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http://rosettacode.org/wiki/Sorting_algorithms/Merge_sort | Sorting algorithms/Merge sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
The merge sort is a recursive sort of order n*log(n).
It is notable for having a worst case and average complexity of O(n*log(n)), and a best case complexity of O(n) (for pre-sorted input).
The basic idea is to split the collection into smaller groups by halving it until the groups only have one element or no elements (which are both entirely sorted groups).
Then merge the groups back together so that their elements are in order.
This is how the algorithm gets its divide and conquer description.
Task
Write a function to sort a collection of integers using the merge sort.
The merge sort algorithm comes in two parts:
a sort function and
a merge function
The functions in pseudocode look like this:
function mergesort(m)
var list left, right, result
if length(m) ≤ 1
return m
else
var middle = length(m) / 2
for each x in m up to middle - 1
add x to left
for each x in m at and after middle
add x to right
left = mergesort(left)
right = mergesort(right)
if last(left) ≤ first(right)
append right to left
return left
result = merge(left, right)
return result
function merge(left,right)
var list result
while length(left) > 0 and length(right) > 0
if first(left) ≤ first(right)
append first(left) to result
left = rest(left)
else
append first(right) to result
right = rest(right)
if length(left) > 0
append rest(left) to result
if length(right) > 0
append rest(right) to result
return result
See also
the Wikipedia entry: merge sort
Note: better performance can be expected if, rather than recursing until length(m) ≤ 1, an insertion sort is used for length(m) smaller than some threshold larger than 1. However, this complicates the example code, so it is not shown here.
| #Ada | Ada | generic
type Element_Type is private;
type Index_Type is (<>);
type Collection_Type is array(Index_Type range <>) of Element_Type;
with function "<"(Left, Right : Element_Type) return Boolean is <>;
package Mergesort is
function Sort(Item : Collection_Type) return Collection_Type;
end MergeSort; |
http://rosettacode.org/wiki/Sorting_algorithms/Pancake_sort | Sorting algorithms/Pancake sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array of integers (of any convenient size) into ascending order using Pancake sorting.
In short, instead of individual elements being sorted, the only operation allowed is to "flip" one end of the list, like so:
Before: 6 7 8 9 2 5 3 4 1
After: 9 8 7 6 2 5 3 4 1
Only one end of the list can be flipped; this should be the low end, but the high end is okay if it's easier to code or works better, but it must be the same end for the entire solution. (The end flipped can't be arbitrarily changed.)
Show both the initial, unsorted list and the final sorted list.
(Intermediate steps during sorting are optional.)
Optimizations are optional (but recommended).
Related tasks
Number reversal game
Topswops
Also see
Wikipedia article: pancake sorting.
| #JavaScript | JavaScript | Array.prototype.pancake_sort = function () {
for (var i = this.length - 1; i >= 1; i--) {
// find the index of the largest element not yet sorted
var max_idx = 0;
var max = this[0];
for (var j = 1; j <= i; j++) {
if (this[j] > max) {
max = this[j];
max_idx = j;
}
}
if (max_idx == i)
continue; // element already in place
var new_slice;
// flip this max element to index 0
if (max_idx > 0) {
new_slice = this.slice(0, max_idx+1).reverse();
for (var j = 0; j <= max_idx; j++)
this[j] = new_slice[j];
}
// then flip the max element to its place
new_slice = this.slice(0, i+1).reverse();
for (var j = 0; j <= i; j++)
this[j] = new_slice[j];
}
return this;
}
ary = [7,6,5,9,8,4,3,1,2,0]
sorted = ary.concat().pancake_sort(); |
http://rosettacode.org/wiki/Sorting_algorithms/Stooge_sort | Sorting algorithms/Stooge sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Stooge sort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Show the Stooge Sort for an array of integers.
The Stooge Sort algorithm is as follows:
algorithm stoogesort(array L, i = 0, j = length(L)-1)
if L[j] < L[i] then
L[i] ↔ L[j]
if j - i > 1 then
t := (j - i + 1)/3
stoogesort(L, i , j-t)
stoogesort(L, i+t, j )
stoogesort(L, i , j-t)
return L
| #PHP | PHP |
function stoogeSort(&$arr, $i, $j)
{
if($arr[$j] < $arr[$i])
{
list($arr[$j],$arr[$i]) = array($arr[$i], $arr[$j]);
}
if(($j - $i) > 1)
{
$t = ($j - $i + 1) / 3;
stoogesort($arr, $i, $j - $t);
stoogesort($arr, $i + $t, $j);
stoogesort($arr, $i, $j - $t);
}
}
|
http://rosettacode.org/wiki/Sorting_algorithms/Selection_sort | Sorting algorithms/Selection sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array (or list) of elements using the Selection sort algorithm.
It works as follows:
First find the smallest element in the array and exchange it with the element in the first position, then find the second smallest element and exchange it with the element in the second position, and continue in this way until the entire array is sorted.
Its asymptotic complexity is O(n2) making it inefficient on large arrays.
Its primary purpose is for when writing data is very expensive (slow) when compared to reading, eg. writing to flash memory or EEPROM.
No other sorting algorithm has less data movement.
References
Rosetta Code: O (complexity).
Wikipedia: Selection sort.
Wikipedia: [Big O notation].
| #GAP | GAP | SelectionSort := function(v)
local i, j, k, n, m;
n := Size(v);
for i in [1 .. n] do
k := i;
m := v[i];
for j in [i + 1 .. n] do
if v[j] < m then
k := j;
m := v[j];
fi;
od;
v[k] := v[i];
v[i] := m;
od;
end;
v := List([1 .. 100], n -> Random([1 .. 100]));
SelectionSort(v);
v; |
http://rosettacode.org/wiki/Sorting_algorithms/Selection_sort | Sorting algorithms/Selection sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array (or list) of elements using the Selection sort algorithm.
It works as follows:
First find the smallest element in the array and exchange it with the element in the first position, then find the second smallest element and exchange it with the element in the second position, and continue in this way until the entire array is sorted.
Its asymptotic complexity is O(n2) making it inefficient on large arrays.
Its primary purpose is for when writing data is very expensive (slow) when compared to reading, eg. writing to flash memory or EEPROM.
No other sorting algorithm has less data movement.
References
Rosetta Code: O (complexity).
Wikipedia: Selection sort.
Wikipedia: [Big O notation].
| #Go | Go | package main
import "fmt"
var a = []int{170, 45, 75, -90, -802, 24, 2, 66}
func main() {
fmt.Println("before:", a)
selectionSort(a)
fmt.Println("after: ", a)
}
func selectionSort(a []int) {
last := len(a) - 1
for i := 0; i < last; i++ {
aMin := a[i]
iMin := i
for j := i + 1; j < len(a); j++ {
if a[j] < aMin {
aMin = a[j]
iMin = j
}
}
a[i], a[iMin] = aMin, a[i]
}
} |
http://rosettacode.org/wiki/Soundex | Soundex | Soundex is an algorithm for creating indices for words based on their pronunciation.
Task
The goal is for homophones to be encoded to the same representation so that they can be matched despite minor differences in spelling (from the soundex Wikipedia article).
Caution
There is a major issue in many of the implementations concerning the separation of two consonants that have the same soundex code! According to the official Rules [[1]]. So check for instance if Ashcraft is coded to A-261.
If a vowel (A, E, I, O, U) separates two consonants that have the same soundex code, the consonant to the right of the vowel is coded. Tymczak is coded as T-522 (T, 5 for the M, 2 for the C, Z ignored (see "Side-by-Side" rule above), 2 for the K). Since the vowel "A" separates the Z and K, the K is coded.
If "H" or "W" separate two consonants that have the same soundex code, the consonant to the right of the vowel is not coded. Example: Ashcraft is coded A-261 (A, 2 for the S, C ignored, 6 for the R, 1 for the F). It is not coded A-226.
| #J | J | removeDups =: {.;.1~ (1 , }. ~: }: )
codes =: ;: 'BFPV CGJKQSXZ DT L MN R HW'
soundex =: 3 : 0
if. 0=# k=.toupper y do. '0' return. end.
({.k), ,": ,. 3 {. 0-.~ }. removeDups 7 0:`(I.@:=)`]} , k >:@I.@:(e. &>)"0 _ codes
) |
http://rosettacode.org/wiki/Sorting_algorithms/Shell_sort | Sorting algorithms/Shell sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array of elements using the Shell sort algorithm, a diminishing increment sort.
The Shell sort (also known as Shellsort or Shell's method) is named after its inventor, Donald Shell, who published the algorithm in 1959.
Shell sort is a sequence of interleaved insertion sorts based on an increment sequence.
The increment size is reduced after each pass until the increment size is 1.
With an increment size of 1, the sort is a basic insertion sort, but by this time the data is guaranteed to be almost sorted, which is insertion sort's "best case".
Any sequence will sort the data as long as it ends in 1, but some work better than others.
Empirical studies have shown a geometric increment sequence with a ratio of about 2.2 work well in practice.
[1]
Other good sequences are found at the On-Line Encyclopedia of Integer Sequences.
| #ooRexx | ooRexx | /* Rexx */
-- --- Main --------------------------------------------------------------------
call demo
return
exit
-- -----------------------------------------------------------------------------
-- Shell sort implementation
-- -----------------------------------------------------------------------------
::routine shellSort
use arg ra
n = ra~items()
inc = format(n / 2.0,, 0) -- rounding
loop label inc while inc > 0
loop i_ = inc to n - 1
temp = ra~get(i_)
j_ = i_
loop label j_ while j_ >= inc
if \(ra~get(j_ - inc) > temp) then leave j_
ra~set(j_, ra~get(j_ - inc))
j_ = j_ - inc
end j_
ra~set(j_, temp)
end i_
inc = format(inc / 2.2,, 0) -- rounding
end inc
return ra
-- -----------------------------------------------------------------------------
-- Demonstrate the implementation
-- -----------------------------------------------------------------------------
::routine demo
placesList = .nlist~of( -
"UK London", "US New York", "US Boston", "US Washington" -
, "UK Washington", "US Birmingham", "UK Birmingham", "UK Boston" -
)
lists = .array~of( -
placesList -
, shellSort(placesList~copy()) -
)
loop ln = 1 to lists~items()
cl = lists[ln]
loop ct = 0 to cl~items() - 1
say right(ct + 1, 4)':' cl[ct]
end ct
say
end ln
return
-- -----------------------------------------------------------------------------
::routine isTrue
return 1 == 1
-- -----------------------------------------------------------------------------
::routine isFalse
return \isTrue()
-- -----------------------------------------------------------------------------
-- Helper class. Map get and set methods for easier conversion from java.util.List
-- -----------------------------------------------------------------------------
::class NList mixinclass List public
-- Map get() to at()
::method get
use arg ix
return self~at(ix)
-- Map set() to put()
::method set
use arg ix, item
self~put(item, ix)
return
|
http://rosettacode.org/wiki/Stack | Stack |
Data Structure
This illustrates a data structure, a means of storing data within a program.
You may see other such structures in the Data Structures category.
A stack is a container of elements with last in, first out access policy. Sometimes it also called LIFO.
The stack is accessed through its top.
The basic stack operations are:
push stores a new element onto the stack top;
pop returns the last pushed stack element, while removing it from the stack;
empty tests if the stack contains no elements.
Sometimes the last pushed stack element is made accessible for immutable access (for read) or mutable access (for write):
top (sometimes called peek to keep with the p theme) returns the topmost element without modifying the stack.
Stacks allow a very simple hardware implementation.
They are common in almost all processors.
In programming, stacks are also very popular for their way (LIFO) of resource management, usually memory.
Nested scopes of language objects are naturally implemented by a stack (sometimes by multiple stacks).
This is a classical way to implement local variables of a re-entrant or recursive subprogram. Stacks are also used to describe a formal computational framework.
See stack machine.
Many algorithms in pattern matching, compiler construction (e.g. recursive descent parsers), and machine learning (e.g. based on tree traversal) have a natural representation in terms of stacks.
Task
Create a stack supporting the basic operations: push, pop, empty.
See also
Array
Associative array: Creation, Iteration
Collections
Compound data type
Doubly-linked list: Definition, Element definition, Element insertion, List Traversal, Element Removal
Linked list
Queue: Definition, Usage
Set
Singly-linked list: Element definition, Element insertion, List Traversal, Element Removal
Stack
| #Mercury | Mercury | :- module sstack.
:- interface.
% We're going to call the type sstack (simple stack) because we don't want to get it
% accidentally confused with the official stack module in the standard library.
:- type sstack(T).
:- func sstack.new = sstack(T).
:- pred sstack.is_empty(sstack(T)::in) is semidet.
:- func sstack.push(sstack(T), T) = sstack(T).
:- pred sstack.pop(T::out, sstack(T)::in, sstack(T)::out) is semidet.
:- implementation.
:- import_module list.
:- type sstack(T)
---> sstack(list(T)).
sstack.new = sstack([]).
sstack.is_empty(sstack([])).
sstack.push(Stack0, Elem) = Stack1 :-
Stack0 = sstack(Elems),
Stack1 = sstack([Elem | Elems]).
sstack.pop(Elem, !Stack) :-
!.Stack = sstack([Elem | Elems]),
!:Stack = sstack(Elems).
:- end_module sstack. |
http://rosettacode.org/wiki/Spiral_matrix | Spiral matrix | Task
Produce a spiral array.
A spiral array is a square arrangement of the first N2 natural numbers, where the
numbers increase sequentially as you go around the edges of the array spiraling inwards.
For example, given 5, produce this array:
0 1 2 3 4
15 16 17 18 5
14 23 24 19 6
13 22 21 20 7
12 11 10 9 8
Related tasks
Zig-zag matrix
Identity_matrix
Ulam_spiral_(for_primes)
| #Pascal | Pascal | program Spiralmat;
type
tDir = (left,down,right,up);
tdxy = record
dx,dy: longint;
end;
tdeltaDir = array[tDir] of tdxy;
const
Nextdir : array[tDir] of tDir = (down,right,up,left);
cDir : tDeltaDir = ((dx:1;dy:0),(dx:0;dy:1),(dx:-1;dy:0),(dx:0;dy:-1));
cMaxN = 32;
type
tSpiral = array[0..cMaxN,0..cMaxN] of LongInt;
function FillSpiral(n:longint):tSpiral;
var
b,i,k, dn,x,y : longInt;
dir : tDir;
tmpSp : tSpiral;
BEGIN
b := 0;
x := 0;
y := 0;
//only for the first line
k := -1;
dn := n-1;
tmpSp[x,y] := b;
dir := left;
repeat
i := 0;
while i < dn do
begin
inc(b);
tmpSp[x,y] := b;
inc(x,cDir[dir].dx);
inc(y,cDir[dir].dy);
inc(i);
end;
Dir:= NextDir[dir];
inc(k);
IF k > 1 then
begin
k := 0;
//shorten the line every second direction change
dn := dn-1;
if dn <= 0 then
BREAK;
end;
until false;
//the last
tmpSp[x,y] := b+1;
FillSpiral := tmpSp;
end;
var
a : tSpiral;
x,y,n : LongInt;
BEGIN
For n := 1 to 5{cMaxN} do
begin
A:=FillSpiral(n);
For y := 0 to n-1 do
begin
For x := 0 to n-1 do
write(A[x,y]:4);
writeln;
end;
writeln;
end;
END.
|
http://rosettacode.org/wiki/Sorting_algorithms/Radix_sort | Sorting algorithms/Radix sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an integer array with the radix sort algorithm.
The primary purpose is to complete the characterization of sort algorithms task.
| #REXX | REXX | /*REXX program performs a radix sort on an integer array (can be negative/zero/positive)*/
call gen /*call subroutine to generate numbers. */
call radSort n, w /*invoke the radix sort subroutine. */
call show /*display the elements in the @ array*/
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
gen: ILF= 0 2 3 4 5 5 7. 6 6 7 11 7 13 9 8 8 17 8 19 9 10 13 23 9 10 15 ,
9 11 29 10 31 10 14 19 12 10 37 21 16 11 41 12 43 15 11 25 47 11 14 12 20 17 ,
53 11 16 13 22 31 59 12 61 33 13 12 18 16 67 21 26 14 71 12 73 39 13 23 18 18 ,
79 13 12 43 83 14 22 45 32 17 89 13 20 27 34 49 24 13 97 16 17 14 101 ,
'22 103 19 15 55 107 13 109 18 40 15 113 -42'
/*excluding -42, abbreviated above list is called the integer log function*/
n= words(ILF) /* I────── L── F───────*/
w= 0; do m=1 for n; _= word(ILF,m) +0; @.m= _; w= max(w, length(_) )
end /*m*/; return /*W: is the maximum width ↑ of numbers*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
radSort: procedure expose @.; parse arg size,w; mote= c2d(' '); #= 1; !.#._n= size
!.#._b= 1; if w=='' then w= 8
!.#._i= 1; do i=1 for size; [email protected]; @.i= right(abs(y), w, 0); if y<0 then @.i= '-'@.i
end /*i*/ /* [↑] negative case.*/
do while #\==0; ctr.= 0; L= 'ffff'x; low= !.#._b; n= !.#._n; $= !.#._i; H=
#= #-1 /* [↑] is the radix. */
do j=low for n; parse var @.j =($) _ +1; ctr._= ctr._ + 1
if ctr._==1 & _\=='' then do; if _<<L then L=_; if _>>H then H=_
end /* ↑↑ */
end /*j*/ /* └┴─────◄─── << is a strict comparison.*/
_= /* ┌──◄─── >> " " " " */
if L>>H then iterate /*◄─────┘ */
if L==H & ctr._==0 then do; #= #+1; !.#._b= low; !.#._n= n; !.#._i= $+1; iterate
end
L= c2d(L); H= c2d(H); ?= ctr._ + low; top._= ?; ts= mote
max= L
do k=L to H; _= d2c(k, 1); c= ctr._ /* [↓] swap 2 item radices.*/
if c>ts then parse value c k with ts max; ?= ?+c; top._= ?
end /*k*/
piv= low /*set PIVot to the low part of the sort*/
do while piv<low+n
it= @.piv
do forever; parse var it =($) _ +1; c= top._ -1
if piv>=c then leave; top._= c; ?= @.c; @.c= it; it= ?
end /*forever*/
top._= piv; @.piv= it; piv= piv + ctr._
end /*while piv<low+n */
i= max
do until i==max; _= d2c(i, 1); i= i+1; if i>H then i= L; d= ctr._
if d<=mote then do; if d<2 then iterate; b= top._
do k=b+1 for d-1; q= @.k
do j=k-1 by -1 to b while q<<@.j; jp= j+1; @.jp= @.j
end /*j*/
jp= j+1; @.jp= q
end /*k*/
iterate
end
#= #+1; !.#._b= top._; !.#._n= d; !.#._i= $ + 1
end /*until i==max*/
end /*while #\==0 */
#= 0 /* [↓↓↓] handle neg. and pos. arrays. */
do i=size by -1 for size; if @.i>=0 then iterate; #= #+1; @@.#= @.i
end /*i*/
do j=1 for size; if @.j>=0 then do; #= #+1; @@.#= @.j; end; @.j= @@.j+0
end /*j*/ /* [↑↑↑] combine 2 lists into 1 list. */
return
/*──────────────────────────────────────────────────────────────────────────────────────*/
show: do j=1 for n; say 'item' right(j, w) "after the radix sort:" right(@.j, w)
end /*j*/; return /* [↑] display sorted items ───► term.*/ |
http://rosettacode.org/wiki/Sorting_algorithms/Quicksort | Sorting algorithms/Quicksort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Quicksort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Sort an array (or list) elements using the quicksort algorithm.
The elements must have a strict weak order and the index of the array can be of any discrete type.
For languages where this is not possible, sort an array of integers.
Quicksort, also known as partition-exchange sort, uses these steps.
Choose any element of the array to be the pivot.
Divide all other elements (except the pivot) into two partitions.
All elements less than the pivot must be in the first partition.
All elements greater than the pivot must be in the second partition.
Use recursion to sort both partitions.
Join the first sorted partition, the pivot, and the second sorted partition.
The best pivot creates partitions of equal length (or lengths differing by 1).
The worst pivot creates an empty partition (for example, if the pivot is the first or last element of a sorted array).
The run-time of Quicksort ranges from O(n log n) with the best pivots, to O(n2) with the worst pivots, where n is the number of elements in the array.
This is a simple quicksort algorithm, adapted from Wikipedia.
function quicksort(array)
less, equal, greater := three empty arrays
if length(array) > 1
pivot := select any element of array
for each x in array
if x < pivot then add x to less
if x = pivot then add x to equal
if x > pivot then add x to greater
quicksort(less)
quicksort(greater)
array := concatenate(less, equal, greater)
A better quicksort algorithm works in place, by swapping elements within the array, to avoid the memory allocation of more arrays.
function quicksort(array)
if length(array) > 1
pivot := select any element of array
left := first index of array
right := last index of array
while left ≤ right
while array[left] < pivot
left := left + 1
while array[right] > pivot
right := right - 1
if left ≤ right
swap array[left] with array[right]
left := left + 1
right := right - 1
quicksort(array from first index to right)
quicksort(array from left to last index)
Quicksort has a reputation as the fastest sort. Optimized variants of quicksort are common features of many languages and libraries. One often contrasts quicksort with merge sort, because both sorts have an average time of O(n log n).
"On average, mergesort does fewer comparisons than quicksort, so it may be better when complicated comparison routines are used. Mergesort also takes advantage of pre-existing order, so it would be favored for using sort() to merge several sorted arrays. On the other hand, quicksort is often faster for small arrays, and on arrays of a few distinct values, repeated many times." — http://perldoc.perl.org/sort.html
Quicksort is at one end of the spectrum of divide-and-conquer algorithms, with merge sort at the opposite end.
Quicksort is a conquer-then-divide algorithm, which does most of the work during the partitioning and the recursive calls. The subsequent reassembly of the sorted partitions involves trivial effort.
Merge sort is a divide-then-conquer algorithm. The partioning happens in a trivial way, by splitting the input array in half. Most of the work happens during the recursive calls and the merge phase.
With quicksort, every element in the first partition is less than or equal to every element in the second partition. Therefore, the merge phase of quicksort is so trivial that it needs no mention!
This task has not specified whether to allocate new arrays, or sort in place. This task also has not specified how to choose the pivot element. (Common ways to are to choose the first element, the middle element, or the median of three elements.) Thus there is a variety among the following implementations.
| #C.23 | C# | //
// The Tripartite conditional enables Bentley-McIlroy 3-way Partitioning.
// This performs additional compares to isolate islands of keys equal to
// the pivot value. Use unless key-equivalent classes are of small size.
//
#define Tripartite
namespace RosettaCode {
using System;
using System.Diagnostics;
public class QuickSort<T> where T : IComparable {
#region Constants
public const UInt32 INSERTION_LIMIT_DEFAULT = 12;
private const Int32 SAMPLES_MAX = 19;
#endregion
#region Properties
public UInt32 InsertionLimit { get; }
private T[] Samples { get; }
private Int32 Left { get; set; }
private Int32 Right { get; set; }
private Int32 LeftMedian { get; set; }
private Int32 RightMedian { get; set; }
#endregion
#region Constructors
public QuickSort(UInt32 insertionLimit = INSERTION_LIMIT_DEFAULT) {
this.InsertionLimit = insertionLimit;
this.Samples = new T[SAMPLES_MAX];
}
#endregion
#region Sort Methods
public void Sort(T[] entries) {
Sort(entries, 0, entries.Length - 1);
}
public void Sort(T[] entries, Int32 first, Int32 last) {
var length = last + 1 - first;
while (length > 1) {
if (length < InsertionLimit) {
InsertionSort<T>.Sort(entries, first, last);
return;
}
Left = first;
Right = last;
var median = pivot(entries);
partition(median, entries);
//[Note]Right < Left
var leftLength = Right + 1 - first;
var rightLength = last + 1 - Left;
//
// First recurse over shorter partition, then loop
// on the longer partition to elide tail recursion.
