10000000000\n",
"output": "50251233\n"
}
] |
https://atcoder.jp/contests/past202212-open/tasks/past202212_l | Problem Statement
You are given
N
segments
[L_1, R_1], [L_2, R_2], \ldots, [L_N, R_N]
on a number line.
A subset
S
of the set
\lbrace 1, 2, \ldots, N \rbrace
is said to be a
good set
if:
for all
i, j \in S
, at least one of the following two conditions is satisfied:
the segment
[L_i, R_i]
contains the segment
[L_j, R_j]
;
the segment
[L_j, R_j]
contains the segment
[L_i, R_i]
.
Here, a segment
[L, R]
is said to contain another segment
[L', R']
if and only if
L \leq L'
and
R' \leq R
.
Find the maximum possible size of a good set. | [
{
"input": "4\n1 3\n2 4\n3 4\n1 4\n",
"output": "3\n"
},
{
"input": "3\n0 1\n0 1\n0 1\n",
"output": "3\n"
},
{
"input": "9\n1 6\n1 3\n3 6\n4 6\n2 5\n1 2\n3 4\n3 5\n2 7\n",
"output": "4\n"
}
] |
https://atcoder.jp/contests/past202212-open/tasks/past202212_m | Problem Statement
There is a tree with
N
vertices, whose vertices are numbered
1, \dots, N
and edges are numbered
1, \dots, N-1
. Edge
i \, (1 \leq i \leq N - 1)
connects vertices
U_i
and
V_i
.
Find the sum of the following value over all integer pairs
(l, r)
such that
1 \leq l \leq r \leq N - 1
:
the number of vertices that are reachable from vertex
1
using zero or more edges numbered between
l
and
r
, inclusive. | [
{
"input": "5\n2 3\n1 2\n2 4\n3 5\n",
"output": "24\n"
},
{
"input": "2\n1 2\n",
"output": "2\n"
},
{
"input": "7\n1 2\n2 7\n4 6\n3 6\n4 5\n1 5\n",
"output": "49\n"
}
] |
https://atcoder.jp/contests/past202212-open/tasks/past202212_n | Problem Statement
For an integer sequence
X = (X_1, X_2, \dots, X_k)
, let us define a function
f(X)
as follows:
Let
Y = (Y_1, Y_2, \dots, Y_k)
be the sequence obtained by sorting
X
in ascending order.
Then,
\displaystyle f(X) = \sum_{i=1}^{k-1}(Y_{i+1}-Y_i)^2
.
We have an integer sequence
A = (A_1, A_2, \dots, A_N)
. Given
Q
queries in the following format, process them in order.
Given integers
l
and
r
, find
f(B)
, where
B = (A_l, A_{l + 1}, \dots, A_r)
. | [
{
"input": "3\n3 1 4\n4\n1 1\n1 2\n2 3\n1 3\n",
"output": "0\n4\n9\n5\n"
},
{
"input": "10\n19 70 14 11 85 75 72 35 14 50\n10\n1 1\n3 8\n5 7\n1 3\n5 8\n5 5\n2 10\n2 5\n1 5\n2 9\n",
"output": "0\n1928\n109\n2626\n1478\n0\n1188\n3370\n2860\n1788\n"
}
] |
https://atcoder.jp/contests/past202212-open/tasks/past202212_o | Problem Statement
You are given an integer sequence
A = (A_1, A_2, \ldots, A_N)
of length
N
.
Each element
A_1, A_2, \ldots, A_N
of
A
is a
D
-digit integer (without leading zeros) in the decimal notation, and none of its digits are
0
.
You are given
Q
queries. Each query is of one of type
1
, type
2
, and type
3
, which are described below.
Process the given
Q
queries in the order given in the input.
[ Type
1
]
1
x
Apply a left cyclic shift
x
times to the sequence
A
. In other words, if
A = (a_1, a_2, \ldots, a_N)
,
let
A = (a_{x+1}, a_{x+2}, \ldots, a_N, a_1, a_2, \ldots, a_x)
.
[ Type
2
]
2
l
r
y
Do the following for
i = l, l+1, \ldots, r
:
Let
d_1 d_2 \ldots d_D
be the decimal notation of
A_i
. Replace
A_i
with the integer
d_{y+1} d_{y+2} \ldots d_D d_1 d_2 \ldots d_y
, which is obtained by applying a left cyclic shift
y
times to the digits of
A_i
.
[ Type
3
]
3
l
r
Print
A_l \oplus A_{l+1} \oplus \cdots \oplus A_r
, where
\oplus
denotes the bitwise exclusive logical sum. | [
{
"input": "5 3\n123 234 345 456 567\n5\n3 2 4\n1 3\n3 2 4\n2 3 5 2\n3 2 4\n",
"output": "123\n678\n680\n"
},
{
"input": "20 6\n318153 438943 474719 114997 373645 598458 427319 171794 653644 463294 123454 842368 264537 215892 467783 121159 836368 946718 889644 865849\n20\n2 6 9 3\n2 8 13 5\n2 1 6 3\n2 14 20 5\n1 7\n2 14 15 4\n3 8 8\n2 4 5 3\n2 7 17 2\n1 19\n2 13 16 4\n2 4 9 2\n3 11 14\n1 8\n2 2 17 3\n3 6 9\n3 6 16\n2 16 17 2\n1 1\n3 3 20\n",
"output": "346778\n710529\n89337\n796525\n709076\n"
}
] |
https://atcoder.jp/contests/abc279/tasks/abc279_a | Problem Statement
You are given a string
S
consisting of
v
and
w
.
Print the number of "bottoms" in the string
S
(see the figure at Sample Input/Output). | [
{
"input": "vvwvw\n",
"output": "7\n"
},
{
"input": "v\n",
"output": "1\n"
},
{
"input": "wwwvvvvvv\n",
"output": "12\n"
}
] |
https://atcoder.jp/contests/abc279/tasks/abc279_b | Problem Statement
You are given strings
S
and
T
consisting of lowercase English letters. Determine whether
T
is a (contiguous) substring of
S
.
A string
Y
is said to be a (contiguous) substring of
X
if and only if
Y
can be obtained by performing the operation below on
X
zero or more times.
Do one of the following.
Delete the first character in
X
.
Delete the last character in
X
.
For instance,
tag
is a (contiguous) substring of
voltage
, while
ace
is not a (contiguous) substring of
atcoder
. | [
{
"input": "voltage\ntag\n",
"output": "Yes\n"
},
{
"input": "atcoder\nace\n",
"output": "No\n"
},
{
"input": "gorilla\ngorillagorillagorilla\n",
"output": "No\n"
},
{
"input": "toyotasystems\ntoyotasystems\n",
"output": "Yes\n"
}
] |
https://atcoder.jp/contests/abc279/tasks/abc279_c | Problem Statement
You are given patterns
S
and
T
consisting of
#
and
.
, each with
H
rows and
W
columns.
The pattern
S
is given as
H
strings, and the
j
-th character of
S_i
represents the element at the
i
-th row and
j
-th column. The same goes for
T
.
Determine whether
S
can be made equal to
T
by rearranging the columns of
S
.
Here, rearranging the columns of a pattern
X
is done as follows.
Choose a permutation
P=(P_1,P_2,\dots,P_W)
of
(1,2,\dots,W)
.
Then, for every integer
i
such that
1 \le i \le H
, simultaneously do the following.
For every integer
j
such that
1 \le j \le W
, simultaneously replace the element at the
i
-th row and
j
-th column of
X
with the element at the
i
-th row and
P_j
-th column. | [
{
"input": "3 4\n##.#\n##..\n#...\n.###\n..##\n...#\n",
"output": "Yes\n"
},
{
"input": "3 3\n#.#\n.#.\n#.#\n##.\n##.\n.#.\n",
"output": "No\n"
},
{
"input": "2 1\n#\n.\n#\n.\n",
"output": "Yes\n"
},
{
"input": "8 7\n#..#..#\n.##.##.\n#..#..#\n.##.##.\n#..#..#\n.##.##.\n#..#..#\n.##.##.\n....###\n####...\n....###\n####...\n....###\n####...\n....###\n####...\n",
"output": "Yes\n"
}
] |
https://atcoder.jp/contests/abc279/tasks/abc279_d | Problem Statement
A superman, Takahashi, is about to jump off the roof of a building to help a person in trouble on the ground.
Takahashi's planet has a constant value
g
that represents the strength of gravity, and the time it takes for him to reach the ground after starting to fall is
\frac{A}{\sqrt{g}}
.
It is now time
0
, and
g = 1
.
Takahashi will perform the following operation as many times as he wants (possibly zero).
Use a superpower to increase the value of
g
by
1
. This takes a time of
B
.
Then, he will jump off the building. After starting to fall, he cannot change the value of
g
. Additionally, we only consider the time it takes to perform the operation and fall.
Find the earliest time Takahashi can reach the ground. | [
{
"input": "10 1\n",
"output": "7.7735026919\n"
},
{
"input": "5 10\n",
"output": "5.0000000000\n"
},
{
"input": "1000000000000000000 100\n",
"output": "8772053214538.5976562500\n"
}
] |
https://atcoder.jp/contests/abc279/tasks/abc279_e | Problem Statement
You are given a sequence of length
M
consisting of integers between
1
and
N-1
, inclusive:
A=(A_1,A_2,\dots,A_M)
.
Answer the following question for
i=1, 2, \dots, M
.
There is a sequence
B=(B_1,B_2,\dots,B_N)
. Initially, we have
B_j=j
for each
j
. Let us perform the following operation for
k=1, 2, \dots, i-1, i+1, \dots, M
in this order (in other words, for integers
k
between
1
and
M
except
i
in ascending order).
Swap the values of
B_{A_k}
and
B_{A_k+1}
.
