Sorting algorithms/Quicksort: Difference between revisions

From Rosetta Code
m (fix markup)
(2 intermediate revisions by the same user not shown)
Line 4,524: Line 4,524:
 
[0, 1, 2, 2, 3, 4]
 
[0, 1, 2, 2, 3, 4]
 
[Daniel, Ethan, Jacob, Juan, Liam, Miguel, William]
 
[Daniel, Ethan, Jacob, Juan, Liam, Miguel, William]
  +
</pre>
  +
  +
  +
=={{header|FutureBasic}}==
  +
<syntaxhighlight lang="futurebasic">
  +
include "NSLog.incl"
  +
  +
local fn Quicksort( qs as CFMutableArrayRef, l as NSInteger, r as NSInteger )
  +
UInt64 size = r - l + 1
  +
  +
if size < 2 then exit fn
  +
  +
NSinteger i = l, j = r
  +
NSinteger pivot = fn NumberIntegerValue( qs[l+size / 2] )
  +
  +
do
  +
while fn NumberIntegerValue( qs[i] ) < pivot
  +
i++
  +
wend
  +
while pivot < fn NumberIntegerValue( qs[j] )
  +
j--
  +
wend
  +
if ( i <= j )
  +
MutableArrayExchangeObjects( qs, i, j )
  +
i++
  +
j--
  +
end if
  +
until i > j
  +
  +
if l < j then fn Quicksort( qs, l, j )
  +
if i < r then fn Quicksort( qs, i, r )
  +
end fn
  +
  +
CFMutableArrayRef qs
  +
CFArrayRef unsorted
  +
NSUInteger i, amount
  +
  +
qs = fn MutableArrayWithCapacity(0)
  +
  +
for i = 0 to 25
  +
if i mod 2 == 0 then amount = 100 else amount = 10000
  +
MutableArrayInsertObjectAtIndex( qs, fn NumberWithInteger( rnd(amount) ), i )
  +
next
  +
  +
unsorted = fn ArrayWithArray( qs )
  +
  +
fn QuickSort( qs, 0, len(qs) - 1 )
  +
  +
NSLog( @"\n-----------------\nUnsorted : Sorted\n-----------------" )
  +
for i = 0 to 25
  +
NSLog( @"%8ld : %-8ld", fn NumberIntegerValue( unsorted[i] ), fn NumberIntegerValue( qs[i] ) )
  +
next
  +
  +
randomize
  +
  +
HandleEvents
  +
</syntaxhighlight>
  +
{{output}}
  +
<pre>
  +
-----------------
  +
Unsorted : Sorted
  +
-----------------
  +
97 : 5
  +
6168 : 30
  +
61 : 34
  +
8847 : 40
  +
55 : 46
  +
2570 : 49
  +
40 : 55
  +
4676 : 61
  +
94 : 62
  +
693 : 67
  +
62 : 79
  +
3419 : 94
  +
30 : 97
  +
936 : 693
  +
5 : 733
  +
9910 : 936
  +
67 : 1395
  +
8460 : 1796
  +
79 : 2570
  +
9352 : 3419
  +
49 : 4676
  +
1395 : 6168
  +
34 : 8460
  +
733 : 8847
  +
46 : 9352
  +
1796 : 9910
 
</pre>
 
</pre>
   

Revision as of 19:27, 18 September 2022

Task
Sorting algorithms/Quicksort
You are encouraged to solve this task according to the task description, using any language you may know.
This page uses content from Wikipedia. The original article was at Quicksort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)


Task

Sort an array (or list) elements using the   quicksort   algorithm.

The elements must have a   strict weak order   and the index of the array can be of any discrete type.

For languages where this is not possible, sort an array of integers.


Quicksort, also known as   partition-exchange sort,   uses these steps.

  1.   Choose any element of the array to be the pivot.
  2.   Divide all other elements (except the pivot) into two partitions.
    •   All elements less than the pivot must be in the first partition.
    •   All elements greater than the pivot must be in the second partition.
  3.   Use recursion to sort both partitions.
  4.   Join the first sorted partition, the pivot, and the second sorted partition.


The best pivot creates partitions of equal length (or lengths differing by   1).

The worst pivot creates an empty partition (for example, if the pivot is the first or last element of a sorted array).

The run-time of Quicksort ranges from   O(n log n)   with the best pivots, to   O(n2)   with the worst pivots, where   n   is the number of elements in the array.


This is a simple quicksort algorithm, adapted from Wikipedia.

function quicksort(array)
    less, equal, greater := three empty arrays
    if length(array) > 1  
        pivot := select any element of array
        for each x in array
            if x < pivot then add x to less
            if x = pivot then add x to equal
            if x > pivot then add x to greater
        quicksort(less)
        quicksort(greater)
        array := concatenate(less, equal, greater)

A better quicksort algorithm works in place, by swapping elements within the array, to avoid the memory allocation of more arrays.

function quicksort(array)
    if length(array) > 1
        pivot := select any element of array
        left := first index of array
        right := last index of array
        while left ≤ right
            while array[left] < pivot
                left := left + 1
            while array[right] > pivot
                right := right - 1
            if left ≤ right
                swap array[left] with array[right]
                left := left + 1
                right := right - 1
        quicksort(array from first index to right)
        quicksort(array from left to last index)

Quicksort has a reputation as the fastest sort. Optimized variants of quicksort are common features of many languages and libraries. One often contrasts quicksort with   merge sort,   because both sorts have an average time of   O(n log n).

"On average, mergesort does fewer comparisons than quicksort, so it may be better when complicated comparison routines are used. Mergesort also takes advantage of pre-existing order, so it would be favored for using sort() to merge several sorted arrays. On the other hand, quicksort is often faster for small arrays, and on arrays of a few distinct values, repeated many times."http://perldoc.perl.org/sort.html

Quicksort is at one end of the spectrum of divide-and-conquer algorithms, with merge sort at the opposite end.

  • Quicksort is a conquer-then-divide algorithm, which does most of the work during the partitioning and the recursive calls. The subsequent reassembly of the sorted partitions involves trivial effort.
  • Merge sort is a divide-then-conquer algorithm. The partioning happens in a trivial way, by splitting the input array in half. Most of the work happens during the recursive calls and the merge phase.


With quicksort, every element in the first partition is less than or equal to every element in the second partition. Therefore, the merge phase of quicksort is so trivial that it needs no mention!

This task has not specified whether to allocate new arrays, or sort in place. This task also has not specified how to choose the pivot element. (Common ways to are to choose the first element, the middle element, or the median of three elements.) Thus there is a variety among the following implementations.

11l

Translation of: Python
F _quicksort(&array, start, stop) -> N
   I stop - start > 0
      V pivot = array[start]
      V left = start
      V right = stop
      L left <= right
         L array[left] < pivot
            left++
         L array[right] > pivot
            right--
         I left <= right
            swap(&array[left], &array[right])
            left++
            right--
      _quicksort(&array, start, right)
      _quicksort(&array, left, stop)

F quicksort(&array)
   _quicksort(&array, 0, array.len - 1)

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

360 Assembly

Translation of: REXX

Structured version with ASM & ASSIST macros.

*        Quicksort                 14/09/2015 & 23/06/2016
QUICKSOR CSECT
         USING  QUICKSOR,R13       base register
         B      72(R15)            skip savearea
         DC     17F'0'             savearea
         STM    R14,R12,12(R13)    prolog
         ST     R13,4(R15)         "
         ST     R15,8(R13)         " 
         LR     R13,R15            "
         MVC    A,=A(1)            a(1)=1
         MVC    B,=A(NN)           b(1)=hbound(t)
         L      R6,=F'1'           k=1
       DO WHILE=(LTR,R6,NZ,R6)   do while k<>0    ==================
         LR     R1,R6              k 
         SLA    R1,2               ~
         L      R10,A-4(R1)        l=a(k)
         LR     R1,R6              k
         SLA    R1,2               ~
         L      R11,B-4(R1)        m=b(k)
         BCTR   R6,0               k=k-1
         LR     R4,R11             m
         C      R4,=F'2'           if m<2 
         BL     ITERATE            then iterate
         LR     R2,R10             l
         AR     R2,R11             +m
         BCTR   R2,0               -1
         ST     R2,X               x=l+m-1
         LR     R2,R11             m
         SRA    R2,1               m/2
         AR     R2,R10             +l
         ST     R2,Y               y=l+m/2
         L      R1,X               x
         SLA    R1,2               ~
         L      R4,T-4(R1)         r4=t(x)
         L      R1,Y               y
         SLA    R1,2               ~
         L      R5,T-4(R1)         r5=t(y)
         LR     R1,R10             l
         SLA    R1,2               ~
         L      R3,T-4(R1)         r3=t(l)
         IF     CR,R4,LT,R3        if t(x)<t(l)       ---+
         IF     CR,R5,LT,R4          if t(y)<t(x)        |
         LR     R7,R4                  p=t(x)            |
         L      R1,X                   x                 |
         SLA    R1,2                   ~                 |
         ST     R3,T-4(R1)             t(x)=t(l)         |
         ELSEIF CR,R5,GT,R3          elseif t(y)>t(l)    |
         LR     R7,R3                  p=t(l)            |
         ELSE   ,                    else                |
         LR     R7,R5                  p=t(y)            |
         L      R1,Y                   y                 |
         SLA    R1,2                   ~                 |
         ST     R3,T-4(R1)            t(y)=t(l)          |
         ENDIF  ,                    end if              |
         ELSE   ,                  else                  |
         IF     CR,R5,LT,R3          if t(y)<t(l)        |
         LR     R7,R3                  p=t(l)            |
         ELSEIF CR,R5,GT,R4          elseif t(y)>t(x)    |
         LR     R7,R4                  p=t(x)            |
         L      R1,X                   x                 |
         SLA    R1,2                   ~                 |
         ST     R3,T-4(R1)             t(x)=t(l)         |
         ELSE   ,                    else                |
         LR     R7,R5                  p=t(y)            |
         L      R1,Y                   y                 |
         SLA    R1,2                   ~                 |
         ST     R3,T-4(R1)             t(y)=t(l)         |
         ENDIF  ,                    end if              |
         ENDIF  ,                  end if             ---+
         LA     R8,1(R10)          i=l+1
         L      R9,X               j=x
FOREVER  EQU    *                  do forever  --------------------+  
         LR     R1,R8                i                             |
         SLA    R1,2                 ~                             |
         LA     R2,T-4(R1)           @t(i)                         |
         L      R0,0(R2)             t(i)                          |
         DO WHILE=(CR,R8,LE,R9,AND,  while i<=j and   ---+         |   X
               CR,R0,LE,R7)                t(i)<=p       |         |
         AH     R8,=H'1'               i=i+1             |         |
         AH     R2,=H'4'               @t(i)             |         |
         L      R0,0(R2)               t(i)              |         |
         ENDDO  ,                    end while        ---+         |
         LR     R1,R9                j                             |
         SLA    R1,2                 ~                             |
         LA     R2,T-4(R1)           @t(j)                         |
         L      R0,0(R2)             t(j)                          |
         DO WHILE=(CR,R8,LT,R9,AND,  while i<j and    ---+         |   X
               CR,R0,GE,R7)                t(j)>=p       |         |
         SH     R9,=H'1'               j=j-1             |         |
         SH     R2,=H'4'               @t(j)             |         |
         L      R0,0(R2)               t(j)              |         |
         ENDDO  ,                    end while        ---+         |
         CR     R8,R9                if i>=j                       |
         BNL    LEAVE                then leave (segment finished) |
         LR     R1,R8                i                             |
         SLA    R1,2                 ~                             |
         LA     R2,T-4(R1)           @t(i)                         |
         LR     R1,R9                j                             |
         SLA    R1,2                 ~                             |
         LA     R3,T-4(R1)           @t(j)                         |
         L      R0,0(R2)             w=t(i)       +                |
         MVC    0(4,R2),0(R3)        t(i)=t(j)    |swap t(i),t(j)  |
         ST     R0,0(R3)             t(j)=w       +                |
         B      FOREVER            end do forever  ----------------+
LEAVE    EQU    *
         LR     R9,R8              j=i
         BCTR   R9,0               j=i-1
         LR     R1,R9              j
         SLA    R1,2               ~
         LA     R3,T-4(R1)         @t(j)
         L      R2,0(R3)           t(j)
         LR     R1,R10             l
         SLA    R1,2               ~
         ST     R2,T-4(R1)         t(l)=t(j)
         ST     R7,0(R3)           t(j)=p
         LA     R6,1(R6)           k=k+1
         LR     R1,R6              k
         SLA    R1,2               ~
         LA     R4,A-4(R1)         r4=@a(k)
         LA     R5,B-4(R1)         r5=@b(k)
         IF     C,R8,LE,Y          if i<=y           ----+
         ST     R8,0(R4)             a(k)=i              |
         L      R2,X                 x                   |
         SR     R2,R8                -i                  |
         LA     R2,1(R2)             +1                  |
         ST     R2,0(R5)             b(k)=x-i+1          |
         LA     R6,1(R6)             k=k+1               |
         ST     R10,4(R4)            a(k)=l              |
         LR     R2,R9                j                   |
         SR     R2,R10               -l                  |
         ST     R2,4(R5)             b(k)=j-l            |
         ELSE   ,                  else                  |
         ST     R10,4(R4)            a(k)=l              |
         LR     R2,R9                j                   |
         SR     R2,R10               -l                  |
         ST     R2,0(R5)             b(k)=j-l            |
         LA     R6,1(R6)             k=k+1               |
         ST     R8,4(R4)             a(k)=i              |
         L      R2,X                 x                   |
         SR     R2,R8                -i                  |
         LA     R2,1(R2)             +1                  |
         ST     R2,4(R5)             b(k)=x-i+1          |
         ENDIF  ,                  end if            ----+
ITERATE  EQU    *                  
       ENDDO    ,                  end while  =====================
*        ***    *********          print sorted table
         LA     R3,PG              ibuffer
         LA     R4,T               @t(i)
       DO WHILE=(C,R4,LE,=A(TEND)) do i=1 to hbound(t)
         L      R2,0(R4)             t(i)
         XDECO  R2,XD                edit t(i)
         MVC    0(4,R3),XD+8         put in buffer
         LA     R3,4(R3)             ibuffer=ibuffer+1
         LA     R4,4(R4)             i=i+1
       ENDDO    ,                  end do
         XPRNT  PG,80              print buffer
         L      R13,4(0,R13)       epilog 
         LM     R14,R12,12(R13)    "
         XR     R15,R15            "
         BR     R14                exit
T        DC     F'10',F'9',F'9',F'6',F'7',F'16',F'1',F'16',F'17',F'15'
         DC     F'1',F'9',F'18',F'16',F'8',F'20',F'18',F'2',F'19',F'8'
TEND     DS     0F
NN       EQU    (TEND-T)/4)
A        DS     (NN)F              same size as T
B        DS     (NN)F              same size as T
X        DS     F
Y        DS     F
PG       DS     CL80
XD       DS     CL12
         YREGS 
         END    QUICKSOR
Output:
   1   1   2   6   7   8   8   9   9   9  10  15  16  16  16  17  18  18  19  20