//
if (leftLength < rightLength) {
Sort(entries, first, Right);
first = Left;
length = rightLength;
}
else {
Sort(entries, Left, last);
last = Right;
length = leftLength;
}
}
}
/// <summary>Return an odd sample size proportional to the log of a large interval size.</summary>
private static Int32 sampleSize(Int32 length, Int32 max = SAMPLES_MAX) {
var logLen = (Int32)Math.Log10(length);
var samples = Math.Min(2 * logLen + 1, max);
return Math.Min(samples, length);
}
/// <summary>Estimate the median value of entries[Left:Right]</summary>
/// <remarks>A sample median is used as an estimate the true median.</remarks>
private T pivot(T[] entries) {
var length = Right + 1 - Left;
var samples = sampleSize(length);
// Sample Linearly:
for (var sample = 0; sample < samples; sample++) {
// Guard against Arithmetic Overflow:
var index = (Int64)length * sample / samples + Left;
Samples[sample] = entries[index];
}
InsertionSort<T>.Sort(Samples, 0, samples - 1);
return Samples[samples / 2];
}
private void partition(T median, T[] entries) {
var first = Left;
var last = Right;
#if Tripartite
LeftMedian = first;
RightMedian = last;
#endif
while (true) {
//[Assert]There exists some index >= Left where entries[index] >= median
//[Assert]There exists some index <= Right where entries[index] <= median
// So, there is no need for Left or Right bound checks
while (median.CompareTo(entries[Left]) > 0) Left++;
while (median.CompareTo(entries[Right]) < 0) Right--;
//[Assert]entries[Right] <= median <= entries[Left]
if (Right <= Left) break;
Swap(entries, Left, Right);
swapOut(median, entries);
Left++;
Right--;
//[Assert]entries[first:Left - 1] <= median <= entries[Right + 1:last]
}
if (Left == Right) {
Left++;
Right--;
}
//[Assert]Right < Left
swapIn(entries, first, last);
//[Assert]entries[first:Right] <= median <= entries[Left:last]
//[Assert]entries[Right + 1:Left - 1] == median when non-empty
}
#endregion
#region Swap Methods
[Conditional("Tripartite")]
private void swapOut(T median, T[] entries) {
if (median.CompareTo(entries[Left]) == 0) Swap(entries, LeftMedian++, Left);
if (median.CompareTo(entries[Right]) == 0) Swap(entries, Right, RightMedian--);
}
[Conditional("Tripartite")]
private void swapIn(T[] entries, Int32 first, Int32 last) {
// Restore Median entries
while (first < LeftMedian) Swap(entries, first++, Right--);
while (RightMedian < last) Swap(entries, Left++, last--);
}
/// <summary>Swap entries at the left and right indicies.</summary>
public void Swap(T[] entries, Int32 left, Int32 right) {
Swap(ref entries[left], ref entries[right]);
}
/// <summary>Swap two entities of type T.</summary>
public static void Swap(ref T e1, ref T e2) {
var e = e1;
e1 = e2;
e2 = e;
}
#endregion
}
#region Insertion Sort
static class InsertionSort<T> where T : IComparable {
public static void Sort(T[] entries, Int32 first, Int32 last) {
for (var next = first + 1; next <= last; next++)
insert(entries, first, next);
}
/// <summary>Bubble next entry up to its sorted location, assuming entries[first:next - 1] are already sorted.</summary>
private static void insert(T[] entries, Int32 first, Int32 next) {
var entry = entries[next];
while (next > first && entries[next - 1].CompareTo(entry) > 0)
entries[next] = entries[--next];
entries[next] = entry;
}
}
#endregion
} |
http://rosettacode.org/wiki/Sorting_algorithms/Patience_sort | Sorting algorithms/Patience sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Sort an array of numbers (of any convenient size) into ascending order using Patience sorting.
Related task
Longest increasing subsequence
| #OCaml | OCaml | module PatienceSortFn (Ord : Set.OrderedType) : sig
val patience_sort : Ord.t list -> Ord.t list
end = struct
module PilesSet = Set.Make
(struct
type t = Ord.t list
let compare x y = Ord.compare (List.hd x) (List.hd y)
end);;
let sort_into_piles list =
let piles = Array.make (List.length list) [] in
let bsearch_piles x len =
let rec aux lo hi =
if lo > hi then
lo
else
let mid = (lo + hi) / 2 in
if Ord.compare (List.hd piles.(mid)) x < 0 then
aux (mid+1) hi
else
aux lo (mid-1)
in
aux 0 (len-1)
in
let f len x =
let i = bsearch_piles x len in
piles.(i) <- x :: piles.(i);
if i = len then len+1 else len
in
let len = List.fold_left f 0 list in
Array.sub piles 0 len
let merge_piles piles =
let pq = Array.fold_right PilesSet.add piles PilesSet.empty in
let rec f pq acc =
if PilesSet.is_empty pq then
acc
else
let elt = PilesSet.min_elt pq in
match elt with
[] -> failwith "Impossible"
| x::xs ->
let pq' = PilesSet.remove elt pq in
f (if xs = [] then pq' else PilesSet.add xs pq') (x::acc)
in
List.rev (f pq [])
let patience_sort n =
merge_piles (sort_into_piles n)
end |
http://rosettacode.org/wiki/Sorting_algorithms/Insertion_sort | Sorting algorithms/Insertion sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Insertion sort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
An O(n2) sorting algorithm which moves elements one at a time into the correct position.
The algorithm consists of inserting one element at a time into the previously sorted part of the array, moving higher ranked elements up as necessary.
To start off, the first (or smallest, or any arbitrary) element of the unsorted array is considered to be the sorted part.
Although insertion sort is an O(n2) algorithm, its simplicity, low overhead, good locality of reference and efficiency make it a good choice in two cases:
small n,
as the final finishing-off algorithm for O(n logn) algorithms such as mergesort and quicksort.
The algorithm is as follows (from wikipedia):
function insertionSort(array A)
for i from 1 to length[A]-1 do
value := A[i]
j := i-1
while j >= 0 and A[j] > value do
A[j+1] := A[j]
j := j-1
done
A[j+1] = value
done
Writing the algorithm for integers will suffice.
| #BASIC_2 | BASIC | DECLARE SUB InsertionSort (theList() AS INTEGER)
DIM n(10) AS INTEGER, L AS INTEGER, o AS STRING
FOR L = 0 TO 10
n(L) = INT(RND * 32768)
NEXT
InsertionSort n()
FOR L = 1 TO 10
PRINT n(L); ";";
NEXT
SUB InsertionSort (theList() AS INTEGER)
DIM insertionElementIndex AS INTEGER
FOR insertionElementIndex = 1 TO UBOUND(theList)
DIM insertionElement AS INTEGER
insertionElement = theList(insertionElementIndex)
DIM j AS INTEGER
j = insertionElementIndex - 1
DO WHILE (j >= 0)
'necessary for BASICs without short-circuit evaluation
IF (insertionElement < theList(j)) THEN
theList(j + 1) = theList(j)
j = j - 1
ELSE
EXIT DO
END IF
LOOP
theList(j + 1) = insertionElement
NEXT
END SUB |
http://rosettacode.org/wiki/Sorting_algorithms/Permutation_sort | Sorting algorithms/Permutation sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Implement a permutation sort, which proceeds by generating the possible permutations
of the input array/list until discovering the sorted one.
Pseudocode:
while not InOrder(list) do
nextPermutation(list)
done
| #Ring | Ring |
# Project : Sorting algorithms/Permutation sort
a = [4, 65, 2, 31, 0, 99, 2, 83, 782]
result = []
permute(a,1)
for n = 1 to len(result)
num = 0
for m = 1 to len(result[n]) - 1
if result[n][m] <= result[n][m+1]
num = num + 1
ok
next
if num = len(result[n]) - 1
nr = n
exit
ok
next
see "" + nr + " permutations required to sort " + len(a) + " items." + nl
func permute(a,k)
if k = len(a)
add(result,a)
else
for i = k to len(a)
temp=a[k]
a[k]=a[i]
a[i]=temp
permute(a,k+1)
temp=a[k]
a[k]=a[i]
a[i]=temp
next
ok
return a
|
http://rosettacode.org/wiki/Sorting_algorithms/Permutation_sort | Sorting algorithms/Permutation sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Implement a permutation sort, which proceeds by generating the possible permutations
of the input array/list until discovering the sorted one.
Pseudocode:
while not InOrder(list) do
nextPermutation(list)
done
| #Ruby | Ruby | class Array
def permutationsort
permutation.each{|perm| return perm if perm.sorted?}
end
def sorted?
each_cons(2).all? {|a, b| a <= b}
end
end |
http://rosettacode.org/wiki/Sorting_algorithms/Heapsort | Sorting algorithms/Heapsort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Heapsort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Heapsort is an in-place sorting algorithm with worst case and average complexity of O(n logn).
The basic idea is to turn the array into a binary heap structure, which has the property that it allows efficient retrieval and removal of the maximal element.
We repeatedly "remove" the maximal element from the heap, thus building the sorted list from back to front.
A heap sort requires random access, so can only be used on an array-like data structure.
Pseudocode:
function heapSort(a, count) is
input: an unordered array a of length count
(first place a in max-heap order)
heapify(a, count)
end := count - 1
while end > 0 do
(swap the root(maximum value) of the heap with the
last element of the heap)
swap(a[end], a[0])
(decrement the size of the heap so that the previous
max value will stay in its proper place)
end := end - 1
(put the heap back in max-heap order)
siftDown(a, 0, end)
function heapify(a,count) is
(start is assigned the index in a of the last parent node)
start := (count - 2) / 2
while start ≥ 0 do
(sift down the node at index start to the proper place
such that all nodes below the start index are in heap
order)
siftDown(a, start, count-1)
start := start - 1
(after sifting down the root all nodes/elements are in heap order)
function siftDown(a, start, end) is
(end represents the limit of how far down the heap to sift)
root := start
while root * 2 + 1 ≤ end do (While the root has at least one child)
child := root * 2 + 1 (root*2+1 points to the left child)
(If the child has a sibling and the child's value is less than its sibling's...)
if child + 1 ≤ end and a[child] < a[child + 1] then
child := child + 1 (... then point to the right child instead)
if a[root] < a[child] then (out of max-heap order)
swap(a[root], a[child])
root := child (repeat to continue sifting down the child now)
else
return
Write a function to sort a collection of integers using heapsort.
| #AppleScript | AppleScript | -- In-place binary heap sort.
-- Heap sort algorithm: J.W.J. Williams.
on heapSort(theList, l, r) -- Sort items l thru r of theList.
set listLen to (count theList)
if (listLen < 2) then return
-- Convert negative and/or transposed range indices.
if (l < 0) then set l to listLen + l + 1
if (r < 0) then set r to listLen + r + 1
if (l > r) then set {l, r} to {r, l}
script o
-- The list as a script property to allow faster references to its items.
property lst : theList
-- In a binary heap, the list index of each node's first child is (node index * 2) - (l - 1). Preset the constant part.
property const : l - 1
-- Private subhandler: sift a value down into the heap from a given node.
on siftDown(siftV, node, endOfHeap)
set child to node * 2 - const
repeat until (child comes after endOfHeap)
set childV to my lst's item child
if (child comes before endOfHeap) then
set child2 to child + 1
set child2V to my lst's item child2
if (child2V > childV) then
set child to child2
set childV to child2V
end if
end if
if (childV > siftV) then
set my lst's item node to childV
set node to child
set child to node * 2 - const
else
exit repeat
end if
end repeat
-- Insert the sifted-down value at the node reached.
set my lst's item node to siftV
end siftDown
end script
-- Arrange the sort range into a "heap" with its "top" at the leftmost position.
repeat with i from (l + r) div 2 to l by -1
tell o to siftDown(its lst's item i, i, r)
end repeat
-- Unpick the heap.
repeat with endOfHeap from r to (l + 1) by -1
set endV to o's lst's item endOfHeap
set o's lst's item endOfHeap to o's lst's item l
tell o to siftDown(endV, l, endOfHeap - 1)
end repeat
return -- nothing
end heapSort
property sort : heapSort
-- Demo:
local aList
set aList to {74, 95, 9, 56, 76, 33, 51, 27, 62, 55, 86, 60, 65, 32, 10, 62, 72, 87, 86, 85, 36, 20, 44, 17, 60}
sort(aList, 1, -1) -- Sort items 1 thru -1 of aList.
return aList |
http://rosettacode.org/wiki/Sorting_algorithms/Merge_sort | Sorting algorithms/Merge sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
The merge sort is a recursive sort of order n*log(n).
It is notable for having a worst case and average complexity of O(n*log(n)), and a best case complexity of O(n) (for pre-sorted input).
The basic idea is to split the collection into smaller groups by halving it until the groups only have one element or no elements (which are both entirely sorted groups).
Then merge the groups back together so that their elements are in order.
This is how the algorithm gets its divide and conquer description.
Task
Write a function to sort a collection of integers using the merge sort.
The merge sort algorithm comes in two parts:
a sort function and
a merge function
The functions in pseudocode look like this:
function mergesort(m)
var list left, right, result
if length(m) ≤ 1
return m
else
var middle = length(m) / 2
for each x in m up to middle - 1
add x to left
for each x in m at and after middle
add x to right
left = mergesort(left)
right = mergesort(right)
if last(left) ≤ first(right)
append right to left
return left
result = merge(left, right)
return result
function merge(left,right)
var list result
while length(left) > 0 and length(right) > 0
if first(left) ≤ first(right)
append first(left) to result
left = rest(left)
else
append first(right) to result
right = rest(right)
if length(left) > 0
append rest(left) to result
if length(right) > 0
append rest(right) to result
return result
See also
the Wikipedia entry: merge sort
Note: better performance can be expected if, rather than recursing until length(m) ≤ 1, an insertion sort is used for length(m) smaller than some threshold larger than 1. However, this complicates the example code, so it is not shown here.
| #ALGOL_68 | ALGOL 68 | MODE DATA = CHAR;
PROC merge sort = ([]DATA m)[]DATA: (
IF LWB m >= UPB m THEN
m
ELSE
INT middle = ( UPB m + LWB m ) OVER 2;
[]DATA left = merge sort(m[:middle]);
[]DATA right = merge sort(m[middle+1:]);
flex merge(left, right)[AT LWB m]
FI
);
# FLEX version: A demonstration of FLEX for manipulating arrays #
PROC flex merge = ([]DATA in left, in right)[]DATA:(
[UPB in left + UPB in right]DATA result;
FLEX[0]DATA left := in left;
FLEX[0]DATA right := in right;
FOR index TO UPB result DO
# change the direction of this comparison to change the direction of the sort #
IF LWB right > UPB right THEN
result[index:] := left;
stop iteration
ELIF LWB left > UPB left THEN
result[index:] := right;
stop iteration
ELIF left[1] <= right[1] THEN
result[index] := left[1];
left := left[2:]
ELSE
result[index] := right[1];
right := right[2:]
FI
OD;
stop iteration:
result
);
[32]CHAR char array data := "big fjords vex quick waltz nymph";
print((merge sort(char array data), new line)); |
http://rosettacode.org/wiki/Sorting_algorithms/Pancake_sort | Sorting algorithms/Pancake sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array of integers (of any convenient size) into ascending order using Pancake sorting.
In short, instead of individual elements being sorted, the only operation allowed is to "flip" one end of the list, like so:
Before: 6 7 8 9 2 5 3 4 1
After: 9 8 7 6 2 5 3 4 1
Only one end of the list can be flipped; this should be the low end, but the high end is okay if it's easier to code or works better, but it must be the same end for the entire solution. (The end flipped can't be arbitrarily changed.)
Show both the initial, unsorted list and the final sorted list.
(Intermediate steps during sorting are optional.)
Optimizations are optional (but recommended).
Related tasks
Number reversal game
Topswops
Also see
Wikipedia article: pancake sorting.
| #jq | jq | def pancakeSort:
def flip(i):
. as $in | ($in[0:i+1]|reverse) + $in[i+1:] ;
# If input is [] then return null
def index_of_max:
. as $in
| reduce range(1; length) as $i
# state: [ix, max]
( [ 0, $in[0] ];
if $in[$i] > .[1] then [ $i, $in[$i] ] else . end )
| .[0] ;
reduce range(0; length) as $iup
(.;
(length - $iup - 1) as $i
| (.[0:$i+1] | index_of_max) as $max
# flip about $max and then about $i unless $i == $max
| if ($i == $max) then .
else flip($max) | flip($i)
end ) ; |
http://rosettacode.org/wiki/Sorting_algorithms/Pancake_sort | Sorting algorithms/Pancake sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array of integers (of any convenient size) into ascending order using Pancake sorting.
In short, instead of individual elements being sorted, the only operation allowed is to "flip" one end of the list, like so:
Before: 6 7 8 9 2 5 3 4 1
After: 9 8 7 6 2 5 3 4 1
Only one end of the list can be flipped; this should be the low end, but the high end is okay if it's easier to code or works better, but it must be the same end for the entire solution. (The end flipped can't be arbitrarily changed.)
Show both the initial, unsorted list and the final sorted list.
(Intermediate steps during sorting are optional.)
Optimizations are optional (but recommended).
Related tasks
Number reversal game
Topswops
Also see
Wikipedia article: pancake sorting.
| #Julia | Julia | function pancakesort!(arr::Vector{<:Real})
len = length(arr)
if len < 2 return arr end
for i in len:-1:2
j = indmax(arr[1:i])
if i == j continue end
arr[1:j] = reverse(arr[1:j])
arr[1:i] = reverse(arr[1:i])
end
return arr
end
v = rand(-10:10, 10)
println("# unordered: $v\n -> ordered: ", pancakesort!(v)) |
http://rosettacode.org/wiki/Sorting_algorithms/Stooge_sort | Sorting algorithms/Stooge sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Stooge sort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Show the Stooge Sort for an array of integers.
The Stooge Sort algorithm is as follows:
algorithm stoogesort(array L, i = 0, j = length(L)-1)
if L[j] < L[i] then
L[i] ↔ L[j]
if j - i > 1 then
t := (j - i + 1)/3
stoogesort(L, i , j-t)
stoogesort(L, i+t, j )
stoogesort(L, i , j-t)
return L
| #PicoLisp | PicoLisp | (de stoogeSort (L N)
(default N (length L))
(let P (nth L N)
(when (> (car L) (car P))
(xchg L P) ) )
(when (> N 2)
(let D (/ N 3)
(stoogeSort L (- N D))
(stoogeSort (nth L (inc D)) (- N D))
(stoogeSort L (- N D)) ) )
L ) |
http://rosettacode.org/wiki/Sorting_algorithms/Stooge_sort | Sorting algorithms/Stooge sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Stooge sort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Show the Stooge Sort for an array of integers.
The Stooge Sort algorithm is as follows:
algorithm stoogesort(array L, i = 0, j = length(L)-1)
if L[j] < L[i] then
L[i] ↔ L[j]
if j - i > 1 then
t := (j - i + 1)/3
stoogesort(L, i , j-t)
stoogesort(L, i+t, j )
stoogesort(L, i , j-t)
return L
| #PL.2FI | PL/I | stoogesort: procedure (L) recursive; /* 16 August 2010 */
declare L(*) fixed binary;
declare (i, j, t, temp) fixed binary;
j = hbound(L,1);
do i = lbound(L, 1) to j;
if L(j) < L(i) then
do; temp = L(i); L(i) = L(j); L(j) = temp; end;
if j - i > 1 then
do;
t = (j - i + 1)/3;
call stoogesort(L, i , j-t);
call stoogesort(L, i+t, j );
call stoogesort(L, i , j-t);
end;
end;
end stoogesort; |
http://rosettacode.org/wiki/Sorting_algorithms/Selection_sort | Sorting algorithms/Selection sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array (or list) of elements using the Selection sort algorithm.
It works as follows:
First find the smallest element in the array and exchange it with the element in the first position, then find the second smallest element and exchange it with the element in the second position, and continue in this way until the entire array is sorted.
Its asymptotic complexity is O(n2) making it inefficient on large arrays.
Its primary purpose is for when writing data is very expensive (slow) when compared to reading, eg. writing to flash memory or EEPROM.
No other sorting algorithm has less data movement.
References
Rosetta Code: O (complexity).
Wikipedia: Selection sort.
Wikipedia: [Big O notation].
| #Haskell | Haskell | import Data.List (delete)
selSort :: (Ord a) => [a] -> [a]
selSort [] = []
selSort xs = selSort (delete x xs) ++ [x]
where x = maximum xs |
http://rosettacode.org/wiki/Soundex | Soundex | Soundex is an algorithm for creating indices for words based on their pronunciation.
Task
The goal is for homophones to be encoded to the same representation so that they can be matched despite minor differences in spelling (from the soundex Wikipedia article).
Caution
There is a major issue in many of the implementations concerning the separation of two consonants that have the same soundex code! According to the official Rules [[1]]. So check for instance if Ashcraft is coded to A-261.
If a vowel (A, E, I, O, U) separates two consonants that have the same soundex code, the consonant to the right of the vowel is coded. Tymczak is coded as T-522 (T, 5 for the M, 2 for the C, Z ignored (see "Side-by-Side" rule above), 2 for the K). Since the vowel "A" separates the Z and K, the K is coded.
If "H" or "W" separate two consonants that have the same soundex code, the consonant to the right of the vowel is not coded. Example: Ashcraft is coded A-261 (A, 2 for the S, C ignored, 6 for the R, 1 for the F). It is not coded A-226.
| #Java | Java | public static void main(String[] args){
System.out.println(soundex("Soundex"));
System.out.println(soundex("Example"));
System.out.println(soundex("Sownteks"));
System.out.println(soundex("Ekzampul"));
}
private static String getCode(char c){
switch(c){
case 'B': case 'F': case 'P': case 'V':
return "1";
case 'C': case 'G': case 'J': case 'K':
case 'Q': case 'S': case 'X': case 'Z':
return "2";
case 'D': case 'T':
return "3";
case 'L':
return "4";
case 'M': case 'N':
return "5";
case 'R':
return "6";
default:
return "";
}
}
public static String soundex(String s){
String code, previous, soundex;
code = s.toUpperCase().charAt(0) + "";
// EDITED : previous = "7";
previous = getCode(s.toUpperCase().charAt(0));
for(int i = 1;i < s.length();i++){
String current = getCode(s.toUpperCase().charAt(i));
if(current.length() > 0 && !current.equals(previous)){
code = code + current;
}
previous = current;
}
soundex = (code + "0000").substring(0, 4);
return soundex;
} |
http://rosettacode.org/wiki/Sorting_algorithms/Shell_sort | Sorting algorithms/Shell sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array of elements using the Shell sort algorithm, a diminishing increment sort.
The Shell sort (also known as Shellsort or Shell's method) is named after its inventor, Donald Shell, who published the algorithm in 1959.
Shell sort is a sequence of interleaved insertion sorts based on an increment sequence.
The increment size is reduced after each pass until the increment size is 1.
With an increment size of 1, the sort is a basic insertion sort, but by this time the data is guaranteed to be almost sorted, which is insertion sort's "best case".
Any sequence will sort the data as long as it ends in 1, but some work better than others.
Empirical studies have shown a geometric increment sequence with a ratio of about 2.2 work well in practice.
[1]
Other good sequences are found at the On-Line Encyclopedia of Integer Sequences.
| #PARI.2FGP | PARI/GP | shellSort(v)={
my(inc=#v\2);
while(inc,
for(i=inc+1,#v,
my(t=v[i],j=i);
while(j>inc && v[j-inc]>t,
v[j]=v[j-=inc]
);
v[j]=t
);
inc \= 2.2
);
v
}; |
http://rosettacode.org/wiki/Sorting_algorithms/Shell_sort | Sorting algorithms/Shell sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array of elements using the Shell sort algorithm, a diminishing increment sort.
The Shell sort (also known as Shellsort or Shell's method) is named after its inventor, Donald Shell, who published the algorithm in 1959.
Shell sort is a sequence of interleaved insertion sorts based on an increment sequence.
The increment size is reduced after each pass until the increment size is 1.
With an increment size of 1, the sort is a basic insertion sort, but by this time the data is guaranteed to be almost sorted, which is insertion sort's "best case".
Any sequence will sort the data as long as it ends in 1, but some work better than others.
Empirical studies have shown a geometric increment sequence with a ratio of about 2.2 work well in practice.
[1]
Other good sequences are found at the On-Line Encyclopedia of Integer Sequences.
| #Pascal | Pascal | Const
MaxN = 100; { number of elements (my example is 100) }
Type
TArray = Array [0..MaxN] of Integer;
Procedure ShellSort ( var A : TArray; N : Integer );
Var
i, j, step, tmp : Integer;
Begin
step:=N div 2; // step:=step shr 1
While step>0 Do Begin
For i:=step to N Do Begin
tmp:=A[i];
j:=i;
While (j>=step) and (A[j-step]>tmp) Do Begin
A[j]:=A[j-step];
dec(j,step);
End;
A[j]:=tmp;
End;
step:=step div 2; // step:=step shr 1
End;
End;
|
http://rosettacode.org/wiki/Stack | Stack |
Data Structure
This illustrates a data structure, a means of storing data within a program.
You may see other such structures in the Data Structures category.
A stack is a container of elements with last in, first out access policy. Sometimes it also called LIFO.
The stack is accessed through its top.
The basic stack operations are:
push stores a new element onto the stack top;
pop returns the last pushed stack element, while removing it from the stack;
empty tests if the stack contains no elements.
Sometimes the last pushed stack element is made accessible for immutable access (for read) or mutable access (for write):
top (sometimes called peek to keep with the p theme) returns the topmost element without modifying the stack.
Stacks allow a very simple hardware implementation.
They are common in almost all processors.
In programming, stacks are also very popular for their way (LIFO) of resource management, usually memory.
Nested scopes of language objects are naturally implemented by a stack (sometimes by multiple stacks).
This is a classical way to implement local variables of a re-entrant or recursive subprogram. Stacks are also used to describe a formal computational framework.
See stack machine.
Many algorithms in pattern matching, compiler construction (e.g. recursive descent parsers), and machine learning (e.g. based on tree traversal) have a natural representation in terms of stacks.
Task
Create a stack supporting the basic operations: push, pop, empty.
See also
Array
Associative array: Creation, Iteration
Collections
Compound data type
Doubly-linked list: Definition, Element definition, Element insertion, List Traversal, Element Removal
Linked list
Queue: Definition, Usage
Set
Singly-linked list: Element definition, Element insertion, List Traversal, Element Removal
Stack
| #MiniScript | MiniScript | // Note in Miniscript, a value of zero is false,
// and any other number is true.
// therefore the .len function works as the inverse of a .empty function
stack = [2, 4, 6]
stack.push 8
print "Stack is " + stack
print "Adding '9' to stack " + stack.push(9)
print "Top of stack is " + stack.pop
print "Stack is " + stack
if stack.len then
print "Stack is not empty"
else
print "Stack is empty"
end if |
http://rosettacode.org/wiki/Spiral_matrix | Spiral matrix | Task
Produce a spiral array.
A spiral array is a square arrangement of the first N2 natural numbers, where the
numbers increase sequentially as you go around the edges of the array spiraling inwards.
