# Sorting algorithms/Permutation sort

Sorting algorithms/Permutation sort
You are encouraged to solve this task according to the task description, using any language you may know.

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

O(n log2n) sorts
Shell Sort

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
```

## 11l

```F is_sorted(arr)
L(i) 1..arr.len-1
I arr[i-1] > arr[i]
R 0B
R 1B

F permutation_sort(&arr)
L !is_sorted(arr)
arr.next_permutation()

V arr = [7, 6, 5, 9, 8, 4, 3, 1, 2, 0]
permutation_sort(&arr)
print(arr)```
Output:
```[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
```

## AArch64 Assembly

Works with: as version Raspberry Pi 3B version Buster 64 bits
```/* ARM assembly AARCH64 Raspberry PI 3B */
/*  program permutationSort64.s  */

/*******************************************/
/* Constantes file                         */
/*******************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeConstantesARM64.inc"

/*******************************************/
/* Structures                               */
/********************************************/
/* structure permutations  */
.struct  0
perm_size:                        // elements number
.struct  perm_size + 8
perm_adrheap:                     // Init to zéro at the first call
perm_end:
/*********************************/
/* Initialized data              */
/*********************************/
.data
szMessSortOk:       .asciz "Table sorted.\n"
szMessSortNok:      .asciz "Table not sorted !!!!!.\n"
sMessCounter:       .asciz "sorted in  @ permutations \n"
sMessResult:        .asciz "Value  : @ \n"

szCarriageReturn:   .asciz "\n"

.align 4
.equ NBELEMENTS, (. - TableNumber) / 8
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss
sZoneConv:       .skip 24
stPermutation:   .skip perm_end
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main
main:                                              // entry of program
mov x1,NBELEMENTS                              // elements number
str x1,[x0,perm_size]
mov x1,0                                       // first call
mov x20,0                                      // counter
1:
bl newPermutation                              // call for each permutation
cmp x0,0                                       // end ?
blt 99f                                        // yes -> error
//bl displayTable                              // for display after each permutation
mov x1,NBELEMENTS                              // number of élements
bl isSorted                                    // control sort
cmp x0,1                                       // sorted ?
bne 1b                                         // no -> loop

bl displayTable
bl affichageMess
mov x0,x20                                     // display counter
bl conversion10S                               // décimal conversion
bl strInsertAtCharInc
bl affichageMess                               // display message
b 100f
99:
bl displayTable
bl affichageMess
100:                                               // standard end of the program
mov x0,0                                       // return code
mov x8,EXIT                                    // request to exit program
svc 0                                          // perform the system call

/******************************************************************/
/*     control sorted table                                   */
/******************************************************************/
/* x0 contains the address of table */
/* x1 contains the number of elements  > 0  */
/* x0 return 0  if not sorted   1  if sorted */
isSorted:
stp x2,lr,[sp,-16]!             // save  registers
stp x3,x4,[sp,-16]!             // save  registers
mov x2,0
ldr x4,[x0,x2,lsl 3]
1:
cmp x2,x1
bge 99f
ldr x3,[x0,x2, lsl 3]
cmp x3,x4
blt 98f
mov x4,x3
b 1b
98:
mov x0,0                       // not sorted
b 100f
99:
mov x0,1                       // sorted
100:
ldp x3,x4,[sp],16              // restaur  2 registers
ldp x2,lr,[sp],16              // restaur  2 registers
/***************************************************/
/*   return permutation one by one                 */
/* sur une idée de vincent Moresmau                */
/* use algorytm heap iteratif see wikipedia        */
/***************************************************/
/* x0 contains the address of structure permutations */
/* x0 return address  of value table or zéro if end */
newPermutation:
stp x1,lr,[sp,-16]!             // save  registers
stp x2,x3,[sp,-16]!             // save  registers
stp x4,x5,[sp,-16]!             // save  registers
stp x6,x7,[sp,-16]!             // save  registers
cmp x2,0
bne 2f
// first call -> init area on heap
mov x7,x0
ldr x1,[x7,perm_size]
lsl x3,x1,3                     // 8 bytes by count table
add x3,x3,8                     // 8 bytes for current index
mov x0,0                        // allocation place heap
mov x8,BRK                      // call system 'brk'
svc 0
mov x2,x0                       // save address heap
mov x8,BRK                      // call system 'brk'
svc #0
cmp x0,-1                       // allocation error
beq 100f
mov x3,0
1:                                  // loop init
str xzr,[x8,x3,lsl 3]           // init to zéro area heap
cmp x3,x1
blt 1b
str xzr,[x2]                    // store zero to index
ldr x0,[x7,perm_adrtable]       // return first permutation
b 100f

2:                                  // other calls x2 contains heap address
ldr x1,[x7,perm_size]           // elements number
ldr x3,[x2]                     // load current index
3:
ldr x4,[x8,x3,lsl 3]            // load count [i]
cmp x4,x3                       // compare with i
bge 6f
tst x3,#1                       // even ?
bne 4f
ldr x5,[x0]                     // yes load value A[0]
ldr x6,[x0,x3,lsl 3]            // and swap with value A[i]
str x6,[x0]
str x5,[x0,x3,lsl 3]
b 5f
4:
ldr x5,[x0,x4,lsl 3]            // no load value A[count[i]]
ldr x6,[x0,x3,lsl 3]            // and swap with value A[i]
str x6,[x0,x4,lsl 3]
str x5,[x0,x3,lsl 3]
5:
str x4,[x8,x3,lsl 3]            // store new count [i]
str xzr,[x2]                    // store new index
b 100f                          // and return new permutation in x0
6:
str xzr,[x8,x3,lsl 3]           // store zero in count [i]
cmp x3,x1                       // end
blt 3b                          // loop
mov x0,0                        // if end -> return zero

100:                               // end function
ldp x6,x7,[sp],16               // restaur  1 register
ldp x4,x5,[sp],16               // restaur  1 register
ldp x2,x3,[sp],16               // restaur  2 registers
ldp x1,lr,[sp],16               // restaur  2 registers

/******************************************************************/
/*      Display table elements                                */
/******************************************************************/
/* x0 contains the address of table */
displayTable:
stp x1,lr,[sp,-16]!              // save  registers
stp x2,x3,[sp,-16]!              // save  registers
mov x3,0
1:                                   // loop display table
ldr x0,[x2,x3,lsl 3]
bl conversion10S                  // décimal conversion
bl strInsertAtCharInc            // insert result at // character
bl affichageMess                 // display message
cmp x3,NBELEMENTS - 1
ble 1b
bl affichageMess
mov x0,x2
100:
ldp x2,x3,[sp],16               // restaur  2 registers
ldp x1,lr,[sp],16               // restaur  2 registers
/********************************************************/
/*        File Include fonctions                        */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"```
```Value  : -5
Value  : +1
Value  : +2
Value  : +3
Value  : +4
Value  : +6
Value  : +7
Value  : +8
Value  : +9
Value  : +10

Table sorted.
sorted in  +3467024 permutations
```

## ActionScript

```//recursively builds the permutations of permutable, appended to front, and returns the first sorted permutation it encounters
function permutations(front:Array, permutable:Array):Array {
//If permutable has length 1, there is only one possible permutation. Check whether it's sorted
if (permutable.length==1)
return isSorted(front.concat(permutable));
else
//There are multiple possible permutations. Generate them.
var i:uint=0,tmp:Array=null;
do
{
tmp=permutations(front.concat([permutable[i]]),remove(permutable,i));
i++;
}while (i< permutable.length && tmp == null);
//If tmp != null, it contains the sorted permutation. If it does not contain the sorted permutation, return null. Either way, return tmp.
return tmp;
}
//returns the array if it's sorted, or null otherwise
function isSorted(data:Array):Array {
for (var i:uint = 1; i < data.length; i++)
if (data[i]<data[i-1])
return null;
return data;
}
//returns a copy of array with the i'th element removed
function remove(array:Array, i:uint):Array {
return array.filter(function(item,index,array){return(index !=i)}) ;
}
//wrapper around the permutation function to provide a more logical interface
function permutationSort(array:Array):Array {
return permutations([],array);
}
```

## ARM Assembly

Works with: as version Raspberry Pi
```/* ARM assembly Raspberry PI  */
/*  program permutationSort.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   1,3,6,2,5,9,10,8,5,7       @ for test 2 sames values
TableNumber:       .int   10,9,8,7,6,5,4,3,2,1
#TableNumber:       .int   1,2,3
.equ NBELEMENTS, (. - TableNumber) / 4
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss
sZoneConv:            .skip 24
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main
main:                                              @ entry of program
mov r1,#NBELEMENTS                             @ number of élements
bl heapIteratif
bl displayTable