AArch64 Assembly

Works with: as version Raspberry Pi 3B version Buster 64 bits
/* ARM assembly AARCH64 Raspberry PI 3B */
/*  program quickSort64.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"
sMessResult:        .asciz "Value  : @ \n"
szCarriageReturn:   .asciz "\n"
 
.align 4
TableNumber:      .quad   1,3,6,2,5,9,10,8,4,7,11
#TableNumber:     .quad   10,9,8,7,6,-5,4,3,2,1
                 .equ NBELEMENTS, (. - TableNumber) / 8 
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss
sZoneConv:       .skip 24
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main 
main:                                              // entry of program 
    ldr x0,qAdrTableNumber                         // address number table
    mov x1,0                                       // first element
    mov x2,NBELEMENTS                              // number of élements 
    bl quickSort
    ldr x0,qAdrTableNumber                         // address number table
    bl displayTable
 
    ldr x0,qAdrTableNumber                         // address number table
    mov x1,NBELEMENTS                              // number of élements 
    bl isSorted                                    // control sort
    cmp x0,1                                       // sorted ?
    beq 1f                                    
    ldr x0,qAdrszMessSortNok                       // no !! error sort
    bl affichageMess
    b 100f
1:                                                 // yes
    ldr x0,qAdrszMessSortOk
    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
 
qAdrsZoneConv:            .quad sZoneConv
qAdrszCarriageReturn:     .quad szCarriageReturn
qAdrsMessResult:          .quad sMessResult
qAdrTableNumber:          .quad TableNumber
qAdrszMessSortOk:         .quad szMessSortOk
qAdrszMessSortNok:        .quad szMessSortNok
/******************************************************************/
/*     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:
    add x2,x2,1
    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
    ret                            // return to address lr x30
/***************************************************/
/*   Appel récursif Tri Rapide quicksort           */
/***************************************************/
/* x0 contains the address of table */
/* x1 contains index of first item  */
/* x2 contains the number of elements  > 0  */
quickSort:
    stp x2,lr,[sp,-16]!             // save  registers
    stp x3,x4,[sp,-16]!             // save  registers
    str x5,   [sp,-16]!             // save  registers
    sub x2,x2,1                     // last item index
    cmp x1,x2                       // first > last ? 
    bge 100f                        // yes -> end
    mov x4,x0                       // save x0
    mov x5,x2                       // save x2
    bl partition1                   // cutting into 2 parts
    mov x2,x0                       // index partition
    mov x0,x4                       // table address
    bl quickSort                    // sort lower part
    add x1,x2,1                     // index begin = index partition + 1
    add x2,x5,1                     // number of elements
    bl quickSort                    // sort higter part
 
 100:                               // end function
    ldr x5,   [sp],16               // restaur  1 register
    ldp x3,x4,[sp],16               // restaur  2 registers
    ldp x2,lr,[sp],16               // restaur  2 registers
    ret                             // return to address lr x30
 
/******************************************************************/
/*      Partition table elements                                */ 
/******************************************************************/
/* x0 contains the address of table */
/* x1 contains index of first item  */
/* x2 contains index of last item   */
partition1:
    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
    ldr x3,[x0,x2,lsl 3]            // load value last index
    mov x4,x1                       // init with first index
    mov x5,x1                       // init with first index
1:                                  // begin loop
    ldr x6,[x0,x5,lsl 3]            // load value
    cmp x6,x3                       // compare value
    bge 2f
    ldr x7,[x0,x4,lsl 3]            // if < swap value table
    str x6,[x0,x4,lsl 3]
    str x7,[x0,x5,lsl 3]
    add x4,x4,1                     // and increment index 1
2:
    add x5,x5,1                     // increment index 2
    cmp x5,x2                       // end ?
    blt 1b                          // no loop
    ldr x7,[x0,x4,lsl 3]            // swap value
    str x3,[x0,x4,lsl 3]
    str x7,[x0,x2,lsl 3]
    mov x0,x4                       // return index partition
100:
    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
    ret                             // return to address lr x30
 
/******************************************************************/
/*      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 x2,x0                        // table address
    mov x3,0
1:                                   // loop display table
    ldr x0,[x2,x3,lsl 3]
    ldr x1,qAdrsZoneConv
    bl conversion10S                  // décimal conversion
    ldr x0,qAdrsMessResult
    ldr x1,qAdrsZoneConv
    bl strInsertAtCharInc            // insert result at // character
    bl affichageMess                 // display message
    add x3,x3,1
    cmp x3,NBELEMENTS - 1
    ble 1b
    ldr x0,qAdrszCarriageReturn
    bl affichageMess
    mov x0,x2
100:
    ldp x2,x3,[sp],16               // restaur  2 registers
    ldp x1,lr,[sp],16               // restaur  2 registers
    ret                             // return to address lr x30
/********************************************************/
/*        File Include fonctions                        */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"
Value  : +1
Value  : +2
Value  : +3
Value  : +4
Value  : +5
Value  : +6
Value  : +7
Value  : +8
Value  : +9
Value  : +10
Value  : +11

Table sorted.

ABAP

This works for ABAP Version 7.40 and above

report z_quicksort.

data(numbers) = value int4_table( ( 4 ) ( 65 ) ( 2 ) ( -31 ) ( 0 ) ( 99 ) ( 2 ) ( 83 ) ( 782 ) ( 1 ) ).
perform quicksort changing numbers.

write `[`.
loop at numbers assigning field-symbol(<numbers>).
  write <numbers>.
endloop.
write `]`.

form quicksort changing numbers type int4_table.
  data(less) = value int4_table( ).
  data(equal) = value int4_table( ).
  data(greater) = value int4_table( ).

  if lines( numbers ) > 1.
    data(pivot) = numbers[ lines( numbers ) / 2 ].

    loop at numbers assigning field-symbol(<number>).
      if <number> < pivot.
        append <number> to less.
      elseif <number> = pivot.
        append <number> to equal.
      elseif <number> > pivot.
        append <number> to greater.
      endif.
    endloop.

    perform quicksort changing less.
    perform quicksort changing greater.

    clear numbers.
    append lines of less to numbers.
    append lines of equal to numbers.
    append lines of greater to numbers.
  endif.
endform.
Output:
[        31-         0          1          2          2          4         65         83         99        782  ]

ACL2

(defun partition (p xs)
   (if (endp xs)
       (mv nil nil)
       (mv-let (less more)
               (partition p (rest xs))
          (if (< (first xs) p)
              (mv (cons (first xs) less) more)
              (mv less (cons (first xs) more))))))

(defun qsort (xs)
   (if (endp xs)
       nil
       (mv-let (less more)
               (partition (first xs) (rest xs))
          (append (qsort less)
                  (list (first xs))
                  (qsort more)))))

Usage:

> (qsort '(8 6 7 5 3 0 9))
(0 3 5 6 7 8 9)

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 QuickSort(INT ARRAY a INT size)
  INT low,high,part

  InitStack()
  Push(0,size-1)
  WHILE IsEmpty()=0
  DO
    Pop(@low,@high)
    part=Partition(a,low,high)
    IF part-1>low THEN
      Push(low,part-1)      
    FI
    IF part+1<high THEN
      Push(part+1,high)
    FI
  OD
RETURN

PROC Test(INT ARRAY a INT size)
  PrintE("Array before sort:")
  PrintArray(a,size)
  QuickSort(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:

Screenshot from Atari 8-bit computer

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]

ActionScript

Works with: ActionScript version 3

The functional programming way

function quickSort (array:Array):Array
{
    if (array.length <= 1)
        return array;

    var pivot:Number = array[Math.round(array.length / 2)];

    return quickSort(array.filter(function (x:Number, index:int, array:Array):Boolean { return x <  pivot; })).concat(
            array.filter(function (x:Number, index:int, array:Array):Boolean { return x == pivot; })).concat(
        quickSort(array.filter(function (x:Number, index:int, array:Array):Boolean { return x > pivot; })));
}

The faster way

function quickSort (array:Array):Array
{
    if (array.length <= 1)
        return array;

    var pivot:Number = array[Math.round(array.length / 2)];

    var less:Array = [];
    var equal:Array = [];
    var greater:Array = [];

    for each (var x:Number in array) {
        if (x < pivot)
            less.push(x);
        if (x == pivot)
            equal.push(x);
        if (x > pivot)
            greater.push(x);
    }

    return quickSort(less).concat(
            equal).concat(
            quickSort(greater));
}

Ada

This example is implemented as a generic procedure.

