# Sorting Algorithms/Circle Sort

(Redirected from Circle sort)
Sorting Algorithms/Circle 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

Sort an array of integers (of any convenient size) into ascending order using Circlesort.

In short, compare the first element to the last element, then the second element to the second last element, etc.

Then split the array in two and recurse until there is only one single element in the array, like this:

```Before:
6 7 8 9 2 5 3 4 1
After:
1 4 3 5 2 9 8 7 6
```

Repeat this procedure until quiescence (i.e. until there are no swaps).

Show both the initial, unsorted list and the final sorted list. (Intermediate steps during sorting are optional.)

Optimizations (like doing 0.5 log2(n) iterations and then continue with an Insertion sort) are optional.

Pseudo code:

``` function circlesort (index lo, index hi, swaps)
{
if lo == hi return (swaps)
high := hi
low := lo
mid := int((hi-lo)/2)
while lo < hi {
if  (value at lo) > (value at hi) {
swap.values (lo,hi)
swaps++
}
lo++
hi--
}
if lo == hi
if (value at lo) > (value at hi+1) {
swap.values (lo,hi+1)
swaps++
}
swaps := circlesort(low,low+mid,swaps)
swaps := circlesort(low+mid+1,high,swaps)
return(swaps)
}
while circlesort (0, sizeof(array)-1, 0)
```

## 11l

Translation of: Python
```F circle_sort_backend(&A, Int l, r)
V n = r - l
I n < 2
R 0
V swaps = 0
V m = n I/ 2
L(i) 0 .< m
I A[r - (i + 1)] < A[l + i]
swap(&A[r - (i + 1)], &A[l + i])
swaps++
I (n [&] 1) != 0 & (A[l + m] < A[l + m - 1])
swap(&A[l + m - 1], &A[l + m])
swaps++
R swaps + circle_sort_backend(&A, l, l + m) + circle_sort_backend(&A, l + m, r)

F circle_sort(&l)
V swaps = 0
V s = 1
L s != 0
s = circle_sort_backend(&l, 0, l.len)
swaps += s
R swaps

L(i) 309
V l = Array(0 .< i)
V m = copy(l)
random:shuffle(&l)
V n = copy(l)
circle_sort(&l)
I l != m
print(l.len)
print(n)
print(l)```

## AArch64 Assembly

Works with: as version Raspberry Pi 3B version Buster 64 bits
```/* ARM assembly AARCH64 Raspberry PI 3B */
/*  program circleSort64.s  */

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

/*********************************/
/* Initialized data              */
/*********************************/
.data
szMessSortOk:       .asciz "Table sorted.\n"
szMessSortNok:      .asciz "Table not sorted !!!!!.\n"
szMessSortBefore:   .asciz "Display table before sort.\n"
sMessResult:        .asciz "Value  : @ \n"
szCarriageReturn:   .asciz "\n"

.align 4
.equ NBELEMENTS, (. - TableNumber) / 8
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss
sZoneConv:            .skip 24
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main
main:                               // entry of program
bl affichageMess
bl displayTable
1:
mov x1,#0
mov x2,#NBELEMENTS -1           // number of élements
mov x3,#0
bl circleSort
cmp x0,#0
bne 1b
mov x1,#NBELEMENTS              // number of élements
bl displayTable

mov x1,#NBELEMENTS              // number of élements
bl isSorted                     // control sort
cmp x0,#1                       // sorted ?
beq 2f
ldr x0,qAdrszMessSortNok        // no !! error sort
bl affichageMess
b 100f
2:                                  // yes
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                      // smaller -> error
mov x4,x3                    // A[i-1] = A[i]
b 1b                         // else loop
98:
mov x0,#0                    // error
b 100f
99:
mov x0,#1                    // ok -> return
100:
ldp x2,x3,[sp],16            // restaur  2 registers
ldp x1,lr,[sp],16            // restaur  2 registers
/******************************************************************/
/*         circle sort                                              */
/******************************************************************/
/* x0 contains the address of table */
/* x1 contains the first index */
/* x2 contains the last index */
/* x3 contains number of swaps */
circleSort:
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
stp x8,x9,[sp,-16]!          // save  registers
stp x10,x11,[sp,-16]!        // save  registers
cmp x1,x2
beq 99f
mov x8,x1                    // low
mov x9,x2                    // high
sub x4,x2,x1
lsr x4,x4,#1
mov x10,x4                   // mid
1:                               // start loop
cmp x1,x2
bge 3f
ldr x5,[x0,x1,lsl #3]
ldr x6,[x0,x2,lsl #3]
cmp x5,x6
ble 2f
str x6,[x0,x1,lsl #3]        // swap values
str x5,[x0,x2,lsl #3]
2:
sub x2,x2,#1                 // decrement hi
b 1b                         // and loop
3:
cmp x1,x2                    // compare lo hi
bne 4f                       // not egal
ldr x5,[x0,x1,lsl #3]
ldr x6,[x0,x2,lsl #3]
cmp x5,x6
ble 4f
str x6,[x0,x1,lsl #3]        //  swap
str x5,[x0,x2,lsl #3]
4:
mov x1,x8                    // low
mov x2,x10                   // mid
bl circleSort
mov x3,x0                    // swaps
mov x1,x8                    // low
mov x2,x10                   // mid
mov x2,x9                    // high
bl circleSort
mov x3,x0                    // swaps
99:
mov x0,x3                    // return number swaps
100:
ldp x10,x11,[sp],16          // restaur  2 registers
ldp x8,x9,[sp],16            // restaur  2 registers
ldp x6,x7,[sp],16            // restaur  2 registers
ldp x4,x5,[sp],16            // restaur  2 registers
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 conversion10              // décimal conversion
bl strInsertAtCharInc
bl affichageMess             // display message
cmp x3,#NBELEMENTS - 1
ble 1b
bl affichageMess
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"```
```Display table before sort.
Value  : 10
Value  : 9
Value  : 8
Value  : 7
Value  : 6
Value  : 5
Value  : 4
Value  : 3
Value  : 2
Value  : 1

Value  : 1
Value  : 2
Value  : 3
Value  : 4
Value  : 5
Value  : 6
Value  : 7
Value  : 8
Value  : 9
Value  : 10

Table sorted.
```

## Action!

Action! language does not support recursion. Therefore an iterative approach with a stack has been proposed.

```DEFINE MAX_COUNT="100"
INT ARRAY stack(MAX_COUNT)
INT stackSize

PROC PrintArray(INT ARRAY a INT size)
INT i

Put('[)
FOR i=0 TO size-1
DO
IF i>0 THEN Put(' ) FI
PrintI(a(i))
OD
Put(']) PutE()
RETURN

PROC InitStack()
stackSize=0
RETURN

BYTE FUNC IsEmpty()
IF stackSize=0 THEN
RETURN (1)
FI
RETURN (0)

PROC Push(INT low,high)
stack(stackSize)=low  stackSize==+1
stack(stackSize)=high stackSize==+1
RETURN

PROC Pop(INT POINTER low,high)
stackSize==-1 high^=stack(stackSize)
stackSize==-1 low^=stack(stackSize)
RETURN

INT FUNC Partition(INT ARRAY a INT low,high)
INT part,v,i,tmp

v=a(high)
part=low-1

FOR i=low TO high-1
DO
IF a(i)<=v THEN
part==+1
tmp=a(part) a(part)=a(i) a(i)=tmp
FI
OD

part==+1
tmp=a(part) a(part)=a(high) a(high)=tmp
RETURN (part)

PROC CircleSort(INT ARRAY a INT size)
INT swaps,low,high,lo,hi,tmp,mid

InitStack()
DO
swaps=0
Push(0,size-1)
WHILE IsEmpty()=0
DO
Pop(@low,@high)
IF low<high THEN
lo=low hi=high
WHILE lo<hi
DO
IF a(hi)<a(lo) THEN
tmp=a(lo) a(lo)=a(hi) a(hi)=tmp
swaps==+1
FI
lo==+1 hi==-1
OD
IF lo=hi AND a(lo+1)<a(lo) THEN
tmp=a(lo) a(lo)=a(lo+1) a(lo+1)=tmp
swaps==+1
FI
mid=(lo+hi)/2
Push(low,mid)
Push(mid+1,high)
FI
OD
UNTIL swaps=0
OD
RETURN

PROC Test(INT ARRAY a INT size)
PrintE("Array before sort:")
PrintArray(a,size)
CircleSort(a,size)
PrintE("Array after sort:")
PrintArray(a,size)
PutE()
RETURN

PROC Main()
INT ARRAY
a(10)=[1 4 65535 0 3 7 4 8 20 65530],
b(21)=[10 9 8 7 6 5 4 3 2 1 0
65535 65534 65533 65532 65531
65530 65529 65528 65527 65526],
c(8)=[101 102 103 104 105 106 107 108],
d(12)=[1 65535 1 65535 1 65535 1
65535 1 65535 1 65535]

Test(a,10)
Test(b,21)
Test(c,8)
Test(d,12)
RETURN```
Output:
```Array before sort:
[1 4 -1 0 3 7 4 8 20 -6]
Array after sort:
[-6 -1 0 1 3 4 4 7 8 20]

Array before sort:
[10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10]
Array after sort:
[-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10]

Array before sort:
[101 102 103 104 105 106 107 108]
Array after sort:
[101 102 103 104 105 106 107 108]

Array before sort:
[1 -1 1 -1 1 -1 1 -1 1 -1 1 -1]
Array after sort:
[-1 -1 -1 -1 -1 -1 1 1 1 1 1 1]
```

## ALGOL 68

```BEGIN # circlesort                                                           #

# swaps a and b                                                          #
PRIO =:= = 9;
OP   =:= = ( REF INT a, b )VOID: BEGIN INT t = a; a := b; b := t END;

# sorts data in-place and returns a reference to data                    #
OP   CIRCLESORT = ( REF[]INT data )REF[]INT:
BEGIN
PROC circlesort = ( REF[]INT data, INT low, high, swaps so far )INT:
IF low >= high THEN swaps so far
ELSE
INT swaps := swaps so far;
INT hi    := high;
INT lo    := low;
INT mid    = ( hi - lo ) OVER 2;
WHILE lo < hi DO
IF  data[ lo ] > data[ hi ] THEN
data[ lo ] =:= data[ hi ];
swaps      +:= 1
FI;
lo +:= 1;
hi -:= 1
OD;
IF lo = hi AND hi < UPB data THEN
IF data[ lo ] > data[ hi + 1 ] THEN
data[ lo ] =:= data[ hi + 1 ];
swaps      +:= 1
FI
FI;
swaps := circlesort( data, low, low + mid,      swaps );
swaps := circlesort( data, low + mid + 1, high, swaps )
FI # circlesort # ;