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
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

/******************************************************************/
/*     permutation by heap iteratif (wikipedia)                                   */
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the eléments number  */
heapIteratif:
push {r3-r9,lr}                @ save registers
mov r8,r0                      @ save table address
lsl r9,r1,#2                   @ four bytes by count
sub sp,sp,r9
mov fp,sp
mov r3,#0
mov r4,#0                      @ index
1:                                 @ init area counter
str r4,[fp,r3,lsl #2]
cmp r3,r1
blt 1b

//bl displayTable
bl isSorted                     @ control sort
cmp r0,#1                       @ sorted ?
beq 99f
mov r0,r8                       @ restaur table address

mov r3,#0                       @ index
2:
ldr r4,[fp,r3,lsl #2]           @ load count [i]
cmp r4,r3                       @ compare with i
bge 5f
tst r3,#1                       @ even ?
bne 3f
ldr r5,[r0]                     @ yes load value A[0]
ldr r6,[r0,r3,lsl #2]           @ ans swap with value A[i]
str r6,[r0]
str r5,[r0,r3,lsl #2]
b 4f
3:
ldr r5,[r0,r4,lsl #2]         @ load value A[count[i]]
ldr r6,[r0,r3,lsl #2]         @ and swap with value A[i]
str r6,[r0,r4,lsl #2]
str r5,[r0,r3,lsl #2]
4:
//bl displayTable
bl isSorted                     @ control sort
cmp r0,#1                       @ sorted ?
beq 99f                         @ yes
mov r0,r8                       @ restaur table address
add r4,r4,#1                    @ increment count i
str r4,[fp,r3,lsl #2]           @ and store on stack
mov r3,#0                       @ raz index
b 2b                            @ and loop
5:
mov r4,#0                       @ raz count [i]
str r4,[fp,r3,lsl #2]
cmp r3,r1                       @ end ?
blt 2b                          @ no -> loop

99:
100:
pop {r3-r9,lr}
bx lr                           @ return
/******************************************************************/
/*     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:
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

/******************************************************************/
/*      Display table elements                                */
/******************************************************************/
/* r0 contains the address of table */
displayTable:
push {r0-r3,lr}                                    @ save registers
mov r3,#0
1:                                                     @ loop display table
ldr r0,[r2,r3,lsl #2]
bl conversion10S                                    @ décimal conversion
bl strInsertAtCharInc
bl affichageMess                                   @ display message
cmp r3,#NBELEMENTS - 1
ble 1b
bl affichageMess
mov r0,r2
100:
pop {r0-r3,lr}
bx lr
/***************************************************/
/*      ROUTINES INCLUDE                           */
/***************************************************/
.include "../affichage.inc"```

## Arturo

```sorted?: function [arr][
previous: first arr

loop slice arr 1 (size arr)-1 'item [
if not? item > previous -> return false
previous: item
]
return true
]

permutationSort: function [items][
loop permutate items 'perm [
if sorted? perm -> return perm
]
]

print permutationSort [3 1 2 8 5 7 9 4 6]
```
Output:
`1 2 3 4 5 6 7 8 9`

## AutoHotkey

ahk forum: discussion

```MsgBox % PermSort("")
MsgBox % PermSort("xxx")
MsgBox % PermSort("3,2,1")
MsgBox % PermSort("dog,000000,xx,cat,pile,abcde,1,cat")

PermSort(var) {                          ; SORT COMMA SEPARATED LIST
Local i, sorted
StringSplit a, var, `,                ; make array, size = a0

v0 := a0                              ; auxiliary array for permutations
Loop %v0%
v%A_Index% := A_Index

While unSorted("a","v")               ; until sorted
NextPerm("v")                      ; try new permutations

Loop % a0                             ; construct string from sorted array
i := v%A_Index%, sorted .= "," . a%i%
Return SubStr(sorted,2)               ; drop leading comma
}

unSorted(a,v) {
Loop % %a%0-1 {
i := %v%%A_Index%, j := A_Index+1, j := %v%%j%
If (%a%%i% > %a%%j%)
Return 1
}
}

NextPerm(v) { ; the lexicographically next LARGER permutation of v1..v%v0%
Local i, i1, j, t
i := %v%0, i1 := i-1
While %v%%i1% >= %v%%i% {
--i, --i1
IfLess i1,1, Return 1 ; Signal the end
}
j := %v%0
While %v%%j% <= %v%%i1%
--j
t := %v%%i1%, %v%%i1% := %v%%j%, %v%%j% := t,  j := %v%0
While i < j
t := %v%%i%, %v%%i% := %v%%j%, %v%%j% := t, ++i, --j
}
```

## BBC BASIC

```      DIM test(9)
test() = 4, 65, 2, 31, 0, 99, 2, 83, 782, 1

perms% = 0
WHILE NOT FNsorted(test())
perms% += 1
PROCnextperm(test())
ENDWHILE
PRINT ;perms% " permutations required to sort "; DIM(test(),1)+1 " items."
END

DEF PROCnextperm(a())
LOCAL last%, maxindex%, p%
maxindex% = DIM(a(),1)
IF maxindex% < 1 THEN ENDPROC
p% = maxindex%-1
WHILE a(p%) >= a(p%+1)
p% -= 1
IF p% < 0 THEN
PROCreverse(a(), 0, maxindex%)
ENDPROC
ENDIF
ENDWHILE
last% = maxindex%
WHILE a(last%) <= a(p%)
last% -= 1
ENDWHILE
SWAP a(p%), a(last%)
PROCreverse(a(), p%+1, maxindex%)
ENDPROC

DEF PROCreverse(a(), first%, last%)
WHILE first% < last%
SWAP a(first%), a(last%)
first% += 1
last% -= 1
ENDWHILE
ENDPROC

DEF FNsorted(d())
LOCAL I%
FOR I% = 1 TO DIM(d(),1)
IF d(I%) < d(I%-1) THEN = FALSE
NEXT
= TRUE
```
Output:
```980559 permutations required to sort 10 items.
```

## C

Just keep generating next lexicographic permutation until the last one; it's sorted by definition.

```#include <stdio.h>
#include <stdlib.h>
#include <string.h>

typedef int(*cmp_func)(const void*, const void*);

void perm_sort(void *a, int n, size_t msize, cmp_func _cmp)
{
char *p, *q, *tmp = malloc(msize);
#	define A(i) ((char *)a + msize * (i))
#	define swap(a, b) {\
memcpy(tmp, a, msize);\
memcpy(a, b, msize);\
memcpy(b, tmp, msize);	}
while (1) {
/* find largest k such that a[k - 1] < a[k] */
for (p = A(n - 1); (void*)p > a; p = q)
if (_cmp(q = p - msize, p) > 0)
break;

if ((void*)p <= a) break;

/* find largest l such that a[l] > a[k - 1] */
for (p = A(n - 1); p > q; p-= msize)
if (_cmp(q, p) > 0) break;

swap(p, q); /* swap a[k - 1], a[l] */
/* flip a[k] through a[end] */
for (q += msize, p = A(n - 1); q < p; q += msize, p -= msize)
swap(p, q);
}
free(tmp);
}

int scmp(const void *a, const void *b) { return strcmp(*(const char *const *)a, *(const char *const *)b); }

int main()
{
int i;
const char *strs[] = { "spqr", "abc", "giant squid", "stuff", "def" };
perm_sort(strs, 5, sizeof(*strs), scmp);

for (i = 0; i < 5; i++)
printf("%s\n", strs[i]);
return 0;
}
```