After all the operations, let
S_i
be the value of
j
such that
B_j=1
. Find
S_i
. | [
{
"input": "5 4\n1 2 3 2\n",
"output": "1\n3\n2\n4\n"
},
{
"input": "3 3\n2 2 2\n",
"output": "1\n1\n1\n"
},
{
"input": "10 10\n1 1 1 9 4 4 2 1 3 3\n",
"output": "2\n2\n2\n3\n3\n3\n1\n3\n4\n4\n"
}
] |
https://atcoder.jp/contests/abc279/tasks/abc279_f | Problem Statement
There are
N
boxes numbered
1,2,\ldots,N
, and
10^{100}
balls numbered
1,2,\dots,10^{100}
.
Initially, box
i
contains just ball
i
.
Process a total of
Q
operations that will be performed.
There are three types of operations:
1
,
2
, and
3
.
Type
1
: Put all contents of box
Y
into box
X
. It is guaranteed that
X \neq Y
.
1
X
Y
Type
2
: Put ball
k+1
into box
X
, where
k
is the current total number of balls contained in the boxes.
2
X
Type
3
: Report the number of the box that contains ball
X
.
3
X | [
{
"input": "5 10\n3 5\n1 1 4\n2 1\n2 4\n3 7\n1 3 1\n3 4\n1 1 4\n3 7\n3 6\n",
"output": "5\n4\n3\n1\n3\n"
}
] |
https://atcoder.jp/contests/abc279/tasks/abc279_g | Problem Statement
There is a grid with
1 \times N
squares, numbered
1,2,\dots,N
from left to right.
Takahashi prepared paints of
C
colors and painted each square in one of the
C
colors.
Then, there were at most two colors in any consecutive
K
squares.
Formally, for every integer
i
such that
1 \le i \le N-K+1
, there were at most two colors in squares
i,i+1,\dots,i+K-1
.
In how many ways could Takahashi paint the squares?
Since this number can be enormous, find it modulo
998244353
. | [
{
"input": "3 3 3\n",
"output": "21\n"
},
{
"input": "10 5 2\n",
"output": "1024\n"
},
{
"input": "998 244 353\n",
"output": "952364159\n"
}
] |
https://atcoder.jp/contests/abc279/tasks/abc279_h | Problem Statement
You are given positive integers
N
and
M
. Here, it is guaranteed that
N\leq M \leq 2N
.
Print the sum, modulo
200\ 003
(a prime), of the following value over all sequences of positive integers
S=(S_1,S_2,\dots,S_N)
such that
\displaystyle \sum_{i=1}^{N} S_i = M
(notice the unusual modulo):
\displaystyle \prod_{k=1}^{N} \min(k,S_k)
. | [
{
"input": "3 5\n",
"output": "14\n"
},
{
"input": "1126 2022\n",
"output": "40166\n"
},
{
"input": "1000000000000 1500000000000\n",
"output": "180030\n"
}
] |
https://atcoder.jp/contests/arc152/tasks/arc152_a | Problem Statement
There is a row of
L
chairs. Now,
N
groups of people will come and take seats in order.
Each group consists of one or two people, and the
i
-th group to come consists of
a_i
people.
The total number of people equals
L
.
Each group will randomly choose unoccupied chairs where all group members can sit consecutively, and occupy those chairs.
However, if there are not enough consecutive unoccupied chairs, they will leave without taking seats.
Determine whether it is guaranteed that all
N
groups can take seats. | [
{
"input": "2 4\n2 2\n",
"output": "No\n"
},
{
"input": "3 4\n1 2 1\n",
"output": "Yes\n"
}
] |
https://atcoder.jp/contests/arc152/tasks/arc152_b | Problem Statement
There is a narrow straight road of length
L
stretching east to west. Two travelers will visit this road.
Along the road, there are
N
rest areas. The distance from the west end of the road to the
i
-th rest area is
a_i
(no rest area is at either end of the road).
The road is so narrow that the two travelers cannot pass each other or walk side by side except at the rest areas.
The two travelers will take a trip along the road as follows.
At time
0
, each traveler starts at a rest area of their choice (the two may start at the same rest area).
Then, each visits both ends of the road, and returns to their own starting rest area.
During the trip, they can walk along the road at a speed of at most
1
, or rest at a rest area.
As long as they only pass each other at the rest areas, it is always allowed to change direction.
What is the smallest number of seconds needed for both travelers to visit both ends of the road and return to their starting rest areas?
It can be proved that the answer is always an integer under the Constraints of this problem. | [
{
"input": "2 6\n2 5\n",
"output": "14\n"
},
{
"input": "2 3\n1 2\n",
"output": "6\n"
}
] |
https://atcoder.jp/contests/arc152/tasks/arc152_c | Problem Statement
We have a sequence of
N
terms:
a_1,a_2,\ldots,a_N
.
You can perform the following operation on this sequence any number of times (possibly zero).
Choose a term of the sequence at that point, and let
s
be its value.
Then, for every
1\leq i\leq N
, replace
a_i
with
2s-a_i
.
However, this operation may not be performed in a way that produces a term with a negative value.
You want to make the greatest value among the terms of the sequence as small as possible.
What will this value be after an optimal sequence of operations for this objective? | [
{
"input": "3\n1 3 6\n",
"output": "5\n"
},
{
"input": "5\n400 500 600 700 800\n",
"output": "400\n"
}
] |
https://atcoder.jp/contests/arc152/tasks/arc152_d | Problem Statement
We have an undirected graph with
N
vertices numbered
0
through
N-1
and no edges at first.
You may add edges to this graph as you like.
When you are done with adding edges, the following operation will be performed once using a given integer
K
.
For each edge you have added, let
u
and
v
be its endpoints, and an edge will be added between two vertices
(u+K)
\mathrm{mod}
N
and
(v+K)
\mathrm{mod}
N
.
This edge will be added even if there is already an edge between these vertices, resulting in multi-edges.
For the given
N
and
K
, find a set of edges that you should add so that the graph will be a tree after the operation.
If there is no such set of edges, indicate that fact. | [
{
"input": "5 2\n",
"output": "2\n2 3\n2 4\n"
},
{
"input": "2 1\n",
"output": "-1\n"
},
{
"input": "7 1\n",
"output": "3\n0 1\n2 3\n4 5\n"
}
] |
https://atcoder.jp/contests/arc152/tasks/arc152_e | Problem Statement
On a number line, there are
2^N-1
balls at the coordinates
x=1,2,3,...,2^N-1
, and the ball at
x=i
has a weight of
w_i
. Here,
w_1, w_2,...,w_{2^N-1}
is a permutation of the integers from
1
through
2^N-1
. You will choose a non-negative integer
Z
at most
2^N-1
and attach a weight of
Z
at each of the coordinates
x=\pm 100^{100^{100}}
.
Then, the balls will simultaneously start moving as follows.
At each time, let
R
be the total
\mathrm{XOR}
of the weights of the balls and attached weights that are strictly to the right of the coordinate of a ball, and
L
be the total
\mathrm{XOR}
of the weights of the balls and attached weights that are strictly to the left. If
R>L
, the ball moves to the right at a speed of
1
per second; if
L>R
, the ball moves to the left at a speed of
1
per second; if
L=R
, the ball stands still.
If multiple balls exist at the same coordinate (when, for instance, two balls coming from the left and right reach there), the balls combine into one whose weight is the total
\mathrm{XOR}
of their former weights.
For how many values of
Z
will all balls come to rest within
100^{100}
seconds?
What is
\mathrm{XOR}
?
The bitwise
\mathrm{XOR}
of non-negative integers
A
and
B
,
A \oplus B
, is defined as follows.
When
A \oplus B
is written in binary, the
k
-th lowest bit (
k \geq 0
) is
1
if exactly one of the
k
-th lowest bits of
A
and
B
is
1
, and
0
otherwise.
For instance,
3 \oplus 5 = 6
(in binary:
011 \oplus 101 = 110
).
Generally, the bitwise
\mathrm{XOR}
of
k
non-negative integers
p_1, p_2, p_3, \dots, p_k
is defined as
(\dots ((p_1 \oplus p_2) \oplus p_3) \oplus \dots \oplus p_k)
, which can be proved to be independent of the order of
p_1, p_2, p_3, \dots, p_k
. | [
{
"input": "2\n1 2 3\n",
"output": "1\n"
},
{
"input": "3\n7 1 2 3 4 5 6\n",
"output": "2\n"
}
] |
https://atcoder.jp/contests/arc152/tasks/arc152_f | Problem Statement
You are given a tree with
N
vertices numbered
1
to
N
.
The
i
-th edge connects two vertices
a_i
and
b_i
(1\leq i\leq N-1)
.
Initially, a piece is placed at vertex
1
. You will perform the following operation exactly
N
times.
Choose a vertex that is not occupied by the piece at that moment and is never chosen in the previous operations, and move the piece one vertex toward the chosen vertex.
A way to perform the operation
N
times is called a
good procedure
if the piece ends up at vertex
N
.
Additionally, a good procedure is called an
ideal procedure
if the number of vertices visited by the piece at least once during the procedure (including vertices
1
and
N
) is the minimum possible.
Find the number of vertices visited by the piece at least once during an ideal procedure.
If there is no good procedure, print
-1
instead. | [
{
"input": "4\n1 2\n2 4\n3 4\n",
"output": "3\n"
},
{
"input": "6\n1 6\n2 6\n2 3\n3 4\n4 5\n",
"output": "-1\n"
},
{
"input": "14\n1 2\n1 3\n3 4\n3 5\n5 6\n6 7\n5 8\n8 9\n8 14\n14 10\n10 11\n14 12\n12 13\n",
"output": "5\n"
}
] |
https://atcoder.jp/contests/abc278/tasks/abc278_a | Problem Statement
You are given a sequence
A = (A_1, A_2, \dots, A_N)
of length
N
.
You perform the following operation exactly
K
times:
remove the initial element of
A
and append a
0
to the tail of
A
.
Print all the elements of
A
after the operations. | [
{
"input": "3 2\n2 7 8\n",
"output": "8 0 0\n"
},
{
"input": "3 4\n9 9 9\n",
"output": "0 0 0\n"
},
{
"input": "9 5\n1 2 3 4 5 6 7 8 9\n",
"output": "6 7 8 9 0 0 0 0 0\n"
}
] |
https://atcoder.jp/contests/abc278/tasks/abc278_b | Problem Statement
Takahashi bought a table clock.