WHILE circlesort( data, LWB data, UPB data, 0 ) > 0 DO SKIP OD;
data
END # CIRCLESORT # ;

# prints the elements of an array of integers separated by spaces         #
OP   SHOW = ( []INT list )VOID:
FOR i FROM LWB list TO UPB list DO
print( ( " ", whole( list[ i ], 0 ) ) )
OD # SHOW # ;

# tests the CIRCLESORT operator                                          #
PROC test circle sort = ( []INT unsorted )VOID:
BEGIN
[ LWB unsorted : UPB unsorted ]INT data := unsorted;
print( ( "[" ) );
SHOW unsorted;
print( ( " ]", newline, "    -> [" ) );
SHOW CIRCLESORT data;
print( ( " ]", newline ) )
END # test circle sort # ;

test circle sort( ( 6, 7, 8, 9, 2, 5, 3, 4, 1 ) );
# test cases from the Action! sample                                     #
test circle sort( ( 1, 4, -1, 0, 3, 7, 4, 8, 20, -6 ) );
test circle sort( ( 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10 ) );
test circle sort( ( 101, 102, 103, 104, 105, 106, 107, 108 ) );
test circle sort( ( 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1 ) );
test circle sort( ( ) );
test circle sort( ( 1 ) )

END```
Output:
```[ 6 7 8 9 2 5 3 4 1 ]
-> [ 1 2 3 4 5 6 7 8 9 ]
[ 1 4 -1 0 3 7 4 8 20 -6 ]
-> [ -6 -1 0 1 3 4 4 7 8 20 ]
[ 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 ]
-> [ -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 ]
[ 101 102 103 104 105 106 107 108 ]
-> [ 101 102 103 104 105 106 107 108 ]
[ 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 ]
-> [ -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 ]
[ ]
-> [ ]
[ 1 ]
-> [ 1 ]
```

## ARM Assembly

Works with: as version Raspberry Pi
```/* ARM assembly Raspberry PI  */
/*  program circleSort.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"
szMessSortBefore:   .asciz "Display table before sort.\n"
sMessResult:        .asciz "Value  : @ \n"
szCarriageReturn:   .asciz "\n"

.align 4
#TableNumber:      .int   1,3,6,2,5,9,10,8,4,7
#TableNumber:       .int   1,2,3,4,5,6,7,8,9,10
TableNumber:       .int   9,5,12,8,2,12,6
#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
bl affichageMess
bl displayTable
1:
mov r1,#0
mov r2,#NBELEMENTS -1           @ number of élements
mov r3,#0
bl circleSort
cmp r0,#0
bne 1b
mov r1,#NBELEMENTS              @ number of élements
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

/******************************************************************/
/*     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
/******************************************************************/
/*         circle sort                                              */
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the first index */
/* r2 contains the last index */
/* r3 contains number of swaps */
circleSort:
push {r1-r10,lr}           @ save registers
cmp r1,r2
beq 99f
mov r8,r1                  @ low
mov r9,r2                  @ high
sub r4,r2,r1
lsr r4,#1
mov r10,r4                 @ mid
1:                             @ start loop
cmp r1,r2
bge 3f
ldr r5,[r0,r1,lsl #2]
ldr r6,[r0,r2,lsl #2]
cmp r5,r6
ble 2f
str r6,[r0,r1,lsl #2]      @ swap values
str r5,[r0,r2,lsl #2]
2:
sub r2,r2,#1               @ decrement hi
b 1b                       @ and loop
3:
cmp r1,r2                  @ compare lo hi
bne 4f                     @ not egal
ldr r5,[r0,r1,lsl #2]
ldr r6,[r0,r2,lsl #2]
cmp r5,r6
ble 4f
str r6,[r0,r1,lsl #2]      @  swap
str r5,[r0,r2,lsl #2]
4:
mov r1,r8                  @ low
mov r2,r10                 @ mid
bl circleSort
mov r3,r0                 @ swaps
mov r1,r8                 @ low
mov r2,r10                @ mid
mov r2,r9                 @ high
bl circleSort
mov r3,r0                 @ swaps
99:
mov r0,r3                 @ return number swaps
100:
pop {r1-r10,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 conversion10                   @ décimal conversion
bl strInsertAtCharInc
bl affichageMess                  @ display message
cmp r3,#NBELEMENTS - 1
ble 1b
bl affichageMess
100:
pop {r0-r3,lr}
bx lr
/***************************************************/
/*      ROUTINES INCLUDE                           */
/***************************************************/
.include "../affichage.inc"```
```Display table before sort.
Value  : 9
Value  : 5
Value  : 12
Value  : 8
Value  : 2
Value  : 12
Value  : 6

Value  : 2
Value  : 5
Value  : 6
Value  : 8
Value  : 9
Value  : 12
Value  : 12

Table sorted.
```

## Arturo

```innerCircleSort: function [ar, lo, hi, swaps][
localSwaps: swaps
localHi: hi
localLo: lo
if localLo = localHi -> return swaps

high: localHi
low: localLo
mid: (localHi - localLo) / 2

while [localLo < localHi] [
if ar\[localLo] > ar\[localHi] [
tmp: ar\[localLo]
ar\[localLo]: ar\[localHi]
ar\[localHi]: tmp
localSwaps: localSwaps + 1
]
localLo: localLo + 1
localHi: localHi - 1
]
if localLo = localHi [
if ar\[localLo] > ar\[localHi + 1] [
tmp: ar\[localLo]
ar\[localLo]: ar\[localHi + 1]
ar\[localHi + 1]: tmp
localSwaps: localSwaps + 1
]
]

localSwaps: innerCircleSort ar low low + mid localSwaps
localSwaps: innerCircleSort ar low + mid + 1 high localSwaps
return localSwaps
]

circleSort: function [arr][
result: new arr
while [not? zero? innerCircleSort result 0 dec size result 0][]
return result
]

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

## AutoHotkey

```nums := [6, 7, 8, 9, 2, 5, 3, 4, 1]
while circlesort(nums, 1, nums.Count(), 0)		; 1-based
continue
for i, v in nums
output .= v ", "
MsgBox % "[" Trim(output, ", ") "]"
return

circlesort(Arr, lo, hi, swaps){
if (lo = hi)
return swaps
high:= hi
low := lo
mid := Floor((hi - lo) / 2)
while (lo < hi) {
if (Arr[lo] > Arr[hi]){
tempVal := Arr[lo], Arr[lo] := Arr[hi], Arr[hi] := tempVal
swaps++
}
lo++
hi--
}
if (lo = hi)
if (Arr[lo] > Arr[hi+1]){
tempVal := Arr[lo], Arr[lo] := Arr[hi+1], Arr[hi+1] := tempVal
swaps++
}
swaps := circlesort(Arr, low, low+mid, swaps)
swaps := circlesort(Arr, low+mid+1, high, swaps)
return swaps
}
```
Output:
`[1, 2, 3, 4, 5, 6, 7, 8, 9]`

## C

```#include <stdio.h>

int circle_sort_inner(int *start, int *end)
{
int *p, *q, t, swapped;

if (start == end) return 0;

// funny "||" on next line is for the center element of odd-lengthed array
for (swapped = 0, p = start, q = end; p<q || (p==q && ++q); p++, q--)
if (*p > *q)
t = *p, *p = *q, *q = t, swapped = 1;

// q == p-1 at this point
return swapped | circle_sort_inner(start, q) | circle_sort_inner(p, end);
}

//helper function to show arrays before each call
void circle_sort(int *x, int n)
{
do {
int i;
for (i = 0; i < n; i++) printf("%d ", x[i]);
putchar('\n');
} while (circle_sort_inner(x, x + (n - 1)));
}

int main(void)
{
int x[] = {5, -1, 101, -4, 0, 1, 8, 6, 2, 3};
circle_sort(x, sizeof(x) / sizeof(*x));

return 0;
}
```
Output:
```5 -1 101 -4 0 1 8 6 2 3
-4 -1 0 3 6 1 2 8 5 101
-4 -1 0 1 2 3 5 6 8 101
```

## C#

```using System;
using System.Linq;

namespace CircleSort
{
internal class Program
{
public static int[] CircleSort(int[] array)
{
if (array.Length > 0)
while (CircleSortR(array, 0, array.Length - 1, 0) != 0)
continue;
return array;
}

private static int CircleSortR(int[] arr, int lo, int hi, int numSwaps)
{
if (lo == hi)
return numSwaps;

var high = hi;
var low = lo;
var mid = (hi - lo) / 2;

while (lo < hi)
{
if (arr[lo] > arr[hi])
{
(arr[lo], arr[hi]) = (arr[hi], arr[lo]);
numSwaps++;
}
lo++;
hi--;
}

if (lo == hi && arr[lo] > arr[hi + 1])
{
(arr[lo], arr[hi + 1]) = (arr[hi + 1], arr[lo]);
numSwaps++;
}

numSwaps = CircleSortR(arr, low, low + mid, numSwaps);
numSwaps = CircleSortR(arr, low + mid + 1, high, numSwaps);

return numSwaps;
}

private static void Main(string[] args)
{
var sortedArray = CircleSort(new int[] { 6, 7, 8, 9, 2, 5, 3, 4, 1 });
sortedArray.ToList().ForEach(i => Console.Write(i.ToString() + " "));
Console.WriteLine();
var sortedArray2 = CircleSort(new int[] { 2, 14, 4, 6, 8, 1, 3, 5, 7, 11, 0, 13, 12, -1 });
sortedArray2.ToList().ForEach(i => Console.Write(i.ToString() + " "));
Console.WriteLine();
var sortedArray3 = CircleSort(new int[] { 2, 3, 3, 5, 5, 1, 1, 7, 7, 6, 6, 4, 4, 0, 0 });
sortedArray3.ToList().ForEach(i => Console.Write(i.ToString() + " "));
}
}
}
```
Output:
```1 2 3 4 5 6 7 8 9
-1 0 1 2 3 4 5 6 7 8 11 12 13 14
0 0 1 1 2 3 3 4 4 5 5 6 6 7 7
```

## C++

```#include <iostream>

int circlesort(int* arr, int lo, int hi, int swaps) {
if(lo == hi) {
return swaps;
}
int high = hi;
int low = lo;
int mid = (high - low) / 2;
while(lo < hi) {
if(arr[lo] > arr[hi]) {
int temp = arr[lo];
arr[lo] = arr[hi];
arr[hi] = temp;
swaps++;
}
lo++;
hi--;
}

if(lo == hi) {
if(arr[lo] > arr[hi+1]) {
int temp = arr[lo];
arr[lo] = arr[hi+1];
arr[hi+1] = temp;
swaps++;
}
}
swaps = circlesort(arr, low, low+mid, swaps);
swaps = circlesort(arr, low+mid+1, high, swaps);
return swaps;
}

void circlesortDriver(int* arr, int n) {
do {
for(int i = 0; i < n; i++) {
std::cout << arr[i] << ' ';
}
std::cout << std::endl;
} while(circlesort(arr, 0, n-1, 0));
}

int main() {
int arr[] = { 6, 7, 8, 9, 2, 5, 3, 4, 1 };
circlesortDriver(arr, sizeof(arr)/sizeof(int));
return 0;
}
```