The procedure specification is:

-----------------------------------------------------------------------
-- Generic Quick_Sort procedure
-----------------------------------------------------------------------
generic
   type Element is private;
   type Index is (<>);
   type Element_Array is array(Index range <>) of Element;
   with function "<" (Left, Right : Element) return Boolean is <>;
procedure Quick_Sort(A : in out Element_Array);

The procedure body deals with any discrete index type, either an integer type or an enumerated type.

-----------------------------------------------------------------------
-- Generic Quick_Sort procedure
----------------------------------------------------------------------- 

procedure Quick_Sort (A : in out Element_Array) is
   
   procedure Swap(Left, Right : Index) is
      Temp : Element := A (Left);
   begin
      A (Left) := A (Right);
      A (Right) := Temp;
   end Swap;
  
begin
   if A'Length > 1 then
   declare
      Pivot_Value : Element := A (A'First);
      Right       : Index := A'Last;
      Left        : Index := A'First;
   begin
       loop
          while Left < Right and not (Pivot_Value < A (Left)) loop
             Left := Index'Succ (Left);
          end loop;
          while Pivot_Value < A (Right) loop
             Right := Index'Pred (Right);
          end loop;
          exit when Right <= Left;
          Swap (Left, Right);
          Left := Index'Succ (Left);
          Right := Index'Pred (Right);
       end loop;
       if Right = A'Last then
          Right := Index'Pred (Right);
          Swap (A'First, A'Last);
       end if;
       if Left = A'First then
          Left := Index'Succ (Left);
       end if;
       Quick_Sort (A (A'First .. Right));
       Quick_Sort (A (Left .. A'Last));
   end;
   end if;
end Quick_Sort;

An example of how this procedure may be used is:

with Ada.Text_Io;
with Ada.Float_Text_IO; use Ada.Float_Text_IO; 
with Quick_Sort;

procedure Sort_Test is
   type Days is (Mon, Tue, Wed, Thu, Fri, Sat, Sun);
   type Sales is array (Days range <>) of Float;
   procedure Sort_Days is new Quick_Sort(Float, Days, Sales);
   
   procedure Print (Item : Sales) is
   begin
      for I in Item'range loop
         Put(Item => Item(I), Fore => 5, Aft => 2, Exp => 0);
      end loop;
   end Print;
  
   Weekly_Sales : Sales := (Mon => 300.0, 
      Tue => 700.0, 
      Wed => 800.0, 
      Thu => 500.0, 
      Fri => 200.0, 
      Sat => 100.0, 
      Sun => 900.0);
  
begin
  
   Print(Weekly_Sales);
   Ada.Text_Io.New_Line(2);
   Sort_Days(Weekly_Sales);
   Print(Weekly_Sales);
  
end Sort_Test;

ALGOL 68

#--- Swap function ---#
PROC swap = (REF []INT array, INT first, INT second) VOID:
(
    INT temp := array[first];
    array[first] := array[second];
    array[second]:= temp
);

#--- Quick sort 3 arg function ---#
PROC quick = (REF [] INT array, INT first, INT last) VOID:
(
    INT smaller := first + 1,  
        larger  := last,
        pivot   := array[first];
  
    WHILE smaller <= larger DO
        WHILE array[smaller] < pivot   AND   smaller < last DO   
            smaller +:= 1        
        OD;
        WHILE array[larger]  > pivot   AND   larger > first DO   
            larger  -:= 1       
        OD; 
        IF smaller < larger THEN 
            swap(array, smaller, larger); 
            smaller +:= 1;
            larger  -:= 1
        ELSE
            smaller +:= 1
        FI
    OD;
    
    swap(array, first, larger);    

    IF first < larger-1 THEN
        quick(array, first, larger-1)  
    FI;
    IF last > larger +1 THEN
        quick(array, larger+1, last)   
    FI
);

#--- Quick sort 1 arg function ---#
PROC quicksort = (REF []INT array) VOID:
(
  IF UPB array > 1 THEN
    quick(array, 1, UPB array) 
  FI
);

#***************************************************************#
main:
(
    [10]INT a; 
    FOR i FROM 1 TO UPB a DO 
        a[i] := ROUND(random*1000)
    OD;                             

    print(("Before:", a));
    quicksort(a);
    print((newline, newline));
    print(("After: ", a))
)
Output:
Before:        +73       +921       +179       +961        +50       +324        +82       +178       +243       +458
                                                                                                                     
After:         +50        +73        +82       +178       +179       +243       +324       +458       +921       +961

ALGOL W

% Quicksorts in-place the array of integers v, from lb to ub %
procedure quicksort ( integer array v( * )
                    ; integer value lb, ub
                    ) ;
if ub > lb then begin
    % more than one element, so must sort %
    integer left, right, pivot;
    left   := lb;
    right  := ub;
    % choosing the middle element of the array as the pivot %
    pivot  := v( left + ( ( right + 1 ) - left ) div 2 );
    while begin
        while left  <= ub and v( left  ) < pivot do left  := left  + 1;
        while right >= lb and v( right ) > pivot do right := right - 1;
        left <= right
    end do begin
        integer swap;
        swap       := v( left  );
        v( left  ) := v( right );
        v( right ) := swap;
        left       := left  + 1;
        right      := right - 1
    end while_left_le_right ;
    quicksort( v, lb,   right );
    quicksort( v, left, ub    )
end quicksort ;

APL

Works with: Dyalog APL
Translation of: J
      qsort  {1≥⍴⍵:⍵  e[?⍴]  ((<e)/) , ((=e)/) , ((>e)/)}
      qsort 31 4 1 5 9 2 6 5 3 5 8
1 2 3 4 5 5 5 6 8 9 31

Of course, in real APL applications, one would use ⍋ (Grade Up) to sort (which will pick a sorting algorithm suited to the argument):

      sort  {[]}
      sort 31 4 1 5 9 2 6 5 3 5 8
1 2 3 4 5 5 5 6 8 9 31

AppleScript

Functional

Emphasising clarity and simplicity more than run-time performance. (Practical scripts will often delegate sorting to the OS X shell, or, since OS X Yosemite, to Foundation classes through the ObjC interface).

Translation of: JavaScript

(Functional ES5 version)

-- quickSort :: (Ord a) => [a] -> [a]
on quickSort(xs)
    if length of xs > 1 then
        set {h, t} to uncons(xs)
        
        -- lessOrEqual :: a -> Bool
        script lessOrEqual
            on |λ|(x)
                x  h
            end |λ|
        end script
        
        set {less, more} to partition(lessOrEqual, t)
        
        quickSort(less) & h & quickSort(more)
    else
        xs
    end if
end quickSort


-- TEST -----------------------------------------------------------------------
on run
    
    quickSort([11.8, 14.1, 21.3, 8.5, 16.7, 5.7])
    
    --> {5.7, 8.5, 11.8, 14.1, 16.7, 21.3}
    
end run


-- GENERIC FUNCTIONS ----------------------------------------------------------

-- partition :: predicate -> List -> (Matches, nonMatches)
-- partition :: (a -> Bool) -> [a] -> ([a], [a])
on partition(f, xs)
    tell mReturn(f)
        set lst to {{}, {}}
        repeat with x in xs
            set v to contents of x
            set end of item ((|λ|(v) as integer) + 1) of lst to v
        end repeat
        return {item 2 of lst, item 1 of lst}
    end tell
end partition

-- uncons :: [a] -> Maybe (a, [a])
on uncons(xs)
    if length of xs > 0 then
        {item 1 of xs, rest of xs}
    else
        missing value
    end if
end uncons

-- Lift 2nd class handler function into 1st class script wrapper 
-- mReturn :: Handler -> Script
on mReturn(f)
    if class of f is script then
        f
    else
        script
            property |λ| : f
        end script
    end if
end mReturn
Output:
{5.7, 8.5, 11.8, 14.1, 16.7, 21.3}

Straightforward

Emphasising clarity, quick sorting, and correct AppleScript:

-- In-place Quicksort (basic algorithm).
-- Algorithm: S.A.R. (Tony) Hoare, 1960.
on quicksort(theList, l, r) -- Sort items l thru r of theList.
    set listLength to (count theList)
    if (listLength < 2) then return
    -- Convert negative and/or transposed range indices.
    if (l < 0) then set l to listLength + l + 1
    if (r < 0) then set r to listLength + r + 1
    if (l > r) then set {l, r} to {r, l}
    
    -- Script object containing the list as a property (to allow faster references to its items)
    -- and the recursive subhandler.
    script o
        property lst : theList
        
        on qsrt(l, r)
            set pivot to my lst's item ((l + r) div 2)
            set i to l
            set j to r
            repeat until (i > j)
                set lv to my lst's item i
                repeat while (pivot > lv)
                    set i to i + 1
                    set lv to my lst's item i
                end repeat
                
                set rv to my lst's item j
                repeat while (rv > pivot)
                    set j to j - 1
                    set rv to my lst's item j
                end repeat
                
                if (j > i) then
                    set my lst's item i to rv
                    set my lst's item j to lv
                else if (i > j) then
                    exit repeat
                end if
                
                set i to i + 1
                set j to j - 1
            end repeat
            
            if (j > l) then qsrt(l, j)
            if (i < r) then qsrt(i, r)
        end qsrt
    end script
    
    tell o to qsrt(l, r)
    
    return -- nothing.
end quicksort
property sort : quicksort

-- Demo:
local aList
set aList to {28, 9, 95, 22, 67, 55, 20, 41, 60, 53, 100, 72, 19, 67, 14, 42, 29, 20, 74, 39}
sort(aList, 1, -1) -- Sort items 1 thru -1 of aList.
return aList
Output:
{9, 14, 19, 20, 20, 22, 28, 29, 39, 41, 42, 53, 55, 60, 67, 67, 72, 74, 95, 100}

Arc

(def qs (seq)
  (if (empty seq) nil
      (let pivot (car seq)
	(join (qs (keep [< _ pivot] (cdr seq)))
	      (list pivot)
	      (qs (keep [>= _ pivot] (cdr seq)))))))

ARM Assembly

Works with: as version Raspberry Pi
/* ARM assembly Raspberry PI  */
/*  program quickSort.s   */
/* look pseudo code in wikipedia  quicksort */

/************************************/
/* Constantes                       */
/************************************/
.equ STDOUT, 1     @ Linux output console
.equ EXIT,   1     @ Linux syscall
.equ WRITE,  4     @ Linux syscall
/*********************************/
/* Initialized data              */
/*********************************/
.data
szMessSortOk:       .asciz "Table sorted.\n"
szMessSortNok:      .asciz "Table not sorted !!!!!.\n"
sMessResult:        .ascii "Value  : "
sMessValeur:        .fill 11, 1, ' '            @ size => 11
szCarriageReturn:   .asciz "\n"
 
.align 4
iGraine:  .int 123456
.equ NBELEMENTS,      10
#TableNumber:	     .int   9,5,6,1,2,3,10,8,4,7
#TableNumber:	     .int   1,3,5,2,4,6,10,8,4,7
#TableNumber:	     .int   1,3,5,2,4,6,10,8,4,7
#TableNumber:	     .int   1,2,3,4,5,6,10,8,4,7
TableNumber:	     .int   10,9,8,7,6,5,4,3,2,1
#TableNumber:	     .int   13,12,11,10,9,8,7,6,5,4,3,2,1
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss  
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main 
main:                                              @ entry of program 
 