## C#

```public static class PermutationSorter
{
public static void Sort<T>(List<T> list) where T : IComparable
{
PermutationSort(list, 0);
}
public static bool PermutationSort<T>(List<T> list, int i) where T : IComparable
{
int j;
if (issorted(list, i))
{
return true;
}
for (j = i + 1; j < list.Count; j++)
{
T temp = list[i];
list[i] = list[j];
list[j] = temp;
if (PermutationSort(list, i + 1))
{
return true;
}
temp = list[i];
list[i] = list[j];
list[j] = temp;
}
return false;
}
public static bool issorted<T>(List<T> list, int i) where T : IComparable
{
for (int j = list.Count-1; j > 0; j--)
{
if(list[j].CompareTo(list[j-1])<0)
{
return false;
}
}
return true;
}
}```

## C++

Since next_permutation already returns whether the resulting sequence is sorted, the code is quite simple:

```#include <algorithm>

template<typename ForwardIterator>
void permutation_sort(ForwardIterator begin, ForwardIterator end)
{
while (std::next_permutation(begin, end))
{
// -- this block intentionally left empty --
}
}
```

## Clojure

```(use '[clojure.contrib.combinatorics :only (permutations)])

(defn permutation-sort [s]
(first (filter (partial apply <=) (permutations s))))

(permutation-sort [2 3 5 3 5])
```

## CoffeeScript

```# This code takes a ridiculously inefficient algorithm and rather futilely
# optimizes one part of it.  Permutations are computed lazily.

sorted_copy = (a) ->
# This returns a sorted copy of an array by lazily generating
# permutations of indexes and stopping when the indexes yield
# a sorted array.
indexes = [0...a.length]
ans = find_matching_permutation indexes, (permuted_indexes) ->
new_array = (a[i] for i in permuted_indexes)
console.log permuted_indexes, new_array
in_order(new_array)
(a[i] for i in ans)

in_order = (a) ->
# return true iff array a is in increasing order.
return true if a.length <= 1
for i in [0...a.length-1]
return false if a[i] > a[i+1]
true

get_factorials = (n) ->
# return an array of the first n+1 factorials, starting with 0!
ans = [1]
f = 1
for i in [1..n]
f *= i
ans.push f
ans

permutation = (a, i, factorials) ->
# Return the i-th permutation of an array by
# using remainders of factorials to determine
# elements.
while a.length > 0
f = factorials[a.length-1]
n = Math.floor(i / f)
i = i % f
elem = a[n]
a = a[0...n].concat(a[n+1...])
elem
# The above loop gets treated like
# an array expression, so it returns
# all the elements.

find_matching_permutation = (a, f_match) ->
factorials = get_factorials(a.length)
for i in [0...factorials[a.length]]
permuted_array = permutation(a, i, factorials)
if f_match permuted_array
return permuted_array
null

do ->
a = ['c', 'b', 'a', 'd']
console.log 'input:', a
ans = sorted_copy a
console.log 'DONE!'
console.log 'sorted copy:', ans
```
Output:
```> coffee permute_sort.coffee
input: [ 'c', 'b', 'a', 'd' ]
[ 0, 1, 2, 3 ] [ 'c', 'b', 'a', 'd' ]
[ 0, 1, 3, 2 ] [ 'c', 'b', 'd', 'a' ]
[ 0, 2, 1, 3 ] [ 'c', 'a', 'b', 'd' ]
[ 0, 2, 3, 1 ] [ 'c', 'a', 'd', 'b' ]
[ 0, 3, 1, 2 ] [ 'c', 'd', 'b', 'a' ]
[ 0, 3, 2, 1 ] [ 'c', 'd', 'a', 'b' ]
[ 1, 0, 2, 3 ] [ 'b', 'c', 'a', 'd' ]
[ 1, 0, 3, 2 ] [ 'b', 'c', 'd', 'a' ]
[ 1, 2, 0, 3 ] [ 'b', 'a', 'c', 'd' ]
[ 1, 2, 3, 0 ] [ 'b', 'a', 'd', 'c' ]
[ 1, 3, 0, 2 ] [ 'b', 'd', 'c', 'a' ]
[ 1, 3, 2, 0 ] [ 'b', 'd', 'a', 'c' ]
[ 2, 0, 1, 3 ] [ 'a', 'c', 'b', 'd' ]
[ 2, 0, 3, 1 ] [ 'a', 'c', 'd', 'b' ]
[ 2, 1, 0, 3 ] [ 'a', 'b', 'c', 'd' ]
DONE!
sorted copy: [ 'a', 'b', 'c', 'd' ]
```

## Common Lisp

Too bad `sorted?` vector code has to be copypasta'd. Could use map nil but that would in turn make it into spaghetti code.

The `nth-permutation` function is some classic algorithm from Wikipedia.

```(defun factorial (n)
(loop for result = 1 then (* i result)
for i from 2 to n
finally (return result)))

(defun nth-permutation (k sequence)
(if (zerop (length sequence))
(coerce () (type-of sequence))
(let ((seq (etypecase sequence
(vector (copy-seq sequence))
(sequence (coerce sequence 'vector)))))
(loop for j from 2 to (length seq)
do (setq k (truncate (/ k (1- j))))
do (rotatef (aref seq (mod k j))
(aref seq (1- j)))
finally (return (coerce seq (type-of sequence)))))))

(defun sortedp (fn sequence)
(etypecase sequence
(list (loop for previous = #1='#:foo then i
for i in sequence
always (or (eq previous #1#)
(funcall fn i previous))))
;; copypasta
(vector (loop for previous = #1# then i
for i across sequence
always (or (eq previous #1#)
(funcall fn i previous))))))

(defun permutation-sort (fn sequence)
(loop for i below (factorial (length sequence))
for permutation = (nth-permutation i sequence)
when (sortedp fn permutation)
do (return permutation)))
```
```CL-USER> (time (permutation-sort #'> '(8 3 10 6 1 9 7 2 5 4)))
Evaluation took:
5.292 seconds of real time
5.204325 seconds of total run time (5.176323 user, 0.028002 system)
[ Run times consist of 0.160 seconds GC time, and 5.045 seconds non-GC time. ]
98.34% CPU
12,337,938,025 processor cycles
611,094,240 bytes consed

(1 2 3 4 5 6 7 8 9 10)
```

## Crystal

```def sorted?(items : Array)
prev = items[0]
items.each do |item|
if item < prev
return false
end
prev = item
end
return true
end

def permutation_sort(items : Array)
items.each_permutation do |permutation|
if sorted?(permutation)
return permutation
end
end
end
```

## D

### Basic Version

This uses the second (lazy) permutations from the Permutations Task.

```import std.stdio, std.algorithm, permutations2;

void permutationSort(T)(T[] items) pure nothrow @safe @nogc {
foreach (const perm; items.permutations!false)
if (perm.isSorted)
break;
}

void main() {
auto data = [2, 7, 4, 3, 5, 1, 0, 9, 8, 6, -1];
data.permutationSort;
data.writeln;
}
```
Output:
`[-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]`

The run-time is about 0.52 seconds with ldc2.

### Alternative Version

Translation of: C++
```import std.stdio, std.algorithm;

void permutationSort(T)(T[] items) pure nothrow @safe @nogc {
while (items.nextPermutation) {}
}

void main() {
auto data = [2, 7, 4, 3, 5, 1, 0, 9, 8, 6, -1];
data.permutationSort;
data.writeln;
}
```

The output is the same. Run-time about 1.04 seconds with ldc2 (the C++ entry with G++ takes about 0.4 seconds).

## E

Translation of: C++
```def swap(container, ixA, ixB) {
def temp := container[ixA]
container[ixA] := container[ixB]
container[ixB] := temp
}