The clock shows the time as shown in Figure 1 at
\mathrm{AB}
:
\mathrm{CD}
in the
24
-hour system.
For example, the clock in Figure 2 shows 7:58.
The format of the time is formally described as follows.
Suppose that the current time is
m
minutes past
h
in the
24
-hour system. Here, the
24
-hour system represents the hour by an integer between
0
and
23
(inclusive), and the minute by an integer between
0
and
59
(inclusive).
Let
A
be the tens digit of
h
,
B
be the ones digit of
h
,
C
be the tens digit of
m
, and
D
be the ones digit of
m
. (Here, if
h
has only one digit, we consider that it has a leading zero; the same applies to
m
.)
Then, the clock shows
A
in its top-left,
B
in its bottom-left,
C
in its top-right, and
D
in its bottom-right.
Takahashi has decided to call a time
a confusing time
if it satisfies the following condition:
after swapping the top-right and bottom-left digits on the clock, it still reads a valid time in the
24
-hour system.
For example, the clock in Figure 3 shows 20:13. After swapping its top-right and bottom-left digits, it reads 21:03. Thus, 20:13 is a confusing time.
The clock now shows
H
:
M
.
Find the next confusing time (including now) in the
24
-hour system. | [
{
"input": "1 23\n",
"output": "1 23\n"
},
{
"input": "19 57\n",
"output": "20 0\n"
},
{
"input": "20 40\n",
"output": "21 0\n"
}
] |
https://atcoder.jp/contests/abc278/tasks/abc278_c | Problem Statement
Takahashi runs an SNS "Twidai," which has
N
users from user
1
through user
N
.
In Twidai, users can follow or unfollow other users.
Q
operations have been performed since Twidai was launched.
The
i
-th
(1\leq i\leq Q)
operation is represented by three integers
T_i
,
A_i
, and
B_i
, whose meanings are as follows:
If
T_i = 1
: it means that user
A_i
follows user
B_i
. If user
A_i
is already following user
B_i
at the time of this operation, it does not make any change.
If
T_i = 2
: it means that user
A_i
unfollows user
B_i
. If user
A_i
is not following user
B_i
at the time of this operation, it does not make any change.
If
T_i = 3
: it means that you are asked to determine if users
A_i
and
B_i
are following each other. You need to print
Yes
if user
A_i
is following user
B_i
and user
B_i
is following user
A_i
, and
No
otherwise.
When the service was launched, no users were following any users.
Print the correct answers for all operations such that
T_i = 3
in ascending order of
i
. | [
{
"input": "3 9\n1 1 2\n3 1 2\n1 2 1\n3 1 2\n1 2 3\n1 3 2\n3 1 3\n2 1 2\n3 1 2\n",
"output": "No\nYes\nNo\nNo\n"
},
{
"input": "2 8\n1 1 2\n1 2 1\n3 1 2\n1 1 2\n1 1 2\n1 1 2\n2 1 2\n3 1 2\n",
"output": "Yes\nNo\n"
},
{
"input": "10 30\n3 1 6\n3 5 4\n1 6 1\n3 1 7\n3 8 4\n1 1 6\n2 4 3\n1 6 5\n1 5 6\n1 1 8\n1 8 1\n2 3 10\n1 7 6\n3 5 6\n1 6 7\n3 6 7\n1 9 5\n3 8 6\n3 3 8\n2 6 9\n1 7 1\n3 10 8\n2 9 2\n1 10 9\n2 6 10\n2 6 8\n3 1 6\n3 1 8\n2 8 5\n1 9 10\n",
"output": "No\nNo\nNo\nNo\nYes\nYes\nNo\nNo\nNo\nYes\nYes\n"
}
] |
https://atcoder.jp/contests/abc278/tasks/abc278_d | Problem Statement
You are given a sequence
A = (A_1, A_2, \dots, A_N)
of length
N
.
Given
Q
queries, process all of them in order.
The
q
-th
(1\leq q\leq Q)
query is in one of the following three formats, which represents the following queries:
1\ x _ q
: assign
x_q
to every element of
A
.
2\ i _ q\ x _ q
: add
x_q
to
A _ {i _ q}
.
3\ i _ q
: print the value of
A _ {i _ q}
. | [
{
"input": "5\n3 1 4 1 5\n6\n3 2\n2 3 4\n3 3\n1 1\n2 3 4\n3 3\n",
"output": "1\n8\n5\n"
},
{
"input": "1\n1000000000\n8\n2 1 1000000000\n2 1 1000000000\n2 1 1000000000\n2 1 1000000000\n2 1 1000000000\n2 1 1000000000\n2 1 1000000000\n3 1\n",
"output": "8000000000\n"
},
{
"input": "10\n1 8 4 15 7 5 7 5 8 0\n20\n2 7 0\n3 7\n3 8\n1 7\n3 3\n2 4 4\n2 4 9\n2 10 5\n1 10\n2 4 2\n1 10\n2 3 1\n2 8 11\n2 3 14\n2 1 9\n3 8\n3 8\n3 1\n2 6 5\n3 7\n",
"output": "7\n5\n7\n21\n21\n19\n10\n"
}
] |
https://atcoder.jp/contests/abc278/tasks/abc278_e | Problem Statement
You have a grid with
H
rows from top to bottom and
W
columns from left to right.
We denote by
(i, j)
the square at the
i
-th row from the top and
j
-th column from the left.
(i,j)\ (1\leq i\leq H,1\leq j\leq W)
has an integer
A _ {i,j}
between
1
and
N
written on it.
You are given integers
h
and
w
. For all pairs
(k,l)
such that
0\leq k\leq H-h
and
0\leq l\leq W-w
, solve the following problem:
If you black out the squares
(i,j)
such that
k\lt i\leq k+h
and
l\lt j\leq l+w
, how many distinct integers are written on the squares that are not blacked out?
Note, however, that you do not actually black out the squares (that is, the problems are independent). | [
{
"input": "3 4 5 2 2\n2 2 1 1\n3 2 5 3\n3 4 4 3\n",
"output": "4 4 3\n5 3 4\n"
},
{
"input": "5 6 9 3 4\n7 1 5 3 9 5\n4 5 4 5 1 2\n6 1 6 2 9 7\n4 7 1 5 8 8\n3 4 3 3 5 3\n",
"output": "8 8 7\n8 9 7\n8 9 8\n"
},
{
"input": "9 12 30 4 7\n2 2 2 2 2 2 2 2 2 2 2 2\n2 2 20 20 2 2 5 9 10 9 9 23\n2 29 29 29 29 29 28 28 26 26 26 15\n2 29 29 29 29 29 25 25 26 26 26 15\n2 29 29 29 29 29 25 25 8 25 15 15\n2 18 18 18 18 1 27 27 25 25 16 16\n2 19 22 1 1 1 7 3 7 7 7 7\n2 19 22 22 6 6 21 21 21 7 7 7\n2 19 22 22 22 22 21 21 21 24 24 24\n",
"output": "21 20 19 20 18 17\n20 19 18 19 17 15\n21 19 20 19 18 16\n21 19 19 18 19 18\n20 18 18 18 19 18\n18 16 17 18 19 17\n"
}
] |
https://atcoder.jp/contests/abc278/tasks/abc278_f | Problem Statement
You are given
N
strings
S _ 1,S _ 2,\ldots,S _ N
.
S _ i\ (1\leq i\leq N)
is a non-empty string of length at most
10
consisting of lowercase English letters, and the strings are pairwise distinct.
Taro the First and Jiro the Second play a word-chain game.
In this game, the two players take alternating turns,
with Taro the First going first.
In each player's turn, the player chooses an integer
i\ (1\leq i\leq N)
,
which should satisfy the following two conditions:
i
is different from any integer chosen by the two players so far since the game started;
the current turn is the first turn of the game, or the last character of
S_j
equals the first character of
S_i
, where
j
is the last integer chosen.
The player who is unable to choose a conforming
i
loses; the other player wins.
Determine which player will win if the two players play optimally. | [
{
"input": "6\nenum\nfloat\nif\nmodint\ntakahashi\ntemplate\n",
"output": "First\n"
},
{
"input": "10\ncatch\nchokudai\nclass\ncontinue\ncopy\nexec\nhavoc\nintrinsic\nstatic\nyucatec\n",
"output": "Second\n"
},
{
"input": "16\nmnofcmzsdx\nlgeowlxuqm\nouimgdjxlo\njhwttcycwl\njbcuioqbsj\nmdjfikdwix\njhvdpuxfil\npeekycgxco\nsbvxszools\nxuuqebcrzp\njsciwvdqzl\nobblxzjhco\nptobhnpfpo\nmuizaqtpgx\njtgjnbtzcl\nsivwidaszs\n",
"output": "First\n"
}
] |
https://atcoder.jp/contests/abc278/tasks/abc278_g | Problem Statement
This is an
interactive task
(where your program interacts with the judge's program via Standard Input and Output).
You are given integers
N
,
L
, and
R
.
You play the following game against the judge:
There are
N
cards numbered
1
through
N
on the table.
The players alternately perform the following operation:
choose an integer pair
(x, y)
satisfying
1 \leq x \leq N
,
L \leq y \leq R
such that all of the
y
cards
x, x+1, \dots, x+y-1
remain on the table, and remove cards
x, x+1, \dots, x+y-1
from the table.
The first player to become unable to perform the operation loses, and the other player wins.
Choose whether to go first or second, and play the game against the judge to win. | [] |
https://atcoder.jp/contests/abc278/tasks/abc278_h | Problem Statement
A sequence
S
of non-negative integers is said to be a
good sequence
if:
there exists a non-empty (not necessarily contiguous) subsequence
T
of
S
such that the bitwise XOR of all elements in
T
is
1
.
There are an empty sequence
A
, and
2^B
cards with each of the integers between
0
and
2^B-1
written on them.
You repeat the following operation until
A
becomes a good sequence:
You freely choose a card and append the integer written on it to the tail of
A
. Then, you eat the card. (Once eaten, the card cannot be chosen anymore.)
How many sequences of length
N
can be the final
A
after the operations? Find the count modulo
998244353
.