1:
    ldr r0,iAdrTableNumber                         @ address number table

    mov r1,#0                                      @ indice first item
    mov r2,#NBELEMENTS                             @ number of élements 
    bl triRapide                                   @ call quicksort
    ldr r0,iAdrTableNumber                         @ address number table
    bl displayTable
 
    ldr r0,iAdrTableNumber                         @ address number table
    mov r1,#NBELEMENTS                             @ number of élements 
    bl isSorted                                    @ control sort
    cmp r0,#1                                      @ sorted ?
    beq 2f                                    
    ldr r0,iAdrszMessSortNok                       @ no !! error sort
    bl affichageMess
    b 100f
2:                                                 @ yes
    ldr r0,iAdrszMessSortOk
    bl affichageMess
100:                                               @ standard end of the program 
    mov r0, #0                                     @ return code
    mov r7, #EXIT                                  @ request to exit program
    svc #0                                         @ perform the system call
 
iAdrsMessValeur:          .int sMessValeur
iAdrszCarriageReturn:    .int szCarriageReturn
iAdrsMessResult:          .int sMessResult
iAdrTableNumber:          .int TableNumber
iAdrszMessSortOk:         .int szMessSortOk
iAdrszMessSortNok:        .int szMessSortNok
/******************************************************************/
/*     control sorted table                                   */ 
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the number of elements  > 0  */
/* r0 return 0  if not sorted   1  if sorted */
isSorted:
    push {r2-r4,lr}                                    @ save registers
    mov r2,#0
    ldr r4,[r0,r2,lsl #2]
1:
    add r2,#1
    cmp r2,r1
    movge r0,#1
    bge 100f
    ldr r3,[r0,r2, lsl #2]
    cmp r3,r4
    movlt r0,#0
    blt 100f
    mov r4,r3
    b 1b
100:
    pop {r2-r4,lr}
    bx lr                                              @ return 


/***************************************************/
/*   Appel récursif Tri Rapide quicksort           */
/***************************************************/
/* r0 contains the address of table */
/* r1 contains index of first item  */
/* r2 contains the number of elements  > 0  */
triRapide:
    push {r2-r5,lr}                                   @ save registers
    sub r2,#1                                         @ last item index
    cmp r1,r2                                         @ first > last ? 
    bge 100f                                          @ yes -> end
    mov r4,r0                                         @ save r0
    mov r5,r2                                         @ save r2
    bl partition1                                     @ cutting into 2 parts
    mov r2,r0                                         @ index partition
    mov r0,r4                                         @ table address
    bl triRapide                                      @ sort lower part
    add r1,r2,#1                                      @ index begin = index partition + 1
    add r2,r5,#1                                      @ number of elements
    bl triRapide                                      @ sort higter part
   
 100:                                                 @ end function
    pop {r2-r5,lr}                                    @ restaur  registers 
    bx lr                                             @ return


/******************************************************************/
/*      Partition table elements                                */ 
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains index of first item  */
/* r2 contains index of last item   */

partition1:
    push {r1-r7,lr}                                    @ save registers
    ldr r3,[r0,r2,lsl #2]                              @ load value last index
    mov r4,r1                                          @ init with first index
    mov r5,r1                                          @ init with first index
1:                                                     @ begin loop
    ldr r6,[r0,r5,lsl #2]                              @ load value
    cmp r6,r3                                          @ compare value
    ldrlt r7,[r0,r4,lsl #2]                            @ if < swap value table
    strlt r6,[r0,r4,lsl #2]
    strlt r7,[r0,r5,lsl #2]
    addlt r4,#1                                        @ and increment index 1
    add    r5,#1                                       @ increment index 2
    cmp r5,r2                                          @ end ?
    blt 1b                                             @ no loop
    ldr r7,[r0,r4,lsl #2]                              @ swap value
    str r3,[r0,r4,lsl #2]
    str r7,[r0,r2,lsl #2]
    mov r0,r4                                          @ return index partition
100:
    pop {r1-r7,lr}
    bx lr

/******************************************************************/
/*      Display table elements                                */ 
/******************************************************************/
/* r0 contains the address of table */
displayTable:
    push {r0-r3,lr}                                    @ save registers
    mov r2,r0                                          @ table address
    mov r3,#0
1:                                                     @ loop display table
    ldr r0,[r2,r3,lsl #2]
    ldr r1,iAdrsMessValeur                             @ display value
    bl conversion10                                    @ call function
    ldr r0,iAdrsMessResult
    bl affichageMess                                   @ display message
    add r3,#1
    cmp r3,#NBELEMENTS - 1
    ble 1b
    ldr r0,iAdrszCarriageReturn
    bl affichageMess
100:
    pop {r0-r3,lr}
    bx lr
/******************************************************************/
/*     display text with size calculation                         */ 
/******************************************************************/
/* r0 contains the address of the message */
affichageMess:
    push {r0,r1,r2,r7,lr}                          @ save  registres
    mov r2,#0                                      @ counter length 
1:                                                 @ loop length calculation 
    ldrb r1,[r0,r2]                                @ read octet start position + index 
    cmp r1,#0                                      @ if 0 its over 
    addne r2,r2,#1                                 @ else add 1 in the length 
    bne 1b                                         @ and loop 
                                                   @ so here r2 contains the length of the message 
    mov r1,r0                                      @ address message in r1 
    mov r0,#STDOUT                                 @ code to write to the standard output Linux 
    mov r7, #WRITE                                 @ code call system "write" 
    svc #0                                         @ call systeme 
    pop {r0,r1,r2,r7,lr}                           @ restaur des  2 registres */ 
    bx lr                                          @ return  
/******************************************************************/
/*     Converting a register to a decimal unsigned                */ 
/******************************************************************/
/* r0 contains value and r1 address area   */
/* r0 return size of result (no zero final in area) */
/* area size => 11 bytes          */
.equ LGZONECAL,   10
conversion10:
    push {r1-r4,lr}                                 @ save registers 
    mov r3,r1
    mov r2,#LGZONECAL
 
1:	                                            @ start loop
    bl divisionpar10U                               @ unsigned  r0 <- dividende. quotient ->r0 reste -> r1
    add r1,#48                                      @ digit
    strb r1,[r3,r2]                                 @ store digit on area
    cmp r0,#0                                       @ stop if quotient = 0 
    subne r2,#1                                     @ else previous position
    bne 1b	                                    @ and loop
                                                    @ and move digit from left of area
    mov r4,#0
2:
    ldrb r1,[r3,r2]
    strb r1,[r3,r4]
    add r2,#1
    add r4,#1
    cmp r2,#LGZONECAL
    ble 2b
                                                      @ and move spaces in end on area
    mov r0,r4                                         @ result length 
    mov r1,#' '                                       @ space
3:
    strb r1,[r3,r4]                                   @ store space in area
    add r4,#1                                         @ next position
    cmp r4,#LGZONECAL
    ble 3b                                            @ loop if r4 <= area size
 
100:
    pop {r1-r4,lr}                                    @ restaur registres 
    bx lr                                             @return
 
/***************************************************/
/*   division par 10   unsigned                    */
/***************************************************/
/* r0 dividende   */
/* r0 quotient */	
/* r1 remainder  */
divisionpar10U:
    push {r2,r3,r4, lr}
    mov r4,r0                                          @ save value
    //mov r3,#0xCCCD                                   @ r3 <- magic_number lower  raspberry 3
    //movt r3,#0xCCCC                                  @ r3 <- magic_number higter raspberry 3
    ldr r3,iMagicNumber                                @ r3 <- magic_number    raspberry 1 2
    umull r1, r2, r3, r0                               @ r1<- Lower32Bits(r1*r0) r2<- Upper32Bits(r1*r0) 
    mov r0, r2, LSR #3                                 @ r2 <- r2 >> shift 3
    add r2,r0,r0, lsl #2                               @ r2 <- r0 * 5 
    sub r1,r4,r2, lsl #1                               @ r1 <- r4 - (r2 * 2)  = r4 - (r0 * 10)
    pop {r2,r3,r4,lr}
    bx lr                                              @ leave function 
iMagicNumber:  	.int 0xCCCCCCCD

Arturo

quickSort: function [items][
	if 2 > size items -> return items
	
	pivot: first items
	left:  select slice items 1 (size items)-1 'x -> x < pivot
	right: select slice items 1 (size items)-1 'x -> x >= pivot

	((quickSort left) ++ pivot) ++ quickSort right
]

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

ATS

A quicksort working on non-linear linked lists

(*------------------------------------------------------------------*)
(* Quicksort in ATS2, for non-linear lists.                         *)
(*------------------------------------------------------------------*)

#include "share/atspre_staload.hats"

#define NIL list_nil ()
#define ::  list_cons

(*------------------------------------------------------------------*)

(* A simple quicksort working on "garbage-collected" linked lists,
   with first element as pivot. This is meant as a demonstration, not
   as a superior sort algorithm.

   It is based on the "not-in-place" task pseudocode. *)

datatype comparison_result =
| first_is_less_than_second of ()
| first_is_equal_to_second of ()
| first_is_greater_than_second of ()

extern fun {a : t@ype}
list_quicksort$comparison (x : a, y : a) :<> comparison_result

extern fun {a : t@ype}
list_quicksort {n   : int}
               (lst : list (a, n)) :<> list (a, n)

(* -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  - *)

implement {a}
list_quicksort {n} (lst) =
  let
    fun
    partition {n     : nat}
              .<n>.             (* Proof of termination. *)
              (lst   : list (a, n),
               pivot : a)
        :<> [n1, n2, n3 : int | n1 + n2 + n3 == n]
            @(list (a, n1), list (a, n2), list (a, n3)) =
      (* This implementation is *not* tail recursive. I may get a
         scolding for using ATS to risk stack overflow! However, I
         need more practice writing non-tail routines. :) Also, a lot
         of programmers in other languages would do it this
         way--especially if the lists are evaluated lazily. *)
      case+ lst of
      | NIL => @(NIL, NIL, NIL)
      | head :: tail =>
        let
          val @(lt, eq, gt) = partition (tail, pivot)
          prval () = lemma_list_param lt
          prval () = lemma_list_param eq
          prval () = lemma_list_param gt
        in
          case+ list_quicksort$comparison<a> (head, pivot) of
          | first_is_less_than_second ()    => @(head :: lt, eq, gt)
          | first_is_equal_to_second ()     => @(lt, head :: eq, gt)
          | first_is_greater_than_second () => @(lt, eq, head :: gt)
        end

    fun
    quicksort {n   : nat}
              .<n>.             (* Proof of termination. *)
              (lst : list (a, n))
        :<> list (a, n) =
      case+ lst of
      | NIL => lst
      | _ :: NIL => lst
      | head :: tail =>
        let
          (* We are careful here to run "partition" on "tail" rather
             than "lst", so the termination metric will be provably
             decreasing. (Really the compiler *forces* us to take such
             care, or else to change :<> to :<!ntm>) *)
          val pivot = head
          prval () = lemma_list_param tail
          val @(lt, eq, gt) = partition {n - 1} (tail, pivot)
          prval () = lemma_list_param lt
          prval () = lemma_list_param eq
          prval () = lemma_list_param gt
          val eq = pivot :: eq
          and lt = quicksort lt
          and gt = quicksort gt
        in
          lt + (eq + gt)
        end

    prval () = lemma_list_param lst
  in
    quicksort {n} lst
  end

(*------------------------------------------------------------------*)

val example_strings =
  $list ("choose", "any", "element", "of", "the", "array",
         "to", "be", "the", "pivot",
         "divide", "all", "other", "elements", "except",
         "the", "pivot", "into", "two", "partitions",
         "all", "elements", "less", "than", "the", "pivot",
         "must", "be", "in", "the", "first", "partition",
         "all", "elements", "greater", "than", "the", "pivot",
         "must", "be", "in", "the", "second", "partition",
         "use", "recursion", "to", "sort", "both", "partitions",
         "join", "the", "first", "sorted", "partition", "the",
         "pivot", "and", "the", "second", "sorted", "partition")

implement
list_quicksort$comparison<string> (x, y) =
  let
    val i = strcmp (x, y)
  in
    if i < 0 then
      first_is_less_than_second
    else if i = 0 then
      first_is_equal_to_second
    else
      first_is_greater_than_second
  end

implement
main0 () =
  let
    val sorted_strings = list_quicksort<string> example_strings

    fun
    print_strings {n       : nat} .<n>.
                  (strings : list (string, n),
                   i       : int) : void =
      case+ strings of
      | NIL => if i <> 1 then println! () else ()
      | head :: tail =>
        begin
          print! head;
          if i = 8 then
            begin
              println! ();
              print_strings (tail, 1)
            end
          else
            begin
              print! " ";
              print_strings (tail, succ i)
            end
        end
  in
    println! (length example_strings);
    println! (length sorted_strings);
    print_strings (sorted_strings, 1)
  end

(*------------------------------------------------------------------*)
Output:
$ patscc -O3 -DATS_MEMALLOC_GCBDW quicksort_task_for_lists.dats -lgc && ./a.out
62
62
all all all and any array be be
be both choose divide element elements elements elements
except first first greater in in into join
less must must of other partition partition partition
partition partitions partitions pivot pivot pivot pivot pivot
recursion second second sort sorted sorted than than
the the the the the the the the
the the to to two use

A quicksort working on linear linked lists

This program was derived from the quicksort for non-linear linked lists.