/** Reverse order of elements of 'sequence' whose indexes are in the interval [ixLow, ixHigh] */
def reverseRange(sequence, var ixLow, var ixHigh) {
while (ixLow < ixHigh) {
swap(sequence, ixLow, ixHigh)
ixLow += 1
ixHigh -= 1
}
}

/** Algorithm from <http://marknelson.us/2002/03/01/next-permutation>, allegedly from a version of the C++ STL */
def nextPermutation(sequence) {
def last := sequence.size() - 1
var i := last
while (true) {
var ii := i
i -= 1
if (sequence[i] < sequence[ii]) {
var j := last + 1
while (!(sequence[i] < sequence[j -= 1])) {} # buried side effect
swap(sequence, i, j)
reverseRange(sequence, ii, last)
return true
}
if (i == 0) {
reverseRange(sequence, 0, last)
return false
}
}
}

/** Note: Worst case on sorted list */
def permutationSort(flexList) {
while (nextPermutation(flexList)) {}
}```

## EasyLang

```global perm[] .
proc nextperm . a[] .
n = len perm[]
k = n - 1
while k >= 1 and perm[k + 1] <= perm[k]
k -= 1
.
if k = 0
a[] = [ ]
return
.
l = n
while perm[l] <= perm[k]
l -= 1
.
swap perm[l] perm[k]
swap a[l] a[k]
k += 1
while k < n
swap perm[k] perm[n]
swap a[k] a[n]
k += 1
n -= 1
.
.
proc perminit . a[] .
for i to len a[]
perm[] &= i
.
.
proc permsort . a[] .
perminit a[]
repeat
for i = 2 to len a[]
if a[i - 1] > a[i]
break 1
.
.
until i > len a[]
nextperm a[]
if len a[] = 0
print "error"
break 1
.
.
.
arr[] = [ 7 6 5 9 8 4 3 1 2 0 ]
permsort arr[]
print arr[]```
Output:
```[ 0 1 2 3 4 5 6 7 8 9 ]
```

## EchoLisp

```;; This efficient sort method uses the list library for permutations

(lib 'list)
(define (in-order L)
(cond
((empty? L) #t)
((empty? (rest L)) #t)
(else (and ( < (first L) (second  L)) (in-order (rest L))))))

(define L (shuffle (iota 6)))
→ (1 5 4 2 0 3)

(for ((p (in-permutations (length L ))))
#:when (in-order (list-permute L p))
(writeln (list-permute L p)) #:break #t)

→ (0 1 2 3 4 5)
```

## Elixir

```defmodule Sort do
def permutation_sort([]), do: []
def permutation_sort(list) do
Enum.find(permutation(list), fn [h|t] -> in_order?(t, h) end)
end

defp permutation([]), do: [[]]
defp permutation(list) do
for x <- list, y <- permutation(list -- [x]), do: [x|y]
end

defp in_order?([], _), do: true
defp in_order?([h|_], pre) when h<pre, do: false
defp in_order?([h|t], _), do: in_order?(t, h)
end

IO.inspect list = for _ <- 1..9, do: :rand.uniform(20)
IO.inspect Sort.permutation_sort(list)
```
Output:
```[18, 2, 19, 10, 17, 10, 14, 8, 3]
[2, 3, 8, 10, 10, 14, 17, 18, 19]
```

## EMal

Translation of: Java
```type PermutationSort
fun isSorted = logic by List a
for int i = 1; i < a.length; ++i
if a[i - 1] > a[i] do return false end
end
return true
end
fun permute = void by List a, int n, List lists
if n == 1
List b = int[]
for int i = 0; i < a.length; ++i
b.append(a[i])
end
lists.append(b)
return
end
int i = 0
while i < n
a.swap(i, n - 1)
permute(a, n - 1, lists)
a.swap(i, n - 1)
i = i + 1
end
end
fun sort = List by List a
List lists = List[]
permute(a, a.length, lists)
for each List list in lists
if isSorted(list) do return list end
end
return a
end
type Main
List a = int[3,2,1,8,9,4,6]
writeLine("Unsorted: " + a)
a = PermutationSort.sort(a)
writeLine("  Sorted: " + a)```
Output:
```Unsorted: [3,2,1,8,9,4,6]
Sorted: [1,2,3,4,6,8,9]
```

## Factor

```USING: grouping io math.combinatorics math.order prettyprint ;
IN: rosetta-code.permutation-sort

: permutation-sort ( seq -- seq' )
[ [ before=? ] monotonic? ] find-permutation ;

{ 10 2 6 8 1 4 3 } permutation-sort .
"apple" permutation-sort print
```
Output:
```{ 1 2 3 4 6 8 10 }
aelpp
```

## FreeBASIC

```' version 07-04-2017
' compile with: fbc -s console

' Heap's algorithm non-recursive
Function permutation_sort(a() As ULong) As ULong

Dim As ULong i, j, count
Dim As ULong lb = LBound(a), ub = UBound(a)
Dim As ULong n = ub - lb +1
Dim As ULong c(lb To ub)

While i < n
If c(i) < i Then
If (i And 1) = 0 Then
Swap a(0), a(i)
Else
Swap a(c(i)), a(i)
End If
count += 1
For j = lb To ub -1
If a(j) > a(j +1) Then j = 99
Next
If j < 99 Then Return count
c(i) += 1
i = 0
Else
c(i) = 0
i += 1
End If
Wend

End Function

' ------=< MAIN >=------

Dim As ULong k, p, arr(0 To 9)
Randomize Timer

Print "unsorted array"
For k = LBound(arr) To UBound(arr)
arr(k) = Rnd * 1000
Print arr(k) & IIf(k = UBound(arr), "", ", ");
Next
Print : Print

p = permutation_sort(arr())

Print "sorted array"
For k = LBound(arr) To UBound(arr)
Print arr(k) & IIf(k = UBound(arr), "", ", ");
Next
Print : Print
Print "sorted array in "; p; " permutations"

' empty keyboard buffer
While Inkey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End```
Output:
```unsorted array
81, 476, 915, 357, 934, 683, 413, 450, 2, 407

sorted array
2, 81, 357, 407, 413, 450, 476, 683, 915, 934

sorted array in 1939104 permutations```

## Go

Not following the pseudocode, it seemed simpler to just test sorted at the bottom of a recursive permutation generator.

```package main

import "fmt"

var a = []int{170, 45, 75, -90, -802, 24, 2, 66}

// in place permutation sort of slice a
func main() {
fmt.Println("before:", a)
if len(a) > 1 && !recurse(len(a) - 1) {
// recurse should never return false from the top level.
// if it does, it means some code somewhere is busted,
// either the the permutation generation code or the
// sortedness testing code.
}
fmt.Println("after: ", a)
}

// recursive permutation generator
func recurse(last int) bool {
if last <= 0 {
// bottom of recursion.  test if sorted.
for i := len(a) - 1; a[i] >= a[i-1]; i-- {
if i == 1 {
return true
}
}
return false
}
for i := 0; i <= last; i++ {
a[i], a[last] = a[last], a[i]
if recurse(last - 1) {
return true
}
a[i], a[last] = a[last], a[i]
}
return false
}
```

## Groovy

Permutation sort is an astonishingly inefficient sort algorithm. To even begin to make it tractable, we need to be able to create enumerated permutations on the fly, rather than relying on Groovy's List.permutations() method. For a list of length N there are N! permutations. In this solution, makePermutation creates the Ith permutation to order based on a recursive construction of a unique indexed permutation. The sort method then checks to see if that permutation is sorted, and stops when it is.