Output:

```6 7 8 9 2 5 3 4 1
1 3 4 2 5 6 7 8 9
1 2 3 4 5 6 7 8 9```

## CoffeeScript

```circlesort = (arr, lo, hi, swaps) ->
if lo == hi
return (swaps)

high = hi
low  = lo
mid = Math.floor((hi-lo)/2)

while lo < hi
if arr[lo] > arr[hi]
t = arr[lo]
arr[lo] = arr[hi]
arr[hi] = t
swaps++
lo++
hi--

if lo == hi
if arr[lo] > arr[hi+1]
t = arr[lo]
arr[lo] = arr[hi+1]
arr[hi+1] = t
swaps++

swaps = circlesort(arr,low,low+mid,swaps)
swaps = circlesort(arr,low+mid+1,high,swaps)

return(swaps)

VA = [2,14,4,6,8,1,3,5,7,9,10,11,0,13,12,-1]

while circlesort(VA,0,VA.length-1,0)
console.log VA
```

Output:

```console: -1,1,0,3,4,5,8,12,2,9,6,10,7,13,11,14
console: -1,0,1,3,2,5,4,8,6,7,9,12,10,11,13,14
console: -1,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14```

## D

```import std.stdio, std.algorithm, std.array, std.traits;

void circlesort(T)(T[] items) if (isMutable!T) {
uint inner(size_t lo, size_t hi, uint swaps) {
if (lo == hi)
return swaps;
auto high = hi;
auto low = lo;
immutable mid = (hi - lo) / 2;

while (lo < hi) {
if (items[lo] > items[hi]) {
swap(items[lo], items[hi]);
swaps++;
}
lo++;
hi--;
}

if (lo == hi && items[lo] > items[hi + 1]) {
swap(items[lo], items[hi + 1]);
swaps++;
}
swaps = inner(low, low + mid, swaps);
swaps = inner(low + mid + 1, high, swaps);
return swaps;
}

if (!items.empty)
while (inner(0, items.length - 1, 0)) {}
}

void main() {
import std.random, std.conv;

auto a = [5, -1, 101, -4, 0, 1, 8, 6, 2, 3];
a.circlesort;
a.writeln;
assert(a.isSorted);

// Fuzzy test.
int[30] items;
foreach (immutable _; 0 .. 100_000) {
auto data = items[0 .. uniform(0, items.length)];
foreach (ref x; data)
x = uniform(-items.length.signed * 3, items.length.signed * 3);
data.circlesort;
assert(data.isSorted);
}
}
```
Output:
`[-4, -1, 0, 1, 2, 3, 5, 6, 8, 101]`

## Delphi

Translation of: Go
```program Sorting_Algorithms;

{\$APPTYPE CONSOLE}

uses
System.SysUtils;

function CircleSort(a: TArray<Integer>; lo, hi, swaps: Integer): Integer;
begin
if lo = hi then
exit(swaps);

var high := hi;
var low := lo;
var mid := (hi - lo) div 2;

while lo < hi do
begin
if a[lo] > a[hi] then
begin
var tmp := a[lo];
a[lo] := a[hi];
a[hi] := tmp;
inc(swaps);
end;
inc(lo);
dec(hi);
end;

if lo = hi then
begin
if a[lo] > a[hi + 1] then
begin
var tmp := a[lo];
a[lo] := a[hi + 1];
a[hi + 1] := tmp;
inc(swaps);
end;
end;
swaps := CircleSort(a, low, low + mid, swaps);
swaps := CircleSort(a, low + mid + 1, high, swaps);
result := swaps;
end;

function ToString(a: TArray<Integer>): string;
begin
Result := '[';
for var e in a do
Result := Result + e.ToString + ',';
Result := Result + ']';
end;

const
aa: TArray<TArray<Integer>> = [[6, 7, 8, 9, 2, 5, 3, 4, 1], [2, 14, 4, 6, 8, 1,
3, 5, 7, 11, 0, 13, 12, -1]];

begin
for var a in aa do
begin
write('Original: ');
write(ToString(a));
while CircleSort(a, 0, high(a), 0) <> 0 do
;
writeln;
write('Sorted  : ');
write(ToString(a));
writeln(#10#10);
end;
end.
```

## EasyLang

```global d[] .
func circsort lo hi swaps .
if lo = hi
return swaps
.
high = hi
low = lo
mid = (hi - lo) div 2
while lo < hi
if d[lo] > d[hi]
swap d[lo] d[hi]
swaps += 1
.
lo += 1
hi -= 1
.
if lo = hi
if d[lo] > d[hi + 1]
swap d[lo] d[hi + 1]
swaps += 1
.
.
swaps = circsort low (low + mid) swaps
swaps = circsort (low + mid + 1) high swaps
return swaps
.
d[] = [ -4 -1 1 0 5 -7 -2 4 -6 -3 2 6 3 7 -5 ]
while circsort 1 len d[] 0 > 0
#
.
print d[]```
Output:
```[ -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 ]
```

## Elixir

```defmodule Sort do
def circle_sort(data) do
List.to_tuple(data)
|> circle_sort(0, length(data)-1)
|> Tuple.to_list
end

defp circle_sort(data, lo, hi) do
case circle_sort(data, lo, hi, 0) do
{result, 0} -> result
{result, _} -> circle_sort(result, lo, hi)
end
end

defp circle_sort(data, lo, lo, swaps), do: {data, swaps}
defp circle_sort(data, lo, hi, swaps) do
mid = div(lo + hi, 2)
{data, swaps} = do_circle_sort(data, lo, hi, swaps)
{data, swaps} = circle_sort(data, lo, mid, swaps)
circle_sort(data, mid+1, hi, swaps)
end

def do_circle_sort(data, lo, hi, swaps) when lo>=hi do
if lo==hi and elem(data, lo) > elem(data, hi+1),
do:   {swap(data, lo, hi+1), swaps+1},
else: {data, swaps}
end
def do_circle_sort(data, lo, hi, swaps) do
if elem(data, lo) > elem(data, hi),
do:   do_circle_sort(swap(data, lo, hi), lo+1, hi-1, swaps+1),
else: do_circle_sort(data, lo+1, hi-1, swaps)
end

defp swap(data, i, j) do
vi = elem(data, i)
vj = elem(data, j)
data |> put_elem(i, vj) |> put_elem(j, vi)
end
end

data = [6, 7, 8, 9, 2, 5, 3, 4, 1]
IO.puts "before sort: #{inspect data}"
IO.puts " after sort: #{inspect Sort.circle_sort(data)}"
```
Output:
```before sort: [6, 7, 8, 9, 2, 5, 3, 4, 1]
after sort: [1, 2, 3, 4, 5, 6, 7, 8, 9]
```

## Forth

This one features the newest version of the algorithm on Sourceforge.

```[UNDEFINED] cell- [IF] : cell- 1 cells - ; [THEN]

variable (sorted?)                     \ is the array sorted?

: (compare)                            ( a1 a2 -- a1 a2)
over @ over @ precedes               \ flag if swapped
if over over over @ over @ swap rot ! swap ! false (sorted?) ! then
;

: (circlesort)                         ( a1 a2 --)
over over = if drop drop exit then   \ quit if indexes are equal
over over swap                       \ swap indexes (end begin)
begin
over over >                        \ as long as middle isn't passed
while
(compare) swap cell- swap cell+    \ check and swap opposite elements
repeat rot recurse recurse           \ split array and recurse
;

: sort                                 ( a n --)
1- cells over +                      \ calculate addresses
begin true (sorted?) ! over over (circlesort) (sorted?) @ until drop drop
;

:noname < ; is precedes

10 constant /sample
create sample 5 , -1 , 101 , -4 , 0 , 1 , 8 , 6 , 2 , 3 ,

: .sample sample /sample cells bounds do i ? 1 cells +loop ;

sample /sample sort .sample
```

## Fortran

```!
module circlesort
! I have commented the code that was here and also 'tightened up' various pieces such as how swap detection was done as well
! as fixing an error where the code would exceed array bounds for odd number sized arrays.
! Also, giving some some attribution to the author. - Pete
! This code is a Fortran adaptation of a Forth algorithm laid out by "thebeez" at this URL;
! https://sourceforge.net/p/forth-4th/wiki/Circle%20sort/
!
implicit none
logical, private :: csr
public :: circle_sort

contains

recursive logical function csr(a, left, right,n) result(swapped)
implicit none
integer, intent(in) :: left, right,n
integer, intent(inout) :: a(n)
integer :: lo, hi, mid
integer :: temp
logical :: lefthalf,righthalf
!
swapped = .FALSE.
if (right <= left) return
lo = left   !Store the upper and lower bounds of list for
hi = right  !Recursion later
!
do while (lo < hi)
!   Swap the pair of elements if hi < lo
if (a(hi) < a(lo)) then
swapped = .TRUE.
temp = a(lo)
a(lo) = a(hi)
a(hi) = temp
endif
lo = lo + 1
hi = hi - 1
end do
!   Special case if array is an odd size (not even)
if (lo == hi)then
if(a(hi+1) .lt. a(lo))then
swapped = .TRUE.
temp = a(hi+1)
a(hi+1) = a(lo)
a(lo) = temp
endif
endif
mid = (left + right) / 2 ! Bisection point
lefthalf = csr(a, left, mid,n)
righthalf = csr(a, mid + 1, right,n)
swapped = swapped .or. lefthalf .or. righthalf
end function csr
!
subroutine circle_sort(a, n)
use iso_c_binding, only: c_ptr, c_loc
implicit none
integer, intent(in) :: n
integer, target,intent(inout) :: a(n)

do while ( csr(a, 1, n,n))
! This is the canonical algorithm. However, if you want to
! speed it up, count the iterations and when you have approached
! 0.5*ln(n) iterations, perform a binary insertion sort then exit the loop.
end do
end subroutine circle_sort

end module circlesort
program sort
use circlesort
implicit none
integer :: a(9)
data a/6,7,8,9,2,5,3,4,1/
call circle_sort(a, size(a))
print *, a
end program sort
```

## FreeBASIC

```' version 21-10-2016
' compile with: fbc -s console
' for boundry checks on array's compile with: fbc -s console -exx
' converted pseudo code into FreeBASIC code

' shared variables need to be declared before first use
Dim Shared As Long cs(-7 To 7)

Function circlesort(lo As Long, hi As Long, swaps As ULong) As ULong

' array is declared shared
' sort from lower bound to the highter bound
' array's can have subscript range from -2147483648 to +2147483647