(*------------------------------------------------------------------*)
(* Quicksort in ATS2, for linear lists.                             *)
(*------------------------------------------------------------------*)

#include "share/atspre_staload.hats"

#define NIL list_vt_nil ()
#define ::  list_vt_cons

(*------------------------------------------------------------------*)

(* A simple quicksort working on linear linked lists, with first
   element as pivot. This is meant as a demonstration, not as a
   superior sort algorithm.

   It is based on the "not-in-place" task pseudocode. *)

#define FIRST_IS_LESS_THAN_SECOND     1
#define FIRST_IS_EQUAL_TO_SECOND      2
#define FIRST_IS_GREATER_THAN_SECOND  3

typedef comparison_result =
  [i : int | (i == FIRST_IS_LESS_THAN_SECOND    ||
              i == FIRST_IS_EQUAL_TO_SECOND     ||
              i == FIRST_IS_GREATER_THAN_SECOND)]
  int i

extern fun {a : vt@ype}
list_vt_quicksort$comparison (x : !a, y : !a) :<> comparison_result

extern fun {a : vt@ype}
list_vt_quicksort {n   : int}
                  (lst : list_vt (a, n)) :<!wrt> list_vt (a, n)

(* -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  - *)

implement {a}
list_vt_quicksort {n} (lst) =
  let
    fun
    partition {n     : nat}
              .<n>.             (* Proof of termination. *)
              (lst   : list_vt (a, n),
               pivot : !a)
        :<> [n1, n2, n3 : int | n1 + n2 + n3 == n]
            @(list_vt (a, n1), list_vt (a, n2), list_vt (a, n3)) =
      (* This implementation is *not* tail recursive. I may get a
         scolding for using ATS to risk stack overflow! However, I
         need more practice writing non-tail routines. :) Also, a lot
         of programmers in other languages would do it this
         way--especially if the lists are evaluated lazily. *)
      case+ lst of
      | ~ NIL => @(NIL, NIL, NIL)
      | ~ head :: tail =>
        let
          val @(lt, eq, gt) = partition (tail, pivot)
          prval () = lemma_list_vt_param lt
          prval () = lemma_list_vt_param eq
          prval () = lemma_list_vt_param gt
        in
          case+ list_vt_quicksort$comparison<a> (head, pivot) of
          | FIRST_IS_LESS_THAN_SECOND    => @(head :: lt, eq, gt)
          | FIRST_IS_EQUAL_TO_SECOND     => @(lt, head :: eq, gt)
          | FIRST_IS_GREATER_THAN_SECOND => @(lt, eq, head :: gt)
        end

    fun
    quicksort {n   : nat}
              .<n>.             (* Proof of termination. *)
              (lst : list_vt (a, n))
        :<!wrt> list_vt (a, n) =
      case+ lst of
      | NIL => lst
      | _ :: NIL => lst
      | ~ head :: tail =>
        let
          (* We are careful here to run "partition" on "tail" rather
             than "lst", so the termination metric will be provably
             decreasing. (Really the compiler *forces* us to take such
             care, or else to add !ntm to the effects.) *)
          val pivot = head
          prval () = lemma_list_vt_param tail
          val @(lt, eq, gt) = partition {n - 1} (tail, pivot)
          prval () = lemma_list_vt_param lt
          prval () = lemma_list_vt_param eq
          prval () = lemma_list_vt_param gt
          val eq = pivot :: eq
          and lt = quicksort lt
          and gt = quicksort gt
        in
          list_vt_append (lt, list_vt_append (eq, gt))
        end

    prval () = lemma_list_vt_param lst
  in
    quicksort {n} lst
  end

(*------------------------------------------------------------------*)

implement
list_vt_quicksort$comparison<Strptr1> (x, y) =
  let
    val i = compare (x, y)
  in
    if i < 0 then
      FIRST_IS_LESS_THAN_SECOND
    else if i = 0 then
      FIRST_IS_EQUAL_TO_SECOND
    else
      FIRST_IS_GREATER_THAN_SECOND
  end

implement
list_vt_map$fopr<string><Strptr1> (s) = string0_copy s

implement
list_vt_freelin$clear<Strptr1> (x) = strptr_free x

implement
main0 () =
  let
    val example_strings =
      $list_vt
        ("choose", "any", "element", "of", "the", "array",
         "to", "be", "the", "pivot",
         "divide", "all", "other", "elements", "except",
         "the", "pivot", "into", "two", "partitions",
         "all", "elements", "less", "than", "the", "pivot",
         "must", "be", "in", "the", "first", "partition",
         "all", "elements", "greater", "than", "the", "pivot",
         "must", "be", "in", "the", "second", "partition",
         "use", "recursion", "to", "sort", "both", "partitions",
         "join", "the", "first", "sorted", "partition", "the",
         "pivot", "and", "the", "second", "sorted", "partition")

    val example_strptrs =
      list_vt_map<string><Strptr1> (example_strings)
    val sorted_strptrs = list_vt_quicksort<Strptr1> example_strptrs

    fun
    print_strptrs {n       : nat} .<n>.
                  (strptrs : !list_vt (Strptr1, n),
                   i       : int) : void =
      case+ strptrs of
      | NIL => if i <> 1 then println! () else ()
      | @ head :: tail =>
        begin
          print! head;
          if i = 8 then
            begin
              println! ();
              print_strptrs (tail, 1)
            end
          else
            begin
              print! " ";
              print_strptrs (tail, succ i)
            end;
          fold@ strptrs
        end
  in
    println! (length example_strings);
    println! (length sorted_strptrs);
    print_strptrs (sorted_strptrs, 1);
    list_vt_freelin<Strptr1> sorted_strptrs;
    list_vt_free<string> example_strings
  end

(*------------------------------------------------------------------*)
Output:
$ patscc -O3 -DATS_MEMALLOC_LIBC quicksort_task_for_list_vt.dats && ./a.out
62
62
all all all and any array be be
be both choose divide element elements elements elements
except first first greater in in into join
less must must of other partition partition partition
partition partitions partitions pivot pivot pivot pivot pivot
recursion second second sort sorted sorted than than
the the the the the the the the
the the to to two use

A quicksort working on arrays of non-linear elements

(*------------------------------------------------------------------*)
(* Quicksort in ATS2, for arrays of non-linear values.              *)
(*------------------------------------------------------------------*)

#include "share/atspre_staload.hats"

#define NIL list_nil ()
#define ::  list_cons

(*------------------------------------------------------------------*)

(* A simple quicksort working on arrays of non-linear values, using
   a programmer-selectible pivot.

   It is based on the "in-place" task pseudocode. *)

extern fun {a : t@ype}          (* A "less-than" predicate. *)
array_quicksort$lt (x : a, y : a) : bool

extern fun {a : t@ype}
array_quicksort$select_pivot {n     : int}
                             {i, j  : nat | i < j; j < n}
                             (arr   : &array (a, n) >> _,
                              first : size_t i,
                              last  : size_t j) : a

extern fun {a : t@ype}
array_quicksort {n   : int}
                (arr : &array (a, n) >> _,
                 n   : size_t n) : void

(* -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  - *)

fn {a : t@ype}
swap {n    : int}
     {i, j : nat | i < n; j < n}
     (arr  : &array(a, n) >> _,
      i    : size_t i,
      j    : size_t j) : void =
  {
    val x = arr[i] and y = arr[j]
    val () = (arr[i] := y) and () = (arr[j] := x)
  }

implement {a}
array_quicksort {n} (arr, n) =
  let
    sortdef index = {i : nat | i < n}
    typedef index (i : int) = [0 <= i; i < n] size_t i
    typedef index = [i : index] index i

    macdef lt = array_quicksort$lt<a>

    fun
    quicksort {i, j  : index}
              (arr   : &array(a, n) >> _,
               first : index i,
               last  : index j) : void =
      if first < last then
        {
          val pivot : a =
            array_quicksort$select_pivot<a> (arr, first, last)

          fun
          search_rightwards (arr  : &array (a, n),
                             left : index) : index =
            if arr[left] \lt pivot then
              let
                val () = assertloc (succ left <> n)
              in
                search_rightwards (arr, succ left)
              end
            else
              left

          fun
          search_leftwards (arr   : &array (a, n),
                            left  : index,
                            right : index) : index =
            if right < left then
              right
            else if pivot \lt arr[right] then
              let
                val () = assertloc (right <> i2sz 0)
              in
                search_leftwards (arr, left, pred right)
              end
            else
              right

          fun
          partition (arr    : &array (a, n) >> _,
                     left0  : index,
                     right0 : index) : @(index, index) =
            let
              val left = search_rightwards (arr, left0)
              val right = search_leftwards (arr, left, right0)
            in
              if left <= right then
                let
                  val () = assertloc (succ left <> n)
                  and () = assertloc (right <> i2sz 0)
                in
                  swap (arr, left, right);
                  partition (arr, succ left, pred right)
                end
              else
                @(left, right)
            end

          val @(left, right) = partition (arr, first, last)

          val () = quicksort (arr, first, right)
          and () = quicksort (arr, left, last)
        }
  in
    if i2sz 2 <= n then
      quicksort {0, n - 1} (arr, i2sz 0, pred n)
  end

(*------------------------------------------------------------------*)

val example_strings =
  $list ("choose", "any", "element", "of", "the", "array",
         "to", "be", "the", "pivot",
         "divide", "all", "other", "elements", "except",
         "the", "pivot", "into", "two", "partitions",
         "all", "elements", "less", "than", "the", "pivot",
         "must", "be", "in", "the", "first", "partition",
         "all", "elements", "greater", "than", "the", "pivot",
         "must", "be", "in", "the", "second", "partition",
         "use", "recursion", "to", "sort", "both", "partitions",
         "join", "the", "first", "sorted", "partition", "the",
         "pivot", "and", "the", "second", "sorted", "partition")

implement
array_quicksort$lt<string> (x, y) =
  strcmp (x, y) < 0

implement
array_quicksort$select_pivot<string> {n} (arr, first, last) =
  (* Median of three, with swapping around of elements during pivot
     selection. See https://archive.ph/oYENx *)
  let
    macdef lt = array_quicksort$lt<string>

    val middle = first + ((last - first) / i2sz 2)

    val xfirst = arr[first]
    and xmiddle = arr[middle]
    and xlast = arr[last]
  in
    if (xmiddle \lt xfirst) xor (xlast \lt xfirst) then
      begin
        swap (arr, first, middle);
        if xlast \lt xmiddle then
          swap (arr, first, last);
        xfirst
      end
    else if (xmiddle \lt xfirst) xor (xmiddle \lt xlast) then
      begin
        if xlast \lt xfirst then
          swap (arr, first, last);
        xmiddle
      end
    else
      begin
        swap (arr, middle, last);
        if xmiddle \lt xfirst then
          swap (arr, first, last);
        xlast
      end
  end

implement
main0 () =
  let
    prval () = lemma_list_param example_strings
    val n = length example_strings

    val @(pf, pfgc | p) = array_ptr_alloc<string> (i2sz n)
    macdef arr = !p

    val () = array_initize_list (arr, n, example_strings)
    val () = array_quicksort<string> (arr, i2sz n)
    val sorted_strings = list_vt2t (array2list (arr, i2sz n))

    val () = array_ptr_free (pf, pfgc | p)

    fun
    print_strings {n       : nat} .<n>.
                  (strings : list (string, n),
                   i       : int) : void =
      case+ strings of
      | NIL => if i <> 1 then println! () else ()
      | head :: tail =>
        begin
          print! head;
          if i = 8 then
            begin
              println! ();
              print_strings (tail, 1)
            end
          else
            begin
              print! " ";
              print_strings (tail, succ i)
            end
        end
  in
    println! (length example_strings);
    println! (length sorted_strings);
    print_strings (sorted_strings, 1)
  end

(*------------------------------------------------------------------*)
Output:
$ patscc -O3 -DATS_MEMALLOC_GCBDW quicksort_task_for_arrays.dats -lgc && ./a.out
62
62
all all all and any array be be
be both choose divide element elements elements elements
except first first greater in in into join
less must must of other partition partition partition
partition partitions partitions pivot pivot pivot pivot pivot
recursion second second sort sorted sorted than than
the the the the the the the the
the the to to two use

A quicksort working on arrays of linear elements

The quicksort for arrays of non-linear elements makes a copy of the pivot value, and compares this copy with array elements by value. Here, however, the array elements are linear values. They cannot be copied, unless a special "copy" procedure is provided. We do not want to require such a procedure. So we must do something else.