I believe that this method of constructing permutations results in a stable sort, but I have not actually proven that assertion.

```def factorial = { (it > 1) ? (2..it).inject(1) { i, j -> i*j } : 1 }

def makePermutation;
makePermutation = { list, i ->
def n = list.size()
if (n < 2) return list
def fact = factorial(n-1)
assert i < fact*n

def index = i.intdiv(fact)
[list[index]] + makePermutation(list[0..<index] + list[(index+1)..<n], i % fact)
}

def sorted = { a -> (1..<(a.size())).every { a[it-1] <= a[it] } }

def permutationSort = { a ->
def n = a.size()
def fact = factorial(n)
def permuteA = makePermutation.curry(a)
def pIndex = (0..<fact).find { print "."; sorted(permuteA(it)) }
permuteA(pIndex)
}
```

Test:

```println permutationSort([7,0,12,-45,-1])
println ()
println permutationSort([10, 10.0, 10.00, 1])
println permutationSort([10, 10.00, 10.0, 1])
println permutationSort([10.0, 10, 10.00, 1])
println permutationSort([10.0, 10.00, 10, 1])
println permutationSort([10.00, 10, 10.0, 1])
println permutationSort([10.00, 10.0, 10, 1])
```

The examples with distinct integer and decimal values that compare as equal are there to demonstrate, but not to prove, that the sort is stable.

Output:
```.............................................................................................[-45, -1, 0, 7, 12]

...................[1, 10, 10.0, 10.00]
...................[1, 10, 10.00, 10.0]
...................[1, 10.0, 10, 10.00]
...................[1, 10.0, 10.00, 10]
...................[1, 10.00, 10, 10.0]
...................[1, 10.00, 10.0, 10]```

```import Control.Monad

permutationSort l = head [p | p <- permute l, sorted p]

sorted (e1 : e2 : r) = e1 <= e2 && sorted (e2 : r)
sorted _             = True

permute              = foldM (flip insert) []

insert e []          = return [e]
insert e l@(h : t)   = return (e : l) `mplus`
do { t' <- insert e t ; return (h : t') }
```
Works with: GHC version 6.10
```import Data.List (permutations)

permutationSort l = head [p | p <- permutations l, sorted p]

sorted (e1 : e2 : r) = e1 <= e2 && sorted (e2 : r)
sorted _             = True
```

## Icon and Unicon

Partly from here

```procedure do_permute(l, i, n)
if i >= n then
return l
else
suspend l[i to n] <-> l[i] & do_permute(l, i+1, n)
end

procedure permute(l)
suspend do_permute(l, 1, *l)
end

procedure sorted(l)
local i
if (i := 2 to *l & l[i] >= l[i-1]) then return &fail else return 1
end

procedure main()
local l
l := [6,3,4,5,1]
|( l := permute(l) & sorted(l)) \1 & every writes(" ",!l)
end
```

## J

Generally, this task should be accomplished in J using `/:~`. Here we take an approach that's more comparable with the other examples on this page.

A function to locate the permuation index, in the naive manner prescribed by the task:

```ps =:(1+])^:((-.@-:/:~)@A.~)^:_ 0:
```

Of course, this can be calculated much more directly (and efficiently):

```ps =: A.@:/:
```

Either way:

```   list =: 2 7 4 3 5 1 0 9 8 6

ps list
2380483

2380483 A. list
0 1 2 3 4 5 6 7 8 9

(A.~ps) list
0 1 2 3 4 5 6 7 8 9
```

## Java

```import java.util.List;
import java.util.ArrayList;
import java.util.Arrays;

public class PermutationSort
{
public static void main(String[] args)
{
int[] a={3,2,1,8,9,4,6};
System.out.println("Unsorted: " + Arrays.toString(a));
a=pSort(a);
System.out.println("Sorted: " + Arrays.toString(a));
}
public static int[] pSort(int[] a)
{
List<int[]> list=new ArrayList<int[]>();
permute(a,a.length,list);
for(int[] x : list)
if(isSorted(x))
return x;
return a;
}
private static void permute(int[] a, int n, List<int[]> list)
{
if (n == 1)
{
int[] b=new int[a.length];
System.arraycopy(a, 0, b, 0, a.length);
return;
}
for (int i = 0; i < n; i++)
{
swap(a, i, n-1);
permute(a, n-1, list);
swap(a, i, n-1);
}
}
private static boolean isSorted(int[] a)
{
for(int i=1;i<a.length;i++)
if(a[i-1]>a[i])
return false;
return true;
}
private static void swap(int[] arr,int i, int j)
{
int temp=arr[i];
arr[i]=arr[j];
arr[j]=temp;
}
}```
Output:
```Unsorted: [3, 2, 1, 8, 9, 4, 6]
Sorted: [1, 2, 3, 4, 6, 8, 9]
```

## jq

Infrastructure: The following function generates a stream of permutations of an arbitrary JSON array:

```def permutations:
if length == 0 then []
else
. as \$in
| range(0;length) as \$i
| (\$in|del(.[\$i])|permutations)
| [\$in[\$i]] + .
end ;```

Next is a generic function for checking whether the input array is non-decreasing. If your jq has until/2 then its definition here can be removed.

```def sorted:
def until(cond; next):
def _until: if cond then . else (next|_until) end;
_until;

length as \$length
| if \$length <= 1 then true
else . as \$in
| 1 | until( . == \$length or \$in[.-1] > \$in[.] ; .+1) == \$length
end;```

Permutation-sort:

The first permutation-sort solution presented here works with jq 1.4 but is slower than the subsequent solution, which uses the "foreach" construct introduced after the release of jq 1.4. "foreach" allows a stream generator to be interrupted.

Works with: jq version 1.4
```def permutation_sort_slow:
reduce permutations as \$p (null; if . then . elif (\$p | sorted) then \$p else . end);```
Works with: jq version with foreach
```def permutation_sort:
# emit the first item in stream that satisfies the condition
def first(stream; cond):
label \$out
| foreach stream as \$item
( [false, null];
if .[0] then break \$out else [(\$item | cond), \$item] end;
if .[0] then .[1] else empty end );
first(permutations; sorted);```

Example:

`["too", true, 1, 0, {"a":1},  {"a":0} ] | permutation_sort`
Output:
```\$ jq -c -n -f Permutation_sort.jq
[true,0,1,"too",{"a":0},{"a":1}]
```

## Julia

```# v0.6

using Combinatorics

function permsort(x::Array)
for perm in permutations(x)
if issorted(perm)
return perm
end
end
end

x = randn(10)
@show x permsort(x)
```
Output:
```x = [-0.799206, -2.52542, 0.677947, -1.85139, 0.744764, 1.5327, 0.808935, -0.876105, -0.234308, 0.874579]
permsort(x) = [-2.52542, -1.85139, -0.876105, -0.799206, -0.234308, 0.677947, 0.744764, 0.808935, 0.874579, 1.5327]```

## Kotlin

```// version 1.1.2

fun <T : Comparable<T>> isSorted(list: List<T>): Boolean {
val size = list.size
if (size < 2) return true
for (i in 1 until size) {
if (list[i] < list[i - 1]) return false
}
return true
}

fun <T : Comparable<T>> permute(input: List<T>): List<List<T>> {
if (input.size == 1) return listOf(input)
val perms = mutableListOf<List<T>>()
val toInsert = input[0]
for (perm in permute(input.drop(1))) {
for (i in 0..perm.size) {
val newPerm = perm.toMutableList()
}
}
return perms
}

fun <T : Comparable<T>> permutationSort(input: List<T>): List<T> {
if (input.size == 1) return input
val toInsert = input[0]
for (perm in permute(input.drop(1))) {
for (i in 0..perm.size) {
val newPerm = perm.toMutableList()
if (isSorted(newPerm)) return newPerm
}
}
return input
}

fun main(args: Array<String>) {
val input = listOf('d', 'b', 'e', 'a', 'f', 'c')
println("Before sorting : \$input")
val output = permutationSort(input)
println("After sorting  : \$output")
println()
val input2 = listOf("first", "second", "third", "fourth", "fifth", "sixth")
println("Before sorting : \$input2")
val output2 = permutationSort(input2)
println("After sorting  : \$output2")
}
```
Output:
```Before sorting : [d, b, e, a, f, c]
After sorting  : [a, b, c, d, e, f]

Before sorting : [first, second, third, fourth, fifth, sixth]
After sorting  : [fifth, first, fourth, second, sixth, third]
```

## Lua