For example, given 5, produce this array:
0 1 2 3 4
15 16 17 18 5
14 23 24 19 6
13 22 21 20 7
12 11 10 9 8
Related tasks
Zig-zag matrix
Identity_matrix
Ulam_spiral_(for_primes)
| #Perl | Perl | sub spiral
{my ($n, $x, $y, $dx, $dy, @a) = (shift, 0, 0, 1, 0);
foreach (0 .. $n**2 - 1)
{$a[$y][$x] = $_;
my ($nx, $ny) = ($x + $dx, $y + $dy);
($dx, $dy) =
$dx == 1 && ($nx == $n || defined $a[$ny][$nx])
? ( 0, 1)
: $dy == 1 && ($ny == $n || defined $a[$ny][$nx])
? (-1, 0)
: $dx == -1 && ($nx < 0 || defined $a[$ny][$nx])
? ( 0, -1)
: $dy == -1 && ($ny < 0 || defined $a[$ny][$nx])
? ( 1, 0)
: ($dx, $dy);
($x, $y) = ($x + $dx, $y + $dy);}
return @a;}
foreach (spiral 5)
{printf "%3d", $_ foreach @$_;
print "\n";} |
http://rosettacode.org/wiki/Sorting_algorithms/Radix_sort | Sorting algorithms/Radix sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an integer array with the radix sort algorithm.
The primary purpose is to complete the characterization of sort algorithms task.
| #Ruby | Ruby | class Array
def radix_sort(base=10)
ary = dup
rounds = (Math.log(ary.minmax.map(&:abs).max)/Math.log(base)).floor + 1
rounds.times do |i|
buckets = Array.new(2*base){[]}
base_i = base**i
ary.each do |n|
digit = (n/base_i) % base
digit += base if 0<=n
buckets[digit] << n
end
ary = buckets.flatten
p [i, ary] if $DEBUG
end
ary
end
def radix_sort!(base=10)
replace radix_sort(base)
end
end
p [1, 3, 8, 9, 0, 0, 8, 7, 1, 6].radix_sort
p [170, 45, 75, 90, 2, 24, 802, 66].radix_sort
p [170, 45, 75, 90, 2, 24, -802, -66].radix_sort
p [100000, -10000, 400, 23, 10000].radix_sort |
http://rosettacode.org/wiki/Sorting_algorithms/Quicksort | Sorting algorithms/Quicksort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Quicksort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Sort an array (or list) elements using the quicksort algorithm.
The elements must have a strict weak order and the index of the array can be of any discrete type.
For languages where this is not possible, sort an array of integers.
Quicksort, also known as partition-exchange sort, uses these steps.
Choose any element of the array to be the pivot.
Divide all other elements (except the pivot) into two partitions.
All elements less than the pivot must be in the first partition.
All elements greater than the pivot must be in the second partition.
Use recursion to sort both partitions.
Join the first sorted partition, the pivot, and the second sorted partition.
The best pivot creates partitions of equal length (or lengths differing by 1).
The worst pivot creates an empty partition (for example, if the pivot is the first or last element of a sorted array).
The run-time of Quicksort ranges from O(n log n) with the best pivots, to O(n2) with the worst pivots, where n is the number of elements in the array.
This is a simple quicksort algorithm, adapted from Wikipedia.
function quicksort(array)
less, equal, greater := three empty arrays
if length(array) > 1
pivot := select any element of array
for each x in array
if x < pivot then add x to less
if x = pivot then add x to equal
if x > pivot then add x to greater
quicksort(less)
quicksort(greater)
array := concatenate(less, equal, greater)
A better quicksort algorithm works in place, by swapping elements within the array, to avoid the memory allocation of more arrays.
function quicksort(array)
if length(array) > 1
pivot := select any element of array
left := first index of array
right := last index of array
while left ≤ right
while array[left] < pivot
left := left + 1
while array[right] > pivot
right := right - 1
if left ≤ right
swap array[left] with array[right]
left := left + 1
right := right - 1
quicksort(array from first index to right)
quicksort(array from left to last index)
Quicksort has a reputation as the fastest sort. Optimized variants of quicksort are common features of many languages and libraries. One often contrasts quicksort with merge sort, because both sorts have an average time of O(n log n).
"On average, mergesort does fewer comparisons than quicksort, so it may be better when complicated comparison routines are used. Mergesort also takes advantage of pre-existing order, so it would be favored for using sort() to merge several sorted arrays. On the other hand, quicksort is often faster for small arrays, and on arrays of a few distinct values, repeated many times." — http://perldoc.perl.org/sort.html
Quicksort is at one end of the spectrum of divide-and-conquer algorithms, with merge sort at the opposite end.
Quicksort is a conquer-then-divide algorithm, which does most of the work during the partitioning and the recursive calls. The subsequent reassembly of the sorted partitions involves trivial effort.
Merge sort is a divide-then-conquer algorithm. The partioning happens in a trivial way, by splitting the input array in half. Most of the work happens during the recursive calls and the merge phase.
With quicksort, every element in the first partition is less than or equal to every element in the second partition. Therefore, the merge phase of quicksort is so trivial that it needs no mention!
This task has not specified whether to allocate new arrays, or sort in place. This task also has not specified how to choose the pivot element. (Common ways to are to choose the first element, the middle element, or the median of three elements.) Thus there is a variety among the following implementations.
| #C.2B.2B | C++ | #include <iterator>
#include <algorithm> // for std::partition
#include <functional> // for std::less
// helper function for median of three
template<typename T>
T median(T t1, T t2, T t3)
{
if (t1 < t2)
{
if (t2 < t3)
return t2;
else if (t1 < t3)
return t3;
else
return t1;
}
else
{
if (t1 < t3)
return t1;
else if (t2 < t3)
return t3;
else
return t2;
}
}
// helper object to get <= from <
template<typename Order> struct non_strict_op:
public std::binary_function<typename Order::second_argument_type,
typename Order::first_argument_type,
bool>
{
non_strict_op(Order o): order(o) {}
bool operator()(typename Order::second_argument_type arg1,
typename Order::first_argument_type arg2) const
{
return !order(arg2, arg1);
}
private:
Order order;
};
template<typename Order> non_strict_op<Order> non_strict(Order o)
{
return non_strict_op<Order>(o);
}
template<typename RandomAccessIterator,
typename Order>
void quicksort(RandomAccessIterator first, RandomAccessIterator last, Order order)
{
if (first != last && first+1 != last)
{
typedef typename std::iterator_traits<RandomAccessIterator>::value_type value_type;
RandomAccessIterator mid = first + (last - first)/2;
value_type pivot = median(*first, *mid, *(last-1));
RandomAccessIterator split1 = std::partition(first, last, std::bind2nd(order, pivot));
RandomAccessIterator split2 = std::partition(split1, last, std::bind2nd(non_strict(order), pivot));
quicksort(first, split1, order);
quicksort(split2, last, order);
}
}
template<typename RandomAccessIterator>
void quicksort(RandomAccessIterator first, RandomAccessIterator last)
{
quicksort(first, last, std::less<typename std::iterator_traits<RandomAccessIterator>::value_type>());
} |
http://rosettacode.org/wiki/Sorting_algorithms/Patience_sort | Sorting algorithms/Patience sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Sort an array of numbers (of any convenient size) into ascending order using Patience sorting.
Related task
Longest increasing subsequence
| #Pascal | Pascal | PatienceSortTask (Output);
CONST MaxSortSize = 1024; { A power of two. }
MaxWinnersSize = (2 * MaxSortSize) - 1;
TYPE PilesArrayType = ARRAY [1 .. MaxSortSize] OF INTEGER;
WinnersArrayType = ARRAY [1 .. MaxWinnersSize,
1 .. 2] OF INTEGER;
VAR ExampleNumbers : ARRAY [0 .. 35] OF INTEGER;
SortedIndices : ARRAY [0 .. 25] OF INTEGER;
i : INTEGER;
FUNCTION NextPowerOfTwo (n : INTEGER) : INTEGER;
VAR Pow2 : INTEGER;
BEGIN
{ This need not be a fast implementation. }
Pow2 := 1;
WHILE Pow2 < n DO
Pow2 := Pow2 + Pow2;
NextPowerOfTwo := Pow2;
END;
PROCEDURE InitPilesArray (VAR Arr : PilesArrayType);
VAR i : INTEGER;
BEGIN
FOR i := 1 TO MaxSortSize DO
Arr[i] := 0;
END;
PROCEDURE InitWinnersArray (VAR Arr : WinnersArrayType);
VAR i : INTEGER;
BEGIN
FOR i := 1 TO MaxWinnersSize DO
BEGIN
Arr[i, 1] := 0;
Arr[i, 2] := 0;
END;
END;
PROCEDURE IntegerPatienceSort (iFirst, iLast : INTEGER;
Arr : ARRAY OF INTEGER;
VAR Sorted : ARRAY OF INTEGER);
VAR NumPiles : INTEGER;
Piles, Links : PilesArrayType;
Winners : WinnersArrayType;
FUNCTION FindPile (q : INTEGER) : INTEGER;
{
Bottenbruch search for the leftmost pile whose top is greater
than or equal to some element x. Return an index such that:
* if x is greater than the top element at the far right, then
the index returned will be num-piles.
* otherwise, x is greater than every top element to the left of
index, and less than or equal to the top elements at index
and to the right of index.
References:
* H. Bottenbruch, "Structure and use of ALGOL 60", Journal of
the ACM, Volume 9, Issue 2, April 1962, pp.161-221.
https://doi.org/10.1145/321119.321120
The general algorithm is described on pages 214 and 215.
* https://en.wikipedia.org/w/index.php?title=Binary_search_algorithm&oldid=1062988272#Alternative_procedure
}
VAR i, j, k, Index : INTEGER;
BEGIN
IF NumPiles = 0 THEN
Index := 1
ELSE
BEGIN
j := 0;
k := NumPiles - 1;
WHILE j <> k DO
BEGIN
i := (j + k) DIV 2;
IF Arr[Piles[j + 1] + iFirst - 1] < Arr[q + iFirst - 1] THEN
j := i + 1
ELSE
k := i
END;
IF j = NumPiles - 1 THEN
BEGIN
IF Arr[Piles[j + 1] + iFirst - 1] < Arr[q + iFirst - 1] THEN
{ A new pile is needed. }
j := j + 1
END;
Index := j + 1
END;
FindPile := Index
END;
PROCEDURE Deal;
VAR i, q : INTEGER;
BEGIN
FOR q := 1 TO iLast - iFirst + 1 DO
BEGIN
i := FindPile (q);
Links[q] := Piles[i];
Piles[i] := q;
IF i = NumPiles + 1 THEN
NumPiles := i
END
END;
PROCEDURE KWayMerge;
{
k-way merge by tournament tree.
See Knuth, volume 3, and also
https://en.wikipedia.org/w/index.php?title=K-way_merge_algorithm&oldid=1047851465#Tournament_Tree
However, I store a winners tree instead of the recommended
losers tree. If the tree were stored as linked nodes, it would
probably be more efficient to store a losers tree. However, I
am storing the tree as an array, and one can find an opponent
quickly by simply toggling the least significant bit of a
competitor's array index.
}
VAR TotalExternalNodes : INTEGER;
TotalNodes : INTEGER;
iSorted, i, Next : INTEGER;
FUNCTION FindOpponent (i : INTEGER) : INTEGER;
VAR Opponent : INTEGER;
BEGIN
IF ODD (i) THEN
Opponent := i - 1
ELSE
Opponent := i + 1;
FindOpponent := Opponent
END;
FUNCTION PlayGame (i : INTEGER) : INTEGER;
VAR j, iWinner : INTEGER;
BEGIN
j := FindOpponent (i);
IF Winners[i, 1] = 0 THEN
iWinner := j
ELSE IF Winners[j, 1] = 0 THEN
iWinner := i
ELSE IF (Arr[Winners[j, 1] + iFirst - 1]
< Arr[Winners[i, 1] + iFirst - 1]) THEN
iWinner := j
ELSE
iWinner := i;
PlayGame := iWinner
END;
PROCEDURE ReplayGames (i : INTEGER);
VAR j, iWinner : INTEGER;
BEGIN
j := i;
WHILE j <> 1 DO
BEGIN
iWinner := PlayGame (j);
j := j DIV 2;
Winners[j, 1] := Winners[iWinner, 1];
Winners[j, 2] := Winners[iWinner, 2];
END
END;
PROCEDURE BuildTree;
VAR iStart, i, iWinner : INTEGER;
BEGIN
FOR i := 1 TO TotalExternalNodes DO
{ Record which pile a winner will have come from. }
Winners[TotalExternalNodes - 1 + i, 2] := i;
FOR i := 1 TO NumPiles DO
{ The top of each pile becomes a starting competitor. }
Winners[TotalExternalNodes + i - 1, 1] := Piles[i];
FOR i := 1 TO NumPiles DO
{ Discard the top of each pile. }
Piles[i] := Links[Piles[i]];
iStart := TotalExternalNodes;
WHILE iStart <> 1 DO
BEGIN
i := iStart;
WHILE i <= (2 * iStart) - 1 DO
BEGIN
iWinner := PlayGame (i);
Winners[i DIV 2, 1] := Winners[iWinner, 1];
Winners[i DIV 2, 2] := Winners[iWinner, 2];
i := i + 2
END;
iStart := iStart DIV 2
END
END;
BEGIN
TotalExternalNodes := NextPowerOfTwo (NumPiles);
TotalNodes := (2 * TotalExternalNodes) - 1;
BuildTree;
iSorted := 0;
WHILE Winners[1, 1] <> 0 DO
BEGIN
Sorted[iSorted] := Winners[1, 1] + iFirst - 1;
iSorted := iSorted + 1;
i := Winners[1, 2];
Next := Piles[i]; { The next top of pile i. }
IF Next <> 0 THEN
Piles[i] := Links[Next]; { Drop that top. }
i := (TotalNodes DIV 2) + i;
Winners[i, 1] := Next;
ReplayGames (i)
END
END;
BEGIN
NumPiles := 0;
InitPilesArray (Piles);
InitPilesArray (Links);
InitWinnersArray (Winners);
IF MaxSortSize < iLast - iFirst + 1 THEN
BEGIN
Write ('This subarray is too large for the program.');
WriteLn;
HALT
END
ELSE
BEGIN
Deal;
KWayMerge
END
END;
BEGIN
ExampleNumbers[10] := 22;
ExampleNumbers[11] := 15;
ExampleNumbers[12] := 98;
ExampleNumbers[13] := 82;
ExampleNumbers[14] := 22;
ExampleNumbers[15] := 4;
ExampleNumbers[16] := 58;
ExampleNumbers[17] := 70;
ExampleNumbers[18] := 80;
ExampleNumbers[19] := 38;
ExampleNumbers[20] := 49;
ExampleNumbers[21] := 48;
ExampleNumbers[22] := 46;
ExampleNumbers[23] := 54;
ExampleNumbers[24] := 93;
ExampleNumbers[25] := 8;
ExampleNumbers[26] := 54;
ExampleNumbers[27] := 2;
ExampleNumbers[28] := 72;
ExampleNumbers[29] := 84;
ExampleNumbers[30] := 86;
ExampleNumbers[31] := 76;
ExampleNumbers[32] := 53;
ExampleNumbers[33] := 37;
ExampleNumbers[34] := 90;
IntegerPatienceSort (10, 34, ExampleNumbers, SortedIndices);
Write ('unsorted ');
FOR i := 10 TO 34 DO
BEGIN
Write (' ');
Write (ExampleNumbers[i])
END;
WriteLn;
Write ('sorted ');
FOR i := 0 TO 24 DO
BEGIN
Write (' ');
Write (ExampleNumbers[SortedIndices[i]]);
END;
WriteLn
END. |
http://rosettacode.org/wiki/Sorting_algorithms/Insertion_sort | Sorting algorithms/Insertion sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Insertion sort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
An O(n2) sorting algorithm which moves elements one at a time into the correct position.
The algorithm consists of inserting one element at a time into the previously sorted part of the array, moving higher ranked elements up as necessary.
To start off, the first (or smallest, or any arbitrary) element of the unsorted array is considered to be the sorted part.
Although insertion sort is an O(n2) algorithm, its simplicity, low overhead, good locality of reference and efficiency make it a good choice in two cases:
small n,
as the final finishing-off algorithm for O(n logn) algorithms such as mergesort and quicksort.
The algorithm is as follows (from wikipedia):
function insertionSort(array A)
for i from 1 to length[A]-1 do
value := A[i]
j := i-1
while j >= 0 and A[j] > value do
A[j+1] := A[j]
j := j-1
done
A[j+1] = value
done
Writing the algorithm for integers will suffice.
| #BCPL | BCPL | get "libhdr"
let insertionSort(A, len) be
for i = 1 to len-1 do
$( let value = A!i
let j = i-1
while j >= 0 & A!j > value do
$( A!(j+1) := A!j
j := j-1
$)
A!(j+1) := value
$)
let write(s, A, len) be
$( writes(s)
for i=0 to len-1 do writed(A!i, 4)
wrch('*N')
$)
let start() be
$( let array = table 4,65,2,-31,0,99,2,83,782,1
let length = 10
write("Before: ", array, length)
insertionSort(array, length)
write("After: ", array, length)
$) |
http://rosettacode.org/wiki/Sorting_algorithms/Permutation_sort | Sorting algorithms/Permutation sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Implement a permutation sort, which proceeds by generating the possible permutations
of the input array/list until discovering the sorted one.
Pseudocode:
while not InOrder(list) do
nextPermutation(list)
done
| #Scheme | Scheme | (define (insertions e list)
(if (null? list)
(cons (cons e list) list)
(cons (cons e list)
(map (lambda (tail) (cons (car list) tail))
(insertions e (cdr list))))))
(define (permutations list)
(if (null? list)
(cons list list)
(apply append (map (lambda (permutation)
(insertions (car list) permutation))
(permutations (cdr list))))))
(define (sorted? list)
(cond ((null? list) #t)
((null? (cdr list)) #t)
((<= (car list) (cadr list)) (sorted? (cdr list)))
(else #f)))
(define (permutation-sort list)
(let loop ((permutations (permutations list)))
(if (sorted? (car permutations))
(car permutations)
(loop (cdr permutations))))) |
http://rosettacode.org/wiki/Sorting_algorithms/Heapsort | Sorting algorithms/Heapsort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Heapsort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Heapsort is an in-place sorting algorithm with worst case and average complexity of O(n logn).
The basic idea is to turn the array into a binary heap structure, which has the property that it allows efficient retrieval and removal of the maximal element.
We repeatedly "remove" the maximal element from the heap, thus building the sorted list from back to front.
A heap sort requires random access, so can only be used on an array-like data structure.
Pseudocode:
function heapSort(a, count) is
input: an unordered array a of length count
(first place a in max-heap order)
heapify(a, count)
end := count - 1
while end > 0 do
(swap the root(maximum value) of the heap with the
last element of the heap)
swap(a[end], a[0])
(decrement the size of the heap so that the previous
max value will stay in its proper place)
end := end - 1
(put the heap back in max-heap order)
siftDown(a, 0, end)
function heapify(a,count) is
(start is assigned the index in a of the last parent node)
start := (count - 2) / 2
while start ≥ 0 do
(sift down the node at index start to the proper place
such that all nodes below the start index are in heap
order)
siftDown(a, start, count-1)
start := start - 1
(after sifting down the root all nodes/elements are in heap order)
function siftDown(a, start, end) is
(end represents the limit of how far down the heap to sift)
root := start
while root * 2 + 1 ≤ end do (While the root has at least one child)
child := root * 2 + 1 (root*2+1 points to the left child)
(If the child has a sibling and the child's value is less than its sibling's...)
if child + 1 ≤ end and a[child] < a[child + 1] then
child := child + 1 (... then point to the right child instead)
if a[root] < a[child] then (out of max-heap order)
swap(a[root], a[child])
root := child (repeat to continue sifting down the child now)
else
return
Write a function to sort a collection of integers using heapsort.
| #ARM_Assembly | ARM Assembly |
/* ARM assembly Raspberry PI */
/* program heapSort.s */
/* look Pseudocode begin this task */
/************************************/
/* Constantes */
/************************************/
.equ STDOUT, 1 @ Linux output console
.equ EXIT, 1 @ Linux syscall
.equ WRITE, 4 @ Linux syscall
/*********************************/
/* Initialized data */
/*********************************/
.data
szMessSortOk: .asciz "Table sorted.\n"
szMessSortNok: .asciz "Table not sorted !!!!!.\n"
sMessResult: .ascii "Value : "
sMessValeur: .fill 11, 1, ' ' @ size => 11
szCarriageReturn: .asciz "\n"
.align 4
iGraine: .int 123456
.equ NBELEMENTS, 10
TableNumber: .int 1,3,6,2,5,9,10,8,4,7
#TableNumber: .int 10,9,8,7,6,5,4,3,2,1
/*********************************/
/* UnInitialized data */
/*********************************/
.bss
/*********************************/
/* code section */
/*********************************/
.text
.global main
main: @ entry of program
1:
ldr r0,iAdrTableNumber @ address number table
mov r1,#NBELEMENTS @ number of élements
bl heapSort
ldr r0,iAdrTableNumber @ address number table
bl displayTable
ldr r0,iAdrTableNumber @ address number table
mov r1,#NBELEMENTS @ number of élements
bl isSorted @ control sort
cmp r0,#1 @ sorted ?
beq 2f
ldr r0,iAdrszMessSortNok @ no !! error sort
bl affichageMess
b 100f
2: @ yes
ldr r0,iAdrszMessSortOk
bl affichageMess
100: @ standard end of the program
mov r0, #0 @ return code
mov r7, #EXIT @ request to exit program
svc #0 @ perform the system call
iAdrsMessValeur: .int sMessValeur
iAdrszCarriageReturn: .int szCarriageReturn
iAdrsMessResult: .int sMessResult
iAdrTableNumber: .int TableNumber
iAdrszMessSortOk: .int szMessSortOk
iAdrszMessSortNok: .int szMessSortNok
/******************************************************************/
/* control sorted table */
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the number of elements > 0 */
/* r0 return 0 if not sorted 1 if sorted */
isSorted:
push {r2-r4,lr} @ save registers
mov r2,#0
ldr r4,[r0,r2,lsl #2]
1:
add r2,#1
cmp r2,r1
movge r0,#1
bge 100f
ldr r3,[r0,r2, lsl #2]
cmp r3,r4
movlt r0,#0
blt 100f
mov r4,r3
b 1b
100:
pop {r2-r4,lr}
bx lr @ return
/******************************************************************/
/* heap sort */
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the number of element */
heapSort:
push {r2,r3,r4,lr} @ save registers
bl heapify @ first place table in max-heap order
sub r3,r1,#1
1:
cmp r3,#0
ble 100f
mov r1,#0 @ swap the root(maximum value) of the heap with the last element of the heap)
mov r2,r3
bl swapElement
sub r3,#1
mov r1,#0
mov r2,r3 @ put the heap back in max-heap order
bl siftDown
b 1b
100:
pop {r2,r3,r4,lr}
bx lr @ return
/******************************************************************/
/* place table in max-heap order */
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the number of element */
heapify:
push {r1,r2,r3,r4,lr} @ save registers
mov r4,r1
sub r3,r1,#2
lsr r3,#1
1:
cmp r3,#0
blt 100f
mov r1,r3
sub r2,r4,#1
bl siftDown
sub r3,#1
b 1b
100:
pop {r1,r2,r3,r4,lr}
bx lr @ return
/******************************************************************/
/* swap two elements of table */
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the first index */
/* r2 contains the second index */
swapElement:
push {r3,r4,lr} @ save registers
ldr r3,[r0,r1,lsl #2] @ swap number on the table
ldr r4,[r0,r2,lsl #2]
str r4,[r0,r1,lsl #2]
str r3,[r0,r2,lsl #2]
100:
pop {r3,r4,lr}
bx lr @ return
/******************************************************************/
/* put the heap back in max-heap order */
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the first index */
/* r2 contains the last index */
siftDown:
push {r1-r7,lr} @ save registers
@ r1 = root = start
mov r3,r2 @ save last index
1:
lsl r4,r1,#1
add r4,#1
cmp r4,r3
bgt 100f
add r5,r4,#1
cmp r5,r3
bgt 2f
ldr r6,[r0,r4,lsl #2] @ compare elements on the table
ldr r7,[r0,r5,lsl #2]
cmp r6,r7
movlt r4,r5
2:
ldr r7,[r0,r4,lsl #2] @ compare elements on the table
ldr r6,[r0,r1,lsl #2] @ root
cmp r6,r7
bge 100f
mov r2,r4 @ and r1 is root
bl swapElement
mov r1,r4 @ root = child
b 1b
100:
pop {r1-r7,lr}
bx lr @ return
/******************************************************************/
/* Display table elements */
/******************************************************************/
/* r0 contains the address of table */
displayTable:
push {r0-r3,lr} @ save registers
mov r2,r0 @ table address
mov r3,#0
1: @ loop display table
ldr r0,[r2,r3,lsl #2]
ldr r1,iAdrsMessValeur @ display value
bl conversion10 @ call function
ldr r0,iAdrsMessResult
bl affichageMess @ display message
add r3,#1
cmp r3,#NBELEMENTS - 1
ble 1b
ldr r0,iAdrszCarriageReturn
bl affichageMess
100:
pop {r0-r3,lr}
bx lr
/******************************************************************/
/* display text with size calculation */
/******************************************************************/
/* r0 contains the address of the message */
affichageMess:
push {r0,r1,r2,r7,lr} @ save registres
mov r2,#0 @ counter length
1: @ loop length calculation
ldrb r1,[r0,r2] @ read octet start position + index
cmp r1,#0 @ if 0 its over
addne r2,r2,#1 @ else add 1 in the length
bne 1b @ and loop
@ so here r2 contains the length of the message
mov r1,r0 @ address message in r1
mov r0,#STDOUT @ code to write to the standard output Linux
mov r7, #WRITE @ code call system "write"
svc #0 @ call systeme
pop {r0,r1,r2,r7,lr} @ restaur des 2 registres */
bx lr @ return
/******************************************************************/
/* Converting a register to a decimal unsigned */
/******************************************************************/
/* r0 contains value and r1 address area */
/* r0 return size of result (no zero final in area) */
/* area size => 11 bytes */
.equ LGZONECAL, 10
conversion10:
push {r1-r4,lr} @ save registers
mov r3,r1
mov r2,#LGZONECAL
1: @ start loop
bl divisionpar10U @ unsigned r0 <- dividende. quotient ->r0 reste -> r1
add r1,#48 @ digit
strb r1,[r3,r2] @ store digit on area
cmp r0,#0 @ stop if quotient = 0
subne r2,#1 @ else previous position
bne 1b @ and loop
@ and move digit from left of area
mov r4,#0
2:
ldrb r1,[r3,r2]
strb r1,[r3,r4]
add r2,#1
add r4,#1
cmp r2,#LGZONECAL
ble 2b
@ and move spaces in end on area
mov r0,r4 @ result length
mov r1,#' ' @ space
3:
strb r1,[r3,r4] @ store space in area
add r4,#1 @ next position
cmp r4,#LGZONECAL
ble 3b @ loop if r4 <= area size
100:
pop {r1-r4,lr} @ restaur registres
bx lr @return
/***************************************************/
/* division par 10 unsigned */
/***************************************************/
/* r0 dividende */
/* r0 quotient */
/* r1 remainder */
divisionpar10U:
push {r2,r3,r4, lr}
mov r4,r0 @ save value
//mov r3,#0xCCCD @ r3 <- magic_number lower raspberry 3
//movt r3,#0xCCCC @ r3 <- magic_number higter raspberry 3
ldr r3,iMagicNumber @ r3 <- magic_number raspberry 1 2
umull r1, r2, r3, r0 @ r1<- Lower32Bits(r1*r0) r2<- Upper32Bits(r1*r0)
mov r0, r2, LSR #3 @ r2 <- r2 >> shift 3
add r2,r0,r0, lsl #2 @ r2 <- r0 * 5
sub r1,r4,r2, lsl #1 @ r1 <- r4 - (r2 * 2) = r4 - (r0 * 10)
pop {r2,r3,r4,lr}
bx lr @ leave function
iMagicNumber: .int 0xCCCCCCCD
|
http://rosettacode.org/wiki/Sorting_algorithms/Merge_sort | Sorting algorithms/Merge sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
The merge sort is a recursive sort of order n*log(n).