What we do is move the pivot to the last element of the array, by safely swapping it with the original last element. We partition the array to the left of the last element, comparing array elements with the pivot (that is, the last element) by reference.

(*------------------------------------------------------------------*)
(* Quicksort in ATS2, for arrays of (possibly) linear values.       *)
(*------------------------------------------------------------------*)

#include "share/atspre_staload.hats"

#define NIL list_vt_nil ()
#define ::  list_vt_cons

(*------------------------------------------------------------------*)

(* A simple quicksort working on arrays of non-linear values, using
   a programmer-selectible pivot.

   It is based on the "in-place" task pseudocode. *)

extern fun {a : vt@ype}          (* A "less-than" predicate. *)
array_quicksort$lt {px, py : addr}
                   (pfx    : !(a @ px),
                    pfy    : !(a @ py) |
                    px     : ptr px,
                    py     : ptr py) : bool

extern fun {a : vt@ype}
array_quicksort$select_pivot_index {n     : int}
                                   {i, j  : nat | i < j; j < n}
                                   (arr   : &array (a, n),
                                    first : size_t i,
                                    last  : size_t j)
    : [k : int | i <= k; k <= j] size_t k

extern fun {a : vt@ype}
array_quicksort {n   : int}
                (arr : &array (a, n) >> _,
                 n   : size_t n) : void

(* -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  - *)

prfn                   (* Subdivide an array view into three views. *)
array_v_subdivide3 {a : vt@ype} {p : addr} {n1, n2, n3 : nat}
                   (pf : @[a][n1 + n2 + n3] @ p)
    :<prf> @(@[a][n1] @ p,
           @[a][n2] @ (p + n1 * sizeof a),
           @[a][n3] @ (p + (n1 + n2) * sizeof a)) =
  let
    prval (pf1, pf23) =
      array_v_split {a} {p} {n1 + n2 + n3} {n1} pf
    prval (pf2, pf3) =
      array_v_split {a} {p + n1 * sizeof a} {n2 + n3} {n2} pf23
  in
    @(pf1, pf2, pf3)
  end

prfn            (* Join three contiguous array views into one view. *)
array_v_join3 {a : vt@ype} {p : addr} {n1, n2, n3 : nat}
              (pf1 : @[a][n1] @ p,
               pf2 : @[a][n2] @ (p + n1 * sizeof a),
               pf3 : @[a][n3] @ (p + (n1 + n2) * sizeof a))
    :<prf> @[a][n1 + n2 + n3] @ p =
  let
    prval pf23 =
      array_v_unsplit {a} {p + n1 * sizeof a} {n2, n3} (pf2, pf3)
    prval pf = array_v_unsplit {a} {p} {n1, n2 + n3} (pf1, pf23)
  in
    pf
  end

fn {a : vt@ype}            (* Safely swap two elements of an array. *)
swap_elems_1 {n     : int}
             {i, j  : nat | i <= j; j < n}
             {p     : addr}
             (pfarr : !array_v(a, p, n) >> _ |
              p     : ptr p,
              i     : size_t i,
              j     : size_t j) : void =

  let
    fn {a : vt@ype}
    swap {n     : int}
         {i, j  : nat | i < j; j < n}
         {p     : addr}
         (pfarr : !array_v(a, p, n) >> _ |
          p     : ptr p,
          i     : size_t i,
          j     : size_t j) : void =
      {

        (* Safely swapping linear elements requires that views of
           those elements be split off from the rest of the
           array. Why? Because those elements will temporarily be in
           an uninitialized state. (Actually they will be "?!", but
           the difference is unimportant here.)

           Remember, a linear value is consumed by using it.

           The view for the whole array can be reassembled only after
           new values have been stored, making the entire array once
           again initialized. *)

        prval @(pf1, pf2, pf3) =
          array_v_subdivide3 {a} {p} {i, j - i, n - j} pfarr
        prval @(pfi, pf2_) = array_v_uncons pf2
        prval @(pfj, pf3_) = array_v_uncons pf3

        val pi = ptr_add<a> (p, i)
        and pj = ptr_add<a> (p, j)

        val xi = ptr_get<a> (pfi | pi)
        and xj = ptr_get<a> (pfj | pj)

        val () = ptr_set<a> (pfi | pi, xj)
        and () = ptr_set<a> (pfj | pj, xi)

        prval pf2 = array_v_cons (pfi, pf2_)
        prval pf3 = array_v_cons (pfj, pf3_)
        prval () = pfarr := array_v_join3 (pf1, pf2, pf3)
      }
  in
    if i < j then
      swap {n} {i, j} {p} (pfarr | p, i, j)
    else
      ()   (* i = j must be handled specially, due to linear typing.*)
  end

fn {a : vt@ype}            (* Safely swap two elements of an array. *)
swap_elems_2 {n    : int}
             {i, j : nat | i <= j; j < n}
             (arr  : &array(a, n) >> _,
              i     : size_t i,
              j     : size_t j) : void =
  swap_elems_1 (view@ arr | addr@ arr, i, j)

overload swap_elems with swap_elems_1
overload swap_elems with swap_elems_2
overload swap with swap_elems

fn {a : vt@ype}         (* Safely compare two elements of an array. *)
lt_elems_1 {n     : int}
           {i, j  : nat | i < n; j < n}
           {p     : addr}
           (pfarr : !array_v(a, p, n) |
            p     : ptr p,
            i     : size_t i,
            j     : size_t j) : bool =
  let
    fn
    compare {n     : int}
            {i, j  : nat | i < j; j < n}
            {p     : addr}
            (pfarr : !array_v(a, p, n) |
             p     : ptr p,
             i     : size_t i,
             j     : size_t j,
             gt    : bool) : bool =
      let
        prval @(pf1, pf2, pf3) =
          array_v_subdivide3 {a} {p} {i, j - i, n - j} pfarr
        prval @(pfi, pf2_) = array_v_uncons pf2
        prval @(pfj, pf3_) = array_v_uncons pf3

        val pi = ptr_add<a> (p, i)
        and pj = ptr_add<a> (p, j)

        val retval =
          if gt then
            array_quicksort$lt<a> (pfj, pfi | pj, pi)
          else
            array_quicksort$lt<a> (pfi, pfj | pi, pj)

        prval pf2 = array_v_cons (pfi, pf2_)
        prval pf3 = array_v_cons (pfj, pf3_)
        prval () = pfarr := array_v_join3 (pf1, pf2, pf3)
      in
        retval
      end
  in
    if i < j then
      compare {n} {i, j} {p} (pfarr | p, i, j, false)
    else if j < i then
      compare {n} {j, i} {p} (pfarr | p, j, i, true)
    else
      false
  end

fn {a : vt@ype}         (* Safely compare two elements of an array. *)
lt_elems_2 {n    : int}
           {i, j : nat | i < n; j < n}
           (arr  : &array (a, n),
            i    : size_t i,
            j    : size_t j) : bool =
  lt_elems_1 (view@ arr | addr@ arr, i, j)

overload lt_elems with lt_elems_1
overload lt_elems with lt_elems_2

implement {a}
array_quicksort {n} (arr, n) =
  let
    sortdef index = {i : nat | i < n}
    typedef index (i : int) = [0 <= i; i < n] size_t i
    typedef index = [i : index] index i

    macdef lt = array_quicksort$lt<a>

    fun
    quicksort {i, j  : index}
              (arr   : &array(a, n) >> _,
               first : index i,
               last  : index j) : void =
      if first < last then
        {
          val pivot =
            array_quicksort$select_pivot_index<a> (arr, first, last)

          (* Swap the pivot with the last element. *)
          val () = swap (arr, pivot, last)
          val pivot = last

          fun
          search_rightwards (arr  : &array (a, n),
                             left : index) : index =
            if lt_elems<a> (arr, left, pivot) then
              let
                val () = assertloc (succ left <> n)
              in
                search_rightwards (arr, succ left)
              end
            else
              left

          fun
          search_leftwards (arr   : &array (a, n),
                            left  : index,
                            right : index) : index =
            if right < left then
              right
            else if lt_elems<a> (arr, pivot, right) then
              let
                val () = assertloc (right <> i2sz 0)
              in
                search_leftwards (arr, left, pred right)
              end
            else
              right

          fun
          partition (arr    : &array (a, n) >> _,
                     left0  : index,
                     right0 : index) : @(index, index) =
            let
              val left = search_rightwards (arr, left0)
              val right = search_leftwards (arr, left, right0)
            in
              if left <= right then
                let
                  val () = assertloc (succ left <> n)
                  and () = assertloc (right <> i2sz 0)
                in
                  swap (arr, left, right);
                  partition (arr, succ left, pred right)
                end
              else
                @(left, right)
            end

          val @(left, right) = partition (arr, first, pred last)

          val () = quicksort (arr, first, right)
          and () = quicksort (arr, left, last)
        }
  in
    if i2sz 2 <= n then
      quicksort {0, n - 1} (arr, i2sz 0, pred n)
  end

(*------------------------------------------------------------------*)

implement
array_quicksort$lt<Strptr1> (pfx, pfy | px, py) =
  compare (!px, !py) < 0

implement
array_quicksort$select_pivot_index<Strptr1> {n} (arr, first, last) =
  (* Median of three. *)
  let
    val middle = first + ((last - first) / i2sz 2)
  in
    if lt_elems<Strptr1> (arr, middle, first)
          xor lt_elems<Strptr1> (arr, last, first) then
      first
    else if lt_elems<Strptr1> (arr, middle, first)
              xor lt_elems<Strptr1> (arr, middle, last) then
      middle
    else
      last
  end

implement
list_vt_map$fopr<string><Strptr1> (s) = string0_copy s

implement
list_vt_freelin$clear<Strptr1> (x) = strptr_free x

implement
main0 () =
  let
    val example_strings =
      $list_vt
        ("choose", "any", "element", "of", "the", "array",
         "to", "be", "the", "pivot",
         "divide", "all", "other", "elements", "except",
         "the", "pivot", "into", "two", "partitions",
         "all", "elements", "less", "than", "the", "pivot",
         "must", "be", "in", "the", "first", "partition",
         "all", "elements", "greater", "than", "the", "pivot",
         "must", "be", "in", "the", "second", "partition",
         "use", "recursion", "to", "sort", "both", "partitions",
         "join", "the", "first", "sorted", "partition", "the",
         "pivot", "and", "the", "second", "sorted", "partition")

    val example_strptrs =
      list_vt_map<string><Strptr1> (example_strings)

    prval () = lemma_list_vt_param example_strptrs
    val n = length example_strptrs

    val @(pf, pfgc | p) = array_ptr_alloc<Strptr1> (i2sz n)
    macdef arr = !p

    val () = array_initize_list_vt<Strptr1> (arr, n, example_strptrs)
    val () = array_quicksort<Strptr1> (arr, i2sz n)
    val sorted_strptrs = array2list (arr, i2sz n)

    fun
    print_strptrs {n       : nat} .<n>.
                  (strptrs : !list_vt (Strptr1, n),
                   i       : int) : void =
      case+ strptrs of
      | NIL => if i <> 1 then println! () else ()
      | @ head :: tail =>
        begin
          print! head;
          if i = 8 then
            begin
              println! ();
              print_strptrs (tail, 1)
            end
          else
            begin
              print! " ";
              print_strptrs (tail, succ i)
            end;
          fold@ strptrs
        end
  in
    println! (length example_strings);
    println! (length sorted_strptrs);
    print_strptrs (sorted_strptrs, 1);
    list_vt_freelin<Strptr1> sorted_strptrs;
    array_ptr_free (pf, pfgc | p);
    list_vt_free<string> example_strings
  end

(*------------------------------------------------------------------*)
Output:
$ patscc -O3 -DATS_MEMALLOC_LIBC quicksort_task_for_arrays_2.dats
62
62
all all all and any array be be
be both choose divide element elements elements elements
except first first greater in in into join
less must must of other partition partition partition
partition partitions partitions pivot pivot pivot pivot pivot
recursion second second sort sorted sorted than than
the the the the the the the the
the the to to two use

A stable quicksort working on linear lists

See the code at the quickselect task.