If lo = hi Then Return swaps

Dim As Long high = hi
Dim As Long low = lo
Dim As Long mid_ = (hi - lo) \ 2

While lo < hi
If cs(lo) > cs(hi) Then
Swap cs(lo), cs(hi)
swaps += 1
End If
lo += 1
hi -= 1
Wend
If lo = hi Then
If cs(lo) > cs(hi +1) Then
Swap cs(lo), cs(hi +1)
swaps += 1
End If
End If
swaps = circlesort(low          , low + mid_, swaps)
swaps = circlesort(low + mid_ +1,       high, swaps)

Return swaps

End Function

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

Dim As Long i, a = LBound(cs), b = UBound(cs)

Randomize Timer
For i = a To b : cs(i) = i  : Next
For i = a To b ' little shuffle
Swap cs(i), cs(Int(Rnd * (b - a +1)) + a)
Next

Print "unsorted ";
For i = a To b : Print Using "####"; cs(i); : Next : Print

' sort the array, loop until sorted
While circlesort(a, b, 0) : Wend

Print "  sorted ";
For i = a To b : Print Using "####"; cs(i); : Next : Print

' empty keyboard buffer
While InKey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End```
Output:
```unsorted   -4  -1   1   0   5  -7  -2   4  -6  -3   2   6   3   7  -5
sorted   -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7```

## Go

```package main

import "fmt"

func circleSort(a []int, lo, hi, swaps int) int {
if lo == hi {
return swaps
}
high, low := hi, lo
mid := (hi - lo) / 2
for lo < hi {
if a[lo] > a[hi] {
a[lo], a[hi] = a[hi], a[lo]
swaps++
}
lo++
hi--
}
if lo == hi {
if a[lo] > a[hi+1] {
a[lo], a[hi+1] = a[hi+1], a[lo]
swaps++
}
}
swaps = circleSort(a, low, low+mid, swaps)
swaps = circleSort(a, low+mid+1, high, swaps)
return swaps
}

func main() {
aa := [][]int{
{6, 7, 8, 9, 2, 5, 3, 4, 1},
{2, 14, 4, 6, 8, 1, 3, 5, 7, 11, 0, 13, 12, -1},
}
for _, a := range aa {
fmt.Printf("Original: %v\n", a)
for circleSort(a, 0, len(a)-1, 0) != 0 {
// empty block
}
fmt.Printf("Sorted  : %v\n\n", a)
}
}
```
Output:
```Original: [6 7 8 9 2 5 3 4 1]
Sorted  : [1 2 3 4 5 6 7 8 9]

Original: [2 14 4 6 8 1 3 5 7 11 0 13 12 -1]
Sorted  : [-1 0 1 2 3 4 5 6 7 8 11 12 13 14]
```

This code uses the tortoise-and-the-hare technique to split the input list in two and compare the relevant positions.

```import Data.Bool (bool)

circleSort :: Ord a => [a] -> [a]
circleSort xs = if swapped then circleSort ks else ks
where
(swapped,ks) = go False xs (False,[])

go d []  sks = sks
go d [x] (s,ks) = (s,x:ks)
go d xs  (s,ks) =
let (st,_,ls,rs) = halve d s xs xs
in go False ls (go True rs (st,ks))

halve d s (y:ys) (_:_:zs) = swap d y (halve d s ys zs)
halve d s ys     []       = (s,ys,[],[])
halve d s (y:ys) [_]      = (s,ys,[y | e],[y | not e])
where e = y <= head ys

swap d x (s,y:ys,ls,rs)
| bool (<=) (<) d x y = (    d || s,ys,x:ls,y:rs)
| otherwise           = (not d || s,ys,y:ls,x:rs)
```
Output:
```>>> circleSort [6,7,8,9,2,5,3,4,1]
[1,2,3,4,5,6,7,8,9]

>>> circleSort [2,14,4,6,8,1,3,5,7,11,0,13,12,-1]
[-1,0,1,2,3,4,5,6,7,8,11,12,13,14]
```

## J

Of more parsing and atomic data, or less parsing with large data groups the latter produces faster J programs. Consequently each iteration laminates the original with its reverse. It joins the recursive call to the pairwise minima of the left block to the recursive call of the pairwise maxima of the right block, repeating the operations while the output changes. This is sufficient for power of 2 length data. The pre verb adjusts the data length. And post recovers the original data. This implementation discards the "in place" property described at the sourceforge link.

```circle_sort =: post  power_of_2_length@pre    NB. the main sorting verb
power_of_2_length =: even_length_iteration^:_ NB. repeat while the answer changes
even_length_iteration =: (<./ (,&\$: |.) >./)@(-:@# ({. ,: |.@}.) ])^:(1<#)
pre =: ,   (-~ >.&.(2&^.))@# # >./            NB. extend data to next power of 2 length
post =: ({.~ #)~                              NB. remove the extra data
```

Examples:

```   show =: [ smoutput

8 ([: circle_sort&.>@show ;&(?~)) 13  NB. sort lists length 8 and 13
┌───────────────┬────────────────────────────┐
│0 6 7 3 4 5 2 1│3 10 1 4 7 8 5 6 2 0 9 11 12│
└───────────────┴────────────────────────────┘
┌───────────────┬────────────────────────────┐
│0 1 2 3 4 5 6 7│0 1 2 3 4 5 6 7 8 9 10 11 12│
└───────────────┴────────────────────────────┘

8 ([: circle_sort&.>@show ;&(1 }. 2 # ?~)) 13  NB. data has repetition
┌─────────────────────────────┬──────────────────────────────────────────────────────┐
│2 3 3 5 5 1 1 7 7 6 6 4 4 0 0│12 11 11 4 4 3 3 9 9 7 7 10 10 6 6 2 2 1 1 5 5 8 8 0 0│
└─────────────────────────────┴──────────────────────────────────────────────────────┘
┌─────────────────────────────┬──────────────────────────────────────────────────────┐
│0 0 1 1 2 3 3 4 4 5 5 6 6 7 7│0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12│
└─────────────────────────────┴──────────────────────────────────────────────────────┘
```

## Java

```import java.util.Arrays;

public class CircleSort {

public static void main(String[] args) {
circleSort(new int[]{2, 14, 4, 6, 8, 1, 3, 5, 7, 11, 0, 13, 12, -1});
}

public static void circleSort(int[] arr) {
if (arr.length > 0)
do {
System.out.println(Arrays.toString(arr));
} while (circleSortR(arr, 0, arr.length - 1, 0) != 0);
}

private static int circleSortR(int[] arr, int lo, int hi, int numSwaps) {
if (lo == hi)
return numSwaps;

int high = hi;
int low = lo;
int mid = (hi - lo) / 2;

while (lo < hi) {
if (arr[lo] > arr[hi]) {
swap(arr, lo, hi);
numSwaps++;
}
lo++;
hi--;
}

if (lo == hi && arr[lo] > arr[hi + 1]) {
swap(arr, lo, hi + 1);
numSwaps++;
}

numSwaps = circleSortR(arr, low, low + mid, numSwaps);
numSwaps = circleSortR(arr, low + mid + 1, high, numSwaps);

return numSwaps;
}

private static void swap(int[] arr, int idx1, int idx2) {
int tmp = arr[idx1];
arr[idx1] = arr[idx2];
arr[idx2] = tmp;
}
}
```
```[2, 14, 4, 6, 8, 1, 3, 5, 7, 11, 0, 13, 12, -1]
[-1, 1, 0, 4, 3, 8, 12, 2, 7, 6, 11, 5, 13, 14]
[-1, 0, 1, 3, 2, 4, 7, 5, 6, 8, 12, 11, 13, 14]
[-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14]```

## jq

Works with: jq version 1.4

With kudos to #Raku.

"circlesort" as defined in this section can be used to sort any JSON array. In case your jq does not have "until" as a builtin, here is its definition:

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

def swap(i;j): .[i] as \$t | .[i] = .[j] | .[j] = \$t;

# state: [lo, hi, swaps, array]
def cs:

# increment lo, decrement hi, and if they are equal, increment hi again
# i.e. ++hi if --hi == \$lo
def next: # [lo, hi]
.[0] += 1 | .[1] -= 1 | (if .[0] == .[1] then .[1] += 1 else . end) ;

.[0] as \$start | .[1] as \$stop
| if \$start < \$stop then
until(.[0] >= .[1];
.[0] as \$lo | .[1] as \$hi | .[3] as \$array
| if \$array[\$lo] > \$array[\$hi] then
.[3] = (\$array | swap(\$lo; \$hi))
| .[2] += 1         # swaps++
else .
end
| next)
| .[0] as \$lo | .[1] as \$hi
| [\$start, \$hi, .[2], .[3]] | cs
| [\$lo, \$stop,  .[2], .[3]] | cs
else .
end ;

[0, length-1, 0, .] | cs
| .[2] as \$swaps
| .[3]
| if \$swaps == 0 then .
else circlesort
end ;```

Example:

`"The quick brown fox jumps over the lazy dog" | split(" ") | circlesort`
Output:
```\$ jq -n -c -f -M circleSort.jq
["The","brown","dog","fox","jumps","lazy","over","quick","the"]
```

## Julia

Works with: Julia version 0.6
```function _ciclesort!(arr::Vector, lo::Int, hi::Int, swaps::Int)
lo == hi && return swaps
high = hi
low  = lo
mid  = (hi - lo) ÷ 2
while lo < hi
if arr[lo] > arr[hi]
arr[lo], arr[hi] = arr[hi], arr[lo]
swaps += 1
end
lo += 1
hi -= 1
end
if lo == hi
if arr[lo] > arr[hi+1]
arr[lo], arr[hi+1] = arr[hi+1], arr[lo]
swaps += 1
end
end
swaps = _ciclesort!(arr, low, low + mid, swaps)
swaps = _ciclesort!(arr, low + mid + 1, high, swaps)
return swaps
end

function ciclesort!(arr::Vector)
while !iszero(_ciclesort!(arr, 1, endof(arr), 0)) end
return arr
end

v = rand(10)
println("# \$v\n -> ", ciclesort!(v))
```
Output:
```# [0.603704, 0.293639, 0.51395, 0.74624, 0.245282, 0.930508, 0.550865, 0.62253, 0.00608894, 0.270426]
-> [0.00608894, 0.245282, 0.270426, 0.293639, 0.51395, 0.550865, 0.603704, 0.62253, 0.74624, 0.930508]```

## Kotlin

```// version 1.1.0

fun<T: Comparable<T>> circleSort(array: Array<T>, lo: Int, hi: Int, nSwaps: Int): Int {
if (lo == hi) return nSwaps

fun swap(array: Array<T>, i: Int, j: Int) {
val temp  = array[i]
array[i]  = array[j]
array[j]  = temp
}

var high  = hi
var low   = lo
val mid   = (hi - lo) / 2
var swaps = nSwaps
while (low < high) {
if (array[low] > array[high]) {
swap(array, low, high)
swaps++
}
low++
high--
}
if (low == high)
if (array[low] > array[high + 1]) {
swap(array, low, high + 1)
swaps++
}
swaps = circleSort(array, lo, lo + mid, swaps)
swaps = circleSort(array, lo + mid + 1, hi, swaps)
return swaps
}

fun main(args: Array<String>) {
val array = arrayOf(6, 7, 8, 9, 2, 5, 3, 4, 1)
println("Original: \${array.asList()}")
while (circleSort(array, 0, array.size - 1, 0) != 0) ; // empty statement
println("Sorted  : \${array.asList()}")
println()
val array2 = arrayOf("the", "quick", "brown", "fox", "jumps", "over", "the", "lazy", "dog")
println("Original: \${array2.asList()}")
while (circleSort(array2, 0, array2.size - 1, 0) != 0) ;
println("Sorted  : \${array2.asList()}")
}
```
Output:
```Original: [6, 7, 8, 9, 2, 5, 3, 4, 1]
Sorted  : [1, 2, 3, 4, 5, 6, 7, 8, 9]

Original: [the, quick, brown, fox, jumps, over, the, lazy, dog]
Sorted  : [brown, dog, fox, jumps, lazy, over, quick, the, the]
```

## Lua

The first argument to the 'inner' function needs to be a reference to the table as Lua cannot use a pointer to the first element's memory address. Conversely the 'outer' function only needs one argument as the size of the table is innately knowable.