What is bitwise XOR?
The bitwise
\mathrm{XOR}
of non-negative integers
A
and
B
,
A \oplus B
, is defined as follows.
When
A \oplus B
is written in binary, the
k
-th lowest bit (
k \geq 0
) is
1
if exactly one of the
k
-th lowest bits of
A
and
B
is
1
, and
0
otherwise.
For instance,
3 \oplus 5 = 6
(in binary:
011 \oplus 101 = 110
). | [
{
"input": "2 2\n",
"output": "5\n"
},
{
"input": "2022 1119\n",
"output": "293184537\n"
},
{
"input": "200000 10000000\n",
"output": "383948354\n"
}
] |
https://atcoder.jp/contests/joi2023yo1c/tasks/joi2023_yo1c_a | 問題文
2
つの数字
A, B
が与えられる．
十の位が
A
であり，一の位が
B
である
2
桁の正の整数を出力せよ． | [
{
"input": "2\n2\n",
"output": "22\n"
},
{
"input": "1\n0\n",
"output": "10\n"
},
{
"input": "1\n9\n",
"output": "19\n"
}
] |
https://atcoder.jp/contests/joi2023yo1c/tasks/joi2023_yo1c_b | 問題文
2
つの整数
A, B
が与えられる．
2022
年
11
月
A
日の
B
週間後の日が
2022
年
11
月ならば
1
を，
2022
年
11
月でないならば
0
を出力せよ．
ただし，
2022
年
11
月は
2022
年
11
月
1
日から
2022
年
11
月
30
日までの
30
日間であり，
x
週間後の日とは
(7\times x)
日後の日のことを指す． | [
{
"input": "19\n1\n",
"output": "1\n"
},
{
"input": "3\n4\n",
"output": "0\n"
},
{
"input": "8\n3\n",
"output": "1\n"
}
] |
https://atcoder.jp/contests/joi2023yo1c/tasks/joi2023_yo1c_c | 問題文
ただ奇妙な発明で知られる JOI 社は，最近 JOI Editor というテキストエディタを開発した．
このテキストエディタは，
j
，
o
，
i
の
3
つのキーで操作することができる．
j
，
o
，
i
のいずれかのキーを押すと，そのキーに書かれている英小文字が入力されるが，同じ英小文字が
2
つ隣接すると，ただちにその
2
文字が対応する英大文字に置換される．すなわち，
jj
は
JJ
に，
oo
は
OO
に，
ii
は
II
に置換される．
例えば，
j
，
o
，
o
，
o
，
i
のキーをこの順番で押すと，
j
，
o
，
o
までキーを押した直後，
2
文字目と
3
文字目の並びが
oo
となる．同じ英小文字が
2
つ隣接しているので，この
2
文字がただちに
OO
に置換される．最終的に JOI Editor に書かれている文字列は
jOOoi
となる．
joOOi
や
jOOOi
とはならないことに注意せよ．
長さ
N
の文字列
S
が与えられる．
S
の各文字は
j
，
o
，
i
のいずれかである．
N
回キーを押す．
S
の
i
文字目 (
1 \leqq i \leqq N
) は
i
回目に押すキーを表す．最終的に JOI Editor に書かれている文字列を出力せよ． | [
{
"input": "6\njjoiii\n",
"output": "JJoIIi\n"
},
{
"input": "6\njoijoi\n",
"output": "joijoi\n"
},
{
"input": "7\nooooooo\n",
"output": "OOOOOOo\n"
}
] |
https://atcoder.jp/contests/joi2023yo1c/tasks/joi2023_yo1c_d | 問題文
JOI 高校には
N
人の生徒がおり，
1
から
N
までの番号が付けられている．
先月 JOI 高校ではマラソン大会が開催され，生徒全員がこれに参加した．生徒
i
(
1 \leqq i \leqq N
) の記録は
A_i
分であった．
マラソン大会における各生徒の順位を求めよ．ただし，生徒
i
(
1 \leqq i \leqq N
) の順位は，(記録が
A_i
分未満の生徒の人数)
{} + 1
で計算される． | [
{
"input": "3\n44 42 69\n",
"output": "2\n1\n3\n"
},
{
"input": "4\n40 60 40 60\n",
"output": "1\n3\n1\n3\n"
},
{
"input": "10\n766 152 595 926 663 509 368 595 175 622\n",
"output": "9\n1\n5\n10\n8\n4\n3\n5\n2\n7\n"
}
] |
https://atcoder.jp/contests/abc277/tasks/abc277_a | Problem Statement
You are given a sequence
P
that is a permutation of
(1,2,…,N)
, and an integer
X
.
The
i
-th term of
P
has a value of
P_i
.
Print
k
such that
P_k = X
. | [
{
"input": "4 3\n2 3 1 4\n",
"output": "2\n"
},
{
"input": "5 2\n3 5 1 4 2\n",
"output": "5\n"
},
{
"input": "6 6\n1 2 3 4 5 6\n",
"output": "6\n"
}
] |
https://atcoder.jp/contests/abc277/tasks/abc277_b | Problem Statement
You are given
N
strings, each of length
2
, consisting of uppercase English letters and digits. The
i
-th string is
S_i
.
Determine whether the following three conditions are all satisfied.
・For every string, the first character is one of
H
,
D
,
C
, and
S
.
・For every string, the second character is one of
A
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
,
T
,
J
,
Q
,
K
.
・All strings are pairwise different. That is, if
i \neq j
, then
S_i \neq S_j
. | [
{
"input": "4\nH3\nDA\nD3\nSK\n",
"output": "Yes\n"
},
{
"input": "5\nH3\nDA\nCK\nH3\nS7\n",
"output": "No\n"
},
{
"input": "4\n3H\nAD\n3D\nKS\n",
"output": "No\n"
},
{
"input": "5\n00\nAA\nXX\nYY\nZZ\n",
"output": "No\n"
}
] |
https://atcoder.jp/contests/abc277/tasks/abc277_c | Problem Statement
There is a
10^9
-story building with
N
ladders.
Takahashi, who is on the
1
-st (lowest) floor, wants to reach the highest floor possible by using ladders (possibly none).
The ladders are numbered from
1
to
N
, and ladder
i
connects the
A_i
-th and
B_i
-th floors. One can use ladder
i
in either direction to move from the
A_i
-th floor to the
B_i
-th floor or vice versa, but not between other floors.
Takahashi can freely move within the same floor, but cannot move between floors without using ladders.
What is the highest floor Takahashi can reach? | [
{
"input": "4\n1 4\n4 3\n4 10\n8 3\n",
"output": "10\n"
},
{
"input": "6\n1 3\n1 5\n1 12\n3 5\n3 12\n5 12\n",
"output": "12\n"
},
{
"input": "3\n500000000 600000000\n600000000 700000000\n700000000 800000000\n",
"output": "1\n"
}
] |
https://atcoder.jp/contests/abc277/tasks/abc277_d | Problem Statement
Takahashi has
N
cards in his hand.
For
i = 1, 2, \ldots, N
, the
i
-th card has an non-negative integer
A_i
written on it.
First, Takahashi will freely choose a card from his hand and put it on a table.
Then, he will repeat the following operation as many times as he wants (possibly zero).
Let
X
be the integer written on the last card put on the table. If his hand contains cards with the integer
X
or the integer
(X+1)\bmod M
written on them, freely choose one of those cards and put it on the table. Here,
(X+1)\bmod M
denotes the remainder when
(X+1)
is divided by
M
.
Print the smallest possible sum of the integers written on the cards that end up remaining in his hand. | [
{
"input": "9 7\n3 0 2 5 5 3 0 6 3\n",
"output": "11\n"
},
{
"input": "1 10\n4\n",
"output": "0\n"
},
{
"input": "20 20\n18 16 15 9 8 8 17 1 3 17 11 9 12 11 7 3 2 14 3 12\n",
"output": "99\n"
}
] |
https://atcoder.jp/contests/abc277/tasks/abc277_e | Problem Statement
You are given an undirected graph consisting of
N
vertices and
M
edges.
For
i = 1, 2, \ldots, M
, the
i
-th edge is an undirected edge connecting vertex
u_i
and
v_i
that is initially passable if
a_i = 1
and initially impassable if
a_i = 0
.
Additionally, there are switches on
K
of the vertices: vertex
s_1
, vertex
s_2
,
\ldots
, vertex
s_K
.
Takahashi is initially on vertex
1
, and will repeat performing one of the two actions below,
Move
or
Hit Switch
, which he may choose each time, as many times as he wants.
Move
: Choose a vertex adjacent to the vertex he is currently on via an edge, and move to that vertex.
Hit Switch
: If there is a switch on the vertex he is currently on, hit it. This will invert the passability of every edge in the graph. That is, a passable edge will become impassable, and vice versa.
Determine whether Takahashi can reach vertex
N
, and if he can, print the minimum possible number of times he performs
Move
before reaching vertex
N
. | [
{
"input": "5 5 2\n1 3 0\n2 3 1\n5 4 1\n2 1 1\n1 4 0\n3 4\n",
"output": "5\n"
},
{
"input": "4 4 2\n4 3 0\n1 2 1\n1 2 0\n2 1 1\n2 4\n",
"output": "-1\n"
}
] |
https://atcoder.jp/contests/abc277/tasks/abc277_f | Problem Statement
You are given a matrix
A
whose elements are non-negative integers.
For a pair of integers
(i, j)
such that
1 \leq i \leq H
and
1 \leq j \leq W
,
let
A_{i, j}
denote the element at the
i
-th row and
j
-th column of
A
.
Let us perform the following procedure on
A
.
First, replace each element of
A
that is
0
with an arbitrary
positive integer
(if multiple elements are
0
, they may be replaced with different positive integers).
Then, repeat performing one of the two operations below, which may be chosen each time, as many times as desired (possibly zero).
Choose a pair of integers
(i, j)
such that
1 \leq i \lt j \leq H
and swap the
i
-th and
j
-th rows of
A
.
Choose a pair of integers
(i, j)
such that
1 \leq i \lt j \leq W
and swap the
i
-th and
j
-th columns of
A
.