Output:
$ patscc -O3 -DATS_MEMALLOC_LIBC quickselect_task_for_list_vt.dats && ./a.out quicksort
stable sort by first character:
duck, deer, dolphin, elephant, earwig, giraffe, pronghorn, wildebeest, woodlouse, whip-poor-will

AutoHotkey

Translated from the python example:

a := [4, 65, 2, -31, 0, 99, 83, 782, 7]
for k, v in QuickSort(a)
	Out .= "," v
MsgBox, % SubStr(Out, 2)
return

QuickSort(a)
{
	if (a.MaxIndex() <= 1)
		return a
	Less := [], Same := [], More := []
	Pivot := a[1]
	for k, v in a
	{
		if (v < Pivot)
			less.Insert(v)
		else if (v > Pivot)
			more.Insert(v)
		else
			same.Insert(v)
	}
	Less := QuickSort(Less)
	Out := QuickSort(More)
	if (Same.MaxIndex())
		Out.Insert(1, Same*) ; insert all values of same at index 1
	if (Less.MaxIndex())
		Out.Insert(1, Less*) ; insert all values of less at index 1
	return Out
}

Old implementation for AutoHotkey 1.0:

MsgBox % quicksort("8,4,9,2,1")

quicksort(list)
{
  StringSplit, list, list, `,
  If (list0 <= 1)
    Return list
  pivot := list1
  Loop, Parse, list, `,
  {
    If (A_LoopField < pivot)
      less = %less%,%A_LoopField%
    Else If (A_LoopField > pivot)
      more = %more%,%A_LoopField%
    Else
      pivotlist = %pivotlist%,%A_LoopField%
  }
  StringTrimLeft, less, less, 1
  StringTrimLeft, more, more, 1
  StringTrimLeft, pivotList, pivotList, 1
  less := quicksort(less)
  more := quicksort(more)
  Return less . pivotList . more
}

AWK

# the following qsort implementation extracted from:
#
#       ftp://ftp.armory.com/pub/lib/awk/qsort
#
# Copyleft GPLv2 John DuBois
#
# @(#) qsort 1.2.1 2005-10-21
# 1990 john h. dubois iii (john@armory.com)
#
# qsortArbIndByValue(): Sort an array according to the values of its elements.
#
# Input variables:
#
# Arr[] is an array of values with arbitrary (associative) indices.
#
# Output variables:
#
# k[] is returned with numeric indices 1..n.  The values assigned to these
# indices are the indices of Arr[], ordered so that if Arr[] is stepped
# through in the order Arr[k[1]] .. Arr[k[n]], it will be stepped through in
# order of the values of its elements.
#
# Return value: The number of elements in the arrays (n).
#
# NOTES:
#
# Full example for accessing results:
#
#       foolist["second"] = 2;
#       foolist["zero"] = 0;
#       foolist["third"] = 3;
#       foolist["first"] = 1;
#
#       outlist[1] = 0;
#       n = qsortArbIndByValue(foolist, outlist)
#
#       for (i = 1; i <= n; i++) {
#               printf("item at %s has value %d\n", outlist[i], foolist[outlist[i]]);
#       }
#      delete outlist; 
#
function qsortArbIndByValue(Arr, k,
                            ArrInd, ElNum)
{
        ElNum = 0;
        for (ArrInd in Arr) {
                k[++ElNum] = ArrInd;
        }
        qsortSegment(Arr, k, 1, ElNum);
        return ElNum;
}
#
# qsortSegment(): Sort a segment of an array.
#
# Input variables:
#
# Arr[] contains data with arbitrary indices.
#
# k[] has indices 1..nelem, with the indices of Arr[] as values.
#
# Output variables:
#
# k[] is modified by this function.  The elements of Arr[] that are pointed to
# by k[start..end] are sorted, with the values of elements of k[] swapped
# so that when this function returns, Arr[k[start..end]] will be in order.
#
# Return value: None.
#
function qsortSegment(Arr, k, start, end,
                      left, right, sepval, tmp, tmpe, tmps)
{
        if ((end - start) < 1) {        # 0 or 1 elements
                return;
        }
        # handle two-element case explicitly for a tiny speedup
        if ((end - start) == 1) {
                if (Arr[tmps = k[start]] > Arr[tmpe = k[end]]) {
                        k[start] = tmpe;
                        k[end] = tmps;
                }
                return;
        }
        # Make sure comparisons act on these as numbers
        left = start + 0;
        right = end + 0;
        sepval = Arr[k[int((left + right) / 2)]];
        # Make every element <= sepval be to the left of every element > sepval
        while (left < right) {
                while (Arr[k[left]] < sepval) {
                        left++;
                }
                while (Arr[k[right]] > sepval) {
                        right--;
                }
                if (left < right) {
                        tmp = k[left];
                        k[left++] = k[right];
                        k[right--] = tmp;
                }
        }
        if (left == right)
                if (Arr[k[left]] < sepval) {
                        left++;
                } else {
                        right--;
                }
        if (start < right) {
                qsortSegment(Arr, k, start, right);
        }
        if (left < end) {
                qsortSegment(Arr, k, left, end);
        }
}

BASIC

Works with: FreeBASIC
Works with: PowerBASIC for DOS
Works with: QB64
Works with: QBasic

This is specifically for INTEGERs, but can be modified for any data type by changing arr()'s type.

DECLARE SUB quicksort (arr() AS INTEGER, leftN AS INTEGER, rightN AS INTEGER)

DIM q(99) AS INTEGER
DIM n AS INTEGER

RANDOMIZE TIMER

FOR n = 0 TO 99
    q(n) = INT(RND * 9999)
NEXT

OPEN "output.txt" FOR OUTPUT AS 1
    FOR n = 0 TO 99
        PRINT #1, q(n),
    NEXT
    PRINT #1,
    quicksort q(), 0, 99
    FOR n = 0 TO 99
        PRINT #1, q(n),
    NEXT
CLOSE

SUB quicksort (arr() AS INTEGER, leftN AS INTEGER, rightN AS INTEGER)
    DIM pivot AS INTEGER, leftNIdx AS INTEGER, rightNIdx AS INTEGER
    leftNIdx = leftN
    rightNIdx = rightN
    IF (rightN - leftN) > 0 THEN
        pivot = (leftN + rightN) / 2
        WHILE (leftNIdx <= pivot) AND (rightNIdx >= pivot)
            WHILE (arr(leftNIdx) < arr(pivot)) AND (leftNIdx <= pivot)
                leftNIdx = leftNIdx + 1
            WEND
            WHILE (arr(rightNIdx) > arr(pivot)) AND (rightNIdx >= pivot)
                rightNIdx = rightNIdx - 1
            WEND
            SWAP arr(leftNIdx), arr(rightNIdx)
            leftNIdx = leftNIdx + 1
            rightNIdx = rightNIdx - 1
            IF (leftNIdx - 1) = pivot THEN
                rightNIdx = rightNIdx + 1
                pivot = rightNIdx
            ELSEIF (rightNIdx + 1) = pivot THEN
                leftNIdx = leftNIdx - 1
                pivot = leftNIdx
            END IF
        WEND
        quicksort arr(), leftN, pivot - 1
        quicksort arr(), pivot + 1, rightN
    END IF
END SUB

BBC BASIC

      DIM test(9)
      test() = 4, 65, 2, -31, 0, 99, 2, 83, 782, 1
      PROCquicksort(test(), 0, 10)
      FOR i% = 0 TO 9
        PRINT test(i%) ;
      NEXT
      PRINT
      END
      
      DEF PROCquicksort(a(), s%, n%)
      LOCAL l%, p, r%, t%
      IF n% < 2 THEN ENDPROC
      t% = s% + n% - 1
      l% = s%
      r% = t%
      p = a((l% + r%) DIV 2)
      REPEAT
        WHILE a(l%) < p l% += 1 : ENDWHILE
        WHILE a(r%) > p r% -= 1 : ENDWHILE
        IF l% <= r% THEN
          SWAP a(l%), a(r%)
          l% += 1
          r% -= 1
        ENDIF
      UNTIL l% > r%
      IF s% < r% PROCquicksort(a(), s%, r% - s% + 1)
      IF l% < t% PROCquicksort(a(), l%, t% - l% + 1 )
      ENDPROC
Output:
       -31         0         1         2         2         4        65        83        99       782

IS-BASIC

100 PROGRAM "QuickSrt.bas"
110 RANDOMIZE
120 NUMERIC A(5 TO 19)
130 CALL INIT(A)
140 CALL WRITE(A)
150 CALL QSORT(LBOUND(A),UBOUND(A))
160 CALL WRITE(A)
170 DEF INIT(REF A)
180   FOR I=LBOUND(A) TO UBOUND(A)
190     LET A(I)=RND(98)+1
200   NEXT
210 END DEF
220 DEF WRITE(REF A)
230   FOR I=LBOUND(A) TO UBOUND(A)
240     PRINT A(I);
250   NEXT
260   PRINT
270 END DEF
280 DEF QSORT(AH,FH)
290   NUMERIC E
300   LET E=AH:LET U=FH:LET K=A(E)
310   DO UNTIL E=U
320     DO UNTIL E=U OR A(U)<K
330       LET U=U-1
340     LOOP
350     IF E<U THEN
360       LET A(E)=A(U):LET E=E+1
370       DO UNTIL E=U OR A(E)>K
380         LET E=E+1
390       LOOP
400       IF E<U THEN LET A(U)=A(E):LET U=U-1
410     END IF
420   LOOP
430   LET A(E)=K
440   IF AH<E-1 THEN CALL QSORT(AH,E-1)
450   IF E+1<FH THEN CALL QSORT(E+1,FH)
460 END DEF

QB64

' Written by Sanmayce, 2021-Oct-29
' The indexes are signed, but the elements are unsigned.
_Define A-Z As _INTEGER64
Sub Quicksort_QB64 (QWORDS~&&())
    Left = LBound(QWORDS~&&)
    Right = UBound(QWORDS~&&)
    LeftMargin = Left
    ReDim Stack&&(Left To Right)
    StackPtr = 0
    StackPtr = StackPtr + 1
    Stack&&(StackPtr + LeftMargin) = Left
    StackPtr = StackPtr + 1
    Stack&&(StackPtr + LeftMargin) = Right
    Do 'Until StackPtr = 0
        Right = Stack&&(StackPtr + LeftMargin)
        StackPtr = StackPtr - 1
        Left = Stack&&(StackPtr + LeftMargin)
        StackPtr = StackPtr - 1
        Do 'Until Left >= Right
            Pivot~&& = QWORDS~&&((Left + Right) \ 2)
            Indx = Left
            Jndx = Right
            Do
                Do While (QWORDS~&&(Indx) < Pivot~&&)
                    Indx = Indx + 1
                Loop
                Do While (QWORDS~&&(Jndx) > Pivot~&&)
                    Jndx = Jndx - 1
                Loop
                If Indx <= Jndx Then
                    If Indx < Jndx Then Swap QWORDS~&&(Indx), QWORDS~&&(Jndx)
                    Indx = Indx + 1
                    Jndx = Jndx - 1
                End If
            Loop While Indx <= Jndx
            If Indx < Right Then
                StackPtr = StackPtr + 1
                Stack&&(StackPtr + LeftMargin) = Indx
                StackPtr = StackPtr + 1
                Stack&&(StackPtr + LeftMargin) = Right
            End If
            Right = Jndx
        Loop Until Left >= Right
    Loop Until StackPtr = 0
End Sub

BCPL

// This can be run using Cintcode BCPL freely available from www.cl.cam.ac.uk/users/mr10.