```-- Perform one iteration of a circle sort
function innerCircle (t, lo, hi, swaps)
if lo == hi then return swaps end
local high, low, mid = hi, lo, math.floor((hi - lo) / 2)
while lo < hi do
if t[lo] > t[hi] then
t[lo], t[hi] = t[hi], t[lo]
swaps = swaps + 1
end
lo = lo + 1
hi = hi - 1
end
if lo == hi then
if t[lo] > t[hi + 1] then
t[lo], t[hi + 1] = t[hi + 1], t[lo]
swaps = swaps + 1
end
end
swaps = innerCircle(t, low, low + mid, swaps)
swaps = innerCircle(t, low + mid + 1, high, swaps)
return swaps
end

-- Keep sorting the table until an iteration makes no swaps
function circleSort (t)
while innerCircle(t, 1, #t, 0) > 0 do end
end

-- Main procedure
local array = {6, 7, 8, 9, 2, 5, 3, 4, 1}
circleSort(array)
print(table.concat(array, " "))
```
Output:
`1 2 3 4 5 6 7 8 9`

## Mathematica/Wolfram Language

```ClearAll[CircleSort, NestedCircleSort]
CircleSort[d_List, l_, h_] :=
Module[{high, low, mid, lo = l, hi = h, data = d},
If[lo == hi, Return[data]];
high = hi;
low = lo;
mid = Floor[(hi - lo)/2];
While[lo < hi,
If[data[[lo]] > data[[hi]],
data[[{lo, hi}]] //= Reverse;
];
lo++;
hi--
];
If[lo == hi,
If[data[[lo]] > data[[hi + 1]],
data[[{lo, hi + 1}]] //= Reverse;
]
];
data = CircleSort[data, low, low + mid];
data = CircleSort[data, low + mid + 1, high];
data
]
NestedCircleSort[{}] := {}
NestedCircleSort[d_List] := FixedPoint[CircleSort[#, 1, Length[#]] &, d]
NestedCircleSort[Echo@{6, 7, 8, 9, 2, 5, 3, 4, 1}]
NestedCircleSort[Echo@{6, 7, 8, 2, 5, 3, 4, 1}]
NestedCircleSort[Echo@{6, 2, 5, 7, 3, 4, 1}]
NestedCircleSort[Echo@{4, 6, 3, 5, 2, 1}]
NestedCircleSort[Echo@{1, 2, 3, 4, 5}]
NestedCircleSort[Echo@{2, 4, 3, 1}]
NestedCircleSort[Echo@{2, 3, 1}]
NestedCircleSort[Echo@{2, 1}]
NestedCircleSort[Echo@{1}]
NestedCircleSort[Echo@{}]
```
Output:
```>>{6,7,8,9,2,5,3,4,1}
{1,2,3,4,5,6,7,8,9}
>>{6,7,8,2,5,3,4,1}
{1,2,3,4,5,6,7,8}
>>{6,2,5,7,3,4,1}
{1,2,3,4,5,6,7}
>>{4,6,3,5,2,1}
{1,2,3,4,5,6}
>>{1,2,3,4,5}
{1,2,3,4,5}
>>{2,4,3,1}
{1,2,3,4}
>>{2,3,1}
{1,2,3}
>>{2,1}
{1,2}
>>{1}
{1}
>>{}
{}```

## Nim

```proc innerCircleSort[T](a: var openArray[T], lo, hi, swaps: int): int =
var localSwaps: int = swaps
var localHi: int = hi
var localLo: int = lo
if localLo == localHi:
return swaps

var `high` = localHi
var `low` = localLo
var mid = (localHi - localLo) div 2

while localLo < localHi:
if a[localLo] > a[localHi]:
swap a[localLo], a[localHi]
inc localSwaps
inc localLo
dec localHi
if localLo == localHi:
if a[localLo] > a[localHi + 1]:
swap a[localLo], a[localHi + 1]
inc localSwaps

localswaps = a.innerCircleSort(`low`, `low` + mid, localSwaps)
localSwaps = a.innerCircleSort(`low` + mid + 1, `high`, localSwaps)
result = localSwaps

proc circleSort[T](a: var openArray[T]) =
while a.innerCircleSort(0, a.high, 0) != 0:

var arr = @[@[6, 7, 8, 9, 2, 5, 3, 4, 1],
@[2, 14, 4, 6, 8, 1, 3, 5, 7, 11, 0, 13, 12, -1]]

for i in 0..arr.high:
echo "Original: ", \$arr[i]
arr[i].circleSort()
echo "Sorted: ", \$arr[i], if i != arr.high: "\n" else: ""
```
Output:
```Original: @[6, 7, 8, 9, 2, 5, 3, 4, 1]
Sorted: @[1, 2, 3, 4, 5, 6, 7, 8, 9]

Original: @[2, 14, 4, 6, 8, 1, 3, 5, 7, 11, 0, 13, 12, -1]
Sorted: @[-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14]```

## Objeck

Translation of: Objeck
```class CircleSort {
function : Main(args : String[]) ~ Nil {
circleSort([2, 14, 4, 6, 8, 1, 3, 5, 7, 11, 0, 13, 12, -1]);
}

function : circleSort(arr : Int[]) ~ Nil {
if(arr->Size() > 0) {
do {
arr->ToString()->PrintLine();
}
while(CircleSort(arr, 0, arr->Size() - 1, 0) <> 0);
};
}

function : CircleSort( arr : Int[], lo : Int, hi : Int, num_swaps : Int) ~ Int {
if(lo = hi) {
return num_swaps;
};

high := hi;
low := lo;
mid := (hi - lo) / 2;

while (lo < hi) {
if(arr[lo] > arr[hi]) {
Swap(arr, lo, hi);
num_swaps++;
};
lo++;
hi--;
};

if(lo = hi & arr[lo] > arr[hi + 1]) {
Swap(arr, lo, hi + 1);
num_swaps++;
};

num_swaps := CircleSort(arr, low, low + mid, num_swaps);
num_swaps := CircleSort(arr, low + mid + 1, high, num_swaps);

return num_swaps;
}

function : Swap(arr : Int[], idx1 : Int, idx2 : Int) ~ Nil {
tmp := arr[idx1];
arr[idx1] := arr[idx2];
arr[idx2] := tmp;
}
}```

Output:

```[2,14,4,6,8,1,3,5,7,11,0,13,12,-1]
[-1,1,0,4,3,8,12,2,7,6,11,5,13,14]
[-1,0,1,3,2,4,7,5,6,8,12,11,13,14]
[-1,0,1,2,3,4,5,6,7,8,11,12,13,14]
```

## PARI/GP

This follows the pseudocode pretty closely.

```circlesort(v)=
{
local(v=v); \\ share with cs
while (cs(1, #v),);
v;
}
cs(lo, hi)=
{
if (lo == hi, return (0));
my(high=hi,low=lo,mid=(hi-lo)\2,swaps);
while (lo < hi,
if (v[lo] > v[hi],
[v[lo],v[hi]]=[v[hi],v[lo]];
swaps++
);
lo++;
hi--
);
if (lo==hi && v[lo] > v[hi+1],
[v[lo],v[hi+1]]=[v[hi+1],v[lo]];
swaps++
);
swaps + cs(low,low+mid) + cs(low+mid+1,high);
}
print(example=[6,7,8,9,2,5,3,4,1]);
print(circlesort(example));```
Output:
```[6, 7, 8, 9, 2, 5, 3, 4, 1]
[1, 2, 3, 4, 5, 6, 7, 8, 9]```

## Pascal

```{
source file name on linux is ./p.p

-*- mode: compilation; default-directory: "/tmp/" -*-
Compilation started at Sat Mar 11 23:55:25

a=./p && pc \$a.p && \$a
Free Pascal Compiler version 3.0.0+dfsg-8 [2016/09/03] for x86_64
Copyright (c) 1993-2015 by Florian Klaempfl and others
Target OS: Linux for x86-64
Compiling ./p.p
/usr/bin/ld.bfd: warning: link.res contains output sections; did you forget -T?
56 lines compiled, 0.0 sec
1 2 3 4 5 6 7 8 9

Compilation finished at Sat Mar 11 23:55:25
}

program sort;

var
a : array[0..999] of integer;
i :  integer;

procedure circle_sort(var a : array of integer; left : integer; right : integer);
var swaps : integer;

procedure csinternal(var a : array of integer; left : integer; right : integer; var swaps : integer);
var
lo, hi, mid : integer;
t           : integer;
begin
if left < right then
begin
lo := left;
hi := right;
while lo < hi do
begin
if a[hi] < a[lo] then
begin
t := a[lo]; a[lo] := a[hi]; a[hi] := t;
swaps := swaps + 1;
end;
lo := lo + 1;
hi := hi - 1;
end;
if (lo = hi) and (a[lo+1] < a[lo]) then
begin
t := a[lo]; a[lo] := a[lo+1]; a[lo+1] := t;
swaps := swaps + 1;
end;
mid := trunc((hi + lo) / 2);
csinternal(a, left, mid, swaps);
csinternal(a, mid + 1, right, swaps)
end
end;

begin;
swaps := 1;
while (0 < swaps) do
begin
swaps := 0;
csinternal(a, left, right, swaps);
end
end;

begin
{
generating polynomial coefficients computed in j:  6 7 8 9 2 5 3 4 1x %. ^/~i.9x
are 6 29999r280 _292519r1120 70219r288 _73271r640 10697r360 _4153r960 667r2016 _139r13440
}
a[1]:=6;a[2]:=7;a[3]:=8;a[4]:=9;a[5]:=2;a[6]:=5;a[7]:=3;a[8]:=4;a[9]:=1;
circle_sort(a,1,9);
for i := 1 to 9 do write(a[i], ' ');
writeln();
end.
```

## Perl

Less flexible than the Raku version, as written does only numeric comparisons.