```-- Return an iterator to produce every permutation of list
function permute (list)
local function perm (list, n)
if n == 0 then coroutine.yield(list) end
for i = 1, n do
list[i], list[n] = list[n], list[i]
perm(list, n - 1)
list[i], list[n] = list[n], list[i]
end
end
return coroutine.wrap(function() perm(list, #list) end)
end

-- Return true if table t is in ascending order or false if not
function inOrder (t)
for pos = 2, #t do
if t[pos] < t[pos - 1] then
return false
end
end
return true
end

-- Main procedure
local list = {2,3,1}                 --\   Written to match task pseudocode,
local nextPermutation = permute(list) --\  more idiomatic would be:
while not inOrder(list) do             --\
list = nextPermutation()             --/   for p in permute(list) do
end                                   --/       stuffWith(p)
print(unpack(list))                  --/     end
```
Output:
`1       2       3`

## Maple

```arr := Array([17,0,-1,72,0]):
len := numelems(arr):
P := Iterator:-Permute(len):
for p in P do
lst:= convert(arr[sort(convert(p,list),output=permutation)],list):
if (ListTools:-Sorted(lst)) then
print(lst):
break:
end if:
end do:```
Output:
`[-1,0,0,17,72]`

## Mathematica/Wolfram Language

Here is a one-line solution. A custom order relation can be defined for the OrderedQ[] function.

```PermutationSort[x_List] := NestWhile[RandomSample, x, Not[OrderedQ[#]] &]
```

## MATLAB / Octave

```function list = permutationSort(list)

permutations = perms(1:numel(list)); %Generate all permutations of the item indicies

%Test every permutation of the indicies of the original list
for i = (1:size(permutations,1))
if issorted( list(permutations(i,:)) )
list = list(permutations(i,:));
return %Once the correct permutation of the original list is found break out of the program
end
end

end
```

Sample Usage:

```>> permutationSort([4 3 1 5 6 2])

ans =

1     2     3     4     5     6
```

## MAXScript

```fn inOrder arr =
(
if arr.count < 2 then return true
else
(
local i = 1
while i < arr.count do
(
if arr[i+1] < arr[i] do return false
i += 1
)
return true
)
)

fn permutations arr =
(
if arr.count <= 1 then return arr
else
(
for i = 1 to arr.count do
(
local rest = for r in 1 to arr.count where r != i collect arr[r]
local permRest = permutations rest
local new = join #(arr[i]) permRest
if inOrder new do return new
)
)
)```

Output:

```a = for i in 1 to 9 collect random 1 20
#(10, 20, 17, 15, 17, 15, 3, 11, 15)
permutations a
#(3, 10, 11, 15, 15, 15, 17, 17, 20)```

Warning: This algorithm is very inefficient and Max will crash very quickly with bigger arrays.

## NetRexx

Uses the permutation iterator RPermutationIterator at Permutations to generate the permutations.

```/* NetRexx */
options replace format comments java crossref symbols nobinary

import java.util.List
import java.util.ArrayList

numeric digits 20

class RSortingPermutationsort public

properties private static
iterations
maxIterations

-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method permutationSort(vlist = List) public static returns List
perm = RPermutationIterator(vlist)
iterations = 0
maxIterations = RPermutationIterator.factorial(vlist.size())
loop while perm.hasNext()
iterations = iterations + 1
pl = List perm.next()
if isSorted(pl) then leave
else pl = null
end
return pl

-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method isSorted(ss = List) private static returns boolean
status = isTrue
loop ix = 1 while ix < ss.size()
vleft  = Rexx ss.get(ix - 1)
vright = Rexx ss.get(ix)
if vleft.datatype('N') & vright.datatype('N')
then vtest = vleft > vright  -- For numeric types we must use regular comparison.
else vtest = vleft >> vright -- For non-numeric/mixed types we must do strict comparison.
if vtest then do
status = isFalse
leave ix
end
end ix
return status

-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method runSample(arg) private static
placesList = -
"UK  London,     US  New York,   US  Boston,     US  Washington" -
"UK  Washington, US  Birmingham, UK  Birmingham, UK  Boston"
anotherList = 'Alpha, Beta, Gamma, Beta'
reversed = '7, 6, 5, 4, 3, 2, 1'
unsorted = '734, 3, 1, 24, 324, -1024, -666, -1, 0, 324, 99999999'
lists = [makeList(placesList), makeList(anotherList), makeList(reversed), makeList(unsorted)]
loop il = 0 while il < lists.length
vlist = lists[il]
say vlist
runtime = System.nanoTime()
rlist = permutationSort(vlist)
runtime = System.nanoTime() - runtime
if rlist \= null then say rlist
else say 'sort failed'
say 'This permutation sort of' vlist.size() 'elements took' iterations 'passes (of' maxIterations') to complete. \-'
say 'Elapsed time:' (runtime / 10 ** 9)'s.'
say
end il
return

-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method makeList(in) public static returns List
lst = ArrayList()
loop while in > ''
parse in val ',' in
end
return lst
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method main(args = String[]) public static
runSample(Rexx(args))
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method isTrue() public static returns boolean
return (1 == 1)
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method isFalse() public static returns boolean
return (1 == 0)```
Output:
```[UK  London, US  New York, US  Boston, US  Washington UK  Washington, US  Birmingham, UK  Birmingham, UK  Boston]
[UK  Birmingham, UK  Boston, UK  London, US  Birmingham, US  Boston, US  New York, US  Washington UK  Washington]
This permutation sort of 7 elements took 4221 passes (of 5040) to complete. Elapsed time: 0.361959s.

[Alpha, Beta, Gamma, Beta]
[Alpha, Beta, Beta, Gamma]
This permutation sort of 4 elements took 2 passes (of 24) to complete. Elapsed time: 0.000113s.

[7, 6, 5, 4, 3, 2, 1]
[1, 2, 3, 4, 5, 6, 7]
This permutation sort of 7 elements took 5040 passes (of 5040) to complete. Elapsed time: 0.267956s.

[734, 3, 1, 24, 324, -1024, -666, -1, 0, 324, 99999999]
[-1024, -666, -1, 0, 1, 3, 24, 324, 324, 734, 99999999]
This permutation sort of 11 elements took 20186793 passes (of 39916800) to complete. Elapsed time: 141.461863s.
```

## Nim

```iterator permutations[T](ys: openarray[T]): seq[T] =
var
d = 1
c = newSeq[int](ys.len)
xs = newSeq[T](ys.len)

for i, y in ys: xs[i] = y
yield xs

block outter:
while true:
while d > 1:
dec d
c[d] = 0
while c[d] >= d:
inc d
if d >= ys.len: break outter

let i = if (d and 1) == 1: c[d] else: 0
swap xs[i], xs[d]
yield xs
inc c[d]

proc isSorted[T](s: openarray[T]): bool =
var last = low(T)
for c in s:
if c < last:
return false
last = c
return true

proc permSort[T](a: openarray[T]): seq[T] =
for p in a.permutations:
if p.isSorted:
return p

var a = @[4, 65, 2, -31, 0, 99, 2, 83, 782]
echo a.permSort
```
Output:
`@[-31, 0, 2, 2, 4, 65, 83, 99, 782]`

## OCaml

Like the Haskell version, except not evaluated lazily. So it always computes all the permutations, before searching through them for a sorted one; which is more expensive than necessary; unlike the Haskell version, which stops generating at the first sorted permutation.