Determine whether
A
can be made to satisfy the following condition.
A_{1, 1} \leq A_{1, 2} \leq \cdots \leq A_{1, W} \leq A_{2, 1} \leq A_{2, 2} \leq \cdots \leq A_{2, W} \leq A_{3, 1} \leq \cdots \leq A_{H, 1} \leq A_{H, 2} \leq \cdots \leq A_{H, W}
.
In other words, for every two pairs of integers
(i, j)
and
(i', j')
such that
1 \leq i, i' \leq H
and
1 \leq j, j' \leq W
, both of the following conditions are satisfied.
If
i \lt i'
, then
A_{i, j} \leq A_{i', j'}
.
If
i = i'
and
j \lt j'
, then
A_{i, j} \leq A_{i', j'}
. | [
{
"input": "3 3\n9 6 0\n0 4 0\n3 0 3\n",
"output": "Yes\n"
},
{
"input": "2 2\n2 1\n1 2\n",
"output": "No\n"
}
] |
https://atcoder.jp/contests/abc277/tasks/abc277_g | Problem Statement
You are given a connected simple undirected graph consisting of
N
vertices and
M
edges.
For
i = 1, 2, \ldots, M
, the
i
-th edge connects vertex
u_i
and vertex
v_i
.
Takahashi starts at
Level
0
on vertex
1
, and will perform the following action exactly
K
times.
First, choose one of the vertices adjacent to the vertex he is currently on, uniformly at random, and move to the chosen vertex.
Then, the following happens according to the vertex
v
he has moved to.
If
C_v = 0
: Takahashi's Level increases by
1
.
If
C_v = 1
: Takahashi receives a money of
X^2
yen, where
X
is his current Level.
Print the expected value of the total amount of money Takahashi receives during the
K
actions above, modulo
998244353
(see Notes). | [
{
"input": "5 4 8\n4 5\n2 3\n2 4\n1 2\n0 0 1 1 0\n",
"output": "89349064\n"
},
{
"input": "8 12 20\n7 6\n2 6\n6 4\n2 1\n8 5\n7 2\n7 5\n3 7\n3 5\n1 8\n6 3\n1 4\n0 0 1 1 0 0 0 0\n",
"output": "139119094\n"
}
] |
https://atcoder.jp/contests/abc277/tasks/abc277_h | Problem Statement
Determine whether there is a sequence of
N
integers
X = (X_1, X_2, \ldots ,X_N)
that satisfies all of the following conditions, and construct one such sequence if it exists.
0 \leq X_i \leq M
for every
1 \leq i \leq N
.
L_i \leq X_{A_i} + X_{B_i} \leq R_i
for every
1 \leq i \leq Q
. | [
{
"input": "4 5 3\n1 3 5 7\n1 4 1 2\n2 2 3 8\n",
"output": "2 4 3 0\n"
},
{
"input": "3 7 3\n1 2 3 4\n3 1 9 12\n2 3 2 4\n",
"output": "-1\n"
}
] |
https://atcoder.jp/contests/ahc016/tasks/ahc016_a | Problem Statement
Given an integer
M
and an error rate
\epsilon
, determine an integer
N
satisfying
4\leq N\leq 100
and output
N
-vertex undirected graphs
G_0,G_1,\cdots,G_{M-1}
.
The graphs may be disconnected.
Then process the following query
100
times.
In the
k
-th query, you are given an
N
-vertex undirected graph
H_k
.
H_k
is a graph generated from some
G_{s_k}
as follows.
Initialize
H_k=G_{s_k}
.
For each
(i,j)
with
0\leq i<j\leq N-1
, flip whether or not
H_k
contains edge
(i,j)
with probability
\epsilon
.
Randomly shuffle the order of the vertices in
H_k
.
After receiving
H_k
, predict from which graph
G_{s_k}
it was generated, and output the predicted value
t_k
of
s_k
. | [] |
https://atcoder.jp/contests/abc276/tasks/abc276_a | Problem Statement
You are given a string
S
consisting of lowercase English letters.
If
a
appears in
S
, print the last index at which it appears; otherwise, print
-1
. (The index starts at
1
.) | [
{
"input": "abcdaxayz\n",
"output": "7\n"
},
{
"input": "bcbbbz\n",
"output": "-1\n"
},
{
"input": "aaaaa\n",
"output": "5\n"
}
] |
https://atcoder.jp/contests/abc276/tasks/abc276_b | Problem Statement
There are
N
cities numbered
1, \dots, N
, and
M
roads connecting cities.
The
i
-th road
(1 \leq i \leq M)
connects city
A_i
and city
B_i
.
Print
N
lines as follows.
Let
d_i
be the number of cities directly connected to city
i \, (1 \leq i \leq N)
, and those cities be city
a_{i, 1}
,
\dots
, city
a_{i, d_i}
, in
ascending order
.
The
i
-th line
(1 \leq i \leq N)
should contain
d_i + 1
integers
d_i, a_{i, 1}, \dots, a_{i, d_i}
in this order, separated by spaces. | [
{
"input": "6 6\n3 6\n1 3\n5 6\n2 5\n1 2\n1 6\n",
"output": "3 2 3 6\n2 1 5\n2 1 6\n0\n2 2 6\n3 1 3 5\n"
},
{
"input": "5 10\n1 2\n1 3\n1 4\n1 5\n2 3\n2 4\n2 5\n3 4\n3 5\n4 5\n",
"output": "4 2 3 4 5\n4 1 3 4 5\n4 1 2 4 5\n4 1 2 3 5\n4 1 2 3 4\n"
}
] |
https://atcoder.jp/contests/abc276/tasks/abc276_c | Problem Statement
You are given a permutation
P = (P_1, \dots, P_N)
of
(1, \dots, N)
, where
(P_1, \dots, P_N) \neq (1, \dots, N)
.
Assume that
P
is the
K
-th lexicographically smallest among all permutations of
(1 \dots, N)
. Find the
(K-1)
-th lexicographically smallest permutation.
What are permutations?
A
permutation
of
(1, \dots, N)
is an arrangement of
(1, \dots, N)
into a sequence.
What is lexicographical order?
For sequences of length
N
,
A = (A_1, \dots, A_N)
and
B = (B_1, \dots, B_N)
,
A
is said to be
strictly lexicographically smaller
than
B
if and only if there is an integer
1 \leq i \leq N
that satisfies both of the following.
(A_{1},\ldots,A_{i-1}) = (B_1,\ldots,B_{i-1}).
A_i < B_i
. | [
{
"input": "3\n3 1 2\n",
"output": "2 3 1\n"
},
{
"input": "10\n9 8 6 5 10 3 1 2 4 7\n",
"output": "9 8 6 5 10 2 7 4 3 1\n"
}
] |
https://atcoder.jp/contests/abc276/tasks/abc276_d | Problem Statement
You are given a sequence of positive integers:
A=(a_1,a_2,\ldots,a_N)
.
You can choose and perform one of the following operations any number of times, possibly zero.
Choose an integer
i
such that
1 \leq i \leq N
and
a_i
is a multiple of
2
, and replace
a_i
with
\frac{a_i}{2}
.
Choose an integer
i
such that
1 \leq i \leq N
and
a_i
is a multiple of
3
, and replace
a_i
with
\frac{a_i}{3}
.
Your objective is to make
A
satisfy
a_1=a_2=\ldots=a_N
.
Find the minimum total number of times you need to perform an operation to achieve the objective. If there is no way to achieve the objective, print
-1
instead. | [
{
"input": "3\n1 4 3\n",
"output": "3\n"
},
{
"input": "3\n2 7 6\n",
"output": "-1\n"
},
{
"input": "6\n1 1 1 1 1 1\n",
"output": "0\n"
}
] |
https://atcoder.jp/contests/abc276/tasks/abc276_e | Problem Statement
We have a grid with
H
rows from top to bottom and
W
columns from left to right. Let
(i, j)
denote the
i
-th row from the top
(1 \leq i \leq H)
and
j
-th column from the left
(1 \leq j \leq W)
.
Each square is one of the following: the initial point, a road, and an obstacle.
A square
(i, j)
is represented by a character
C_{i, j}
. The square is the initial point if
C_{i, j} =
S
, a road if
C_{i, j} =
.
, and an obstacle if
C_{i, j} =
#
. There is exactly one initial point.
Determine whether there is a path of length
4
or greater that starts at the initial point, repeats moving vertically or horizontally to an adjacent square, and returns to the initial point without going through an obstacle or visiting the same square multiple times except at the beginning and the end.
More formally, determine whether there are an integer
n
and a sequence of squares
(x_0, y_0), (x_1, y_1), \dots, (x_n, y_n)
that satisfy the following conditions.
n \geq 4
.
C_{x_0, y_0} = C_{x_n, y_n} =
S
.
If
1 \leq i \leq n - 1
, then
C_{x_i, y_i} =
.
.
If
1 \leq i \lt j \leq n - 1
, then
(x_i, y_i) \neq (x_j, y_j)
.
If
0 \leq i \leq n - 1
, then square
(x_i, y_i)
and square
(x_{i+1}, y_{i+1})
are vertically or horizontally adjacent to each other. | [
{
"input": "4 4\n....\n#.#.\n.S..\n.##.\n",
"output": "Yes\n"
},
{
"input": "2 2\nS.\n.#\n",
"output": "No\n"
},
{
"input": "5 7\n.#...#.\n..#.#..\n...S...\n..#.#..\n.#...#.\n",
"output": "No\n"
}
] |
https://atcoder.jp/contests/abc276/tasks/abc276_f | Problem Statement
There are
N
cards called card
1
, card
2
,
\ldots
, card
N
. On card
i
(1\leq i\leq N)
, an integer
A_i
is written.
For
K=1, 2, \ldots, N
, solve the following problem.
We have a bag that contains
K
cards: card
1
, card
2
,
\ldots
, card
K
.
Let us perform the following operation twice, and let
x
and
y
be the numbers recorded, in the recorded order.
Draw a card from the bag uniformly at random, and record the number written on that card. Then,
return the card to the bag
.