It is notable for having a worst case and average complexity of O(n*log(n)), and a best case complexity of O(n) (for pre-sorted input).
The basic idea is to split the collection into smaller groups by halving it until the groups only have one element or no elements (which are both entirely sorted groups).
Then merge the groups back together so that their elements are in order.
This is how the algorithm gets its divide and conquer description.
Task
Write a function to sort a collection of integers using the merge sort.
The merge sort algorithm comes in two parts:
a sort function and
a merge function
The functions in pseudocode look like this:
function mergesort(m)
var list left, right, result
if length(m) ≤ 1
return m
else
var middle = length(m) / 2
for each x in m up to middle - 1
add x to left
for each x in m at and after middle
add x to right
left = mergesort(left)
right = mergesort(right)
if last(left) ≤ first(right)
append right to left
return left
result = merge(left, right)
return result
function merge(left,right)
var list result
while length(left) > 0 and length(right) > 0
if first(left) ≤ first(right)
append first(left) to result
left = rest(left)
else
append first(right) to result
right = rest(right)
if length(left) > 0
append rest(left) to result
if length(right) > 0
append rest(right) to result
return result
See also
the Wikipedia entry: merge sort
Note: better performance can be expected if, rather than recursing until length(m) ≤ 1, an insertion sort is used for length(m) smaller than some threshold larger than 1. However, this complicates the example code, so it is not shown here.
| #AppleScript | AppleScript | (*
In-place, iterative binary merge sort
Merge sort algorithm: John von Neumann, 1945.
Convenience terminology used here:
run: one of two adjacent source-list ranges containing ordered items for merging.
block: range in the destination list to which two runs are merged.
*)
on mergeSort(theList, l, r) -- Sort items l thru r of theList.
set listLength to (count theList)
if (listLength < 2) then return
-- Convert negative and/or transposed range indices.
if (l < 0) then set l to listLength + l + 1
if (r < 0) then set r to listLength + r + 1
if (l > r) then set {l, r} to {r, l}
-- Script object containing the input list and the sort range indices.
script main
property lst : theList
property l : missing value
property r : missing value
end script
set {main's l, main's r} to {l, r}
-- Just swap adjacent items as necessary on the first pass.
-- (Short insertion sorts would be better, to create larger initial runs.)
repeat with j from (l + 1) to r by 2
set i to j - 1
set lv to main's lst's item i
set rv to main's lst's item j
if (lv > rv) then
set main's lst's item i to rv
set main's lst's item j to lv
end if
end repeat
set rangeLength to r - l + 1
if (rangeLength < 3) then return -- That's all if fewer than three items to sort.
-- Script object to alternate with the one above as the source and destination for the
-- merges. Its list need only contain the items from the sort range as ordered so far.
script aux
property lst : main's lst's items l thru r
property l : 1
property r : rangeLength
end script
-- Work out how many merging passes will be needed and set the script objects' initial
-- source and destination roles so that the final pass will merge back to the original list.
set passesToDo to 0
set blockSize to 2
repeat while (blockSize < rangeLength)
set passesToDo to passesToDo + 1
set blockSize to blockSize + blockSize
end repeat
set {srce, dest} to {{main, aux}, {aux, main}}'s item (passesToDo mod 2 + 1)
-- Do the remaining passes, doubling the run and block sizes on each pass.
-- (The end set in each pass will usually be truncated.)
set blockSize to 2
repeat passesToDo times -- Per pass.
set runSize to blockSize
set blockSize to blockSize + blockSize
set k to (dest's l) - 1 -- Destination traversal index.
repeat with leftStart from srce's l to srce's r by blockSize -- Per merge.
set blockEnd to k + blockSize
if (blockEnd comes after dest's r) then set blockEnd to dest's r
set i to leftStart -- Left run traversal index.
set leftEnd to leftStart + runSize - 1
if (leftEnd comes before srce's r) then
set j to leftEnd + 1 -- Right run traversal index.
set rightEnd to leftEnd + runSize
if (rightEnd comes after srce's r) then set rightEnd to srce's r
-- Merge process:
set lv to srce's lst's item i
set rv to srce's lst's item j
repeat with k from (k + 1) to blockEnd
if (lv > rv) then
set dest's lst's item k to rv
if (j = rightEnd) then exit repeat -- Right run used up.
set j to j + 1
set rv to srce's lst's item j
else
set dest's lst's item k to lv
if (i = leftEnd) then -- Left run used up.
set i to j
exit repeat
end if
set i to i + 1
set lv to srce's lst's item i
end if
end repeat
end if
-- Use up the remaining items from the not-yet-exhausted run.
repeat with k from (k + 1) to blockEnd
set dest's lst's item k to srce's lst's item i
set i to i + 1
end repeat
end repeat -- Per merge.
-- Switch source and destination scripts for the next pass.
tell srce
set srce to dest
set dest to it
end tell
end repeat -- Per pass.
return -- nothing
end mergeSort
property sort : mergeSort
-- Demo:
local aList
set aList to {22, 15, 98, 82, 22, 4, 58, 70, 80, 38, 49, 48, 46, 54, 93, 8, 54, 2, 72, 84, 86, 76, 53, 37, 90}
sort(aList, 1, -1) -- Sort items 1 thru -1 of aList.
return aList |
http://rosettacode.org/wiki/Sorting_algorithms/Pancake_sort | Sorting algorithms/Pancake sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array of integers (of any convenient size) into ascending order using Pancake sorting.
In short, instead of individual elements being sorted, the only operation allowed is to "flip" one end of the list, like so:
Before: 6 7 8 9 2 5 3 4 1
After: 9 8 7 6 2 5 3 4 1
Only one end of the list can be flipped; this should be the low end, but the high end is okay if it's easier to code or works better, but it must be the same end for the entire solution. (The end flipped can't be arbitrarily changed.)
Show both the initial, unsorted list and the final sorted list.
(Intermediate steps during sorting are optional.)
Optimizations are optional (but recommended).
Related tasks
Number reversal game
Topswops
Also see
Wikipedia article: pancake sorting.
| #Kotlin | Kotlin | fun pancakeSort(a: IntArray) {
/** Returns the index of the highest number in the range 0 until n. */
fun indexOfMax(n: Int): Int = (0 until n).maxByOrNull{ a[it] }!!
/** Flips the elements in the range 0 .. n. */
fun flip(index: Int) {
a.reverse(0, index + 1)
}
for (n in a.size downTo 2) { // successively reduce size of array by 1
val index = indexOfMax(n) // find index of largest
if (index != n - 1) { // if it's not already at the end
if (index > 0) { // if it's not already at the beginning
flip(index) // move largest to beginning
println("${a.contentToString()} after flipping first ${index + 1}")
}
flip(n - 1) // move largest to end
println("${a.contentToString()} after flipping first $n")
}
}
}
fun main() {
val a = intArrayOf(7, 6, 9, 2, 4, 8, 1, 3, 5)
println("${a.contentToString()} initially")
pancakeSort(a)
} |
http://rosettacode.org/wiki/Sorting_algorithms/Pancake_sort | Sorting algorithms/Pancake sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array of integers (of any convenient size) into ascending order using Pancake sorting.
In short, instead of individual elements being sorted, the only operation allowed is to "flip" one end of the list, like so:
Before: 6 7 8 9 2 5 3 4 1
After: 9 8 7 6 2 5 3 4 1
Only one end of the list can be flipped; this should be the low end, but the high end is okay if it's easier to code or works better, but it must be the same end for the entire solution. (The end flipped can't be arbitrarily changed.)
Show both the initial, unsorted list and the final sorted list.
(Intermediate steps during sorting are optional.)
Optimizations are optional (but recommended).
Related tasks
Number reversal game
Topswops
Also see
Wikipedia article: pancake sorting.
| #Lua | Lua | -- Initialisation
math.randomseed(os.time())
numList = {step = 0, sorted = 0}
-- Create list of n random values
function numList:build (n)
self.values = {}
for i = 1, n do self.values[i] = math.random(-100, 100) end
end
-- Return boolean indicating whether the list is in order
function numList:isSorted ()
for i = 2, #self.values do
if self.values[i] < self.values[i - 1] then return false end
end
print("Finished!")
return true
end
-- Display list of numbers on one line
function numList:show ()
if self.step == 0 then
io.write("Initial state:\t")
else
io.write("After step " .. self.step .. ":\t")
end
for _, v in ipairs(self.values) do io.write(v .. " ") end
print()
end
-- Reverse n values from the left
function numList:reverse (n)
local flipped = {}
for i, v in ipairs(self.values) do
if i > n then
flipped[i] = v
else
flipped[i] = self.values[n + 1 - i]
end
end
self.values = flipped
end
-- Perform one flip of a pancake sort
function numList:pancake ()
local maxPos = 1
for i = 1, #self.values - self.sorted do
if self.values[i] > self.values[maxPos] then maxPos = i end
end
if maxPos == 1 then
numList:reverse(#self.values - self.sorted)
self.sorted = self.sorted + 1
else
numList:reverse(maxPos)
end
self.step = self.step + 1
end
-- Main procedure
numList:build(10)
numList:show()
repeat
numList:pancake()
numList:show()
until numList:isSorted()
|
http://rosettacode.org/wiki/Sorting_algorithms/Stooge_sort | Sorting algorithms/Stooge sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Stooge sort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Show the Stooge Sort for an array of integers.
The Stooge Sort algorithm is as follows:
algorithm stoogesort(array L, i = 0, j = length(L)-1)
if L[j] < L[i] then
L[i] ↔ L[j]
if j - i > 1 then
t := (j - i + 1)/3
stoogesort(L, i , j-t)
stoogesort(L, i+t, j )
stoogesort(L, i , j-t)
return L
| #PowerBASIC | PowerBASIC | %arraysize = 10
SUB stoogesort (L() AS LONG, i AS LONG, j AS LONG)
IF L(j) < L(i) THEN SWAP L(i), L(j)
IF (j - i) > 1 THEN
DIM t AS LONG
t = (j - i + 1) / 3
stoogesort L(), i, j - t
stoogesort L(), i + t, j
stoogesort L(), i, j - t
END IF
END SUB
FUNCTION PBMAIN () AS LONG
RANDOMIZE TIMER
DIM x(%arraysize) AS LONG
DIM i AS LONG, s AS STRING
s = "Before: "
FOR i = 0 TO %arraysize
x(i) = INT(RND * 100)
s = s & STR$(x(i)) & " "
NEXT
stoogesort x(), 0, %arraysize
#IF %DEF(%PB_CC32)
PRINT s
s = ""
#ELSE
s = s & $CRLF
#ENDIF
s = s & "After: "
FOR i = 0 TO %arraysize
s = s & STR$(x(i)) & " "
NEXT
? s
END FUNCTION |
http://rosettacode.org/wiki/Sorting_algorithms/Stooge_sort | Sorting algorithms/Stooge sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Stooge sort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Show the Stooge Sort for an array of integers.
The Stooge Sort algorithm is as follows:
algorithm stoogesort(array L, i = 0, j = length(L)-1)
if L[j] < L[i] then
L[i] ↔ L[j]
if j - i > 1 then
t := (j - i + 1)/3
stoogesort(L, i , j-t)
stoogesort(L, i+t, j )
stoogesort(L, i , j-t)
return L
| #PowerShell | PowerShell | Function StoogeSort( [Int32[]] $L )
{
$i = 0
$j = $L.length-1
if( $L[$j] -lt $L[$i] )
{
$L[$i] = $L[$i] -bxor $L[$j]
$L[$j] = $L[$i] -bxor $L[$j]
$L[$i] = $L[$i] -bxor $L[$j]
}
if( $j -gt 1 )
{
$t = [int] ( ( $j + 1 ) / 3 )
$k = $j - $t + 1
[Array]::Copy( [Int32[]] ( StoogeSort( $L[0..( $j - $t ) ] ) ), $L, $k )
[Array]::ConstrainedCopy( [Int32[]] ( StoogeSort( $L[$t..$j ] ) ), 0, $L, $t, $k )
[Array]::Copy( [Int32[]] ( StoogeSort( $L[0..( $j - $t ) ] ) ), $L, $k )
}
$L
}
StoogeSort 9, 7, 5, 3, 1, 2, 4, 6, 8 |
http://rosettacode.org/wiki/Sorting_algorithms/Selection_sort | Sorting algorithms/Selection sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array (or list) of elements using the Selection sort algorithm.
It works as follows:
First find the smallest element in the array and exchange it with the element in the first position, then find the second smallest element and exchange it with the element in the second position, and continue in this way until the entire array is sorted.
Its asymptotic complexity is O(n2) making it inefficient on large arrays.
Its primary purpose is for when writing data is very expensive (slow) when compared to reading, eg. writing to flash memory or EEPROM.
No other sorting algorithm has less data movement.
References
Rosetta Code: O (complexity).
Wikipedia: Selection sort.
Wikipedia: [Big O notation].
| #Haxe | Haxe | class SelectionSort {
@:generic
public static function sort<T>(arr:Array<T>) {
var len = arr.length;
for (index in 0...len) {
var minIndex = index;
for (remainingIndex in (index+1)...len) {
if (Reflect.compare(arr[minIndex], arr[remainingIndex]) > 0)
minIndex = remainingIndex;
}
if (index != minIndex) {
var temp = arr[index];
arr[index] = arr[minIndex];
arr[minIndex] = temp;
}
}
}
}
class Main {
static function main() {
var integerArray = [1, 10, 2, 5, -1, 5, -19, 4, 23, 0];
var floatArray = [1.0, -3.2, 5.2, 10.8, -5.7, 7.3,
3.5, 0.0, -4.1, -9.5];
var stringArray = ['We', 'hold', 'these', 'truths', 'to',
'be', 'self-evident', 'that', 'all',
'men', 'are', 'created', 'equal'];
Sys.println('Unsorted Integers:' + integerArray);
SelectionSort.sort(integerArray);
Sys.println('Sorted Integers: ' + integerArray);
Sys.println('Unsorted Floats: ' + floatArray);
SelectionSort.sort(floatArray);
Sys.println('Sorted Floats: ' + floatArray);
Sys.println('Unsorted Strings: ' + stringArray);
SelectionSort.sort(stringArray);
Sys.println('Sorted Strings: ' + stringArray);
}
} |
http://rosettacode.org/wiki/Sorting_algorithms/Selection_sort | Sorting algorithms/Selection sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array (or list) of elements using the Selection sort algorithm.
It works as follows:
First find the smallest element in the array and exchange it with the element in the first position, then find the second smallest element and exchange it with the element in the second position, and continue in this way until the entire array is sorted.
Its asymptotic complexity is O(n2) making it inefficient on large arrays.
Its primary purpose is for when writing data is very expensive (slow) when compared to reading, eg. writing to flash memory or EEPROM.
No other sorting algorithm has less data movement.
References
Rosetta Code: O (complexity).
Wikipedia: Selection sort.
Wikipedia: [Big O notation].
| #Icon_and_Unicon | Icon and Unicon | procedure main() #: demonstrate various ways to sort a list and string
demosort(selectionsort,[3, 14, 1, 5, 9, 2, 6, 3],"qwerty")
end
procedure selectionsort(X,op) #: return sorted list ascending(or descending)
local i,m
op := sortop(op,X) # select how and what we sort
every i := 1 to *X-1 do {
m := i
every j := i + 1 to *X do
if op(X[j],X[m]) then m := j # find X that belongs @i low (or high)
X[m ~= i] :=: X[m]
}
return X
end |
http://rosettacode.org/wiki/Soundex | Soundex | Soundex is an algorithm for creating indices for words based on their pronunciation.
Task
The goal is for homophones to be encoded to the same representation so that they can be matched despite minor differences in spelling (from the soundex Wikipedia article).
Caution
There is a major issue in many of the implementations concerning the separation of two consonants that have the same soundex code! According to the official Rules [[1]]. So check for instance if Ashcraft is coded to A-261.
If a vowel (A, E, I, O, U) separates two consonants that have the same soundex code, the consonant to the right of the vowel is coded. Tymczak is coded as T-522 (T, 5 for the M, 2 for the C, Z ignored (see "Side-by-Side" rule above), 2 for the K). Since the vowel "A" separates the Z and K, the K is coded.
If "H" or "W" separate two consonants that have the same soundex code, the consonant to the right of the vowel is not coded. Example: Ashcraft is coded A-261 (A, 2 for the S, C ignored, 6 for the R, 1 for the F). It is not coded A-226.
| #JavaScript | JavaScript | var soundex = function (s) {
var a = s.toLowerCase().split('')
f = a.shift(),
r = '',
codes = {
a: '', e: '', i: '', o: '', u: '',
b: 1, f: 1, p: 1, v: 1,
c: 2, g: 2, j: 2, k: 2, q: 2, s: 2, x: 2, z: 2,
d: 3, t: 3,
l: 4,
m: 5, n: 5,
r: 6
};
r = f +
a
.map(function (v, i, a) { return codes[v] })
.filter(function (v, i, a) { return ((i === 0) ? v !== codes[f] : v !== a[i - 1]); })
.join('');
return (r + '000').slice(0, 4).toUpperCase();
};
var tests = {
"Soundex": "S532",
"Example": "E251",
"Sownteks": "S532",
"Ekzampul": "E251",
"Euler": "E460",
"Gauss": "G200",
"Hilbert": "H416",
"Knuth": "K530",
"Lloyd": "L300",
"Lukasiewicz": "L222",
"Ellery": "E460",
"Ghosh": "G200",
"Heilbronn": "H416",
"Kant": "K530",
"Ladd": "L300",
"Lissajous": "L222",
"Wheaton": "W350",
"Ashcraft": "A226",
"Burroughs": "B622",
"Burrows": "B620",
"O'Hara": "O600"
};
for (var i in tests)
if (tests.hasOwnProperty(i)) {
console.log(
i +
' \t' +
tests[i] +
'\t' +
soundex(i) +
'\t' +
(soundex(i) === tests[i])
);
}
// Soundex S532 S532 true
// Example E251 E251 true
// Sownteks S532 S532 true
// Ekzampul E251 E251 true
// Euler E460 E460 true
// Gauss G200 G200 true
// Hilbert H416 H416 true
// Knuth K530 K530 true
// Lloyd L300 L300 true
// Lukasiewicz L222 L222 true
// Ellery E460 E460 true
// Ghosh G200 G200 true
// Heilbronn H416 H416 true
// Kant K530 K530 true
// Ladd L300 L300 true
// Lissajous L222 L222 true
// Wheaton W350 W350 true
// Ashcraft A226 A226 true
// Burroughs B622 B622 true
// Burrows B620 B620 true
// O'Hara O600 O600 true |
http://rosettacode.org/wiki/Sorting_algorithms/Shell_sort | Sorting algorithms/Shell sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array of elements using the Shell sort algorithm, a diminishing increment sort.
The Shell sort (also known as Shellsort or Shell's method) is named after its inventor, Donald Shell, who published the algorithm in 1959.
Shell sort is a sequence of interleaved insertion sorts based on an increment sequence.
The increment size is reduced after each pass until the increment size is 1.
With an increment size of 1, the sort is a basic insertion sort, but by this time the data is guaranteed to be almost sorted, which is insertion sort's "best case".
Any sequence will sort the data as long as it ends in 1, but some work better than others.
Empirical studies have shown a geometric increment sequence with a ratio of about 2.2 work well in practice.
[1]
Other good sequences are found at the On-Line Encyclopedia of Integer Sequences.
| #Perl | Perl | sub shell_sort {
my (@a, $h, $i, $j, $k) = @_;
for ($h = @a; $h = int $h / 2;) {
for $i ($h .. $#a) {
$k = $a[$i];
for ($j = $i; $j >= $h && $k < $a[$j - $h]; $j -= $h) {
$a[$j] = $a[$j - $h];
}
$a[$j] = $k;
}
}
@a;
}
my @a = map int rand 100, 1 .. $ARGV[0] || 10;
say "@a";
@a = shell_sort @a;
say "@a";
|
http://rosettacode.org/wiki/Stack | Stack |
Data Structure
This illustrates a data structure, a means of storing data within a program.
You may see other such structures in the Data Structures category.
A stack is a container of elements with last in, first out access policy. Sometimes it also called LIFO.
The stack is accessed through its top.
The basic stack operations are:
push stores a new element onto the stack top;
pop returns the last pushed stack element, while removing it from the stack;
empty tests if the stack contains no elements.
Sometimes the last pushed stack element is made accessible for immutable access (for read) or mutable access (for write):
top (sometimes called peek to keep with the p theme) returns the topmost element without modifying the stack.
Stacks allow a very simple hardware implementation.
They are common in almost all processors.
In programming, stacks are also very popular for their way (LIFO) of resource management, usually memory.
Nested scopes of language objects are naturally implemented by a stack (sometimes by multiple stacks).
This is a classical way to implement local variables of a re-entrant or recursive subprogram. Stacks are also used to describe a formal computational framework.
See stack machine.
Many algorithms in pattern matching, compiler construction (e.g. recursive descent parsers), and machine learning (e.g. based on tree traversal) have a natural representation in terms of stacks.
Task
Create a stack supporting the basic operations: push, pop, empty.
See also
Array
Associative array: Creation, Iteration
Collections
Compound data type
Doubly-linked list: Definition, Element definition, Element insertion, List Traversal, Element Removal
Linked list
Queue: Definition, Usage
Set
Singly-linked list: Element definition, Element insertion, List Traversal, Element Removal
Stack
| #Nanoquery | Nanoquery | class Stack
declare internalList
// constructor
def Stack()
internalList = list()
end
def push(val)
internalList.append(val)
end
def pop()
val = internalList[int(len($internalList) - 1)]
internalList.remove(val)
return val
end
def empty()
return len(internalList) = 0
end
end |
http://rosettacode.org/wiki/Spiral_matrix | Spiral matrix | Task
Produce a spiral array.
A spiral array is a square arrangement of the first N2 natural numbers, where the
numbers increase sequentially as you go around the edges of the array spiraling inwards.
For example, given 5, produce this array:
0 1 2 3 4
15 16 17 18 5
14 23 24 19 6
13 22 21 20 7
12 11 10 9 8
Related tasks
Zig-zag matrix
Identity_matrix
Ulam_spiral_(for_primes)
| #Phix | Phix | with javascript_semantics
integer n = 6, x = 1, y = 0, counter = 0,
len = n, dx = 0, dy = 1
string fmt = sprintf("%%%dd",length(sprintf("%d",n*n)))
sequence m = repeat(repeat("??",n),n)
for i=1 to 2*n do -- 2n runs..
for j=1 to len do -- of a length...
x += dx
y += dy
m[x][y] = sprintf(fmt,counter)
counter += 1
end for
len -= odd(i) -- ..-1 every other
{dx,dy} = {dy,-dx} -- in new direction
end for
printf(1,"%s\n",{join(apply(m,join),"\n")})
|
http://rosettacode.org/wiki/Sorting_algorithms/Radix_sort | Sorting algorithms/Radix sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an integer array with the radix sort algorithm.