Translation of: Raku
```sub circlesort {
our @x; local *x = shift;
my(\$beg,\$end) = @_;

my \$swaps = 0;
if (\$beg < \$end) {
my \$lo = \$beg;
my \$hi = \$end;
while (\$lo < \$hi) {
if (\$x[\$lo] > \$x[\$hi]) { # 'gt' here for string comparison
@x[\$lo,\$hi] = @x[\$hi,\$lo];
++\$swaps;
}
++\$hi if --\$hi == ++\$lo
}
\$swaps += circlesort(\@x, \$beg, \$hi);
\$swaps += circlesort(\@x, \$lo, \$end);
}
\$swaps;
}

my @a = <16 35 -64 -29 46 36 -1 -99 20 100 59 26 76 -78 39 85 -7 -81 25 88>;
while (circlesort(\@a, 0, \$#a)) { print join(' ', @a), "\n" }
```
Output:
```-99 -78 16 20 36 -81 -29 46 25 59 -64 -7 39 26 88 -1 35 85 76 100
-99 -78 -29 -81 16 -64 -7 20 -1 39 25 26 36 46 59 35 76 88 85 100
-99 -81 -78 -64 -29 -7 -1 16 20 25 26 35 36 39 46 59 76 85 88 100
-99 -81 -78 -64 -29 -7 -1 16 20 25 26 35 36 39 46 59 76 85 88 100```

## Phix

```with javascript_semantics

sequence array

function circle_sort_inner(integer lo, hi, swaps, level=1)
if lo!=hi then
integer high := hi,
low := lo,
mid := floor((high-low)/2)
while lo <= hi do
hi += (lo=hi)
object alo = array[lo],
ahi = array[hi]
if alo > ahi then
array[lo] = ahi
array[hi] = alo
printf(1,"%V level %d, low %d, high %d\n",{array,level,low,high})
swaps += 1
end if
lo += 1
hi -= 1
end while
swaps = circle_sort_inner(low,low+mid,swaps,level+1)
swaps = circle_sort_inner(low+mid+1,high,swaps,level+1)
end if
return swaps
end function

procedure circle_sort()
printf(1,"%V <== (initial)\n",{array})
while circle_sort_inner(1, length(array), 0) do ?"loop" end while
printf(1,"%V <== (sorted)\n",{array})
end procedure

array = {5, -1, 101, -4, 0, 1, 8, 6, 2, 3}
--array = {-4,-1,1,0,5,-7,-2,4,-6,-3,2,6,3,7,-5}
--array = {6, 7, 8, 9, 2, 5, 3, 4, 1}
--array = {2,14,4,6,8,1,3,5,7,9,10,11,0,13,12,-1}
--array = {"the","quick","brown","fox","jumps","over","the","lazy","dog"}
--array = {0.603704, 0.293639, 0.513965, 0.746246, 0.245282, 0.930508, 0.550878, 0.622534, 0.006089, 0.270426}
--array = shuffle(deep_copy(array))
circle_sort()
```
Output:

Shows the full inner workings: call depth and range being considered, after each swap made.

```{5,-1,101,-4,0,1,8,6,2,3} <== (initial)
{3,-1,101,-4,0,1,8,6,2,5} level 1, low 1, high 10
{3,-1,6,-4,0,1,8,101,2,5} level 1, low 1, high 10
{0,-1,6,-4,3,1,8,101,2,5} level 2, low 1, high 5
{0,-4,6,-1,3,1,8,101,2,5} level 2, low 1, high 5
{0,-4,-1,6,3,1,8,101,2,5} level 2, low 1, high 5
{-1,-4,0,6,3,1,8,101,2,5} level 3, low 1, high 3
{-4,-1,0,6,3,1,8,101,2,5} level 4, low 1, high 2
{-4,-1,0,3,6,1,8,101,2,5} level 3, low 4, high 5
{-4,-1,0,3,6,1,2,101,8,5} level 2, low 6, high 10
{-4,-1,0,3,6,1,2,8,101,5} level 2, low 6, high 10
{-4,-1,0,3,6,1,2,8,5,101} level 3, low 9, high 10
"loop"
{-4,-1,0,2,6,1,3,8,5,101} level 1, low 1, high 10
{-4,-1,0,2,1,6,3,8,5,101} level 1, low 1, high 10
{-4,-1,0,1,2,6,3,8,5,101} level 3, low 4, high 5
{-4,-1,0,1,2,6,3,5,8,101} level 2, low 6, high 10
{-4,-1,0,1,2,5,3,6,8,101} level 3, low 6, high 8
{-4,-1,0,1,2,3,5,6,8,101} level 4, low 6, high 7
"loop"
{-4,-1,0,1,2,3,5,6,8,101} <== (sorted)
```

## Python

The doctest passes with odd and even length lists. As do the random tests. Please see circle_sort.__doc__ for example use and output.

```#python3
#tests: expect no output.
#doctest with  python3 -m doctest thisfile.py

def circle_sort_backend(A:list, L:int, R:int)->'sort A in place, returning the number of swaps':
'''
>>> L = [3, 2, 8, 28, 2,]
>>> circle_sort(L)
3
>>> print(L)
[2, 2, 3, 8, 28]
>>> L = [3, 2, 8, 28,]
>>> circle_sort(L)
1
>>> print(L)
[2, 3, 8, 28]
'''
n = R-L
if n < 2:
return 0
swaps = 0
m = n//2
for i in range(m):
if A[R-(i+1)] < A[L+i]:
(A[R-(i+1)], A[L+i],) = (A[L+i], A[R-(i+1)],)
swaps += 1
if (n & 1) and (A[L+m] < A[L+m-1]):
(A[L+m-1], A[L+m],) = (A[L+m], A[L+m-1],)
swaps += 1
return swaps + circle_sort_backend(A, L, L+m) + circle_sort_backend(A, L+m, R)

def circle_sort(L:list)->'sort A in place, returning the number of swaps':
swaps = 0
s = 1
while s:
s = circle_sort_backend(L, 0, len(L))
swaps += s
return swaps

# more tests!
if __name__ == '__main__':
from random import shuffle
for i in range(309):
L = list(range(i))
M = L[:]
shuffle(L)
N = L[:]
circle_sort(L)
if L != M:
print(len(L))
print(N)
print(L)
```

## Quackery

Having read the information on Sourceforge mentioned in the task description, I note that the circle sort is most elegant when sorting an array the length of which is a power of two. Rather than mess with the central element of an odd length array and forego potential parallelisation I chose to pad the array to the nearest power of two with elements that were guaranteed to be in the right place (here, numbers one larger than the largest item in the array and trim it down to size after sorting. Additionally, rather than flagging exchanges, I use an O(n) test to see if a subarray is sorted to avoid unnecessary recursive calls.

The link at the end of the Sourceforge page to a paper on the subject is broken. This link works.

In the demonstration, I sort the characters in a string. In Quackery a string is a particular use of a nest of numbers (dynamic array of bignums). The string is a word from a famously circular novel. It seemed appropriate for such a novel "circle sort".

```  [ dup size 2 < iff
[ drop true ] done
true swap
dup [] != if
[ tuck > if
[ dip not
conclude ] ] ]
drop ]                    is sorted     ( [ --> b   )

[ 2dup < iff
nip else drop ] ]     is largest    ( [ --> n   )

[ dup largest 1+
over size
dup 1
[ 2dup > while
1 << again ]
nip swap -
dup dip [ of join ]
swap ]                    is pad        (   [ --> n [ )

[ swap dup if
[ negate split drop ] ] is unpad      ( n [ --> [   )

[ dup size times
[ i i^ > not iff
conclude done
dup i peek
over i^ peek
2dup < iff
[ rot i poke
i^ poke ]
else 2drop ] ]          is reorder    (   [ --> [   )

[ [ dup sorted if done
reorder
dup size 2 / split
recurse swap
recurse swap join ]
dup sorted until ]
unpad ]                   is circlesort (   [ --> [   )

dup echo\$ cr
circlesort echo\$ cr```
Output:
```bababadalgharaghtakamminarronnkonnbronntonnerronntuonnthunntrovarrhounawnskawntoohoohoordenenthurnuk
aaaaaaaaaaaabbbbddeeegghhhhhhhikkkklmmnnnnnnnnnnnnnnnnnnnnnoooooooooooooorrrrrrrrrrrstttttttuuuuuvww
```

## Racket

By default this sorts with the numeric `<` but any other (diadic) function can be used to compare... e.g. `string<?`.

```#lang racket
(define (circle-sort v0 [<? <])
(define v (vector-copy v0))

(define (swap-if l r)
(define v.l (vector-ref v l))
(define v.r (vector-ref v r))
(and (<? v.r v.l)
(begin (vector-set! v l v.r) (vector-set! v r v.l) #t)))

(define (inr-cs! L R)
(cond
[(>= L (- R 1)) #f] ; covers 0 or 1 vectors
[else
(define M (quotient (+ L R) 2))
(define I-moved?
(for/or ([l (in-range L M)] [r (in-range (- R 1) L -1)])
(swap-if l r)))
(define M-moved? (and (odd? (- L R)) (> M 0) (swap-if (- M 1) M)))
(define L-moved? (inr-cs! L M))
(define R-moved? (inr-cs! M R))
(or I-moved? L-moved? R-moved? M-moved?)]))

(let loop () (when (inr-cs! 0 (vector-length v)) (loop)))
v)

(define (sort-random-vector)
(define v (build-vector (+ 2 (random 10)) (λ (i) (random 100))))
(define v< (circle-sort v <))
(define sorted? (apply <= (vector->list v<)))
(printf "   ~.a\n-> ~.a [~a]\n\n" v v< sorted?))

(for ([_ 10]) (sort-random-vector))

(circle-sort '#("table" "chair" "cat" "sponge") string<?)
```
Output:
```   #(36 94 63 51 33)
-> #(33 36 51 63 94) [#t]

#(73 74 20 20 79)
-> #(20 20 73 74 79) [#t]

#(83 42)
-> #(42 83) [#t]

#(53 95 43 33 66 47 1 61 28 96)
-> #(1 28 33 43 47 53 61 66 95 96) [#t]

#(71 85)
-> #(71 85) [#t]

#(36 85 50 19 88 17 2 53 21)
-> #(2 17 19 21 36 50 53 85 88) [#t]

#(5 97 62 21 99 73 17 16 37 28)
-> #(5 16 17 21 28 37 62 73 97 99) [#t]

#(12 60 89 90 2 95 9 28)
-> #(2 9 12 28 60 89 90 95) [#t]

#(50 32 30 47 63 74)
-> #(30 32 47 50 63 74) [#t]

#(63 41)
-> #(41 63) [#t]

'#("cat" "chair" "sponge" "table")
```

## Raku

(formerly Perl 6)

The given algorithm can be simplified in several ways. There's no need to compute the midpoint, since the hi/lo will end up there. The extra swap conditional can be eliminated by incrementing hi at the correct moment inside the loop. There's no need to pass accumulated swaps down the call stack.