Print the expected value of
\max(x,y)
, modulo
998244353
(see Notes).
Here,
\max(x,y)
denotes the value of the greater of
x
and
y
(or
x
if they are equal). | [
{
"input": "3\n5 7 5\n",
"output": "5\n499122183\n443664163\n"
},
{
"input": "7\n22 75 26 45 72 81 47\n",
"output": "22\n249561150\n110916092\n873463862\n279508479\n360477194\n529680742\n"
}
] |
https://atcoder.jp/contests/abc276/tasks/abc276_g | Problem Statement
Find the number of sequences of integers with
N
terms,
A=(a_1,a_2,\ldots,a_N)
, that satisfy the following conditions, modulo
998244353
.
0 \leq a_1 \leq a_2 \leq \ldots \leq a_N \leq M
.
For each
i=1,2,\ldots,N-1
, the remainder when
a_i
is divided by
3
is different from the remainder when
a_{i+1}
is divided by
3
. | [
{
"input": "3 4\n",
"output": "8\n"
},
{
"input": "276 10000000\n",
"output": "909213205\n"
}
] |
https://atcoder.jp/contests/abc276/tasks/abc276_h | Problem Statement
Determine whether there is an
N
-by-
N
matrix
X
that satisfies the following conditions, and present one such matrix if it exists. (Let
x_{i,j}
denote the element of
X
at the
i
-th row from the top and
j
-th column from the left.)
x_{i,j} \in \{ 0,1,2 \}
for every
i
and
j
(1 \leq i,j \leq N)
.
The following holds for each
i=1,2,\ldots,Q
.
Let
P = \prod_{a_i \leq j \leq b_i} \prod_{c_i \leq k \leq d_i} x_{j,k}
. Then,
P
is congruent to
e_i
modulo
3
. | [
{
"input": "2 3\n1 1 1 2 0\n1 2 2 2 1\n2 2 1 2 2\n",
"output": "Yes\n0 2\n1 2\n"
},
{
"input": "4 4\n1 4 1 4 0\n1 4 1 4 1\n1 4 1 4 2\n1 4 1 4 0\n",
"output": "No\n"
}
] |
https://atcoder.jp/contests/ttpc2022/tasks/ttpc2022_a | 問題文
TTPC (Tottemo Tanoshii Programming Contest) は、
2015
年に
1
回目が開催され、その後
A
年ごと (
A
は正の整数) に開催されるコンテストです。
より正確には、TTPC は
2015 + A \times n
(
n
は非負整数) と表すことができる年に開催され、それ以外の年には開催されません。
また、TTPC は、
2015
年の他にも
X
年と
Y
年に開催されることが分かっています。
このとき、
A
としてあり得る整数を
昇順に
全て出力してください。 | [
{
"input": "2019 2023\n",
"output": "1\n2\n4\n"
},
{
"input": "999999999995 1000000000000\n",
"output": "1\n5\n"
},
{
"input": "2019 2022\n",
"output": "1\n"
}
] |
https://atcoder.jp/contests/ttpc2022/tasks/ttpc2022_b | 問題文
あなたは
X
円が入った魔法の財布を持っています。
この財布に魔法を使うと、あなたは財布に入っている金額を
10
進の文字列と見て任意に並び替えることができます。
例えば、
120
円が入った魔法の財布に魔法を使うと、入っている金額を
12
円、
21
円、
102
円、
120
円、
201
円、
210
円のいずれかに変えることができます(先頭の
0
は無視されます)。
あなたはこれから魔法の財布を持って
N
個のお店を
順番に
訪れます。
i
番目のお店 (
1 ≤ i ≤ N
) では
A_i
円の商品が
1
つ売っており、もし魔法の財布に
A_i
円以上入っていれば、魔法の財布から
A_i
円を支払ってその商品を買うことができます。
魔法は好きなときに好きなだけ使うことができます。あなたは最大で商品をいくつ買うことができますか？ | [
{
"input": "2 120\n142 90\n",
"output": "2\n"
},
{
"input": "1 119\n911\n",
"output": "1\n"
},
{
"input": "5 1000\n900 90 900 9 900\n",
"output": "3\n"
},
{
"input": "7 1171\n6328 2419 8302 7503 1744 8495 1522\n",
"output": "5\n"
}
] |
https://atcoder.jp/contests/ttpc2022/tasks/ttpc2022_c | 問題文
長さ
N
の整数列
A = (A_1, \dots, A_N), B = (B_1, \dots, B_N), C = (C_1, \dots, C_N), D = (D_1, \dots, D_N), E = (E_1, \dots, E_N)
が与えられます。
以下の値を
998244353
で割ったあまりを求めてください。
\displaystyle\sum_{i=1}^{N}\sum_{j=1}^{N}\sum_{k=1}^{N}\sum_{l=1}^{N}\sum_{m=1}^{N}\mathrm{med}(A_i,B_j,C_k,D_l,E_m)
ただし、
\mathrm{med}(a,b,c,d,e)
は
a,b,c,d,e
の中央値を表します。 | [
{
"input": "1\n1\n2\n3\n4\n5\n",
"output": "3\n"
},
{
"input": "3\n1 2 3\n1 3 2\n2 1 3\n2 3 1\n3 1 2\n",
"output": "486\n"
}
] |
https://atcoder.jp/contests/ttpc2022/tasks/ttpc2022_d | 問題文
頂点に
1, 2, \dots, N
の番号が付いた、頂点
1
を根とする
N
頂点の根付き木があります。
i
番目の辺 (
1 ≤ i ≤ N - 1
) は頂点
U_i
と頂点
V_i
を結んでいます。
木の各頂点は白か黒で塗られており、頂点
i
(
1 ≤ i ≤ N
) は
A_i = 0
のとき白で、
A_i = 1
のとき黒で塗られています。
木を黒くしたい黒木さんは、以下の操作を
0
回以上の任意の回数行って、
黒
で塗られている頂点の数を最大化します。
葉
である頂点
x
を
1
つ選び、根から
x
までのパスに含まれる頂点 (両端を含む) の色を反転させる (白で塗られている場合は黒に、黒で塗られている場合は白に塗り直す)。
黒木さんは何個の頂点が黒に塗られた木を得ることができるでしょうか？ | [
{
"input": "5\n1 0 0 1 0\n1 2\n1 3\n3 4\n3 5\n",
"output": "5\n"
},
{
"input": "6\n1 1 0 0 1 0\n3 1\n2 5\n1 2\n4 1\n2 6\n",
"output": "5\n"
},
{
"input": "9\n1 0 1 0 1 0 1 0 1\n2 9\n1 2\n6 9\n3 8\n4 5\n5 9\n2 8\n7 8\n",
"output": "6\n"
}
] |
https://atcoder.jp/contests/ttpc2022/tasks/ttpc2022_e | 問題文
大学 A と大学 B は統合することになりました。大学 A の大学名は
A
、大学 B の大学名は
B
です。統合後の新しい大学名
C
を考えましょう。具体的には、以下のようにして
C
を定めます。
A
の空でない部分列を
1
つとって
a
とする。
B
の空でない部分列を
1
つとって
b
とする。
C
を
a
と
b
をこの順で連結した文字列とする。
Q
個の文字列
S_1, S_2, \dots, S_Q
が与えられます。それぞれの文字列が
C
としてあり得るかどうか判定し、あり得る場合は、
|\text{len}(a) - \text{len}(b)|
としてあり得る最小値を求めてください。(
\text{len}(x)
は
x
の長さを表す)
部分列とは？
文字列
X
に対し、その文字列を構成する文字を
0
文字以上取り除き、残った文字を元の順番で並べて得られる文字列を
S
の部分列と呼びます。例えば、
ac
や
abc
は
abc
の部分列ですが、
ca
は
abc
の部分列ではありません。 | [
{
"input": "Tokyo Institute of Technology\nTokyo Medical and Dental University\n10\nThe University\nTokyo University\nkyoto University\nTokyo Tech\nTMDU\nKyoto University\nThe University of Tokyo\nTokyo Technology and Medical and Dental University\n Tehnoooorsty\nTokyo\n",
"output": "10\n4\n4\n-1\n2\n-1\n-1\n-1\n3\n1\n"
}
] |
https://atcoder.jp/contests/ttpc2022/tasks/ttpc2022_f | 問題文
整数列
L = (L_1, L_2, \dots, L_N)
と
R = (R_1, R_2, \dots, R_N)
が与えられます。
以下の条件を満たす
実数
列
A = (A_1, A_2, \dots, A_N)
が存在するか判定してください。
1 \leq i \leq N
を満たすすべての整数
i
に対して
L_i \leq A_i \leq R_i
が成り立つ。
2 \leq i \leq N-1
を満たすすべての整数
i
に対して
A_{i-1} + A_{i+1} \geq 2 A_i
が成り立つ。 | [
{
"input": "4\n2 1 2 5\n4 6 5 8\n",
"output": "Yes\n"
},
{
"input": "3\n1 4 2\n3 7 4\n",
"output": "No\n"
}
] |
https://atcoder.jp/contests/ttpc2022/tasks/ttpc2022_g | 問題文
整数列
L = (L_1, L_2, \dots, L_N)
と
R = (R_1, R_2, \dots, R_N)
が与えられます。
以下の条件を満たす整数列
A = (A_1, A_2, \dots, A_N)
の個数を
998244353
で割ったあまりを求めてください。
1 \leq i \leq N
を満たすすべての整数
i
に対して
L_i \leq A_i \leq R_i
が成り立つ。
ある整数
d
が存在して、
1 \leq i \leq N-1
を満たすすべての整数
i
に対して
A_{i+1} - A_i = d
が成り立つ。 | [
{
"input": "3\n5 5 2\n7 6 7\n",
"output": "6\n"
},
{
"input": "4\n2 3 1 6\n5 6 4 8\n",
"output": "0\n"
}
] |
https://atcoder.jp/contests/ttpc2022/tasks/ttpc2022_h | 問題文
N
頂点
M
辺の有向グラフが与えられます。頂点には
1
から
N
の番号が、辺には
1
から
M
の番号がついています。辺
i
(
1 ≤ i ≤ M
) は頂点
A_i