The primary purpose is to complete the characterization of sort algorithms task.
| #Rust | Rust |
fn merge(in1: &[i32], in2: &[i32], out: &mut [i32]) {
let (left, right) = out.split_at_mut(in1.len());
left.clone_from_slice(in1);
right.clone_from_slice(in2);
}
// least significant digit radix sort
fn radix_sort(data: &mut [i32]) {
for bit in 0..31 {
// types of small and big is Vec<i32>.
// It will be infered from the next call of merge function.
let (small, big): (Vec<_>, Vec<_>) = data.iter().partition(|&&x| (x >> bit) & 1 == 0);
merge(&small, &big, data);
}
// last bit is sign
let (negative, positive): (Vec<_>, Vec<_>) = data.iter().partition(|&&x| x < 0);
merge(&negative, &positive, data);
}
fn main() {
let mut data = [170, 45, 75, -90, -802, 24, 2, 66, -17, 2];
println!("Before: {:?}", data);
radix_sort(&mut data);
println!("After: {:?}", data);
}
|
http://rosettacode.org/wiki/Sorting_algorithms/Radix_sort | Sorting algorithms/Radix sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an integer array with the radix sort algorithm.
The primary purpose is to complete the characterization of sort algorithms task.
| #Scala | Scala | object RadixSort extends App {
def sort(toBeSort: Array[Int]): Array[Int] = { // Loop for every bit in the integers
var arr = toBeSort
for (shift <- Integer.SIZE - 1 until -1 by -1) { // The array to put the partially sorted array into
val tmp = new Array[Int](arr.length)
// The number of 0s
var j = 0
// Move the 0s to the new array, and the 1s to the old one
for (i <- arr.indices) // If there is a 1 in the bit we are testing, the number will be negative
// If this is the last bit, negative numbers are actually lower
if ((shift == 0) == (arr(i) << shift >= 0)) arr(i - j) = arr(i)
else {
tmp(j) = arr(i)
j += 1
}
// Copy over the 1s from the old array
arr.copyToArray(tmp, j, arr.length - j)
// And now the tmp array gets switched for another round of sorting
arr = tmp
}
arr
}
println(sort(Array(170, 45, 75, -90, -802, 24, 2, 66)).mkString(", "))
} |
http://rosettacode.org/wiki/Sorting_algorithms/Quicksort | Sorting algorithms/Quicksort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Quicksort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Sort an array (or list) elements using the quicksort algorithm.
The elements must have a strict weak order and the index of the array can be of any discrete type.
For languages where this is not possible, sort an array of integers.
Quicksort, also known as partition-exchange sort, uses these steps.
Choose any element of the array to be the pivot.
Divide all other elements (except the pivot) into two partitions.
All elements less than the pivot must be in the first partition.
All elements greater than the pivot must be in the second partition.
Use recursion to sort both partitions.
Join the first sorted partition, the pivot, and the second sorted partition.
The best pivot creates partitions of equal length (or lengths differing by 1).
The worst pivot creates an empty partition (for example, if the pivot is the first or last element of a sorted array).
The run-time of Quicksort ranges from O(n log n) with the best pivots, to O(n2) with the worst pivots, where n is the number of elements in the array.
This is a simple quicksort algorithm, adapted from Wikipedia.
function quicksort(array)
less, equal, greater := three empty arrays
if length(array) > 1
pivot := select any element of array
for each x in array
if x < pivot then add x to less
if x = pivot then add x to equal
if x > pivot then add x to greater
quicksort(less)
quicksort(greater)
array := concatenate(less, equal, greater)
A better quicksort algorithm works in place, by swapping elements within the array, to avoid the memory allocation of more arrays.
function quicksort(array)
if length(array) > 1
pivot := select any element of array
left := first index of array
right := last index of array
while left ≤ right
while array[left] < pivot
left := left + 1
while array[right] > pivot
right := right - 1
if left ≤ right
swap array[left] with array[right]
left := left + 1
right := right - 1
quicksort(array from first index to right)
quicksort(array from left to last index)
Quicksort has a reputation as the fastest sort. Optimized variants of quicksort are common features of many languages and libraries. One often contrasts quicksort with merge sort, because both sorts have an average time of O(n log n).
"On average, mergesort does fewer comparisons than quicksort, so it may be better when complicated comparison routines are used. Mergesort also takes advantage of pre-existing order, so it would be favored for using sort() to merge several sorted arrays. On the other hand, quicksort is often faster for small arrays, and on arrays of a few distinct values, repeated many times." — http://perldoc.perl.org/sort.html
Quicksort is at one end of the spectrum of divide-and-conquer algorithms, with merge sort at the opposite end.
Quicksort is a conquer-then-divide algorithm, which does most of the work during the partitioning and the recursive calls. The subsequent reassembly of the sorted partitions involves trivial effort.
Merge sort is a divide-then-conquer algorithm. The partioning happens in a trivial way, by splitting the input array in half. Most of the work happens during the recursive calls and the merge phase.
With quicksort, every element in the first partition is less than or equal to every element in the second partition. Therefore, the merge phase of quicksort is so trivial that it needs no mention!
This task has not specified whether to allocate new arrays, or sort in place. This task also has not specified how to choose the pivot element. (Common ways to are to choose the first element, the middle element, or the median of three elements.) Thus there is a variety among the following implementations.
| #Clojure | Clojure | (defn qsort [L]
(if (empty? L)
'()
(let [[pivot & L2] L]
(lazy-cat (qsort (for [y L2 :when (< y pivot)] y))
(list pivot)
(qsort (for [y L2 :when (>= y pivot)] y)))))) |
http://rosettacode.org/wiki/Sorting_algorithms/Patience_sort | Sorting algorithms/Patience sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Sort an array of numbers (of any convenient size) into ascending order using Patience sorting.
Related task
Longest increasing subsequence
| #Perl | Perl | sub patience_sort {
my @s = [shift];
for my $card (@_) {
my @t = grep { $_->[-1] > $card } @s;
if (@t) { push @{shift(@t)}, $card }
else { push @s, [$card] }
}
my @u;
while (my @v = grep @$_, @s) {
my $value = (my $min = shift @v)->[-1];
for (@v) {
($min, $value) =
($_, $_->[-1]) if $_->[-1] < $value
}
push @u, pop @$min;
}
return @u
}
print join ' ', patience_sort qw(4 3 6 2 -1 13 12 9);
|
http://rosettacode.org/wiki/Sorting_algorithms/Insertion_sort | Sorting algorithms/Insertion sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Insertion sort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
An O(n2) sorting algorithm which moves elements one at a time into the correct position.
The algorithm consists of inserting one element at a time into the previously sorted part of the array, moving higher ranked elements up as necessary.
To start off, the first (or smallest, or any arbitrary) element of the unsorted array is considered to be the sorted part.
Although insertion sort is an O(n2) algorithm, its simplicity, low overhead, good locality of reference and efficiency make it a good choice in two cases:
small n,
as the final finishing-off algorithm for O(n logn) algorithms such as mergesort and quicksort.
The algorithm is as follows (from wikipedia):
function insertionSort(array A)
for i from 1 to length[A]-1 do
value := A[i]
j := i-1
while j >= 0 and A[j] > value do
A[j+1] := A[j]
j := j-1
done
A[j+1] = value
done
Writing the algorithm for integers will suffice.
| #C | C | #include <stdio.h>
void insertion_sort(int*, const size_t);
void insertion_sort(int *a, const size_t n) {
for(size_t i = 1; i < n; ++i) {
int key = a[i];
size_t j = i;
while( (j > 0) && (key < a[j - 1]) ) {
a[j] = a[j - 1];
--j;
}
a[j] = key;
}
}
int main (int argc, char** argv) {
int a[] = {4, 65, 2, -31, 0, 99, 2, 83, 782, 1};
const size_t n = sizeof(a) / sizeof(a[0]) ; // array extent
for (size_t i = 0; i < n; i++)
printf("%d%s", a[i], (i == (n - 1))? "\n" : " ");
insertion_sort(a, n);
for (size_t i = 0; i < n; i++)
printf("%d%s", a[i], (i == (n - 1))? "\n" : " ");
return 0;
}
|
http://rosettacode.org/wiki/Sorting_algorithms/Permutation_sort | Sorting algorithms/Permutation sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Implement a permutation sort, which proceeds by generating the possible permutations
of the input array/list until discovering the sorted one.
Pseudocode:
while not InOrder(list) do
nextPermutation(list)
done
| #Sidef | Sidef | func psort(x, d=x.end) {
if (d.is_zero) {
for i in (1 .. x.end) {
(x[i] < x[i-1]) && return false;
}
return true;
}
(d+1).times {
x.prepend(x.splice(d, 1)...);
x[d] < x[d-1] && next;
psort(x, d-1) && return true;
}
return false;
}
var a = 10.of { 100.irand };
say "Before:\t#{a}";
psort(a);
say "After:\t#{a}"; |
http://rosettacode.org/wiki/Sorting_algorithms/Permutation_sort | Sorting algorithms/Permutation sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Implement a permutation sort, which proceeds by generating the possible permutations
of the input array/list until discovering the sorted one.
Pseudocode:
while not InOrder(list) do
nextPermutation(list)
done
| #Tcl | Tcl | package require Tcl 8.5
package require struct::list
proc inorder {list} {::tcl::mathop::<= {*}$list}
proc permutationsort {list} {
while { ! [inorder $list]} {
set list [struct::list nextperm $list]
}
return $list
} |
http://rosettacode.org/wiki/Sorting_algorithms/Heapsort | Sorting algorithms/Heapsort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Heapsort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Heapsort is an in-place sorting algorithm with worst case and average complexity of O(n logn).
The basic idea is to turn the array into a binary heap structure, which has the property that it allows efficient retrieval and removal of the maximal element.
We repeatedly "remove" the maximal element from the heap, thus building the sorted list from back to front.
A heap sort requires random access, so can only be used on an array-like data structure.
Pseudocode:
function heapSort(a, count) is
input: an unordered array a of length count
(first place a in max-heap order)
heapify(a, count)
end := count - 1
while end > 0 do
(swap the root(maximum value) of the heap with the
last element of the heap)
swap(a[end], a[0])
(decrement the size of the heap so that the previous
max value will stay in its proper place)
end := end - 1
(put the heap back in max-heap order)
siftDown(a, 0, end)
function heapify(a,count) is
(start is assigned the index in a of the last parent node)
start := (count - 2) / 2
while start ≥ 0 do
(sift down the node at index start to the proper place
such that all nodes below the start index are in heap
order)
siftDown(a, start, count-1)
start := start - 1
(after sifting down the root all nodes/elements are in heap order)
function siftDown(a, start, end) is
(end represents the limit of how far down the heap to sift)
root := start
while root * 2 + 1 ≤ end do (While the root has at least one child)
child := root * 2 + 1 (root*2+1 points to the left child)
(If the child has a sibling and the child's value is less than its sibling's...)
if child + 1 ≤ end and a[child] < a[child + 1] then
child := child + 1 (... then point to the right child instead)
if a[root] < a[child] then (out of max-heap order)
swap(a[root], a[child])
root := child (repeat to continue sifting down the child now)
else
return
Write a function to sort a collection of integers using heapsort.
| #Arturo | Arturo | siftDown: function [items, start, ending][
root: start
a: new items
while [ending > 1 + 2 * root][
child: 1 + 2 * root
if and? ending > child + 1
a\[child+1] > a\[child] -> child: child + 1
if? a\[root] < a\[child][
tmp: a\[child]
a\[child]: a\[root]
a\[root]: tmp
root: child
]
else -> return a
]
return a
]
heapSort: function [items][
b: new items
count: size b
loop ((count-2)/2) .. 0 'start -> b: siftDown b start count
loop (count-1) .. 1 'ending [
tmp: b\[ending]
b\[ending]: b\0
b\0: tmp
b: siftDown b 0 ending
]
return b
]
print heapSort [3 1 2 8 5 7 9 4 6] |
http://rosettacode.org/wiki/Sorting_algorithms/Merge_sort | Sorting algorithms/Merge sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
The merge sort is a recursive sort of order n*log(n).
It is notable for having a worst case and average complexity of O(n*log(n)), and a best case complexity of O(n) (for pre-sorted input).
The basic idea is to split the collection into smaller groups by halving it until the groups only have one element or no elements (which are both entirely sorted groups).
Then merge the groups back together so that their elements are in order.
This is how the algorithm gets its divide and conquer description.
Task
Write a function to sort a collection of integers using the merge sort.
The merge sort algorithm comes in two parts:
a sort function and
a merge function
The functions in pseudocode look like this:
function mergesort(m)
var list left, right, result
if length(m) ≤ 1
return m
else
var middle = length(m) / 2
for each x in m up to middle - 1
add x to left
for each x in m at and after middle
add x to right
left = mergesort(left)
right = mergesort(right)
if last(left) ≤ first(right)
append right to left
return left
result = merge(left, right)
return result
function merge(left,right)
var list result
while length(left) > 0 and length(right) > 0
if first(left) ≤ first(right)
append first(left) to result
left = rest(left)
else
append first(right) to result
right = rest(right)
if length(left) > 0
append rest(left) to result
if length(right) > 0
append rest(right) to result
return result
See also
the Wikipedia entry: merge sort
Note: better performance can be expected if, rather than recursing until length(m) ≤ 1, an insertion sort is used for length(m) smaller than some threshold larger than 1. However, this complicates the example code, so it is not shown here.
| #ARM_Assembly | ARM Assembly |
/* ARM assembly Raspberry PI */
/* program mergeSort.s */
/* REMARK 1 : this program use routines in a include file
see task Include a file language arm assembly
for the routine affichageMess conversion10
see at end of this program the instruction include */
/* for constantes see task include a file in arm assembly */
/************************************/
/* Constantes */
/************************************/
.include "../constantes.inc"
/*********************************/
/* Initialized data */
/*********************************/
.data
szMessSortOk: .asciz "Table sorted.\n"
szMessSortNok: .asciz "Table not sorted !!!!!.\n"
sMessResult: .asciz "Value : @ \n"
szCarriageReturn: .asciz "\n"
.align 4
#TableNumber: .int 1,11,3,6,2,5,9,10,8,4,7
TableNumber: .int 10,9,8,7,6,5,4,3,2,1
.equ NBELEMENTS, (. - TableNumber) / 4
/*********************************/
/* UnInitialized data */
/*********************************/
.bss
sZoneConv: .skip 24
/*********************************/
/* code section */
/*********************************/
.text
.global main
main: @ entry of program
ldr r0,iAdrTableNumber @ address number table
mov r1,#0 @ first element
mov r2,#NBELEMENTS @ number of élements
bl mergeSort
ldr r0,iAdrTableNumber @ address number table
bl displayTable
ldr r0,iAdrTableNumber @ address number table
mov r1,#NBELEMENTS @ number of élements
bl isSorted @ control sort
cmp r0,#1 @ sorted ?
beq 1f
ldr r0,iAdrszMessSortNok @ no !! error sort
bl affichageMess
b 100f
1: @ yes
ldr r0,iAdrszMessSortOk
bl affichageMess
100: @ standard end of the program
mov r0, #0 @ return code
mov r7, #EXIT @ request to exit program
svc #0 @ perform the system call
iAdrszCarriageReturn: .int szCarriageReturn
iAdrsMessResult: .int sMessResult
iAdrTableNumber: .int TableNumber
iAdrszMessSortOk: .int szMessSortOk
iAdrszMessSortNok: .int szMessSortNok
/******************************************************************/
/* control sorted table */
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the number of elements > 0 */
/* r0 return 0 if not sorted 1 if sorted */
isSorted:
push {r2-r4,lr} @ save registers
mov r2,#0
ldr r4,[r0,r2,lsl #2]
1:
add r2,#1
cmp r2,r1
movge r0,#1
bge 100f
ldr r3,[r0,r2, lsl #2]
cmp r3,r4
movlt r0,#0
blt 100f
mov r4,r3
b 1b
100:
pop {r2-r4,lr}
bx lr @ return
/******************************************************************/
/* merge */
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains first start index
/* r2 contains second start index */
/* r3 contains the last index */
merge:
push {r1-r8,lr} @ save registers
mov r5,r2 @ init index r2->r5
1: @ begin loop first section
ldr r6,[r0,r1,lsl #2] @ load value first section index r1
ldr r7,[r0,r5,lsl #2] @ load value second section index r5
cmp r6,r7
ble 3f @ <= -> location first section OK
str r7,[r0,r1,lsl #2] @ store value second section in first section
add r8,r5,#1
cmp r8,r3 @ end second section ?
strgt r6,[r0,r5,lsl #2]
bgt 3f @ loop
2: @ loop insert element part 1 into part 2
sub r4,r8,#1
ldr r7,[r0,r8,lsl #2] @ load value 2
cmp r6,r7 @ value <
strlt r6,[r0,r4,lsl #2] @ store value
blt 3f
str r7,[r0,r4,lsl #2] @ store value 2
add r8,#1
cmp r8,r3 @ end second section ?
ble 2b @ no loop
sub r8,#1
str r6,[r0,r8,lsl #2] @ store value 1
3:
add r1,#1
cmp r1,r2 @ end first section ?
blt 1b
100:
pop {r1-r8,lr}
bx lr @ return
/******************************************************************/
/* merge sort */
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the index of first element */
/* r2 contains the number of element */
mergeSort:
push {r3-r7,lr} @ save registers
cmp r2,#2
blt 100f
lsr r4,r2,#1 @ number of element of each subset
tst r2,#1
addne r4,#1
mov r5,r1 @ save first element
mov r6,r2 @ save number of element
mov r7,r4 @ save number of element of each subset
mov r2,r4
bl mergeSort
mov r1,r7 @ restaur number of element of each subset
mov r2,r6 @ restaur number of element
sub r2,r1
mov r3,r5 @ restaur first element
add r1,r3 @ + 1
bl mergeSort @ sort first subset
mov r1,r5 @ restaur first element
mov r2,r7 @ restaur number of element of each subset
add r2,r1
mov r3,r6 @ restaur number of element
add r3,r1
sub r3,#1 @ last index
bl merge
100:
pop {r3-r7,lr}
bx lr @ return
/******************************************************************/
/* Display table elements */
/******************************************************************/
/* r0 contains the address of table */
displayTable:
push {r0-r3,lr} @ save registers
mov r2,r0 @ table address
mov r3,#0
1: @ loop display table
ldr r0,[r2,r3,lsl #2]
ldr r1,iAdrsZoneConv @
bl conversion10S @ décimal conversion
ldr r0,iAdrsMessResult
ldr r1,iAdrsZoneConv @ insert conversion
bl strInsertAtCharInc
bl affichageMess @ display message
add r3,#1
cmp r3,#NBELEMENTS - 1
ble 1b
ldr r0,iAdrszCarriageReturn
bl affichageMess
mov r0,r2
100:
pop {r0-r3,lr}
bx lr
iAdrsZoneConv: .int sZoneConv
/***************************************************/
/* ROUTINES INCLUDE */
/***************************************************/
.include "../affichage.inc"
|
http://rosettacode.org/wiki/Sorting_algorithms/Pancake_sort | Sorting algorithms/Pancake sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array of integers (of any convenient size) into ascending order using Pancake sorting.
In short, instead of individual elements being sorted, the only operation allowed is to "flip" one end of the list, like so:
Before: 6 7 8 9 2 5 3 4 1
After: 9 8 7 6 2 5 3 4 1
Only one end of the list can be flipped; this should be the low end, but the high end is okay if it's easier to code or works better, but it must be the same end for the entire solution. (The end flipped can't be arbitrarily changed.)
Show both the initial, unsorted list and the final sorted list.
(Intermediate steps during sorting are optional.)
Optimizations are optional (but recommended).
Related tasks
Number reversal game
Topswops
Also see
Wikipedia article: pancake sorting.
| #Maple | Maple | flip := proc(arr, i)
local start, temp, icopy;
temp, start, icopy := 0,1,i:
while (start < icopy) do
arr[start], arr[icopy] := arr[icopy], arr[start]:
start:=start+1:
icopy:=icopy-1:
end do:
end proc:
findMax := proc(arr, i)
local Max, j:
Max := 1:
for j from 1 to i do
if arr[j] > arr[Max] then Max := j: end if:
end do:
return Max:
end proc:
pancakesort := proc(arr)
local len,i,Max;
len := numelems(arr):
for i from len to 2 by -1 do
print(arr):
Max := findMax(arr, i):
if (not Max = i) then
flip(arr, Max):
flip(arr, i):
end if:
end do:
print(arr);
end proc: |
http://rosettacode.org/wiki/Sorting_algorithms/Pancake_sort | Sorting algorithms/Pancake sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array of integers (of any convenient size) into ascending order using Pancake sorting.
In short, instead of individual elements being sorted, the only operation allowed is to "flip" one end of the list, like so:
Before: 6 7 8 9 2 5 3 4 1
After: 9 8 7 6 2 5 3 4 1
Only one end of the list can be flipped; this should be the low end, but the high end is okay if it's easier to code or works better, but it must be the same end for the entire solution. (The end flipped can't be arbitrarily changed.)
Show both the initial, unsorted list and the final sorted list.
(Intermediate steps during sorting are optional.)
Optimizations are optional (but recommended).
Related tasks
Number reversal game
Topswops
Also see
Wikipedia article: pancake sorting.
| #Mathematica.2FWolfram_Language | Mathematica/Wolfram Language | ClearAll[LMaxPosition, Flip, pancakeSort]
LMaxPosition[a_, n_] := With[{b = Take[a, n]}, First[Ordering[b, -1]]]
SetAttributes[Flip, HoldAll];
Flip[a_] := Set[a, Reverse[a]]
pancakeSort[in_] := Module[{n, lm, a = in, flips = 0},
Do[
lm = LMaxPosition[a, n];
If[lm < n,
Flip[a[[;; lm]]];
Flip[a[[;; n]]];
];
,
{n, Length[a], 2, -1}
];
a
]
pancakeSort[{6, 7, 8, 9, 2, 5, 3, 4, 1}] |
http://rosettacode.org/wiki/Sorting_algorithms/Stooge_sort | Sorting algorithms/Stooge sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Stooge sort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Show the Stooge Sort for an array of integers.
The Stooge Sort algorithm is as follows:
algorithm stoogesort(array L, i = 0, j = length(L)-1)
if L[j] < L[i] then
L[i] ↔ L[j]
if j - i > 1 then
t := (j - i + 1)/3
stoogesort(L, i , j-t)
stoogesort(L, i+t, j )
stoogesort(L, i , j-t)
return L
| #PureBasic | PureBasic | Procedure Stooge_Sort(Array L.i(1), i=0 , j=0)
If j=0
j=ArraySize(L())
EndIf
If L(i)>L(j)
Swap L(i), L(j)
EndIf
If j-i>1
Protected t=(j-i+1)/3
Stooge_Sort(L(), i, j-t)
Stooge_Sort(L(), i+t, j )
Stooge_Sort(L(), i, j-t)
EndIf
EndProcedure |
http://rosettacode.org/wiki/Sorting_algorithms/Stooge_sort | Sorting algorithms/Stooge sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Stooge sort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Show the Stooge Sort for an array of integers.
The Stooge Sort algorithm is as follows:
algorithm stoogesort(array L, i = 0, j = length(L)-1)
if L[j] < L[i] then
L[i] ↔ L[j]
if j - i > 1 then
t := (j - i + 1)/3
stoogesort(L, i , j-t)
stoogesort(L, i+t, j )
stoogesort(L, i , j-t)
return L
| #Python | Python | >>> data = [1, 4, 5, 3, -6, 3, 7, 10, -2, -5, 7, 5, 9, -3, 7]
>>> def stoogesort(L, i=0, j=None):
if j is None:
j = len(L) - 1
if L[j] < L[i]:
L[i], L[j] = L[j], L[i]
if j - i > 1:
t = (j - i + 1) // 3
stoogesort(L, i , j-t)
stoogesort(L, i+t, j )
stoogesort(L, i , j-t)
return L
>>> stoogesort(data)
[-6, -5, -3, -2, 1, 3, 3, 4, 5, 5, 7, 7, 7, 9, 10] |
http://rosettacode.org/wiki/Sorting_algorithms/Selection_sort | Sorting algorithms/Selection sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array (or list) of elements using the Selection sort algorithm.
It works as follows:
First find the smallest element in the array and exchange it with the element in the first position, then find the second smallest element and exchange it with the element in the second position, and continue in this way until the entire array is sorted.
Its asymptotic complexity is O(n2) making it inefficient on large arrays.
Its primary purpose is for when writing data is very expensive (slow) when compared to reading, eg. writing to flash memory or EEPROM.
No other sorting algorithm has less data movement.
References
Rosetta Code: O (complexity).
Wikipedia: Selection sort.
Wikipedia: [Big O notation].
| #Io | Io | List do (
selectionSortInPlace := method(
size repeat(idx,
swapIndices(idx, indexOf(slice(idx, size) min))
)
)
)
l := list(-1, 4, 2, -9)
l selectionSortInPlace println # ==> list(-9, -1, 2, 4) |
http://rosettacode.org/wiki/Sorting_algorithms/Selection_sort | Sorting algorithms/Selection sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array (or list) of elements using the Selection sort algorithm.
It works as follows:
First find the smallest element in the array and exchange it with the element in the first position, then find the second smallest element and exchange it with the element in the second position, and continue in this way until the entire array is sorted.
Its asymptotic complexity is O(n2) making it inefficient on large arrays.
Its primary purpose is for when writing data is very expensive (slow) when compared to reading, eg. writing to flash memory or EEPROM.
No other sorting algorithm has less data movement.
References
Rosetta Code: O (complexity).
Wikipedia: Selection sort.