```let rec sorted = function
| e1 :: e2 :: r -> e1 <= e2 && sorted (e2 :: r)
| _             -> true

let rec insert e = function
| []          -> [[e]]
| h :: t as l -> (e :: l) :: List.map (fun t' -> h :: t') (insert e t)

let permute xs = List.fold_right (fun h z -> List.concat (List.map (insert h) z))
xs [[]]

let permutation_sort l = List.find sorted (permute l)
```

## PARI/GP

```permutationSort(v)={
my(u);
for(k=1,(#v)!,
u=vecextract(v, numtoperm(#v,k));
for(i=2,#u,
if(u[i]<u[i-1], next(2))
);
return(u)
)
};```

## Perl

Pass a list in by reference, and sort in situ.

```sub psort {
my (\$x, \$d) = @_;

unless (\$d //= \$#\$x) {
\$x->[\$_] < \$x->[\$_ - 1] and return for 1 .. \$#\$x;
return 1
}

for (0 .. \$d) {
unshift @\$x, splice @\$x, \$d, 1;
next if \$x->[\$d] < \$x->[\$d - 1];
return 1 if psort(\$x, \$d - 1);
}
}

my @a = map+(int rand 100), 0 .. 10;
print "Before:\t@a\n";
psort(\@a);
print "After:\t@a\n"
```
Output:
```Before: 94 15 42 35 55 24 96 14 61 94 43
After:  14 15 24 35 42 43 55 61 94 94 96```

## Phix

```with javascript_semantics

function inOrder(sequence s)
for i=2 to length(s) do
if s[i]<s[i-1] then return false end if
end for
return true
end function

function permutationSort(sequence s)
for n=1 to factorial(length(s)) do
sequence perm = permute(n,s)
if inOrder(perm) then return perm end if
end for
?9/0 -- should never happen
end function

?permutationSort({"dog",0,15.545,{"cat","pile","abcde",1},"cat"})
```
Output:
```{0,15.545,"cat","dog",{"cat","pile","abcde",1}}
```

## PHP

```function inOrder(\$arr){
for(\$i=0;\$i<count(\$arr);\$i++){
if(isset(\$arr[\$i+1])){
if(\$arr[\$i] > \$arr[\$i+1]){
return false;
}
}
}
return true;
}

function permute(\$items, \$perms = array( )) {
if (empty(\$items)) {
if(inOrder(\$perms)){
return \$perms;
}
}  else {
for (\$i = count(\$items) - 1; \$i >= 0; --\$i) {
\$newitems = \$items;
\$newperms = \$perms;
list(\$foo) = array_splice(\$newitems, \$i, 1);
array_unshift(\$newperms, \$foo);
\$res = permute(\$newitems, \$newperms);
if(\$res){
return \$res;
}
}
}
}

\$arr = array( 8, 3, 10, 6, 1, 9, 7, 2, 5, 4);
\$arr = permute(\$arr);
echo implode(',',\$arr);
```
`1,2,3,4,5,6,7,8,9,10`

## PicoLisp

```(de permutationSort (Lst)
(let L Lst
(recur (L)  # Permute
(if (cdr L)
(do (length L)
(T (recurse (cdr L)) Lst)
(rot L)
NIL )
(apply <= Lst) ) ) ) )```
Output:
```: (permutationSort (make (do 9 (link (rand 1 999)))))
-> (82 120 160 168 205 226 408 708 719)

: (permutationSort (make (do 9 (link (rand 1 999)))))
-> (108 212 330 471 667 716 739 769 938)

: (permutationSort (make (do 9 (link (rand 1 999)))))
-> (118 253 355 395 429 548 890 900 983)```

## PowerShell

```Function PermutationSort( [Object[]] \$indata, \$index = 0, \$k = 0 )
{
\$data = \$indata.Clone()
\$datal = \$data.length - 1
if( \$datal -gt 0 ) {
for( \$j = \$index; \$j -lt \$datal; \$j++ )
{
\$sorted = ( PermutationSort \$data ( \$index + 1 ) \$j )[0]
if( -not \$sorted )
{
\$temp = \$data[ \$index ]
\$data[ \$index ] = \$data[ \$j + 1 ]
\$data[ \$j + 1 ] = \$temp
}
}
if( \$index -lt ( \$datal - 1 ) )
{
PermutationSort \$data ( \$index + 1 ) \$j
} else {
\$sorted = \$true
for( \$i = 0; ( \$i -lt \$datal ) -and \$sorted; \$i++ )
{
\$sorted = ( \$data[ \$i ] -le \$data[ \$i + 1 ] )
}
\$sorted
\$data
}
}
}

0..4 | ForEach-Object { \$a = \$_; 0..4 | Where-Object { -not ( \$_ -match "\$a" ) } |
ForEach-Object { \$b = \$_; 0..4 | Where-Object { -not ( \$_ -match "\$a|\$b" ) } |
ForEach-Object { \$c = \$_; 0..4 | Where-Object { -not ( \$_ -match "\$a|\$b|\$c" ) } |
ForEach-Object { \$d = \$_; 0..4 | Where-Object { -not ( \$_ -match "\$a|\$b|\$c|\$d" ) } |
ForEach-Object { \$e=\$_; "\$( PermutationSort ( \$a, \$b, \$c, \$d, \$e ) )" }
}
}
}
}
\$l = 8; PermutationSort ( 1..\$l | ForEach-Object { \$Rand = New-Object Random }{ \$Rand.Next( 0, \$l - 1 ) } )
```

## Prolog

```permutation_sort(L,S) :- permutation(L,S), sorted(S).

sorted([]).
sorted([_]).
sorted([X,Y|ZS]) :- X =< Y, sorted([Y|ZS]).

permutation([],[]).
permutation([X|XS],YS) :- permutation(XS,ZS), select(X,YS,ZS).
```

## PureBasic

```Macro reverse(firstIndex, lastIndex)
first = firstIndex
last = lastIndex
While first < last
Swap cur(first), cur(last)
first + 1
last - 1
Wend
EndMacro

Procedure nextPermutation(Array cur(1))
Protected first, last, elementCount = ArraySize(cur())
If elementCount < 2
ProcedureReturn #False ;nothing to permute
EndIf

;Find the lowest position pos such that [pos] < [pos+1]
Protected pos = elementCount - 1
While cur(pos) >= cur(pos + 1)
pos - 1
If pos < 0
reverse(0, elementCount)
ProcedureReturn #False ;no higher lexicographic permutations left, return lowest one instead
EndIf
Wend

;Swap [pos] with the highest positional value that is larger than [pos]
last = elementCount
While cur(last) <= cur(pos)
last - 1
Wend
Swap cur(pos), cur(last)

;Reverse the order of the elements in the higher positions
reverse(pos + 1, elementCount)
ProcedureReturn #True ;next lexicographic permutation found
EndProcedure

Procedure display(Array a(1))
Protected i, fin = ArraySize(a())
For i = 0 To fin
Print(Str(a(i)))
If i = fin: Continue: EndIf
Print(", ")
Next
PrintN("")
EndProcedure

If OpenConsole()
Dim a(9)
a(0) = 8: a(1) = 3: a(2) =  10: a(3) =  6: a(4) =  1: a(5) =  9: a(6) =  7: a(7) =  -4: a(8) =  5: a(9) =  3
display(a())
While nextPermutation(a()): Wend
display(a())

Print(#CRLF\$ + #CRLF\$ + "Press ENTER to exit"): Input()
CloseConsole()
EndIf```
Output:
```8, 3, 10, 6, 1, 9, 7, -4, 5, 3
-4, 1, 3, 3, 5, 6, 7, 8, 9, 10```

## Python

Works with: Python version 2.6
```from itertools import permutations

in_order = lambda s: all(x <= s[i+1] for i,x in enumerate(s[:-1]))
perm_sort = lambda s: (p for p in permutations(s) if in_order(p)).next()
```

The `more_itertools` package contains many useful functions, such as `windowed`. This function gives us a sliding window of chosen size over an iterable. We can use this window, among other things, to check if the iterable is sorted.

Works with: Python version 3.7
```from itertools import permutations
from more_itertools import windowed

def is_sorted(seq):
return all(
v1 <= v2
for v1, v2 in windowed(seq, 2)
)

def permutation_sort(seq):
return next(
permutation
for permutation in permutations(seq)
if is_sorted(permutation)
)
```

## Quackery

```  [ 1 swap times [ i 1+ * ] ] is !          (   n --> n )

[ [] unrot 1 - times
[ i 1+ ! /mod
dip join ] drop ]     is factoradic ( n n --> [ )

[ [] unrot witheach
[ pluck
rot swap nested join
swap ]
join ]                    is inversion  ( [ [ --> [ )

[ over size
factoradic inversion ]    is nperm      ( [ n --> [ )

[ true swap
witheach
[ tuck > if
[ dip not conclude ] ]
drop ]                     is sorted     (   [ --> b )

[ 0
[ 2dup nperm
dup sorted not while
drop 1+ again ]
unrot 2drop ]              is sort       (   [ --> [ )

\$ "beings" sort echo\$```
Output:
`begins`

## R

### e1071

Library: e1071

Warning: This function keeps all the possible permutations in memory at once, which becomes silly when x has 10 or more elements.

```permutationsort <- function(x)
{
if(!require(e1071) stop("the package e1071 is required")
is.sorted <- function(x) all(diff(x) >= 0)

perms <- permutations(length(x))
i <- 1
while(!is.sorted(x))
{
x <- x[perms[i,]]
i <- i + 1
}
x
}
permutationsort(c(1, 10, 9, 7, 3, 0))```

### RcppAlgos

Library: RcppAlgos

RcppAlgos lets us do this at the speed of C++ and with some very short code. The while loop with no body strikes me as poor taste, but I know of no better way.