から頂点
B_i
に向かう辺です。
あなたは、このグラフの各頂点を色
1, …, N
のいずれかで塗ります。ただし、頂点
i
(
1 ≤ i ≤ N
) に塗る色を
c_i
としたとき、以下の条件を満たす必要があります。
任意の組
(i, j)
(
1 ≤ i < j ≤ N
) について、
c_i = c_j
ならば、頂点
i
から頂点
j
へのパスか、頂点
j
から頂点
i
へのパスのいずれか (両方でもよい) が存在する。
\max\{c_1, …, c_N\}
が最小になる塗り方を
1
つ構築してください。 | [
{
"input": "5 5\n1 4\n2 3\n1 3\n2 5\n5 1\n",
"output": "1 1 1 2 1\n"
},
{
"input": "5 7\n1 2\n2 1\n4 3\n5 1\n5 4\n4 1\n4 5\n",
"output": "2 2 1 1 1\n"
},
{
"input": "8 6\n6 1\n3 4\n3 6\n2 3\n4 1\n6 4\n",
"output": "4 4 4 4 3 4 2 1\n"
}
] |
https://atcoder.jp/contests/ttpc2022/tasks/ttpc2022_i | 問題文
整数
N,M,K
と
N
頂点
M
辺の無向グラフが与えられます。グラフの頂点には
1
から
N
の番号が、辺には
1
から
M
の番号が付けられています。辺
i
(
1 ≤ i ≤ M
) は頂点
A_i
と頂点
B_i
の間をつないでいて、辺上には非負整数
C_i
が置かれています。
Q
個のクエリが与えられます。
i
番目 (
1 ≤ i ≤ Q
) のクエリでは、整数
D_{i}
が与えられるので、次の条件を全て満たす整数の組
(u,v)
の個数を求めてください。
1\le u\lt v\le N
(C_{j} \oplus D_{i})\lt K
を満たすような辺
j
のみを通って、頂点
u
から頂点
v
まで移動することが可能
ただし
\oplus
はビット単位
\text{XOR}
演算を表します。
ビット単位
\text{XOR}
演算とは
非負整数
X,Y
のビット単位
\text{XOR}
演算、
X\oplus Y
は以下のように定義されます。
X\oplus Y
を二進表記したときの
2^{k}
の位 (
0\le k
) は、
A,B
を二進表記したときの
2^{k}
の位が異なるなら
1
、そうでないなら
0
とする。
例えば、
3\oplus 5=6
となります。(二進表記すると
011\oplus 101=110
) | [
{
"input": "4 5 5\n1 2 17\n1 3 4\n2 3 20\n2 4 3\n3 4 5\n4\n0\n7\n16\n167\n",
"output": "2\n6\n3\n0\n"
},
{
"input": "9 13 488888932\n2 7 771479959\n3 8 783850182\n5 7 430673756\n6 8 350738034\n4 9 400768807\n2 3 83653266\n1 2 829786563\n5 8 357613791\n7 9 579696618\n3 7 423191200\n3 5 867380255\n1 9 907715012\n6 9 1033650694\n8\n498260055\n144262908\n117665696\n848664012\n983408133\n32610599\n478007408\n134182829\n",
"output": "16\n7\n5\n13\n13\n16\n16\n5\n"
}
] |
https://atcoder.jp/contests/ttpc2022/tasks/ttpc2022_j | 問題文
N
頂点
M
辺の有向グラフが与えられます。頂点には
1
から
N
の番号が、辺には
1
から
M
の番号が付けられていて、辺
i
(
1 ≤ i ≤ M
) は頂点
A_i
から頂点
B_i
への辺です。このグラフに自己ループは存在するかもしれませんが、多重辺はありません。どの頂点からも辺が
1
本以上出ていることが保証されます。
頂点のうち
K
個には宝石が置かれています。
i
番目 (
1 ≤ i ≤ K
) の宝石は頂点
V_i
にあり、価値は
W_i
です。
このグラフを使って First 君と Second 君がゲームをします。ゲーム開始時、First 君は頂点
F
に、Second 君は頂点
S
にいます。First 君から始めて、First 君と Second 君が交互に以下の操作を行います。
自分が今いる頂点から出ている辺を
1
つ選び、その辺に沿って次の頂点まで移動する。移動した頂点に宝石があればそれを手に入れ、その宝石はグラフ上から取り除かれる。
全ての宝石を取るか、ゲーム中にあった盤面と同じ盤面 (手番、各プレイヤーの位置、残っている宝石が全く同じ状態) が再び登場するとゲームは終了します。
お互いに、(自分の取る宝石の価値の合計)
-
(相手の取る宝石の価値の合計) ができるだけ大きくなるように行動するとき、ゲーム終了時の (First 君の取る宝石の価値の合計)
-
(Second 君の取る宝石の価値の合計) を求めてください。 | [
{
"input": "5 16 1 1\n1 2\n1 3\n1 4\n1 5\n2 3\n2 4\n2 5\n3 2\n3 4\n3 5\n4 2\n4 3\n4 5\n5 2\n5 3\n5 4\n4\n2 4\n3 84\n4 38\n5 96\n",
"output": "46\n"
},
{
"input": "8 16 8 4\n1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n7 8\n8 1\n1 5\n2 6\n3 7\n4 8\n5 1\n6 2\n7 3\n8 4\n6\n1 29\n2 34\n3 41\n5 7\n6 26\n7 94\n",
"output": "-23\n"
},
{
"input": "5 5 2 1\n1 1\n2 3\n3 4\n4 5\n5 2\n2\n4 1000000\n5 100000\n",
"output": "1100000\n"
},
{
"input": "10 20 1 2\n1 4\n1 7\n2 2\n2 4\n3 6\n3 3\n4 8\n4 7\n5 7\n5 1\n6 9\n6 2\n7 9\n7 3\n8 8\n8 6\n9 7\n9 8\n10 10\n10 2\n8\n3 92067840\n4 2874502\n5 36253165\n6 70758738\n7 4768969\n8 16029185\n9 16207515\n10 44912151\n",
"output": "132484345\n"
}
] |
https://atcoder.jp/contests/ttpc2022/tasks/ttpc2022_k | 問題文
Alice と Bob と Chris はこれから
N
回じゃんけんをします。 ただし、各々が出す手には次のような制限があります。
Alice は グー をちょうど
A_R
回、 パー をちょうど
A_P
回、 チョキ をちょうど
A_S
回 出す。
Bob は グー をちょうど
B_R
回、 パー をちょうど
B_P
回、 チョキ をちょうど
B_S
回 出す。
Chris は グー をちょうど
C_R
回、 パー をちょうど
C_P
回、 チョキ をちょうど
C_S
回 出す。
Alice と Bob と Chris はとても仲良しなので、
N
回すべてで
あいこ
になるようにしたいです。
N
回のじゃんけんにわたる
3
人の手の出し方であってこれを達成する方法の数を
998244353
で割ったあまりを求めてください。
あいことは
1
回のじゃんけんで
3
人の出す手がすべて同じとき、 またはすべて異なるとき、
あいこ
となります。 | [
{
"input": "2\n2 0 0 1 1 0 1 0 1\n",
"output": "2\n"
},
{
"input": "3\n0 1 2 3 0 0 1 1 1\n",
"output": "0\n"
},
{
"input": "333333\n111111 111111 111111 111111 111111 111111 111111 111111 111111\n",
"output": "383902959\n"
}
] |
https://atcoder.jp/contests/ttpc2022/tasks/ttpc2022_l | 問題文
正整数
N,M
が与えられます。
(0,1,...,NM-1)
の順列
P=(P_{0},P_{1},...,P_{NM-1})
のうち、以下の条件を満たすものの個数を
998244353
で割ったあまりを求めてください。
0\le i\lt NM
を満たす全ての整数
i
について、
\left\lfloor \frac{i}{M} \right\rfloor \neq \left\lfloor \frac{P_{i}}{M}\right\rfloor
が成り立つ。
ただし、
\left\lfloor X \right\rfloor
は
X
以下の最大の整数を表します。 | [
{
"input": "2 2\n",
"output": "4\n"
},
{
"input": "5 1\n",
"output": "44\n"
},
{
"input": "167 91\n",
"output": "284830080\n"
}
] |
https://atcoder.jp/contests/ttpc2022/tasks/ttpc2022_m | 問題文
正整数
N, M
が与えられます。
N
個の正整数の組
(x_1,x_2,\dots ,x_N)
であって
\displaystyle\prod_{i=1}^{N}x_i=M
を満たすものすべての集合を
\bm{X}
とします。
\displaystyle\sum_{(x_1,x_2,\dots ,x_N)\in \bm{X}}\prod_{i=1}^{N} (x_i+A_i)
を
998244353
で割ったあまりを求めてください。 | [
{
"input": "2 3\n0 1\n",
"output": "10\n"
},
{
"input": "5 1\n0 1 2 3 4\n",
"output": "120\n"
},
{
"input": "10 314159265358\n0 1 2 3 4 5 6 7 8 9\n",
"output": "658270849\n"
}
] |
https://atcoder.jp/contests/ttpc2022/tasks/ttpc2022_n | 問題文
整数
K
と
3
次元上の
N
個の点
(x_1,y_1,z_1), \dots, (x_N,y_N,z_N)
が与えられます。
N
点
(K x_1,K y_1,K z_1), \dots, (K x_N,K y_N,K z_N)
の凸包の内部または境界に含まれる点であって座標がすべて整数であるようなものの個数を
998244353
で割ったあまりを求めてください。 | [
{
"input": "4 2\n0 0 0\n1 0 0\n0 1 0\n0 0 1\n",
"output": "10\n"
},
{
"input": "4 10000\n0 0 0\n1 0 0\n0 1 0\n0 0 1\n",
"output": "59878050\n"
},
{
"input": "8 314159265358979\n5 -3 -3\n-5 -3 -3\n0 5 -3\n0 0 10\n4 2 6\n-4 2 6\n0 -5 6\n0 0 -5\n",
"output": "152811018\n"
}
] |
https://atcoder.jp/contests/ttpc2022/tasks/ttpc2022_o | 簡単な問題文
謎のモノイド
(M, \oplus)
と、これを計算する CPU が
4
個あります。
整数
N
が与えられるので、
M
の列
A = (A_1, A_2, …, A_N)
から
A
の累積
\oplus
を
4
並列で計算してください。
その際、操作回数を最小化してください。 | [
{
"input": "2\n",
"output": "1\n2 1 2\n2000 2000 2000\n2000 2000 2000\n2000 2000 2000\n"
},
{
"input": "4\n",
"output": "2\n2 1 2\n4 3 4\n2000 2000 2000\n2000 2000 2000\n3 2 3\n4 2 4\n2000 2000 2000\n2000 2000 2000\n"
}
] |
https://atcoder.jp/contests/ahc015/tasks/ahc015_a | Problem Statement
There is a box that can contain
10\times 10
pieces of candy in a grid pattern.