Wikipedia: [Big O notation].
| #IS-BASIC | IS-BASIC | 100 PROGRAM "SelecSrt.bas"
110 RANDOMIZE
120 NUMERIC ARRAY(-5 TO 14)
130 CALL INIT(ARRAY)
140 CALL WRITE(ARRAY)
150 CALL SELECTIONSORT(ARRAY)
160 CALL WRITE(ARRAY)
170 DEF INIT(REF A)
180 FOR I=LBOUND(A) TO UBOUND(A)
190 LET A(I)=RND(98)+1
200 NEXT
210 END DEF
220 DEF WRITE(REF A)
230 FOR I=LBOUND(A) TO UBOUND(A)
240 PRINT A(I);
250 NEXT
260 PRINT
270 END DEF
280 DEF SELECTIONSORT(REF A)
290 FOR I=LBOUND(A) TO UBOUND(A)-1
300 LET MN=A(I):LET INDEX=I
310 FOR J=I+1 TO UBOUND(A)
320 IF MN>A(J) THEN LET MN=A(J):LET INDEX=J
330 NEXT
340 LET A(INDEX)=A(I):LET A(I)=MN
350 NEXT
360 END DEF |
http://rosettacode.org/wiki/Soundex | Soundex | Soundex is an algorithm for creating indices for words based on their pronunciation.
Task
The goal is for homophones to be encoded to the same representation so that they can be matched despite minor differences in spelling (from the soundex Wikipedia article).
Caution
There is a major issue in many of the implementations concerning the separation of two consonants that have the same soundex code! According to the official Rules [[1]]. So check for instance if Ashcraft is coded to A-261.
If a vowel (A, E, I, O, U) separates two consonants that have the same soundex code, the consonant to the right of the vowel is coded. Tymczak is coded as T-522 (T, 5 for the M, 2 for the C, Z ignored (see "Side-by-Side" rule above), 2 for the K). Since the vowel "A" separates the Z and K, the K is coded.
If "H" or "W" separate two consonants that have the same soundex code, the consonant to the right of the vowel is not coded. Example: Ashcraft is coded A-261 (A, 2 for the S, C ignored, 6 for the R, 1 for the F). It is not coded A-226.
| #Julia | Julia |
using Soundex
@assert soundex("Ashcroft") == "A261" # true
# Too trivial? OK. Here is an example not using a package:
function soundex(s)
char2num = Dict('B'=>1,'F'=>1,'P'=>1,'V'=>1,'C'=>2,'G'=>2,'J'=>2,'K'=>2,
'Q'=>2,'S'=>2,'X'=>2,'Z'=>2,'D'=>3,'T'=>3,'L'=>4,'M'=>5,'N'=>5,'R'=>6)
s = replace(s, r"[^a-zA-Z]", "")
if s == ""
return ""
end
ret = "$(uppercase(s[1]))"
hadvowel = false
lastletternum = haskey(char2num, ret[1]) ? char2num[ret[1]] : ""
for c in s[2:end]
c = uppercase(c)
if haskey(char2num, c)
letternum = char2num[c]
if letternum != lastletternum || hadvowel
ret = "$ret$letternum"
lastletternum = letternum
hadvowel = false
end
elseif c in ('A', 'E', 'I', 'O', 'U', 'Y')
hadvowel = true
end
end
while length(ret) < 4
ret *= "0"
end
ret[1:4]
end
@assert soundex("Ascroft") == "A261"
@assert soundex("Euler") == "E460"
@assert soundex("Gausss") == "G200"
@assert soundex("Hilbert") == "H416"
@assert soundex("Knuth") == "K530"
@assert soundex("Lloyd") == "L300"
@assert soundex("Lukasiewicz") == "L222"
@assert soundex("Ellery") == "E460"
@assert soundex("Ghosh") == "G200"
@assert soundex("Heilbronn") == "H416"
@assert soundex("Kant") == "K530"
@assert soundex("Ladd") == "L300"
@assert soundex("Lissajous") == "L222"
@assert soundex("Wheaton") == "W350"
@assert soundex("Ashcraft") == "A261"
@assert soundex("Burroughs") == "B620"
@assert soundex("Burrows") == "B620"
@assert soundex("O'Hara") == "O600"
|
http://rosettacode.org/wiki/Sorting_algorithms/Shell_sort | Sorting algorithms/Shell sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array of elements using the Shell sort algorithm, a diminishing increment sort.
The Shell sort (also known as Shellsort or Shell's method) is named after its inventor, Donald Shell, who published the algorithm in 1959.
Shell sort is a sequence of interleaved insertion sorts based on an increment sequence.
The increment size is reduced after each pass until the increment size is 1.
With an increment size of 1, the sort is a basic insertion sort, but by this time the data is guaranteed to be almost sorted, which is insertion sort's "best case".
Any sequence will sort the data as long as it ends in 1, but some work better than others.
Empirical studies have shown a geometric increment sequence with a ratio of about 2.2 work well in practice.
[1]
Other good sequences are found at the On-Line Encyclopedia of Integer Sequences.
| #Phix | Phix | with javascript_semantics
function shell_sort(sequence s)
integer gap = floor(length(s)/2), j
while gap>0 do
for i=gap to length(s) do
object si = s[i]
j = i-gap
while j>=1 and si<=s[j] do
s[j+gap] = s[j]
j -= gap
end while
s[j+gap] = si
end for
gap = floor(gap/2)
end while
return s
end function
?shell_sort(shuffle(tagset(10)))
|
http://rosettacode.org/wiki/Stack | Stack |
Data Structure
This illustrates a data structure, a means of storing data within a program.
You may see other such structures in the Data Structures category.
A stack is a container of elements with last in, first out access policy. Sometimes it also called LIFO.
The stack is accessed through its top.
The basic stack operations are:
push stores a new element onto the stack top;
pop returns the last pushed stack element, while removing it from the stack;
empty tests if the stack contains no elements.
Sometimes the last pushed stack element is made accessible for immutable access (for read) or mutable access (for write):
top (sometimes called peek to keep with the p theme) returns the topmost element without modifying the stack.
Stacks allow a very simple hardware implementation.
They are common in almost all processors.
In programming, stacks are also very popular for their way (LIFO) of resource management, usually memory.
Nested scopes of language objects are naturally implemented by a stack (sometimes by multiple stacks).
This is a classical way to implement local variables of a re-entrant or recursive subprogram. Stacks are also used to describe a formal computational framework.
See stack machine.
Many algorithms in pattern matching, compiler construction (e.g. recursive descent parsers), and machine learning (e.g. based on tree traversal) have a natural representation in terms of stacks.
Task
Create a stack supporting the basic operations: push, pop, empty.
See also
Array
Associative array: Creation, Iteration
Collections
Compound data type
Doubly-linked list: Definition, Element definition, Element insertion, List Traversal, Element Removal
Linked list
Queue: Definition, Usage
Set
Singly-linked list: Element definition, Element insertion, List Traversal, Element Removal
Stack
| #Nemerle | Nemerle | public class Stack[T]
{
private stack : list[T];
public this()
{
stack = [];
}
public this(init : list[T])
{
stack = init;
}
public Push(item : T) : Stack[T]
{
Stack(item::stack)
}
public Pop() : T * Stack[T]
{
(stack.Head, Stack(stack.Tail))
}
public Peek() : T
{
stack.Head
}
public IsEmpty() : bool
{
stack.Length == 0
}
} |
http://rosettacode.org/wiki/Spiral_matrix | Spiral matrix | Task
Produce a spiral array.
A spiral array is a square arrangement of the first N2 natural numbers, where the
numbers increase sequentially as you go around the edges of the array spiraling inwards.
For example, given 5, produce this array:
0 1 2 3 4
15 16 17 18 5
14 23 24 19 6
13 22 21 20 7
12 11 10 9 8
Related tasks
Zig-zag matrix
Identity_matrix
Ulam_spiral_(for_primes)
| #PicoLisp | PicoLisp | (load "@lib/simul.l")
(de spiral (N)
(prog1 (grid N N)
(let (Dir '(north east south west .) This 'a1)
(for Val (* N N)
(=: val Val)
(setq This
(or
(with ((car Dir) This)
(unless (: val) This) )
(with ((car (setq Dir (cdr Dir))) This)
(unless (: val) This) ) ) ) ) ) ) )
(mapc
'((L)
(for This L (prin (align 3 (: val))))
(prinl) )
(spiral 5) ) |
http://rosettacode.org/wiki/Sorting_algorithms/Radix_sort | Sorting algorithms/Radix sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an integer array with the radix sort algorithm.
The primary purpose is to complete the characterization of sort algorithms task.
| #Scheme | Scheme | ;;; An illustrative implementation of the radix-10 example at
;;; https://en.wikipedia.org/w/index.php?title=Radix_sort&oldid=1070890278#Least_significant_digit
(cond-expand
(r7rs)
(chicken (import (r7rs))))
(import (scheme base))
(import (scheme write))
(define (sort-by-decimal-digit data power-of-10)
(define bins (make-vector 10 '()))
(do ((i (- (vector-length data) 1) (- i 1)))
((= i -1))
(let* ((element (vector-ref data i))
(digit (truncate-remainder
(truncate-quotient element power-of-10)
10)))
(vector-set! bins digit
(cons element (vector-ref bins digit)))))
(let ((non-zero-found
(let loop ((i 1))
(cond ((= i (vector-length bins)) #f)
((pair? (vector-ref bins i)) #t)
(else (loop (+ i 1)))))))
(when non-zero-found
(let ((i 0))
(do ((j 0 (+ j 1)))
((= j (vector-length bins)))
(do ((p (vector-ref bins j) (cdr p)))
((null? p))
(vector-set! data i (car p))
(set! i (+ i 1))))))
(not non-zero-found)))
(define (radix-sort data)
(let loop ((power-of-10 1))
(let ((done (sort-by-decimal-digit data power-of-10)))
(unless done
(loop (* 10 power-of-10))))))
(define data (vector-copy #(170 45 75 90 2 802 2 66)))
(write data)
(newline)
(radix-sort data)
(write data)
(newline) |
http://rosettacode.org/wiki/Sorting_algorithms/Quicksort | Sorting algorithms/Quicksort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Quicksort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Sort an array (or list) elements using the quicksort algorithm.
The elements must have a strict weak order and the index of the array can be of any discrete type.
For languages where this is not possible, sort an array of integers.
Quicksort, also known as partition-exchange sort, uses these steps.
Choose any element of the array to be the pivot.
Divide all other elements (except the pivot) into two partitions.
All elements less than the pivot must be in the first partition.
All elements greater than the pivot must be in the second partition.
Use recursion to sort both partitions.
Join the first sorted partition, the pivot, and the second sorted partition.
The best pivot creates partitions of equal length (or lengths differing by 1).
The worst pivot creates an empty partition (for example, if the pivot is the first or last element of a sorted array).
The run-time of Quicksort ranges from O(n log n) with the best pivots, to O(n2) with the worst pivots, where n is the number of elements in the array.
This is a simple quicksort algorithm, adapted from Wikipedia.
function quicksort(array)
less, equal, greater := three empty arrays
if length(array) > 1
pivot := select any element of array
for each x in array
if x < pivot then add x to less
if x = pivot then add x to equal
if x > pivot then add x to greater
quicksort(less)
quicksort(greater)
array := concatenate(less, equal, greater)
A better quicksort algorithm works in place, by swapping elements within the array, to avoid the memory allocation of more arrays.
function quicksort(array)
if length(array) > 1
pivot := select any element of array
left := first index of array
right := last index of array
while left ≤ right
while array[left] < pivot
left := left + 1
while array[right] > pivot
right := right - 1
if left ≤ right
swap array[left] with array[right]
left := left + 1
right := right - 1
quicksort(array from first index to right)
quicksort(array from left to last index)
Quicksort has a reputation as the fastest sort. Optimized variants of quicksort are common features of many languages and libraries. One often contrasts quicksort with merge sort, because both sorts have an average time of O(n log n).
"On average, mergesort does fewer comparisons than quicksort, so it may be better when complicated comparison routines are used. Mergesort also takes advantage of pre-existing order, so it would be favored for using sort() to merge several sorted arrays. On the other hand, quicksort is often faster for small arrays, and on arrays of a few distinct values, repeated many times." — http://perldoc.perl.org/sort.html
Quicksort is at one end of the spectrum of divide-and-conquer algorithms, with merge sort at the opposite end.
Quicksort is a conquer-then-divide algorithm, which does most of the work during the partitioning and the recursive calls. The subsequent reassembly of the sorted partitions involves trivial effort.
Merge sort is a divide-then-conquer algorithm. The partioning happens in a trivial way, by splitting the input array in half. Most of the work happens during the recursive calls and the merge phase.
With quicksort, every element in the first partition is less than or equal to every element in the second partition. Therefore, the merge phase of quicksort is so trivial that it needs no mention!
This task has not specified whether to allocate new arrays, or sort in place. This task also has not specified how to choose the pivot element. (Common ways to are to choose the first element, the middle element, or the median of three elements.) Thus there is a variety among the following implementations.
| #COBOL | COBOL | IDENTIFICATION DIVISION.
PROGRAM-ID. quicksort RECURSIVE.
DATA DIVISION.
LOCAL-STORAGE SECTION.
01 temp PIC S9(8).
01 pivot PIC S9(8).
01 left-most-idx PIC 9(5).
01 right-most-idx PIC 9(5).
01 left-idx PIC 9(5).
01 right-idx PIC 9(5).
LINKAGE SECTION.
78 Arr-Length VALUE 50.
01 arr-area.
03 arr PIC S9(8) OCCURS Arr-Length TIMES.
01 left-val PIC 9(5).
01 right-val PIC 9(5).
PROCEDURE DIVISION USING REFERENCE arr-area, OPTIONAL left-val,
OPTIONAL right-val.
IF left-val IS OMITTED OR right-val IS OMITTED
MOVE 1 TO left-most-idx, left-idx
MOVE Arr-Length TO right-most-idx, right-idx
ELSE
MOVE left-val TO left-most-idx, left-idx
MOVE right-val TO right-most-idx, right-idx
END-IF
IF right-most-idx - left-most-idx < 1
GOBACK
END-IF
COMPUTE pivot = arr ((left-most-idx + right-most-idx) / 2)
PERFORM UNTIL left-idx > right-idx
PERFORM VARYING left-idx FROM left-idx BY 1
UNTIL arr (left-idx) >= pivot
END-PERFORM
PERFORM VARYING right-idx FROM right-idx BY -1
UNTIL arr (right-idx) <= pivot
END-PERFORM
IF left-idx <= right-idx
MOVE arr (left-idx) TO temp
MOVE arr (right-idx) TO arr (left-idx)
MOVE temp TO arr (right-idx)
ADD 1 TO left-idx
SUBTRACT 1 FROM right-idx
END-IF
END-PERFORM
CALL "quicksort" USING REFERENCE arr-area,
CONTENT left-most-idx, right-idx
CALL "quicksort" USING REFERENCE arr-area, CONTENT left-idx,
right-most-idx
GOBACK
. |
http://rosettacode.org/wiki/Sorting_algorithms/Patience_sort | Sorting algorithms/Patience sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Sort an array of numbers (of any convenient size) into ascending order using Patience sorting.
Related task
Longest increasing subsequence
| #Phix | Phix | with javascript_semantics
function patience_sort(sequence s)
-- create list of sorted lists
sequence piles = {}
for i=1 to length(s) do
object n = s[i]
for p=1 to length(piles)+1 do
if p>length(piles) then
piles = append(piles,{n})
elsif n>=piles[p][$] then
piles[p] = append(deep_copy(piles[p]),n)
exit
end if
end for
end for
-- merge sort the piles
sequence res = ""
while length(piles) do
integer idx = smallest(piles,return_index:=true)
res = append(res,piles[idx][1])
if length(piles[idx])=1 then
piles[idx..idx] = {}
else
piles[idx] = piles[idx][2..$]
end if
end while
return res
end function
constant tests = {{4,65,2,-31,0,99,83,782,1},
{0,8,4,12,2,10,6,14,1,9,5,13,3,11,7,15},
"nonzerosum",
{"dog", "cow", "cat", "ape", "ant", "man", "pig", "ass", "gnu"}}
for i=1 to length(tests) do
pp(patience_sort(tests[i]),{pp_IntCh,false})
end for
|
http://rosettacode.org/wiki/Sorting_algorithms/Insertion_sort | Sorting algorithms/Insertion sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Insertion sort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
An O(n2) sorting algorithm which moves elements one at a time into the correct position.
The algorithm consists of inserting one element at a time into the previously sorted part of the array, moving higher ranked elements up as necessary.
To start off, the first (or smallest, or any arbitrary) element of the unsorted array is considered to be the sorted part.
Although insertion sort is an O(n2) algorithm, its simplicity, low overhead, good locality of reference and efficiency make it a good choice in two cases:
small n,
as the final finishing-off algorithm for O(n logn) algorithms such as mergesort and quicksort.
The algorithm is as follows (from wikipedia):
function insertionSort(array A)
for i from 1 to length[A]-1 do
value := A[i]
j := i-1
while j >= 0 and A[j] > value do
A[j+1] := A[j]
j := j-1
done
A[j+1] = value
done
Writing the algorithm for integers will suffice.
| #C.23 | C# | namespace Sort {
using System;
static class InsertionSort<T> where T : IComparable {
public static void Sort(T[] entries) {
Sort(entries, 0, entries.Length - 1);
}
public static void Sort(T[] entries, Int32 first, Int32 last) {
for (var i = first + 1; i <= last; i++) {
var entry = entries[i];
var j = i;
while (j > first && entries[j - 1].CompareTo(entry) > 0)
entries[j] = entries[--j];
entries[j] = entry;
}
}
}
} |
http://rosettacode.org/wiki/Sorting_algorithms/Permutation_sort | Sorting algorithms/Permutation sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Implement a permutation sort, which proceeds by generating the possible permutations
of the input array/list until discovering the sorted one.
Pseudocode:
while not InOrder(list) do
nextPermutation(list)
done
| #Ursala | Ursala | #import std
permsort "p" = ~&ihB+ ordered"p"*~+ permutations
#cast %sL
example = permsort(lleq) <'pmf','oao','ejw','hhp','oqh','ock','dwj'> |
http://rosettacode.org/wiki/Sorting_algorithms/Permutation_sort | Sorting algorithms/Permutation sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Implement a permutation sort, which proceeds by generating the possible permutations
of the input array/list until discovering the sorted one.
Pseudocode:
while not InOrder(list) do
nextPermutation(list)
done
| #Wren | Wren | import "/sort" for Sort
var a = [170, 45, 75, -90, -802, 24, 2, 66]
// recursive permutation generator
var recurse
recurse = Fn.new { |last|
if (last <= 0) return Sort.isSorted(a)
for (i in 0..last) {
var t = a[i]
a[i] = a[last]
a[last] = t
if (recurse.call(last - 1)) return true
t = a[i]
a[i] = a[last]
a[last] = t
}
return false
}
System.print("Unsorted: %(a)")
var count = a.count
if (count > 1 && !recurse.call(count-1)) Fiber.abort("Sorted permutation not found!")
System.print("Sorted : %(a)") |
http://rosettacode.org/wiki/Sorting_algorithms/Heapsort | Sorting algorithms/Heapsort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Heapsort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Heapsort is an in-place sorting algorithm with worst case and average complexity of O(n logn).
The basic idea is to turn the array into a binary heap structure, which has the property that it allows efficient retrieval and removal of the maximal element.
We repeatedly "remove" the maximal element from the heap, thus building the sorted list from back to front.
A heap sort requires random access, so can only be used on an array-like data structure.
Pseudocode:
function heapSort(a, count) is
input: an unordered array a of length count
(first place a in max-heap order)
heapify(a, count)
end := count - 1
while end > 0 do
(swap the root(maximum value) of the heap with the
last element of the heap)
swap(a[end], a[0])
(decrement the size of the heap so that the previous
max value will stay in its proper place)
end := end - 1
(put the heap back in max-heap order)
siftDown(a, 0, end)
function heapify(a,count) is
(start is assigned the index in a of the last parent node)
start := (count - 2) / 2
while start ≥ 0 do
(sift down the node at index start to the proper place
such that all nodes below the start index are in heap
order)
siftDown(a, start, count-1)
start := start - 1
(after sifting down the root all nodes/elements are in heap order)
function siftDown(a, start, end) is
(end represents the limit of how far down the heap to sift)
root := start
while root * 2 + 1 ≤ end do (While the root has at least one child)
child := root * 2 + 1 (root*2+1 points to the left child)
(If the child has a sibling and the child's value is less than its sibling's...)
if child + 1 ≤ end and a[child] < a[child + 1] then
child := child + 1 (... then point to the right child instead)
if a[root] < a[child] then (out of max-heap order)
swap(a[root], a[child])
root := child (repeat to continue sifting down the child now)
else
return
Write a function to sort a collection of integers using heapsort.
| #AutoHotkey | AutoHotkey | heapSort(a) {
Local end
end := %a%0
heapify(a,end)
While end > 1
%a%%end% := (%a%1 "", %a%1 := %a%%end%)
,siftDown(a, 1, --end)
}
heapify(a, count) {
Local start
start := count // 2
While start
siftDown(a, start--, count)
}
siftDown(a, start, end) {
Local child, c1
While start*2 <= end {
c1 := 1 + child := start*2
If (c1 <= end && %a%%child% < %a%%c1%)
child := c1
If (%a%%start% < %a%%child%)
%a%%start% := (%a%%child% "", %a%%child% := %a%%start%)
,start := child
Else Return
}
}
a = 1,5,2,7,3,4,6,8,1 ; ----- test -----
StringSplit a, a, `,
heapSort("a")
ListVars
MsgBox |
http://rosettacode.org/wiki/Sorting_algorithms/Merge_sort | Sorting algorithms/Merge sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
The merge sort is a recursive sort of order n*log(n).
It is notable for having a worst case and average complexity of O(n*log(n)), and a best case complexity of O(n) (for pre-sorted input).
The basic idea is to split the collection into smaller groups by halving it until the groups only have one element or no elements (which are both entirely sorted groups).
Then merge the groups back together so that their elements are in order.
This is how the algorithm gets its divide and conquer description.
Task
Write a function to sort a collection of integers using the merge sort.
The merge sort algorithm comes in two parts:
a sort function and
a merge function
The functions in pseudocode look like this:
function mergesort(m)
var list left, right, result
if length(m) ≤ 1
return m
else
var middle = length(m) / 2
for each x in m up to middle - 1
add x to left
for each x in m at and after middle
add x to right
left = mergesort(left)
right = mergesort(right)
if last(left) ≤ first(right)
append right to left
return left
result = merge(left, right)
return result
function merge(left,right)
var list result
while length(left) > 0 and length(right) > 0
if first(left) ≤ first(right)
append first(left) to result
left = rest(left)
else
append first(right) to result
right = rest(right)
if length(left) > 0
append rest(left) to result
if length(right) > 0
append rest(right) to result
return result
See also
the Wikipedia entry: merge sort
Note: better performance can be expected if, rather than recursing until length(m) ≤ 1, an insertion sort is used for length(m) smaller than some threshold larger than 1. However, this complicates the example code, so it is not shown here.
| #Astro | Astro | fun mergesort(m):
if m.lenght <= 1: return m
let middle = floor m.lenght / 2
let left = merge(m[:middle])
let right = merge(m[middle-1:]);
fun merge(left, right):
let result = []
while not (left.isempty or right.isempty):
if left[1] <= right[1]:
result.push! left.shift!()
else:
result.push! right.shift!()
result.push! left.push! right
let arr = [7, 6, 5, 9, 8, 4, 3, 1, 2, 0]
print mergesort arr |
http://rosettacode.org/wiki/Sorting_algorithms/Pancake_sort | Sorting algorithms/Pancake sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array of integers (of any convenient size) into ascending order using Pancake sorting.
In short, instead of individual elements being sorted, the only operation allowed is to "flip" one end of the list, like so:
Before: 6 7 8 9 2 5 3 4 1
After: 9 8 7 6 2 5 3 4 1
Only one end of the list can be flipped; this should be the low end, but the high end is okay if it's easier to code or works better, but it must be the same end for the entire solution. (The end flipped can't be arbitrarily changed.)
Show both the initial, unsorted list and the final sorted list.
(Intermediate steps during sorting are optional.)
Optimizations are optional (but recommended).
Related tasks
Number reversal game
Topswops
Also see
Wikipedia article: pancake sorting.
| #MATLAB_.2F_Octave | MATLAB / Octave | function list = pancakeSort(list)
for i = (numel(list):-1:2)
minElem = list(i);
minIndex = i;
%Find the min element in the current subset of the list
for j = (i:-1:1)
if list(j) <= minElem
minElem = list(j);
minIndex = j;
end
end
%If the element is already in the correct position don't flip
if i ~= minIndex
%First flip flips the min element in the stack to the top
list(minIndex:-1:1) = list(1:minIndex);
%Second flip flips the min element into the correct position in
%the stack
list(i:-1:1) = list(1:i);
end
end %for
end %pancakeSort |
http://rosettacode.org/wiki/Sorting_algorithms/Stooge_sort | Sorting algorithms/Stooge sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Stooge sort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Show the Stooge Sort for an array of integers.
The Stooge Sort algorithm is as follows:
algorithm stoogesort(array L, i = 0, j = length(L)-1)
if L[j] < L[i] then
L[i] ↔ L[j]
if j - i > 1 then
t := (j - i + 1)/3
stoogesort(L, i , j-t)
stoogesort(L, i+t, j )
stoogesort(L, i , j-t)
return L
| #Quackery | Quackery | [ 2 * 3 /mod 0 > + ] is twothirds ( n --> n )
[ dup 0 peek over -1 peek
2dup > iff
[ rot 0 poke -1 poke ]
else 2drop ] is swapends ( [ --> [ )
[ swapends
dup size 3 < if done
dup size twothirds split
swap recurse swap join
dup size 3 / split
recurse join
dup size twothirds split
swap recurse swap join ] is stoogesort ( [ --> [ )
[] 33 times [ 90 random 10 + join ]
dup echo cr
stoogesort echo |
http://rosettacode.org/wiki/Sorting_algorithms/Stooge_sort | Sorting algorithms/Stooge sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Stooge sort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Show the Stooge Sort for an array of integers.