This does generic comparisons, so it works on any ordered type, including numbers or strings.

```sub circlesort (@x, \$beg, \$end) {
my \$swaps = 0;
if \$beg < \$end {
my (\$lo, \$hi) = \$beg, \$end;
repeat {
if @x[\$lo] after @x[\$hi] {
@x[\$lo,\$hi] .= reverse;
++\$swaps;
}
++\$hi if --\$hi == ++\$lo
} while \$lo < \$hi;
\$swaps += circlesort(@x, \$beg, \$hi);
\$swaps += circlesort(@x, \$lo, \$end);
}
\$swaps;
}

say my @x = (-100..100).roll(20);
say @x while circlesort(@x, 0, @x.end);

say @x = <The quick brown fox jumps over the lazy dog.>;
say @x while circlesort(@x, 0, @x.end);
```
Output:
```16 35 -64 -29 46 36 -1 -99 20 100 59 26 76 -78 39 85 -7 -81 25 88
-99 -78 16 20 36 -81 -29 46 25 59 -64 -7 39 26 88 -1 35 85 76 100
-99 -78 -29 -81 16 -64 -7 20 -1 39 25 26 36 46 59 35 76 88 85 100
-99 -81 -78 -64 -29 -7 -1 16 20 25 26 35 36 39 46 59 76 85 88 100
The quick brown fox jumps over the lazy dog.
The brown fox jumps lazy dog. quick over the
The brown dog. fox jumps lazy over quick the```

## REXX

This REXX version will work with any numbers that REXX supports, including negative and/or floating point numbers;
it also will work with character strings.

```/*REXX program uses a  circle sort algorithm  to sort an array (or list) of numbers.    */
parse arg x                                      /*obtain optional arguments from the CL*/
if x='' | x=","  then x= 6 7 8 9 2 5 3 4 1       /*Not specified?  Then use the default.*/
call make_array  'before sort:'                  /*display the list and make an array.  */
call circleSort       #                          /*invoke the circle sort subroutine.   */
call make_list   ' after sort:'                  /*make a list and display it to console*/
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
circleSort:      do while  .circleSrt(1, arg(1), 0)\==0;     end;                   return
make_array: #= words(x);    do i=1 for #;  @.i= word(x, i);  end;  say arg(1)  x;   return
make_list:  y= @.1;         do j=2 for #-1;  y= y  @.j;      end;  say arg(1)  y;   return
.swap:      parse arg a,b;  parse  value  @.a @.b  with  @.b @.a;  swaps= swaps+1;  return
/*──────────────────────────────────────────────────────────────────────────────────────*/
.circleSrt: procedure expose @.;  parse arg LO,HI,swaps    /*obtain  LO & HI  arguments.*/
if LO==HI  then return swaps                   /*1 element?  Done with sort.*/
high= HI;      low= LO;     mid= (HI-LO) % 2   /*assign some indices.       */
/* [↓]  sort a section of #'s*/
do  while LO<HI                     /*sort within a section.     */
if @.LO>@.HI  then call .swap LO,HI /*are numbers out of order ? */
LO= LO + 1;        HI= HI - 1       /*add to LO;  shrink the HI. */
end   /*while*/                     /*just process one section.  */
_= HI + 1                                      /*point to  HI  plus one.    */
if LO==HI  &  @.LO>@._  then call .swap LO, _  /*numbers still out of order?*/
swaps= .circleSrt(low,        low+mid,  swaps) /*sort the   lower  section. */
swaps= .circleSrt(low+mid+1,  high,     swaps) /*  "   "   higher     "     */
return swaps                                   /*the section sorting is done*/
```
output   when using the default input:
```before sort:  6 7 8 9 2 5 3 4 1
after sort:  1 2 3 4 5 6 7 8 9
```
output   when using the input of:   2 3 3 5 5 1 1 7 7 6 6 4 4 0 0
```before sort: 2 3 3 5 5 1 1 7 7 6 6 4 4 0 0
after sort: 0 0 1 1 2 3 3 4 4 5 5 6 6 7 7
```
output   when using the input of:   2 3 44 44 5.77 +1 -12345 -3 -3.9 1e7 9
```before sort: 2 3 44 44 5.77 +1 -12345 -3 -3.9 1e7 0
after sort: -12345 -3.9 -3 0 +1 2 3 5.77 44 44 1e7
```
output   when using the using the input of:   assinine donkey bovine cattle canine dog corvine crow equine horse feline cat hircine goat leporine hare lupine wolf murine rodent piscine fish porcine pig ursine bear vulpine fox
```before sort: assinine donkey bovine cattle canine dog corvine crow equine horse feline cat hircine goat leporine hare lupine wolf murine rodent piscine fish porcine pig ursine bear vulpine fox
after sort: assinine bear bovine canine cat cattle corvine crow dog donkey equine feline fish fox goat hare hircine horse leporine lupine murine pig piscine porcine rodent ursine vulpine wolf
```

## Ring

```# Project : Sorting Algorithms/Circle Sort

test = [-4, -1, 1, 0, 5, -7, -2, 4, -6, -3, 2, 6, 3, 7, -5]
while circlesort(1, len(test), 0) end
showarray(test)

func circlesort(lo, hi, swaps)
if lo = hi
return swaps
ok
high = hi
low = lo
mid = floor((hi-lo)/2)
while lo < hi
if test[lo] > test[hi]
temp = test[lo]
test[lo] = test[hi]
test[hi] = temp
swaps = swaps + 1
ok
lo = lo + 1
hi = hi - 1
end
if lo = hi
if test[lo] > test[hi+1]
temp = test[lo]
test[lo] = test[hi+1]
test[hi + 1] = temp
swaps = swaps + 1
ok
ok
swaps = circlesort(low, low+mid, swaps)
swaps = circlesort(low+mid+1 ,high, swaps)
return swaps

func showarray(vect)
see "["
svect = ""
for n = 1 to len(vect)
svect = svect + vect[n] + ", "
next
svect = left(svect, len(svect) - 2)
see svect
see "]" + nl```

Output:

```[-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7]
```

## Ruby

```class Array
def circle_sort!
while _circle_sort!(0, size-1) > 0
end
self
end

private
def _circle_sort!(lo, hi, swaps=0)
return swaps if lo == hi
low, high = lo, hi
mid = (lo + hi) / 2
while lo < hi
if self[lo] > self[hi]
self[lo], self[hi] = self[hi], self[lo]
swaps += 1
end
lo += 1
hi -= 1
end
if lo == hi && self[lo] > self[hi+1]
self[lo], self[hi+1] = self[hi+1], self[lo]
swaps += 1
end
swaps + _circle_sort!(low, mid) + _circle_sort!(mid+1, high)
end
end

ary = [6, 7, 8, 9, 2, 5, 3, 4, 1]
puts "before sort: #{ary}"
puts " after sort: #{ary.circle_sort!}"
```
Output:
```before sort: [6, 7, 8, 9, 2, 5, 3, 4, 1]
after sort: [1, 2, 3, 4, 5, 6, 7, 8, 9]
```

## Rust

```fn _circle_sort<T: PartialOrd>(a: &mut [T], low: usize, high: usize, swaps: usize) -> usize {
if low == high {
return swaps;
}
let mut lo = low;
let mut hi = high;
let mid = (hi - lo) / 2;
let mut s = swaps;
while lo < hi {
if a[lo] > a[hi] {
a.swap(lo, hi);
s += 1;
}
lo += 1;
hi -= 1;
}
if lo == hi {
if a[lo] > a[hi + 1] {
a.swap(lo, hi + 1);
s += 1;
}
}
s = _circle_sort(a, low, low + mid, s);
s = _circle_sort(a, low + mid + 1, high, s);
return s;
}

fn circle_sort<T: PartialOrd>(a: &mut [T]) {
let len = a.len();
loop {
if _circle_sort(a, 0, len - 1, 0) == 0 {
break;
}
}
}

fn main() {
let mut v = vec![10, 8, 4, 3, 1, 9, 0, 2, 7, 5, 6];
println!("before: {:?}", v);
circle_sort(&mut v);
println!("after:  {:?}", v);
}
```
Output:
```before: [10, 8, 4, 3, 1, 9, 0, 2, 7, 5, 6]
after:  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
```

## Scala

```object CircleSort extends App {

def sort(arr: Array[Int]): Array[Int] = {
def circleSortR(arr: Array[Int], _lo: Int, _hi: Int, _numSwaps: Int): Int = {
var lo = _lo
var hi = _hi
var numSwaps = _numSwaps

def swap(arr: Array[Int], idx1: Int, idx2: Int): Unit = {
val tmp = arr(idx1)
arr(idx1) = arr(idx2)
arr(idx2) = tmp
}

if (lo == hi) return numSwaps
val (high, low) = (hi, lo)
val mid = (hi - lo) / 2
while ( lo < hi) {
if (arr(lo) > arr(hi)) {
swap(arr, lo, hi)
numSwaps += 1
}
lo += 1
hi -= 1
}
if (lo == hi && arr(lo) > arr(hi + 1)) {
swap(arr, lo, hi + 1)
numSwaps += 1
}

circleSortR(arr, low + mid + 1, high, circleSortR(arr, low, low + mid, numSwaps))
}

while (circleSortR(arr, 0, arr.length - 1, 0) != 0)()
arr
}

println(sort(Array[Int](2, 14, 4, 6, 8, 1, 3, 5, 7, 11, 0, 13, 12, -1)).mkString(", "))

}
```