```library(RcppAlgos)
permuSort <- function(list)
{
iter <- permuteIter(list)
while(is.unsorted(iter\$nextIter())){}#iter\$nextIter advances iter to the next iteration and returns it.
iter\$currIter()
}
test <- sample(10)
print(test)
permuSort(test)```
Output:
```#Output
> test <- sample(10)
> print(test)
[1]  8 10  6  2  9  4  7  5  3  1
> permuSort(test)
[1]  1  2  3  4  5  6  7  8  9 10```

An alternative solution would be to replace the while loop with the following:

```repeat
{
if(!is.unsorted(iter\$nextIter())) break
}```

This seems more explicit than the empty while loop, but also more complex.

## Racket

```#lang racket
(define (sort l)
(for/first ([p (in-permutations l)] #:when (apply <= p)) p))
(sort '(6 1 5 2 4 3)) ; => '(1 2 3 4 5 6)
```

## Raku

(formerly Perl 6)

```# Lexicographic permuter from "Permutations" task.
sub next_perm ( @a ) {
my \$j = @a.end - 1;
\$j-- while \$j >= 1 and [>] @a[ \$j, \$j+1 ];

my \$aj = @a[\$j];
my \$k  = @a.end;
\$k-- while [>] \$aj, @a[\$k];

@a[ \$j, \$k ] .= reverse;

my Int \$r = @a.end;
my Int \$s = \$j + 1;
while \$r > \$s {
@a[ \$r, \$s ] .= reverse;
\$r--;
\$s++;
}
}

sub permutation_sort ( @a ) {
my @n = @a.keys;
my \$perm_count = [*] 1 .. +@n; # Factorial
for ^\$perm_count {
my @permuted_a = @a[ @n ];
return @permuted_a if [le] @permuted_a;
next_perm(@n);
}
}

my @data  = < c b e d a >; # Halfway between abcde and edcba
say 'Input  = ' ~ @data;
say 'Output = ' ~ @data.&permutation_sort;
```
Output:
```Input  = c b e d a
Output = a b c d e```

## REXX

```/*REXX program  sorts and displays  an array  using the  permutation-sort  method.      */
call gen                                         /*generate the array elements.         */
call show     'before sort'                      /*show the  before  array elements.    */
say  copies('░', 75)  /*show separator line between displays.*/
call pSort  L                                    /*invoke the permutation sort.         */
call show     ' after sort'                      /*show the   after  array elements.    */
say; say 'Permutation sort took '      ?      " permutations to find the sorted list."
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
.pAdd: #=#+1; do j=1 for N;  #.#=#.#  !.j;  end;   return           /*add a permutation.*/
show:    do j=1  for L;  say @e right(j, wL) arg(1)":" translate(@.j, , '_'); end;  return
/*──────────────────────────────────────────────────────────────────────────────────────*/
gen:   @.=;                            @.1 = '---Four_horsemen_of_the_Apocalypse---'
@.2 = '====================================='
@.3 = 'Famine───black_horse'
@.4 = 'Death───pale_horse'
@.5 = 'Pestilence_[Slaughter]───red_horse'
@.6 = 'Conquest_[War]───white_horse'
@e= right('element', 15)                          /*literal used for the display.*/
do L=1  while @.L\=='';  @@.L=@.L;   end;    L= L-1;      wL=length(L);    return
/*──────────────────────────────────────────────────────────────────────────────────────*/
isOrd: parse arg q                                       /*see if  Q  list is in order. */
_= word(q, 1);  do j=2  to words(q);  x= word(q, j);  if x<_  then return 0;   _= x
end   /*j*/                       /* [↑]  Out of order?   ¬sorted*/
do k=1  for #;  _= word(#.?, k);  @.k= @@._;  end  /*k*/;  return 1  /*in order*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
.pNxt: procedure expose !.;    parse arg n,i;         nm= n - 1
do k=nm  by -1  for nm;   kp= k + 1
if !.k<!.kp   then  do;    i= k;         leave;    end
end   /*k*/                  /* [↓]  swap two array elements*/
do j=i+1  while j<n;  parse value  !.j !.n  with  !.n !.j;   n= n-1;  end  /*j*/
if i==0  then return 0                            /*0:  indicates no more perms. */
do j=i+1  while !.j<!.i;   end  /*j*/          /*search perm for a lower value*/
parse value !.j !.i  with  !.i !.j;  return 1     /*swap two values in !.  array.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
pSort: parse arg n,#.;  #= 0                     /*generate  L  items (!)  permutations.*/
do f=1  for n;                !.f= f;        end  /*f*/;            call .pAdd
do while .pNxt(n, 0);         call .pAdd;    end  /*while*/
do ?=1  until isOrd(\$);       \$=                            /*find permutation.*/
do m=1  for #; _= word(#.?, m); \$= \$ @._;  end  /*m*/     /*build the \$ list.*/
end   /*?*/;                  return
```
output   when using the default (internal) inputs:
```        element 1 before sort: ---Four horsemen of the Apocalypse---
element 2 before sort: =====================================
element 3 before sort: Famine───black horse
element 4 before sort: Death───pale horse
element 5 before sort: Pestilence [Slaughter]───red horse
element 6 before sort: Conquest [War]───white horse
░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
element 1  after sort: ---Four horsemen of the Apocalypse---
element 2  after sort: =====================================
element 3  after sort: Conquest [War]───white horse
element 4  after sort: Death───pale horse
element 5  after sort: Famine───black horse
element 6  after sort: Pestilence [Slaughter]───red horse

Permutation sort took  21  permutations to find the sorted list.
```

## 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)
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```

Output:

```169329 permutations required to sort 9 items.
```

## Ruby

Works with: Ruby version 1.8.7+

The Array class has a permutation method that, with no arguments, returns an enumerable object.

```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
```

## 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)))))
```

## Sidef

Translation of: Perl
```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}";
```
Output:
```Before:	60 98 85 85 37 0 62 96 95 2
After:	0 2 37 60 62 85 85 95 96 98
```

## Tcl

Library: Tcllib (Package: struct::list)

The `firstperm` procedure actually returns the lexicographically first permutation of the input list. However, to meet the letter of the problem, let's loop:

```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
}
```

## Ursala

Standard library functions to generate permutations and test for ordering by a given predicate are used.

```#import std

permsort "p" = ~&ihB+ ordered"p"*~+ permutations

#cast %sL

example = permsort(lleq) <'pmf','oao','ejw','hhp','oqh','ock','dwj'>```
Output:
`<'dwj','ejw','hhp','oao','ock','oqh','pmf'>`

## Wren

Translation of: Go
Library: Wren-sort
```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
System.print("Sorted  : %(a)")
```
Output:
```Unsorted: [170, 45, 75, -90, -802, 24, 2, 66]
Sorted  : [-802, -90, 2, 24, 45, 66, 75, 170]
```

## zkl

Performance is horrid

```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();```
Output:
`L(0,1,2,2,4,31,65,83,99,782)`