The Stooge Sort algorithm is as follows:
algorithm stoogesort(array L, i = 0, j = length(L)-1)
if L[j] < L[i] then
L[i] ↔ L[j]
if j - i > 1 then
t := (j - i + 1)/3
stoogesort(L, i , j-t)
stoogesort(L, i+t, j )
stoogesort(L, i , j-t)
return L
| #R | R | stoogesort = function(vect) {
i = 1
j = length(vect)
if(vect[j] < vect[i]) vect[c(j, i)] = vect[c(i, j)]
if(j - i > 1) {
t = (j - i + 1) %/% 3
vect[i:(j - t)] = stoogesort(vect[i:(j - t)])
vect[(i + t):j] = stoogesort(vect[(i + t):j])
vect[i:(j - t)] = stoogesort(vect[i:(j - t)])
}
vect
}
v = sample(21, 20)
k = stoogesort(v)
v
k |
http://rosettacode.org/wiki/Sorting_algorithms/Selection_sort | Sorting algorithms/Selection sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array (or list) of elements using the Selection sort algorithm.
It works as follows:
First find the smallest element in the array and exchange it with the element in the first position, then find the second smallest element and exchange it with the element in the second position, and continue in this way until the entire array is sorted.
Its asymptotic complexity is O(n2) making it inefficient on large arrays.
Its primary purpose is for when writing data is very expensive (slow) when compared to reading, eg. writing to flash memory or EEPROM.
No other sorting algorithm has less data movement.
References
Rosetta Code: O (complexity).
Wikipedia: Selection sort.
Wikipedia: [Big O notation].
| #J | J | selectionSort=: verb define
data=. y
for_xyz. y do.
temp=. xyz_index }. data
nvidx=. xyz_index + temp i. <./ temp
data=. ((xyz_index, nvidx) { data) (nvidx, xyz_index) } data
end.
data
) |
http://rosettacode.org/wiki/Sorting_algorithms/Selection_sort | Sorting algorithms/Selection sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array (or list) of elements using the Selection sort algorithm.
It works as follows:
First find the smallest element in the array and exchange it with the element in the first position, then find the second smallest element and exchange it with the element in the second position, and continue in this way until the entire array is sorted.
Its asymptotic complexity is O(n2) making it inefficient on large arrays.
Its primary purpose is for when writing data is very expensive (slow) when compared to reading, eg. writing to flash memory or EEPROM.
No other sorting algorithm has less data movement.
References
Rosetta Code: O (complexity).
Wikipedia: Selection sort.
Wikipedia: [Big O notation].
| #Java | Java | public static void sort(int[] nums){
for(int currentPlace = 0;currentPlace<nums.length-1;currentPlace++){
int smallest = Integer.MAX_VALUE;
int smallestAt = currentPlace+1;
for(int check = currentPlace; check<nums.length;check++){
if(nums[check]<smallest){
smallestAt = check;
smallest = nums[check];
}
}
int temp = nums[currentPlace];
nums[currentPlace] = nums[smallestAt];
nums[smallestAt] = temp;
}
} |
http://rosettacode.org/wiki/Soundex | Soundex | Soundex is an algorithm for creating indices for words based on their pronunciation.
Task
The goal is for homophones to be encoded to the same representation so that they can be matched despite minor differences in spelling (from the soundex Wikipedia article).
Caution
There is a major issue in many of the implementations concerning the separation of two consonants that have the same soundex code! According to the official Rules [[1]]. So check for instance if Ashcraft is coded to A-261.
If a vowel (A, E, I, O, U) separates two consonants that have the same soundex code, the consonant to the right of the vowel is coded. Tymczak is coded as T-522 (T, 5 for the M, 2 for the C, Z ignored (see "Side-by-Side" rule above), 2 for the K). Since the vowel "A" separates the Z and K, the K is coded.
If "H" or "W" separate two consonants that have the same soundex code, the consonant to the right of the vowel is not coded. Example: Ashcraft is coded A-261 (A, 2 for the S, C ignored, 6 for the R, 1 for the F). It is not coded A-226.
| #Kotlin | Kotlin | // version 1.1.2
fun getCode(c: Char) = when (c) {
'B', 'F', 'P', 'V' -> "1"
'C', 'G', 'J', 'K', 'Q', 'S', 'X', 'Z' -> "2"
'D', 'T' -> "3"
'L' -> "4"
'M', 'N' -> "5"
'R' -> "6"
'H', 'W' -> "-"
else -> ""
}
fun soundex(s: String): String {
if (s == "") return ""
val sb = StringBuilder().append(s[0].toUpperCase())
var prev = getCode(sb[0])
for (i in 1 until s.length) {
val curr = getCode(s[i].toUpperCase())
if (curr != "" && curr != "-" && curr != prev) sb.append(curr)
if (curr != "-") prev = curr
}
return sb.toString().padEnd(4, '0').take(4)
}
fun main(args: Array<String>) {
val pairs = arrayOf(
"Ashcraft" to "A261",
"Ashcroft" to "A261",
"Gauss" to "G200",
"Ghosh" to "G200",
"Hilbert" to "H416",
"Heilbronn" to "H416",
"Lee" to "L000",
"Lloyd" to "L300",
"Moses" to "M220",
"Pfister" to "P236",
"Robert" to "R163",
"Rupert" to "R163",
"Rubin" to "R150",
"Tymczak" to "T522",
"Soundex" to "S532",
"Example" to "E251"
)
for (pair in pairs) {
println("${pair.first.padEnd(9)} -> ${pair.second} -> ${soundex(pair.first) == pair.second}")
}
} |
http://rosettacode.org/wiki/Sorting_algorithms/Shell_sort | Sorting algorithms/Shell sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array of elements using the Shell sort algorithm, a diminishing increment sort.
The Shell sort (also known as Shellsort or Shell's method) is named after its inventor, Donald Shell, who published the algorithm in 1959.
Shell sort is a sequence of interleaved insertion sorts based on an increment sequence.
The increment size is reduced after each pass until the increment size is 1.
With an increment size of 1, the sort is a basic insertion sort, but by this time the data is guaranteed to be almost sorted, which is insertion sort's "best case".
Any sequence will sort the data as long as it ends in 1, but some work better than others.
Empirical studies have shown a geometric increment sequence with a ratio of about 2.2 work well in practice.
[1]
Other good sequences are found at the On-Line Encyclopedia of Integer Sequences.
| #PHP | PHP |
function shellSort($arr)
{
$inc = round(count($arr)/2);
while($inc > 0)
{
for($i = $inc; $i < count($arr);$i++){
$temp = $arr[$i];
$j = $i;
while($j >= $inc && $arr[$j-$inc] > $temp)
{
$arr[$j] = $arr[$j - $inc];
$j -= $inc;
}
$arr[$j] = $temp;
}
$inc = round($inc/2.2);
}
return $arr;
}
|
http://rosettacode.org/wiki/Stack | Stack |
Data Structure
This illustrates a data structure, a means of storing data within a program.
You may see other such structures in the Data Structures category.
A stack is a container of elements with last in, first out access policy. Sometimes it also called LIFO.
The stack is accessed through its top.
The basic stack operations are:
push stores a new element onto the stack top;
pop returns the last pushed stack element, while removing it from the stack;
empty tests if the stack contains no elements.
Sometimes the last pushed stack element is made accessible for immutable access (for read) or mutable access (for write):
top (sometimes called peek to keep with the p theme) returns the topmost element without modifying the stack.
Stacks allow a very simple hardware implementation.
They are common in almost all processors.
In programming, stacks are also very popular for their way (LIFO) of resource management, usually memory.
Nested scopes of language objects are naturally implemented by a stack (sometimes by multiple stacks).
This is a classical way to implement local variables of a re-entrant or recursive subprogram. Stacks are also used to describe a formal computational framework.
See stack machine.
Many algorithms in pattern matching, compiler construction (e.g. recursive descent parsers), and machine learning (e.g. based on tree traversal) have a natural representation in terms of stacks.
Task
Create a stack supporting the basic operations: push, pop, empty.
See also
Array
Associative array: Creation, Iteration
Collections
Compound data type
Doubly-linked list: Definition, Element definition, Element insertion, List Traversal, Element Removal
Linked list
Queue: Definition, Usage
Set
Singly-linked list: Element definition, Element insertion, List Traversal, Element Removal
Stack
| #NetRexx | NetRexx | /* NetRexx ************************************************************
* 13.08.2013 Walter Pachl translated from REXX version 2
**********************************************************************/
options replace format comments java crossref savelog symbols nobinary
stk = create_stk
say push(stk,123) 'from push'
say empty(stk)
say peek(stk) 'from peek'
say pull(stk) 'from pull'
say empty(stk)
Say pull(stk) 'from pull'
method create_stk static returns Rexx
stk = ''
stk[0] = 0
return stk
method push(stk,v) static
stk[0]=stk[0]+1
stk[stk[0]]=v
Return v
method peek(stk) static
x=stk[0]
If x=0 Then
Return 'stk is empty'
Else
Return stk[x]
method pull(stk) static
x=stk[0]
If x=0 Then
Return 'stk is empty'
Else Do
stk[0]=stk[0]-1
Return stk[x]
End
method empty(stk) static
Return stk[0]=0 |
http://rosettacode.org/wiki/Spiral_matrix | Spiral matrix | Task
Produce a spiral array.
A spiral array is a square arrangement of the first N2 natural numbers, where the
numbers increase sequentially as you go around the edges of the array spiraling inwards.
For example, given 5, produce this array:
0 1 2 3 4
15 16 17 18 5
14 23 24 19 6
13 22 21 20 7
12 11 10 9 8
Related tasks
Zig-zag matrix
Identity_matrix
Ulam_spiral_(for_primes)
| #PL.2FI | PL/I | /* Generates a square matrix containing the integers from 0 to N**2-1, */
/* where N is the length of one side of the square. */
/* Written 22 February 2010. */
declare n fixed binary;
put skip list ('Please type the size of the square:');
get list (n);
begin;
declare A(n,n) fixed binary;
declare (i, j, iinc, jinc, q) fixed binary;
A = -1;
i, j = 1; iinc = 0; jinc = 1;
do q = 0 to n**2-1;
if a(i,j) < 0 then
a(i,j) = q;
else
do;
/* back up */
j = j -jinc; i = i - iinc;
/* change direction */
if iinc = 0 & jinc = 1 then do; iinc = 1; jinc = 0; end;
else if iinc = 1 & jinc = 0 then do; iinc = 0; jinc = -1; end;
else if iinc = 0 & jinc = -1 then do; iinc = -1; jinc = 0; end;
else if iinc = -1 & jinc = 0 then do; iinc = 0; jinc = 1; end;
/* Take one step in the new direction */
i = i + iinc; j = j + jinc;
a(i,j) = q;
end;
if i+iinc > n | i+iinc < 1 then
do;
iinc = 0; jinc = 1;
if j+1 > n then jinc = -1; else if j-1 < 1 then jinc = 1;
if a(i+iinc,j+jinc) >= 0 then jinc = -jinc;
/* j = j + jinc; /* to move on from the present (filled) position */
end;
else i = i + iinc;
if j+jinc > n | j+jinc < 1 then
do;
jinc = 0; iinc = 1;
if i+1 > n then iinc = -1; else if i-1 < 1 then iinc = 1;
if a(i+iinc,j+jinc) >= 0 then iinc = -iinc;
i = i + iinc; /* to move on from the present (filled) position */
end;
else j = j + jinc;
end;
/* Display the square. */
do i = 1 to n;
put skip edit (A(i,*)) (F(4));
end;
end; |
http://rosettacode.org/wiki/Sorting_algorithms/Radix_sort | Sorting algorithms/Radix sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an integer array with the radix sort algorithm.
The primary purpose is to complete the characterization of sort algorithms task.
| #Sidef | Sidef | class Array {
method radix_sort(base=10) {
var arr = self.clone
var rounds = ([arr.minmax].map{.abs}.max.ilog(base) + 1)
for i in (0..rounds) {
var buckets = (2*base -> of {[]})
var base_i = base**i
for n in arr {
var digit = (n/base_i % base)
digit += base if (0 <= n)
buckets[digit].append(n)
}
arr = buckets.flat
}
return arr
}
}
for arr in [
[1, 3, 8, 9, 0, 0, 8, 7, 1, 6],
[170, 45, 75, 90, 2, 24, 802, 66],
[170, 45, 75, 90, 2, 24, -802, -66],
[100000, -10000, 400, 23, 10000],
] {
say arr.radix_sort
} |
http://rosettacode.org/wiki/Sorting_algorithms/Quicksort | Sorting algorithms/Quicksort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Quicksort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Sort an array (or list) elements using the quicksort algorithm.
The elements must have a strict weak order and the index of the array can be of any discrete type.
For languages where this is not possible, sort an array of integers.
Quicksort, also known as partition-exchange sort, uses these steps.
Choose any element of the array to be the pivot.
Divide all other elements (except the pivot) into two partitions.
All elements less than the pivot must be in the first partition.
All elements greater than the pivot must be in the second partition.
Use recursion to sort both partitions.
Join the first sorted partition, the pivot, and the second sorted partition.
The best pivot creates partitions of equal length (or lengths differing by 1).
The worst pivot creates an empty partition (for example, if the pivot is the first or last element of a sorted array).
The run-time of Quicksort ranges from O(n log n) with the best pivots, to O(n2) with the worst pivots, where n is the number of elements in the array.
This is a simple quicksort algorithm, adapted from Wikipedia.
function quicksort(array)
less, equal, greater := three empty arrays
if length(array) > 1
pivot := select any element of array
for each x in array
if x < pivot then add x to less
if x = pivot then add x to equal
if x > pivot then add x to greater
quicksort(less)
quicksort(greater)
array := concatenate(less, equal, greater)
A better quicksort algorithm works in place, by swapping elements within the array, to avoid the memory allocation of more arrays.
function quicksort(array)
if length(array) > 1
pivot := select any element of array
left := first index of array
right := last index of array
while left ≤ right
while array[left] < pivot
left := left + 1
while array[right] > pivot
right := right - 1
if left ≤ right
swap array[left] with array[right]
left := left + 1
right := right - 1
quicksort(array from first index to right)
quicksort(array from left to last index)
Quicksort has a reputation as the fastest sort. Optimized variants of quicksort are common features of many languages and libraries. One often contrasts quicksort with merge sort, because both sorts have an average time of O(n log n).
"On average, mergesort does fewer comparisons than quicksort, so it may be better when complicated comparison routines are used. Mergesort also takes advantage of pre-existing order, so it would be favored for using sort() to merge several sorted arrays. On the other hand, quicksort is often faster for small arrays, and on arrays of a few distinct values, repeated many times." — http://perldoc.perl.org/sort.html
Quicksort is at one end of the spectrum of divide-and-conquer algorithms, with merge sort at the opposite end.
Quicksort is a conquer-then-divide algorithm, which does most of the work during the partitioning and the recursive calls. The subsequent reassembly of the sorted partitions involves trivial effort.
Merge sort is a divide-then-conquer algorithm. The partioning happens in a trivial way, by splitting the input array in half. Most of the work happens during the recursive calls and the merge phase.
With quicksort, every element in the first partition is less than or equal to every element in the second partition. Therefore, the merge phase of quicksort is so trivial that it needs no mention!
This task has not specified whether to allocate new arrays, or sort in place. This task also has not specified how to choose the pivot element. (Common ways to are to choose the first element, the middle element, or the median of three elements.) Thus there is a variety among the following implementations.
| #CoffeeScript | CoffeeScript |
quicksort = ([x, xs...]) ->
return [] unless x?
smallerOrEqual = (a for a in xs when a <= x)
larger = (a for a in xs when a > x)
(quicksort smallerOrEqual).concat(x).concat(quicksort larger)
|
http://rosettacode.org/wiki/Sorting_algorithms/Patience_sort | Sorting algorithms/Patience sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Sort an array of numbers (of any convenient size) into ascending order using Patience sorting.
Related task
Longest increasing subsequence
| #PHP | PHP | <?php
class PilesHeap extends SplMinHeap {
public function compare($pile1, $pile2) {
return parent::compare($pile1->top(), $pile2->top());
}
}
function patience_sort(&$n) {
$piles = array();
// sort into piles
foreach ($n as $x) {
// binary search
$low = 0; $high = count($piles)-1;
while ($low <= $high) {
$mid = (int)(($low + $high) / 2);
if ($piles[$mid]->top() >= $x)
$high = $mid - 1;
else
$low = $mid + 1;
}
$i = $low;
if ($i == count($piles))
$piles[] = new SplStack();
$piles[$i]->push($x);
}
// priority queue allows us to merge piles efficiently
$heap = new PilesHeap();
foreach ($piles as $pile)
$heap->insert($pile);
for ($c = 0; $c < count($n); $c++) {
$smallPile = $heap->extract();
$n[$c] = $smallPile->pop();
if (!$smallPile->isEmpty())
$heap->insert($smallPile);
}
assert($heap->isEmpty());
}
$a = array(4, 65, 2, -31, 0, 99, 83, 782, 1);
patience_sort($a);
print_r($a);
?> |
http://rosettacode.org/wiki/Sorting_algorithms/Insertion_sort | Sorting algorithms/Insertion sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Insertion sort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
An O(n2) sorting algorithm which moves elements one at a time into the correct position.
The algorithm consists of inserting one element at a time into the previously sorted part of the array, moving higher ranked elements up as necessary.
To start off, the first (or smallest, or any arbitrary) element of the unsorted array is considered to be the sorted part.
Although insertion sort is an O(n2) algorithm, its simplicity, low overhead, good locality of reference and efficiency make it a good choice in two cases:
small n,
as the final finishing-off algorithm for O(n logn) algorithms such as mergesort and quicksort.
The algorithm is as follows (from wikipedia):
function insertionSort(array A)
for i from 1 to length[A]-1 do
value := A[i]
j := i-1
while j >= 0 and A[j] > value do
A[j+1] := A[j]
j := j-1
done
A[j+1] = value
done
Writing the algorithm for integers will suffice.
| #C.2B.2B | C++ | g++ -std=c++11 insertion.cpp
|
http://rosettacode.org/wiki/Sorting_algorithms/Permutation_sort | Sorting algorithms/Permutation sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Implement a permutation sort, which proceeds by generating the possible permutations
of the input array/list until discovering the sorted one.
Pseudocode:
while not InOrder(list) do
nextPermutation(list)
done
| #zkl | zkl | rns:=T(4, 65, 2, 31, 0, 99, 2, 83, 782, 1);
fcn psort(list){ len:=list.len(); cnt:=Ref(0);
foreach ns in (Utils.Helpers.permuteW(list)){ // lasy permutations
cnt.set(1);
ns.reduce('wrap(p,n){ if(p>n)return(Void.Stop); cnt.inc(); n });
if(cnt.value==len) return(ns);
}
}(rns).println(); |
http://rosettacode.org/wiki/Sorting_algorithms/Heapsort | Sorting algorithms/Heapsort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Heapsort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Heapsort is an in-place sorting algorithm with worst case and average complexity of O(n logn).
The basic idea is to turn the array into a binary heap structure, which has the property that it allows efficient retrieval and removal of the maximal element.
We repeatedly "remove" the maximal element from the heap, thus building the sorted list from back to front.
A heap sort requires random access, so can only be used on an array-like data structure.
Pseudocode:
function heapSort(a, count) is
input: an unordered array a of length count
(first place a in max-heap order)
heapify(a, count)
end := count - 1
while end > 0 do
(swap the root(maximum value) of the heap with the
last element of the heap)
swap(a[end], a[0])
(decrement the size of the heap so that the previous
max value will stay in its proper place)
end := end - 1
(put the heap back in max-heap order)
siftDown(a, 0, end)
function heapify(a,count) is
(start is assigned the index in a of the last parent node)
start := (count - 2) / 2
while start ≥ 0 do
(sift down the node at index start to the proper place
such that all nodes below the start index are in heap
order)
siftDown(a, start, count-1)
start := start - 1
(after sifting down the root all nodes/elements are in heap order)
function siftDown(a, start, end) is
(end represents the limit of how far down the heap to sift)
root := start
while root * 2 + 1 ≤ end do (While the root has at least one child)
child := root * 2 + 1 (root*2+1 points to the left child)
(If the child has a sibling and the child's value is less than its sibling's...)
if child + 1 ≤ end and a[child] < a[child + 1] then
child := child + 1 (... then point to the right child instead)
if a[root] < a[child] then (out of max-heap order)
swap(a[root], a[child])
root := child (repeat to continue sifting down the child now)
else
return
Write a function to sort a collection of integers using heapsort.
| #BBC_BASIC | BBC BASIC | DIM test(9)
test() = 4, 65, 2, -31, 0, 99, 2, 83, 782, 1
PROCheapsort(test())
FOR i% = 0 TO 9
PRINT test(i%) ;
NEXT
PRINT
END
DEF PROCheapsort(a())
LOCAL e%
PROCheapify(a())
FOR e% = DIM(a(),1) TO 1 STEP -1
SWAP a(e%), a(0)
PROCsiftdown(a(), 0, e%-1)
NEXT
ENDPROC
DEF PROCheapify(a())
LOCAL s%, m%
m% = DIM(a(),1)
FOR s% = (m% - 1) / 2 TO 0 STEP -1
PROCsiftdown(a(), s%, m%)
NEXT
ENDPROC
DEF PROCsiftdown(a(), s%, e%)
LOCAL c%, r%
r% = s%
WHILE r% * 2 + 1 <= e%
c% = r% * 2 + 1
IF c% + 1 <= e% IF a(c%) < a(c% + 1) c% += 1
IF a(r%) < a(c%) SWAP a(r%), a(c%) : r% = c% ELSE ENDPROC
ENDWHILE
ENDPROC |
http://rosettacode.org/wiki/Sorting_algorithms/Heapsort | Sorting algorithms/Heapsort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Heapsort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Heapsort is an in-place sorting algorithm with worst case and average complexity of O(n logn).
The basic idea is to turn the array into a binary heap structure, which has the property that it allows efficient retrieval and removal of the maximal element.
We repeatedly "remove" the maximal element from the heap, thus building the sorted list from back to front.
A heap sort requires random access, so can only be used on an array-like data structure.
Pseudocode:
function heapSort(a, count) is
input: an unordered array a of length count
(first place a in max-heap order)
heapify(a, count)
end := count - 1
while end > 0 do
(swap the root(maximum value) of the heap with the
last element of the heap)
swap(a[end], a[0])
(decrement the size of the heap so that the previous
max value will stay in its proper place)
end := end - 1
(put the heap back in max-heap order)
siftDown(a, 0, end)
function heapify(a,count) is
(start is assigned the index in a of the last parent node)
start := (count - 2) / 2
while start ≥ 0 do
(sift down the node at index start to the proper place
such that all nodes below the start index are in heap
order)
siftDown(a, start, count-1)
start := start - 1
(after sifting down the root all nodes/elements are in heap order)
function siftDown(a, start, end) is
(end represents the limit of how far down the heap to sift)
root := start
while root * 2 + 1 ≤ end do (While the root has at least one child)
child := root * 2 + 1 (root*2+1 points to the left child)
(If the child has a sibling and the child's value is less than its sibling's...)
if child + 1 ≤ end and a[child] < a[child + 1] then
child := child + 1 (... then point to the right child instead)
if a[root] < a[child] then (out of max-heap order)
swap(a[root], a[child])
root := child (repeat to continue sifting down the child now)
else
return
Write a function to sort a collection of integers using heapsort.
| #BCPL | BCPL | // This can be run using Cintcode BCPL freely available from www.cl.cam.ac.uk/users/mr10.
GET "libhdr.h"
LET heapify(v, k, i, last) BE
{ LET j = i+i // If there is a son (or two), j = subscript of first.
AND x = k // x will hold the larger of the sons if any.
IF j<=last DO x := v!j // j, x = subscript and key of first son.
IF j< last DO
{ LET y = v!(j+1) // y = key of the other son.
IF x<y DO x,j := y, j+1 // j, x = subscript and key of larger son.
}
IF k>=x DO
{ v!i := k // k is not lower than larger son if any.
RETURN
}
v!i := x
i := j
} REPEAT
AND heapsort(v, upb) BE
{ FOR i = upb/2 TO 1 BY -1 DO heapify(v, v!i, i, upb)
FOR i = upb TO 2 BY -1 DO
{ LET k = v!i
v!i := v!1
heapify(v, k, 1, i-1)
}
}
LET start() = VALOF {
LET v = VEC 1000
FOR i = 1 TO 1000 DO v!i := randno(1_000_000)
heapsort(v, 1000)
FOR i = 1 TO 1000 DO
{ IF i MOD 10 = 0 DO newline()
writef(" %i6", v!i)
}
newline()
} |
http://rosettacode.org/wiki/Sorting_algorithms/Merge_sort | Sorting algorithms/Merge sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
The merge sort is a recursive sort of order n*log(n).
It is notable for having a worst case and average complexity of O(n*log(n)), and a best case complexity of O(n) (for pre-sorted input).
The basic idea is to split the collection into smaller groups by halving it until the groups only have one element or no elements (which are both entirely sorted groups).
Then merge the groups back together so that their elements are in order.
This is how the algorithm gets its divide and conquer description.
Task
Write a function to sort a collection of integers using the merge sort.