## Sidef

```func circlesort(arr, beg=0, end=arr.end) {
var swaps = 0
if (beg < end) {
var (lo, hi) = (beg, end)
do {
if (arr[lo] > arr[hi]) {
arr.swap(lo, hi)
++swaps
}
++hi if (--hi == ++lo)
} while (lo < hi)
swaps += circlesort(arr, beg, hi)
swaps += circlesort(arr, lo, end)
}
return swaps
}

var numbers = %n(2 3 3 5 5 1 1 7 7 6 6 4 4 0 0)
do { say numbers } while circlesort(numbers)

var strs = ["John", "Kate", "Zerg", "Alice", "Joe", "Jane", "Alice"]
do { say strs } while circlesort(strs)
```
Output:
```[2, 3, 3, 5, 5, 1, 1, 7, 7, 6, 6, 4, 4, 0, 0]
[0, 0, 1, 4, 1, 5, 3, 7, 2, 3, 4, 5, 6, 6, 7]
[0, 0, 1, 1, 2, 3, 3, 4, 4, 5, 5, 7, 6, 6, 7]
[0, 0, 1, 1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7]
["John", "Kate", "Zerg", "Alice", "Joe", "Jane", "Alice"]
["Alice", "Jane", "Alice", "Joe", "John", "Kate", "Zerg"]
["Alice", "Alice", "Jane", "Joe", "John", "Kate", "Zerg"]
```

## Swift

```func circleSort<T: Comparable>(_ array: inout [T]) {
func circSort(low: Int, high: Int, swaps: Int) -> Int {
if low == high {
return swaps
}
var lo = low
var hi = high
let mid = (hi - lo) / 2
var s = swaps
while lo < hi {
if array[lo] > array[hi] {
array.swapAt(lo, hi)
s += 1
}
lo += 1
hi -= 1
}
if lo == hi {
if array[lo] > array[hi + 1] {
array.swapAt(lo, hi + 1)
s += 1
}
}
s = circSort(low: low, high: low + mid, swaps: s)
s = circSort(low: low + mid + 1, high: high, swaps: s)
return s
}
while circSort(low: 0, high: array.count - 1, swaps: 0) != 0 {}
}

var array = [10, 8, 4, 3, 1, 9, 0, 2, 7, 5, 6]
print("before: \(array)")
circleSort(&array)
print(" after: \(array)")

var array2 = ["one", "two", "three", "four", "five", "six", "seven", "eight"]
print("before: \(array2)")
circleSort(&array2)
print(" after: \(array2)")
```
Output:
```before: [10, 8, 4, 3, 1, 9, 0, 2, 7, 5, 6]
after: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
before: ["one", "two", "three", "four", "five", "six", "seven", "eight"]
after: ["eight", "five", "four", "one", "seven", "six", "three", "two"]
```

## uBasic/4tH

This one uses the optimized version featured at Sourceforge.

```PRINT "Circle sort:"
n = FUNC (_InitArray)
PROC _ShowArray (n)
PROC _Circlesort (n)
PROC _ShowArray (n)
PRINT

END

_InnerCircle PARAM (2)
LOCAL (3)
c@ = a@
d@ = b@
e@ = 0

IF c@ = d@ THEN RETURN (0)

DO WHILE c@ < d@
IF @(c@) > @(d@) THEN PROC _Swap (c@, d@) : e@ = e@ + 1
c@ = c@ + 1
d@ = d@ - 1
LOOP

e@ = e@ + FUNC (_InnerCircle (a@, d@))
e@ = e@ + FUNC (_InnerCircle (c@, b@))
RETURN (e@)

_Circlesort PARAM(1)                   ' Circle sort
DO WHILE FUNC (_InnerCircle (0, a@-1))
LOOP
RETURN

_Swap PARAM(2)                         ' Swap two array elements
PUSH @(a@)
@(a@) = @(b@)
@(b@) = POP()
RETURN

_InitArray                             ' Init example array
PUSH 4, 65, 2, -31, 0, 99, 2, 83, 782, 1

FOR i = 0 TO 9
@(i) = POP()
NEXT

RETURN (i)

_ShowArray PARAM (1)                   ' Show array subroutine
FOR i = 0 TO a@-1
PRINT @(i),
NEXT

PRINT
RETURN
```

## V (Vlang)

Translation of: go
```fn circle_sort(mut a []int, l int, h int, s int) int {
mut hi := h
mut lo := l
mut swaps := s
if lo == hi {
return swaps
}
high, low := hi, lo
mid := (hi - lo) / 2
for lo < hi {
if a[lo] > a[hi] {
a[lo], a[hi] = a[hi], a[lo]
swaps++
}
lo++
hi--
}
if lo == hi {
if a[lo] > a[hi+1] {
a[lo], a[hi+1] = a[hi+1], a[lo]
swaps++
}
}
swaps = circle_sort(mut a, low, low+mid, swaps)
swaps = circle_sort(mut a, low+mid+1, high, swaps)
return swaps
}

fn main() {
aa := [
[6, 7, 8, 9, 2, 5, 3, 4, 1],
[2, 14, 4, 6, 8, 1, 3, 5, 7, 11, 0, 13, 12, -1],
]
for a1 in aa {
mut a:=a1.clone()
println("Original: \$a")
for circle_sort(mut a, 0, a.len-1, 0) != 0 {
// empty block
}
println("Sorted  : \$a\n")
}
}```
Output:
```Original: [6, 7, 8, 9, 2, 5, 3, 4, 1]
Sorted  : [1, 2, 3, 4, 5, 6, 7, 8, 9]

Original: [2, 14, 4, 6, 8, 1, 3, 5, 7, 11, 0, 13, 12, -1]
Sorted  : [-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14]
```

## Wren

```var circleSort // recursive
circleSort = Fn.new { |a, lo, hi, swaps|
if (lo == hi) return swaps
var high = hi
var low = lo
var mid = ((hi-lo)/2).floor
while (lo < hi) {
if (a[lo] > a[hi]) {
var t = a[lo]
a[lo] = a[hi]
a[hi] = t
swaps = swaps + 1
}
lo = lo + 1
hi = hi - 1
}
if (lo == hi) {
if (a[lo] > a[hi+1]) {
var t = a[lo]
a[lo] = a[hi+1]
a[hi+1] = t
swaps = swaps + 1
}
}
swaps = circleSort.call(a, low, low + mid, swaps)
swaps = circleSort.call(a, low + mid + 1, high, swaps)
return swaps
}

var array = [ [6, 7, 8, 9, 2, 5, 3, 4, 1], [2, 14, 4, 6, 8, 1, 3, 5, 7, 11, 0, 13, 12, -1] ]
for (a in array) {
System.print("Before: %(a)")
while (circleSort.call(a, 0, a.count-1, 0) != 0) {}
System.print("After : %(a)")
System.print()
}
```
Output:
```Before: [6, 7, 8, 9, 2, 5, 3, 4, 1]
After : [1, 2, 3, 4, 5, 6, 7, 8, 9]

Before: [2, 14, 4, 6, 8, 1, 3, 5, 7, 11, 0, 13, 12, -1]
After : [-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14]
```

## XPL0

```int  Array;

func CircleSort(Lo, Hi, Swaps);
int  Lo, Hi, Swaps;
int  Low, High, Mid, T;
[if Lo = Hi then return Swaps;
Low:= Lo;
High:= Hi;
Mid:= (Hi-Lo)/2;
while Lo < Hi do
[if Array(Lo) > Array(Hi) then
[T:= Array(Lo);  Array(Lo):= Array(Hi);  Array(Hi):= T;
Swaps:= Swaps+1;
];
Lo:= Lo+1;
Hi:= Hi-1;
];
if Lo = Hi then
if Array(Lo) > Array(Hi+1) then
[T:= Array(Lo);  Array(Lo):= Array(Hi+1);  Array(Hi+1):= T;
Swaps:= Swaps+1;
];
Swaps:= CircleSort(Low, Low+Mid, Swaps);
Swaps:= CircleSort(Low+Mid+1, High, Swaps);
return Swaps;
];

int I;
[Array:= [5, -1, 101, -4, 0, 1, 8, 6, 2, 3];
while CircleSort(0, 10-1, 0) # 0 do [];
for I:= 0 to 10-1 do
[IntOut(0, Array(I));  ChOut(0, ^ )];
]```
Output:
```-4 -1 0 1 2 3 5 6 8 101
```

## zkl

```fcn circleSort(list){
csort:=fcn(list,lo,hi,swaps){
if(lo==hi) return(swaps);
high,low,mid:=hi,lo,(hi-lo)/2;
while(lo<hi){
if(list[lo]>list[hi]){
list.swap(lo,hi);
swaps+=1;
}
lo+=1; hi-=1;
}
if(lo==hi)
if (list[lo]>list[hi+1]){
list.swap(lo,hi+1);
swaps+=1;
}
swaps=self.fcn(list,low,low + mid,swaps);
swaps=self.fcn(list,low + mid + 1,high,swaps);
return(swaps);
};
list.println();
while(csort(list,0,list.len()-1,0)){ list.println() }
list
}```
```circleSort(L(6,7,8,9,2,5,3,4,1));
circleSort(L(5,-1,101,-4,0,1,8,6,2,3));```
Output:
```L(6,7,8,9,2,5,3,4,1)
L(1,3,4,2,5,6,7,8,9)
L(1,2,3,4,5,6,7,8,9)
L(5,-1,101,-4,0,1,8,6,2,3)
L(-4,-1,0,3,6,1,2,8,5,101)
L(-4,-1,0,1,2,3,5,6,8,101)
```

## ZX Spectrum Basic

A language like ZX BASIC is not the most obvious choice for a routine which depends on local variables and recursion. This program proves that it can be implemented quite efficiently using arrays and global variables. The b and e variables are set up in such a way that they can be used for the first recursive call. The variables for the next recursion are saved in array s() which serves as a stack together with stack pointer p.

The size of the stack is determined by the amount of memory on the ZX Spectrum, which is 64KB (or 216 bytes). Each call requires two array elements. Note the size of a ZX Spectrum floating point number is 5 bytes, so this stack is slightly oversized. The somewhat strange indexing between both recursions is due to an stack pointer adjustment which was optimized away.

This version of Circle sort was based on the optimized version on Sourceforge. It will also show a few asterisks while running, because it will take some time to finish (about two minutes).

```   10 DIM a(100): DIM s(32): RANDOMIZE : LET p=1: GO SUB 3000: GO SUB 2000: GO SUB 4000
20 STOP
1000 IF b=e THEN RETURN
1010 LET s(p)=b: LET s(p+1)=e
1020 IF a(s(p))>a(e) THEN LET t=a(s(p)): LET a(s(p))=a(e): LET a(e)=t: LET c=1
1030 LET s(p)=s(p)+1: LET e=e-1: IF s(p)<e THEN GO TO 1020
1040 LET p=p+2: GO SUB 1000: LET b=s(p-2): LET e=s(p-1): GO SUB 1000: LET p=p-2: RETURN
2000 PRINT "*";: LET b=1: LET e=100: LET c=0: GO SUB 1000: IF c>0 THEN GO TO 2000
2010 CLS : RETURN
3000 FOR x=1 TO 100: LET a(x)=RND: NEXT x: RETURN
4000 FOR x=1 TO 100: PRINT x,a(x): NEXT x: RETURN```