The box is initially empty, and
100
pieces of candy will be placed in order.
There are
3
flavors of candy, and we know in advance the flavor
f_t (1\leq f_t\leq 3)
of the
t
-th candy.
On the other hand, we do not know in advance to which cell each candy will be placed, and it will be chosen uniformly at random among the empty cells.
You cannot change the order in which the pieces of candy are received.
Each time you receive one piece of candy, you must tilt the box forward, backward, left, or right exactly once.
When you tilt the box, each piece of candy moves in that direction simultaneously until it reaches the edge or hits another candy.
For example, if you tilt the box forward in the state shown in the left figure, the box will be in the state shown in the right figure. | [] |
https://atcoder.jp/contests/abc275/tasks/abc275_a | Problem Statement
There are
N
bridges in AtCoder Village. The height of the bridge numbered
i
is
H_i
(
i
is an integer between
1
and
N
).
Every two different bridges in the village have different heights.
Print the number representing the highest bridge in the village. | [
{
"input": "3\n50 80 70\n",
"output": "2\n"
},
{
"input": "1\n1000000000\n",
"output": "1\n"
},
{
"input": "10\n22 75 26 45 72 81 47 29 97 2\n",
"output": "9\n"
}
] |
https://atcoder.jp/contests/abc275/tasks/abc275_b | Problem Statement
There are non-negative integers
A
,
B
,
C
,
D
,
E
, and
F
, which satisfy
A\times B\times C\geq D\times E\times F
.
Find the remainder when
(A\times B\times C)-(D\times E\times F)
is divided by
998244353
. | [
{
"input": "2 3 5 1 2 4\n",
"output": "22\n"
},
{
"input": "1 1 1000000000 0 0 0\n",
"output": "1755647\n"
},
{
"input": "1000000000000000000 1000000000000000000 1000000000000000000 1000000000000000000 1000000000000000000 1000000000000000000\n",
"output": "0\n"
}
] |
https://atcoder.jp/contests/abc275/tasks/abc275_c | Problem Statement
There is a two-dimensional plane. For integers
r
and
c
between
1
and
9
, there is a pawn at the coordinates
(r,c)
if the
c
-th character of
S_{r}
is
#
, and nothing if the
c
-th character of
S_{r}
is
.
.
Find the number of squares in this plane with pawns placed at all four vertices. | [
{
"input": "##.......\n##.......\n.........\n.......#.\n.....#...\n........#\n......#..\n.........\n.........\n",
"output": "2\n"
},
{
"input": ".#.......\n#.#......\n.#.......\n.........\n....#.#.#\n.........\n....#.#.#\n........#\n.........\n",
"output": "3\n"
}
] |
https://atcoder.jp/contests/abc275/tasks/abc275_d | Problem Statement
A function
f(x)
defined for non-negative integers
x
satisfies the following conditions.
f(0) = 1
.
f(k) = f(\lfloor \frac{k}{2}\rfloor) + f(\lfloor \frac{k}{3}\rfloor)
for any positive integer
k
.
Here,
\lfloor A \rfloor
denotes the value of
A
rounded down to an integer.
Find
f(N)
. | [
{
"input": "2\n",
"output": "3\n"
},
{
"input": "0\n",
"output": "1\n"
},
{
"input": "100\n",
"output": "55\n"
}
] |
https://atcoder.jp/contests/abc275/tasks/abc275_e | Problem Statement
Takahashi is playing sugoroku, a board game.
The board has
N+1
squares, numbered
0
to
N
.
Takahashi starts at square
0
and goes for square
N
.
The game uses a roulette wheel with
M
numbers from
1
to
M
that appear with equal probability.
Takahashi spins the wheel and moves by the number of squares indicated by the wheel. If this would send him beyond square
N
, he turns around at square
N
and goes back by the excessive number of squares.
For instance, assume that
N=4
and Takahashi is at square
3
. If the wheel shows
4
, the excessive number of squares beyond square
4
is
3+4-4=3
. Thus, he goes back by three squares from square
4
and arrives at square
1
.
When Takahashi arrives at square
N
, he wins and the game ends.
Find the probability, modulo
998244353
, that Takahashi wins when he may spin the wheel at most
K
times.
How to print a probability modulo
998244353
It can be proved that the sought probability is always a rational number.
Additionally, under the Constraints of this problem, when the sought probability is represented as an irreducible fraction
\frac{y}{x}
, it is guaranteed that
x
is not divisible by
998244353
.
Here, there is a unique integer
z
between
0
and
998244352
such that
xz \equiv y \pmod{998244353}
. Print this
z
. | [
{
"input": "2 2 1\n",
"output": "499122177\n"
},
{
"input": "10 5 6\n",
"output": "184124175\n"
},
{
"input": "100 1 99\n",
"output": "0\n"
}
] |
https://atcoder.jp/contests/abc275/tasks/abc275_f | Problem Statement
You are given an integer array
A=(a_1,a_2,\ldots,a_N)
.
You may perform the following operation any number of times (possibly zero).
Choose a nonempty contiguous subarray of
A
, and delete it from the array.
For each
x=1,2,\ldots,M
, solve the following problem:
Find the minimum possible number of operations to make the sum of elements of
A
equal
x
.
If it is impossible to make the sum of elements of
A
equal
x
, print
-1
instead.
Note that the sum of elements of an empty array is
0
. | [
{
"input": "4 5\n1 2 3 4\n",
"output": "1\n2\n1\n1\n1\n"
},
{
"input": "1 5\n3\n",
"output": "-1\n-1\n0\n-1\n-1\n"
},
{
"input": "12 20\n2 5 6 5 2 1 7 9 7 2 5 5\n",
"output": "2\n1\n2\n2\n1\n2\n1\n2\n2\n1\n2\n1\n1\n1\n2\n2\n1\n1\n1\n1\n"
}
] |
https://atcoder.jp/contests/abc275/tasks/abc275_g | Problem Statement
There are
N
kinds of items, each with infinitely many copies. The
i
-th kind of item has a weight of
A_i
, a volume of
B_i
, and a value of
C_i
.
Level
X
Takahashi can carry items whose total weight is at most
X
and whose total volume is at most
X
. Under this condition, it is allowed to carry any number of items of the same kind, or omit some kinds of items.
Let
f(X)
be the maximum total value of items Level
X
Takahashi can carry. It can be proved that the limit
\displaystyle\lim_{X\to \infty} \frac{f(X)}{X}
exists. Find this limit. | [
{
"input": "2\n100000000 200000000 100000000\n200000000 100000000 100000000\n",
"output": "0.6666666666666667\n"
},
{
"input": "1\n500000000 300000000 123456789\n",
"output": "0.2469135780000000\n"
}
] |
https://atcoder.jp/contests/abc275/tasks/abc275_h | Problem Statement
There are
N
monsters along a number line. At the coordinate
i
(1\leq i\leq N)
is a monster with a stamina of
A_i
.
Additionally, at the coordinate
i
, there is a permanent shield of a strength
B_i
.
This shield persists even when the monster at the same coordinate has a health of
0
or below.
Takahashi, a magician, can perform the following operation any number of times.
Choose integers
l
and
r
satisfying
1\leq l\leq r\leq N
.
Then, consume
\max(B_l, B_{l+1}, \ldots, B_r)
MP (magic points) to decrease by
1
the stamina of each of the monsters at the coordinates
l,l+1,\ldots,r
.
When choosing
l
and
r
, it is fine if some of the monsters at the coordinates
l,l+1,\ldots,r
already have a stamina of
0
or below.
Note, however, that the shields at all those coordinates still exist.
Takahashi wants to make the stamina of every monster
0
or below.
Find the minimum total MP needed to achieve his objective. | [
{
"input": "5\n4 3 5 1 2\n10 40 20 60 50\n",
"output": "210\n"
},
{
"input": "1\n1000000000\n1000000000\n",
"output": "1000000000000000000\n"
},
{
"input": "10\n522 4575 6426 9445 8772 81 3447 629 3497 7202\n7775 4325 3982 4784 8417 2156 1932 5902 5728 8537\n",
"output": "77917796\n"
}
] |
https://atcoder.jp/contests/abc274/tasks/abc274_a | Problem Statement
Takahashi is making a computer baseball game.
He will write a program that shows a batter's batting average with a specified number of digits.
There are integers
A
and
B
, which satisfy
1 \leq A \leq 10
and
0 \leq B \leq A
.
Let
S
be the string obtained as follows.
Round off
\dfrac{B}{A}
to three decimal digits, then write the integer part (
1
digit),
.
(the decimal point), and the decimal part (
3
digits) in this order, with trailing zeros.
For example, if
A=7
and
B=4
, then
\dfrac{B}{A} = \dfrac{4}{7} = 0.571428\dots
rounded off to three decimal digits is
0.571
. Thus,
S
is
0.571
.
You are given
A
and
B
as the input and asked to print
S
. | [
{
"input": "7 4\n",
"output": "0.571\n"
},
{
"input": "7 3\n",
"output": "0.429\n"
},
{
"input": "2 1\n",
"output": "0.500\n"
},
{
"input": "10 10\n",
"output": "1.000\n"
},
{
"input": "1 0\n",
"output": "0.000\n"
}
] |
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