The merge sort algorithm comes in two parts:
a sort function and
a merge function
The functions in pseudocode look like this:
function mergesort(m)
var list left, right, result
if length(m) ≤ 1
return m
else
var middle = length(m) / 2
for each x in m up to middle - 1
add x to left
for each x in m at and after middle
add x to right
left = mergesort(left)
right = mergesort(right)
if last(left) ≤ first(right)
append right to left
return left
result = merge(left, right)
return result
function merge(left,right)
var list result
while length(left) > 0 and length(right) > 0
if first(left) ≤ first(right)
append first(left) to result
left = rest(left)
else
append first(right) to result
right = rest(right)
if length(left) > 0
append rest(left) to result
if length(right) > 0
append rest(right) to result
return result
See also
the Wikipedia entry: merge sort
Note: better performance can be expected if, rather than recursing until length(m) ≤ 1, an insertion sort is used for length(m) smaller than some threshold larger than 1. However, this complicates the example code, so it is not shown here.
| #ATS | ATS | (*------------------------------------------------------------------*)
(* Mergesort in ATS2, for linear lists. *)
(*------------------------------------------------------------------*)
#include "share/atspre_staload.hats"
staload UN = "prelude/SATS/unsafe.sats"
#define NIL list_vt_nil ()
#define :: list_vt_cons
(*------------------------------------------------------------------*)
(* Destructive stable merge. *)
extern fun {a : vt@ype}
list_vt_merge {m, n : int}
(lst1 : list_vt (a, m),
lst2 : list_vt (a, n))
:<!wrt> list_vt (a, m + n)
(* Order predicate for list_vt_merge. You have to implement this to
suit your needs. *)
extern fun {a : vt@ype}
list_vt_merge$lt : (&a, &a) -<> bool
(* Destructive stable mergesort. *)
extern fun {a : vt@ype}
list_vt_mergesort {n : int}
(lst : list_vt (a, n))
:<!wrt> list_vt (a, n)
(* Order predicate for list_vt_mergesort. You have to implement this
to suit your needs. *)
extern fun {a : vt@ype}
list_vt_mergesort$lt : (&a, &a) -<> bool
(*------------------------------------------------------------------*)
implement {a}
list_vt_merge {m, n} (lst1, lst2) =
let
macdef lt = list_vt_merge$lt<a>
fun
loop {m, n : nat} .<m + n>.
(lst1 : list_vt (a, m),
lst2 : list_vt (a, n),
lst_merged : &List_vt a? >> list_vt (a, m + n))
:<!wrt> void =
case+ lst1 of
| ~ NIL => lst_merged := lst2
| @ elem1 :: tail1 =>
begin
case+ lst2 of
| ~ NIL =>
let
prval () = fold@ lst1
in
lst_merged := lst1
end
| @ elem2 :: tail2 =>
if ~(elem2 \lt elem1) then
let
val () = lst_merged := lst1
prval () = fold@ lst2
val () = loop (tail1, lst2, tail1)
prval () = fold@ lst_merged
in
end
else
let
val () = lst_merged := lst2
prval () = fold@ lst1
val () = loop (lst1, tail2, tail2)
prval () = fold@ lst_merged
in
end
end
prval () = lemma_list_vt_param lst1 (* Proves 0 <= m. *)
prval () = lemma_list_vt_param lst2 (* Proves 0 <= n. *)
prval () = prop_verify {0 <= m} ()
prval () = prop_verify {0 <= n} ()
var lst_merged : List_vt a?
val () = loop {m, n} (lst1, lst2, lst_merged)
in
lst_merged
end
(*------------------------------------------------------------------*)
implement {a}
list_vt_mergesort {n} lst =
let
implement
list_vt_merge$lt<a> (x, y) =
list_vt_mergesort$lt<a> (x, y)
(* You can make SMALL larger than 1 and write small_sort as a fast
stable sort for small lists. *)
#define SMALL 1
fn
small_sort {m : pos | m <= SMALL}
(lst : list_vt (a, m),
m : int m)
:<!wrt> list_vt (a, m) =
lst
fun
recurs {m : pos} .<m>.
(lst : list_vt (a, m),
m : int m)
:<!wrt> list_vt (a, m) =
if m <= SMALL then
small_sort (lst, m)
else
let
prval () = prop_verify {2 <= m} ()
val i = m / 2
val @(lst1, lst2) = list_vt_split_at<a> (lst, i)
val lst1 = recurs (lst1, i)
val lst2 = recurs (lst2, m - i)
in
list_vt_merge<a> (lst1, lst2)
end
prval () = lemma_list_vt_param lst (* Proves 0 <= n. *)
prval () = prop_verify {0 <= n} ()
in
case+ lst of
| NIL => lst
| _ :: _ => recurs (lst, length lst)
end
(*------------------------------------------------------------------*)
extern fun
list_vt_mergesort_int {n : int}
(lst : list_vt (int, n))
:<!wrt> list_vt (int, n)
implement
list_vt_mergesort_int {n} lst =
let
implement
list_vt_mergesort$lt<int> (x, y) =
x < y
in
list_vt_mergesort<int> {n} lst
end
implement
main0 () =
let
val lst = $list_vt (22, 15, 98, 82, 22, 4, 58, 70, 80, 38, 49,
48, 46, 54, 93, 8, 54, 2, 72, 84, 86, 76,
53, 37, 90)
val () = println! ("before : ", $UN.castvwtp1{List int} lst)
val lst = list_vt_mergesort_int lst
val () = println! ("after : ", $UN.castvwtp1{List int} lst)
in
list_vt_free<int> lst
end
(*------------------------------------------------------------------*) |
http://rosettacode.org/wiki/Sorting_algorithms/Pancake_sort | Sorting algorithms/Pancake sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array of integers (of any convenient size) into ascending order using Pancake sorting.
In short, instead of individual elements being sorted, the only operation allowed is to "flip" one end of the list, like so:
Before: 6 7 8 9 2 5 3 4 1
After: 9 8 7 6 2 5 3 4 1
Only one end of the list can be flipped; this should be the low end, but the high end is okay if it's easier to code or works better, but it must be the same end for the entire solution. (The end flipped can't be arbitrarily changed.)
Show both the initial, unsorted list and the final sorted list.
(Intermediate steps during sorting are optional.)
Optimizations are optional (but recommended).
Related tasks
Number reversal game
Topswops
Also see
Wikipedia article: pancake sorting.
| #MAXScript | MAXScript | fn flipArr arr index =
(
local new = #()
for i = index to 1 by -1 do
(
append new arr[i]
)
join new (for i in (index+1) to arr.count collect arr[i])
return new
)
fn pancakeSort arr =
(
if arr.count < 2 then return arr
else
(
for i = arr.count to 1 by -1 do
(
local newArr = for n in 1 to i collect arr[n]
local oldArr = for o in (i+1) to arr.count collect arr[o]
local maxIndices = for m in 1 to (newArr.count) where (newArr[m] == amax newArr) collect m
local lastMaxIndex = maxIndices[maxIndices.count]
newArr = flipArr newArr lastMaxIndex
newArr = flipArr newArr newArr.count
arr = join newArr oldArr
)
return arr
)
) |
http://rosettacode.org/wiki/Sorting_algorithms/Pancake_sort | Sorting algorithms/Pancake sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array of integers (of any convenient size) into ascending order using Pancake sorting.
In short, instead of individual elements being sorted, the only operation allowed is to "flip" one end of the list, like so:
Before: 6 7 8 9 2 5 3 4 1
After: 9 8 7 6 2 5 3 4 1
Only one end of the list can be flipped; this should be the low end, but the high end is okay if it's easier to code or works better, but it must be the same end for the entire solution. (The end flipped can't be arbitrarily changed.)
Show both the initial, unsorted list and the final sorted list.
(Intermediate steps during sorting are optional.)
Optimizations are optional (but recommended).
Related tasks
Number reversal game
Topswops
Also see
Wikipedia article: pancake sorting.
| #NetRexx | NetRexx | /* NetRexx */
options replace format comments java crossref symbols nobinary
import java.util.List
runSample(arg)
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method pancakeSort(tlist = List, debug = (1 == 0)) private static returns List
if tlist.size() > 1 then do
loop i_ = tlist.size() by -1 while i_ > 1
maxPos = 0
loop a_ = 0 while a_ < i_
if Rexx tlist.get(a_) > Rexx tlist.get(maxPos) then maxPos = a_
end a_
if maxPos = i_ - 1 then iterate i_
if maxPos > 0 then pancakeFlip(tlist, maxPos + 1, debug)
pancakeFlip(tlist, i_, debug)
end i_
end
return tlist
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method pancakeFlip(tlist = List, offset, debug = (1 == 0)) private static returns List
z_ = offset - 1
pl = 3
if debug then do
plx = offset.length()
if plx > pl then pl = plx
say ' flip{1-'offset.right(pl, 0)'} Before:' tlist
end
loop i_ = 0 while i_ < z_
Collections.swap(tlist, i_, z_)
z_ = z_ - 1
end i_
if debug then do
say ' flip{1-'offset.right(pl, 0)'} After:' tlist
end
return tlist
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method runSample(arg) private static
isTrue = (1 == 1)
isFalse = \isTrue
parse arg debug .
if '-debug'.abbrev(debug.lower(), 2) then debug = isTrue
else debug = isFalse
lists = sampleData()
loop il = 1 to lists[0]
clist = words2list(lists[il])
say ' Input:' clist
say 'Output:' pancakeSort(clist, debug)
say
end il
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method sampleData() private static
lists = ''
i_ = 0
i_ = i_ + 1; lists[0] = i_; lists[i_] = '1 4 3 5 2 9 8 7 6'
i_ = i_ + 1; lists[0] = i_; lists[i_] = '10 -9 8 -7 6 -5 4 -3 2 -1 0 -10 9 -8 7 -6 5 -4 3 -2 1'
i_ = i_ + 1; lists[0] = i_; lists[i_] = '88 18 31 44 4 0 8 81 14 78 20 76 84 33 73 75 82 5 62 70 12 7 1'
i_ = i_ + 1; lists[0] = i_; lists[i_] = '10 10.0 10.00 1 -10.0 10. -1'
i_ = i_ + 1; lists[0] = i_; lists[i_] = 'To be or not to be that is the question'
i_ = i_ + 1; lists[0] = i_; lists[i_] = '1'
return lists
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method words2list(wordlist) private static returns List
clist = ArrayList()
loop w_ = 1 to wordlist.words()
clist.add(wordlist.word(w_))
end w_
return clist
|
http://rosettacode.org/wiki/Sorting_algorithms/Stooge_sort | Sorting algorithms/Stooge sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Stooge sort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Show the Stooge Sort for an array of integers.
The Stooge Sort algorithm is as follows:
algorithm stoogesort(array L, i = 0, j = length(L)-1)
if L[j] < L[i] then
L[i] ↔ L[j]
if j - i > 1 then
t := (j - i + 1)/3
stoogesort(L, i , j-t)
stoogesort(L, i+t, j )
stoogesort(L, i , j-t)
return L
| #Racket | Racket |
#lang racket
(define (stooge-sort xs [i 0] [j (- (vector-length xs) 1)])
(define (x i) (vector-ref xs i))
(define (x! i v) (vector-set! xs i v))
(define (swap! i j) (define t (x i)) (x! i (x j)) (x! j t))
(when (> (x i) (x j)) (swap! i j))
(when (> (- j i) 1)
(define t (quotient (+ j (- i) 1) 3))
(stooge-sort xs i (- j t))
(stooge-sort xs (+ i t) j)
(stooge-sort xs i (- j t)))
xs)
|
http://rosettacode.org/wiki/Sorting_algorithms/Stooge_sort | Sorting algorithms/Stooge sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
This page uses content from Wikipedia. The original article was at Stooge sort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Show the Stooge Sort for an array of integers.
The Stooge Sort algorithm is as follows:
algorithm stoogesort(array L, i = 0, j = length(L)-1)
if L[j] < L[i] then
L[i] ↔ L[j]
if j - i > 1 then
t := (j - i + 1)/3
stoogesort(L, i , j-t)
stoogesort(L, i+t, j )
stoogesort(L, i , j-t)
return L
| #Raku | Raku | sub stoogesort( @L, $i = 0, $j = @L.end ) {
@L[$j,$i] = @L[$i,$j] if @L[$i] > @L[$j];
my $interval = $j - $i;
if $interval > 1 {
my $t = ( $interval + 1 ) div 3;
stoogesort( @L, $i , $j-$t );
stoogesort( @L, $i+$t, $j );
stoogesort( @L, $i , $j-$t );
}
return @L;
}
my @L = 1, 4, 5, 3, -6, 3, 7, 10, -2, -5;
stoogesort(@L).Str.say;
|
http://rosettacode.org/wiki/Sorting_algorithms/Selection_sort | Sorting algorithms/Selection sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array (or list) of elements using the Selection sort algorithm.
It works as follows:
First find the smallest element in the array and exchange it with the element in the first position, then find the second smallest element and exchange it with the element in the second position, and continue in this way until the entire array is sorted.
Its asymptotic complexity is O(n2) making it inefficient on large arrays.
Its primary purpose is for when writing data is very expensive (slow) when compared to reading, eg. writing to flash memory or EEPROM.
No other sorting algorithm has less data movement.
References
Rosetta Code: O (complexity).
Wikipedia: Selection sort.
Wikipedia: [Big O notation].
| #JavaScript | JavaScript | function selectionSort(nums) {
var len = nums.length;
for(var i = 0; i < len; i++) {
var minAt = i;
for(var j = i + 1; j < len; j++) {
if(nums[j] < nums[minAt])
minAt = j;
}
if(minAt != i) {
var temp = nums[i];
nums[i] = nums[minAt];
nums[minAt] = temp;
}
}
return nums;
} |
http://rosettacode.org/wiki/Soundex | Soundex | Soundex is an algorithm for creating indices for words based on their pronunciation.
Task
The goal is for homophones to be encoded to the same representation so that they can be matched despite minor differences in spelling (from the soundex Wikipedia article).
Caution
There is a major issue in many of the implementations concerning the separation of two consonants that have the same soundex code! According to the official Rules [[1]]. So check for instance if Ashcraft is coded to A-261.
If a vowel (A, E, I, O, U) separates two consonants that have the same soundex code, the consonant to the right of the vowel is coded. Tymczak is coded as T-522 (T, 5 for the M, 2 for the C, Z ignored (see "Side-by-Side" rule above), 2 for the K). Since the vowel "A" separates the Z and K, the K is coded.
If "H" or "W" separate two consonants that have the same soundex code, the consonant to the right of the vowel is not coded. Example: Ashcraft is coded A-261 (A, 2 for the S, C ignored, 6 for the R, 1 for the F). It is not coded A-226.
| #Lua | Lua | local d, digits, alpha = '01230120022455012623010202', {}, ('A'):byte()
d:gsub(".",function(c)
digits[string.char(alpha)] = c
alpha = alpha + 1
end)
function soundex(w)
local res = {}
for c in w:upper():gmatch'.'do
local d = digits[c]
if d then
if #res==0 then
res[1] = c
elseif #res==1 or d~= res[#res] then
res[1+#res] = d
end
end
end
if #res == 0 then
return '0000'
else
res = table.concat(res):gsub("0",'')
return (res .. '0000'):sub(1,4)
end
end
-- tests
local tests = {
{"", "0000"}, {"12346", "0000"},
{"he", "H000"}, {"soundex", "S532"},
{"example", "E251"}, {"ciondecks", "C532"},
{"ekzampul", "E251"}, {"résumé", "R250"},
{"Robert", "R163"}, {"Rupert", "R163"},
{"Rubin", "R150"}, {"Ashcraft", "A226"},
{"Ashcroft", "A226"}
}
for i=1,#tests do
local itm = tests[i]
assert( soundex(itm[1])==itm[2] )
end
print"all tests ok" |
http://rosettacode.org/wiki/Sorting_algorithms/Shell_sort | Sorting algorithms/Shell sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array of elements using the Shell sort algorithm, a diminishing increment sort.
The Shell sort (also known as Shellsort or Shell's method) is named after its inventor, Donald Shell, who published the algorithm in 1959.
Shell sort is a sequence of interleaved insertion sorts based on an increment sequence.
The increment size is reduced after each pass until the increment size is 1.
With an increment size of 1, the sort is a basic insertion sort, but by this time the data is guaranteed to be almost sorted, which is insertion sort's "best case".
Any sequence will sort the data as long as it ends in 1, but some work better than others.
Empirical studies have shown a geometric increment sequence with a ratio of about 2.2 work well in practice.
[1]
Other good sequences are found at the On-Line Encyclopedia of Integer Sequences.
| #Picat | Picat | go =>
A = [23, 76, 99, 58, 97, 57, 35, 89, 51, 38, 95, 92, 24, 46, 31, 24, 14, 12, 57, 78],
println(A),
shell_sort(A),
println(A),
nl.
% Inline sort
shell_sort(A) =>
Inc = round(A.length/2),
while (Inc > 0)
foreach(I in Inc+1..A.length)
Temp = A[I],
J := I,
while (J > Inc, A[J-Inc] > Temp)
A[J] := A[J-Inc],
J := J - Inc
end,
A[J] := Temp
end,
Inc := round(Inc/2.2)
end. |
http://rosettacode.org/wiki/Sorting_algorithms/Shell_sort | Sorting algorithms/Shell sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an array of elements using the Shell sort algorithm, a diminishing increment sort.
The Shell sort (also known as Shellsort or Shell's method) is named after its inventor, Donald Shell, who published the algorithm in 1959.
Shell sort is a sequence of interleaved insertion sorts based on an increment sequence.
The increment size is reduced after each pass until the increment size is 1.
With an increment size of 1, the sort is a basic insertion sort, but by this time the data is guaranteed to be almost sorted, which is insertion sort's "best case".
Any sequence will sort the data as long as it ends in 1, but some work better than others.
Empirical studies have shown a geometric increment sequence with a ratio of about 2.2 work well in practice.
[1]
Other good sequences are found at the On-Line Encyclopedia of Integer Sequences.
| #PicoLisp | PicoLisp | (de shellSort (A)
(for (Inc (*/ (length A) 2) (gt0 Inc) (*/ Inc 10 22))
(for (I Inc (get A I) (inc I))
(let (Tmp @ J I)
(while (and (>= J Inc) (> (get A (- J Inc)) Tmp))
(set (nth A J) (get A (- J Inc)))
(dec 'J Inc) )
(set (nth A J) Tmp) ) ) )
A ) |
http://rosettacode.org/wiki/Stack | Stack |
Data Structure
This illustrates a data structure, a means of storing data within a program.
You may see other such structures in the Data Structures category.
A stack is a container of elements with last in, first out access policy. Sometimes it also called LIFO.
The stack is accessed through its top.
The basic stack operations are:
push stores a new element onto the stack top;
pop returns the last pushed stack element, while removing it from the stack;
empty tests if the stack contains no elements.
Sometimes the last pushed stack element is made accessible for immutable access (for read) or mutable access (for write):
top (sometimes called peek to keep with the p theme) returns the topmost element without modifying the stack.
Stacks allow a very simple hardware implementation.
They are common in almost all processors.
In programming, stacks are also very popular for their way (LIFO) of resource management, usually memory.
Nested scopes of language objects are naturally implemented by a stack (sometimes by multiple stacks).
This is a classical way to implement local variables of a re-entrant or recursive subprogram. Stacks are also used to describe a formal computational framework.
See stack machine.
Many algorithms in pattern matching, compiler construction (e.g. recursive descent parsers), and machine learning (e.g. based on tree traversal) have a natural representation in terms of stacks.
Task
Create a stack supporting the basic operations: push, pop, empty.
See also
Array
Associative array: Creation, Iteration
Collections
Compound data type
Doubly-linked list: Definition, Element definition, Element insertion, List Traversal, Element Removal
Linked list
Queue: Definition, Usage
Set
Singly-linked list: Element definition, Element insertion, List Traversal, Element Removal
Stack
| #Nim | Nim | type Stack[T] = distinct seq[T]
func initStack[T](initialSize = 32): Stack[T] =
Stack[T](newSeq[T](initialSize))
func isEmpty[T](stack: Stack[T]): bool =
seq[T](stack).len == 0
func push[T](stack: var Stack[T]; item: sink T) =
seq[T](stack).add(item)
func pop[T](stack: var Stack[T]): T =
if stack.isEmpty:
raise newException(IndexDefect, "stack is empty.")
seq[T](stack).pop()
func top[T](stack: Stack[T]): T =
if stack.isEmpty:
raise newException(IndexDefect, "stack is empty.")
seq[T](stack)[^1]
func mtop[T](stack: var Stack[T]): var T =
if stack.isEmpty:
raise newException(IndexDefect, "stack is empty.")
seq[T](stack)[^1]
func `mtop=`[T](stack: var Stack[T]; value: T) =
if stack.isEmpty:
raise newException(IndexDefect, "stack is empty.")
seq[T](stack)[^1] = value
when isMainModule:
var s = initStack[int]()
s.push 2
echo s.pop
s.push 3
echo s.top
s.mtop += 1
echo s.top
s.mtop = 5
echo s.top |
http://rosettacode.org/wiki/Spiral_matrix | Spiral matrix | Task
Produce a spiral array.
A spiral array is a square arrangement of the first N2 natural numbers, where the
numbers increase sequentially as you go around the edges of the array spiraling inwards.
For example, given 5, produce this array:
0 1 2 3 4
15 16 17 18 5
14 23 24 19 6
13 22 21 20 7
12 11 10 9 8
Related tasks
Zig-zag matrix
Identity_matrix
Ulam_spiral_(for_primes)
| #PowerShell | PowerShell | function Spiral-Matrix ( [int]$N )
{
# Initialize variables
$X = 0
$Y = -1
$i = 0
$Sign = 1
# Intialize array
$A = New-Object 'int[,]' $N, $N
# Set top row
1..$N | ForEach { $Y += $Sign; $A[$X,$Y] = ++$i }
# For each remaining half spiral...
ForEach ( $M in ($N-1)..1 )
{
# Set the vertical quarter spiral
1..$M | ForEach { $X += $Sign; $A[$X,$Y] = ++$i }
# Curve the spiral
$Sign = -$Sign
# Set the horizontal quarter spiral
1..$M | ForEach { $Y += $Sign; $A[$X,$Y] = ++$i }
}
# Convert the array to text output
$Spiral = ForEach ( $X in 1..$N ) { ( 1..$N | ForEach { $A[($X-1),($_-1)] } ) -join "`t" }
return $Spiral
}
Spiral-Matrix 5
""
Spiral-Matrix 7 |
http://rosettacode.org/wiki/Sorting_algorithms/Radix_sort | Sorting algorithms/Radix sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an integer array with the radix sort algorithm.
The primary purpose is to complete the characterization of sort algorithms task.
| #Tailspin | Tailspin |
templates radixsort&{base:}
sink bucketize
def value: $;
$ ~/ [email protected] -> #
when <=0 ?($value <0..>)> do
..|@radixsort.positives: $value;
when <=0> do
..|@radixsort.negatives(last): $value;
otherwise
def bucket: $ mod $base -> \(<?($value<0..>)> $ + 1 ! <=0> $base ! <> $ !\);
..|@radixsort.buckets($bucket): $value;
@radixsort.done: 0;
end bucketize
// Negatives get completed in wrong length-order, we need to collect by length and correct at the end
@: { done: 1, digit: 1"1", positives: [], negatives: [[]], buckets: [1..$base -> []]};
$... -> !bucketize
[email protected] -> #
when <=1> do
[[email protected](last..1:-1)... ..., [email protected]...] !
otherwise
def previous: [email protected];
..|@: {done: 1, digit: [email protected] * $base, buckets:[1..$base -> []]};
..|@.negatives: [];
$previous... ... -> !bucketize
[email protected] -> #
end radixsort
[170, 45, 75, 91, 90, 92, 802, 24, 2, 66] -> radixsort&{base:10} -> !OUT::write
'
' -> !OUT::write
[-170, -45, -91, -90, -92, -802, -24, -2, -76] -> radixsort&{base:10} -> !OUT::write
'
' -> !OUT::write
[170, 45, 75, -91, -90, -92, -802, 24, 2, 66] -> radixsort&{base:10} -> !OUT::write
'
' -> !OUT::write
[170, 45, 75, -91, -90, -92, -802, 24, 2, 66] -> radixsort&{base:3} -> !OUT::write
|
http://rosettacode.org/wiki/Sorting_algorithms/Radix_sort | Sorting algorithms/Radix sort |
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Task
Sort an integer array with the radix sort algorithm.
The primary purpose is to complete the characterization of sort algorithms task.
| #Tcl | Tcl | package require Tcl 8.5
proc splitByRadix {lst base power} {
# create a list of empty lists to hold the split by digit
set out [lrepeat [expr {$base*2}] {}]
foreach item $lst {
# pulls the selected digit
set digit [expr {($item / $base ** $power) % $base + $base * ($item >= 0)}]
# append the number to the list selected by the digit
lset out $digit [list {*}[lindex $out $digit] $item]
}
return $out
}
# largest abs value element of a list
proc tcl::mathfunc::maxabs {lst} {
set max [abs [lindex $lst 0]]
for {set i 1} {$i < [llength $lst]} {incr i} {
set v [abs [lindex $lst $i]]
if {$max < $v} {set max $v}
}
return $max
}
proc radixSort {lst {base 10}} {
# there are as many passes as there are digits in the longest number
set passes [expr {int(log(maxabs($lst))/log($base) + 1)}]
# For each pass...
for {set pass 0} {$pass < $passes} {incr pass} {
# Split by radix, then merge back into the list
set lst [concat {*}[splitByRadix $lst $base $pass]]
}
return $lst
} |
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