GET "libhdr.h"

LET quicksort(v, n) BE qsort(v+1, v+n)

AND qsort(l, r) BE
{ WHILE l+8<r DO
  { LET midpt = (l+r)/2
    // Select a good(ish) median value.
    LET val   = middle(!l, !midpt, !r)
    LET i = partition(val, l, r)
    // Only use recursion on the smaller partition.
    TEST i>midpt THEN { qsort(i, r);   r := i-1 }
                 ELSE { qsort(l, i-1); l := i   }
  }

  FOR p = l+1 TO r DO  // Now perform insertion sort.
   FOR q = p-1 TO l BY -1 TEST q!0<=q!1 THEN BREAK
                                        ELSE { LET t = q!0
                                               q!0 := q!1
                                               q!1 := t
                                             }
}

AND middle(a, b, c) = a<b -> b<c -> b,
                                    a<c -> c,
                                           a,
                             b<c -> a<c -> a,
                                           c,
                                    b

AND partition(median, p, q) = VALOF
{ LET t = ?
  WHILE !p < median DO p := p+1
  WHILE !q > median DO q := q-1
  IF p>=q RESULTIS p
  t  := !p
  !p := !q
  !q := t
  p, q := p+1, q-1
} REPEAT

LET start() = VALOF {
  LET v = VEC 1000
  FOR i = 1 TO 1000 DO v!i := randno(1_000_000)
  quicksort(v, 1000)
  FOR i = 1 TO 1000 DO
  { IF i MOD 10 = 0 DO newline()
    writef(" %i6", v!i)
  }
  newline()
}

Beads

beads 1 program Quicksort

calc main_init
	var arr = [1, 3, 5, 1, 7, 9, 8, 6, 4, 2]
	var arr2 = arr
	quicksort(arr, 1, tree_count(arr))
	var tempStr : str
	loop across:arr index:ix
		tempStr = tempStr & ' ' & to_str(arr[ix])
	log tempStr

calc quicksort(
	arr:array of num
	startIndex
	highIndex
	)
	if (startIndex < highIndex)
		var partitionIndex = partition(arr, startIndex, highIndex)
		quicksort(arr, startIndex, partitionIndex - 1)
		quicksort(arr, partitionIndex+1, highIndex)

calc partition(
	arr:array of num
	startIndex
	highIndex
	):num
	var pivot = arr[highIndex]
	var i = startIndex - 1
	var j = startIndex
	loop while:(j <= highIndex - 1)
		if arr[j] < pivot
			inc i
			swap arr[i] <=> arr[j]
		inc j
	swap arr[i+1] <=> arr[highIndex]
	return (i+1)
Output:
1 1 2 3 4 5 6 7 8 9

Bracmat

Instead of comparing elements explicitly, this solution puts the two elements-to-compare in a sum. After evaluating the sum its terms are sorted. Numbers are sorted numerically, strings alphabetically and compound expressions by comparing nodes and leafs in a left-to right order. Now there are three cases: either the terms stayed put, or they were swapped, or they were equal and were combined into one term with a factor 2 in front. To not let the evaluator add numbers together, each term is constructed as a dotted list.

( ( Q
  =   Less Greater Equal pivot element
    .     !arg:%(?pivot:?Equal) %?arg
        & :?Less:?Greater
        &   whl
          ' ( !arg:%?element ?arg
            &   (.!element)+(.!pivot)               { BAD: 1900+90 adds to 1990,  GOOD: (.1900)+(.90) is sorted to (.90)+(.1900) }
              : (   (.!element)+(.!pivot)
                  & !element !Less:?Less
                |   (.!pivot)+(.!element)
                  & !element !Greater:?Greater
                | ?&!element !Equal:?Equal
                )
            )
        & Q$!Less !Equal Q$!Greater
      | !arg
  )
& out$Q$(1900 optimized variants of 4001/2 Quicksort (quick,sort) are (quick,sober) features of 90 languages)
);
Output:
  90
  1900
  4001/2
  Quicksort
  are
  features
  languages
  of
  of
  optimized
  variants
  (quick,sober)
  (quick,sort)

C

#include <stdio.h>

void quicksort(int *A, int len);

int main (void) {
  int a[] = {4, 65, 2, -31, 0, 99, 2, 83, 782, 1};
  int n = sizeof a / sizeof a[0];

  int i;
  for (i = 0; i < n; i++) {
    printf("%d ", a[i]);
  }
  printf("\n");

  quicksort(a, n);

  for (i = 0; i < n; i++) {
    printf("%d ", a[i]);
  }
  printf("\n");

  return 0;
}

void quicksort(int *A, int len) {
  if (len < 2) return;

  int pivot = A[len / 2];

  int i, j;
  for (i = 0, j = len - 1; ; i++, j--) {
    while (A[i] < pivot) i++;
    while (A[j] > pivot) j--;

    if (i >= j) break;

    int temp = A[i];
    A[i]     = A[j];
    A[j]     = temp;
  }

  quicksort(A, i);
  quicksort(A + i, len - i);
}
Output:
4 65 2 -31 0 99 2 83 782 1
-31 0 1 2 2 4 65 83 99 782

Randomized sort with separated components.

#include <stdlib.h>     // REQ: rand()

void swap(int *a, int *b) {
  int c = *a;
  *a = *b;
  *b = c;
}

int partition(int A[], int p, int q) {
  swap(&A[p + (rand() % (q - p + 1))], &A[q]);   // PIVOT = A[q]

  int i = p - 1;
  for(int j = p; j <= q; j++) {
    if(A[j] <= A[q]) {
      swap(&A[++i], &A[j]);
    }
  }

  return i;
}

void quicksort(int A[], int p, int q) {
  if(p < q) {
    int pivotIndx = partition(A, p, q);

    quicksort(A, p, pivotIndx - 1);
    quicksort(A, pivotIndx + 1, q);
  }
}

C#

//
// The Tripartite conditional enables Bentley-McIlroy 3-way Partitioning.
// This performs additional compares to isolate islands of keys equal to
// the pivot value.  Use unless key-equivalent classes are of small size.
//
#define Tripartite

namespace RosettaCode {
  using System;
  using System.Diagnostics;

  public class QuickSort<T> where T : IComparable {
    #region Constants
    public const UInt32 INSERTION_LIMIT_DEFAULT = 12;
    private const Int32 SAMPLES_MAX = 19;
    #endregion

    #region Properties
    public UInt32 InsertionLimit { get; }
    private T[] Samples { get; }
    private Int32 Left { get; set; }
    private Int32 Right { get; set; }
    private Int32 LeftMedian { get; set; }
    private Int32 RightMedian { get; set; }
    #endregion

    #region Constructors
    public QuickSort(UInt32 insertionLimit = INSERTION_LIMIT_DEFAULT) {
      this.InsertionLimit = insertionLimit;
      this.Samples = new T[SAMPLES_MAX];
    }
    #endregion

    #region Sort Methods
    public void Sort(T[] entries) {
      Sort(entries, 0, entries.Length - 1);
    }

    public void Sort(T[] entries, Int32 first, Int32 last) {
      var length = last + 1 - first;
      while (length > 1) {
        if (length < InsertionLimit) {
          InsertionSort<T>.Sort(entries, first, last);
          return;
        }

        Left = first;
        Right = last;
        var median = pivot(entries);
        partition(median, entries);
        //[Note]Right < Left

        var leftLength = Right + 1 - first;
        var rightLength = last + 1 - Left;

        //
        // First recurse over shorter partition, then loop
        // on the longer partition to elide tail recursion.
        //
        if (leftLength < rightLength) {
          Sort(entries, first, Right);
          first = Left;
          length = rightLength;
        }
        else {
          Sort(entries, Left, last);
          last = Right;
          length = leftLength;
        }
      }
    }

    /// <summary>Return an odd sample size proportional to the log of a large interval size.</summary>
    private static Int32 sampleSize(Int32 length, Int32 max = SAMPLES_MAX) {
      var logLen = (Int32)Math.Log10(length);
      var samples = Math.Min(2 * logLen + 1, max);
      return Math.Min(samples, length);
    }

    /// <summary>Estimate the median value of entries[Left:Right]</summary>
    /// <remarks>A sample median is used as an estimate the true median.</remarks>
    private T pivot(T[] entries) {
      var length = Right + 1 - Left;
      var samples = sampleSize(length);
      // Sample Linearly:
      for (var sample = 0; sample < samples; sample++) {
        // Guard against Arithmetic Overflow:
        var index = (Int64)length * sample / samples + Left;
        Samples[sample] = entries[index];
      }

      InsertionSort<T>.Sort(Samples, 0, samples - 1);
      return Samples[samples / 2];
    }

    private void partition(T median, T[] entries) {
      var first = Left;
      var last = Right;
#if Tripartite
      LeftMedian = first;
      RightMedian = last;
#endif
      while (true) {
        //[Assert]There exists some index >= Left where entries[index] >= median
        //[Assert]There exists some index <= Right where entries[index] <= median
        // So, there is no need for Left or Right bound checks
        while (median.CompareTo(entries[Left]) > 0) Left++;
        while (median.CompareTo(entries[Right]) < 0) Right--;

        //[Assert]entries[Right] <= median <= entries[Left]
        if (Right <= Left) break;

        Swap(entries, Left, Right);
        swapOut(median, entries);
        Left++;
        Right--;
        //[Assert]entries[first:Left - 1] <= median <= entries[Right + 1:last]
      }

      if (Left == Right) {
        Left++;
        Right--;
      }
      //[Assert]Right < Left
      swapIn(entries, first, last);

      //[Assert]entries[first:Right] <= median <= entries[Left:last]
      //[Assert]entries[Right + 1:Left - 1] == median when non-empty
    }
    #endregion

    #region Swap Methods
    [Conditional("Tripartite")]
    private void swapOut(T median, T[] entries) {
      if (median.CompareTo(entries[Left]) == 0) Swap(entries, LeftMedian++, Left);
      if (median.CompareTo(entries[Right]) == 0) Swap(entries, Right, RightMedian--);
    }

    [Conditional("Tripartite")]
    private void swapIn(T[] entries, Int32 first, Int32 last) {
      // Restore Median entries
      while (first < LeftMedian) Swap(entries, first++, Right--);
      while (RightMedian < last) Swap(entries, Left++, last--);
    }

    /// <summary>Swap entries at the left and right indicies.</summary>
    public void Swap(T[] entries, Int32 left, Int32 right) {
      Swap(ref entries[left], ref entries[right]);
    }

    /// <summary>Swap two entities of type T.</summary>
    public static void Swap(ref T e1, ref T e2) {
      var e = e1;
      e1 = e2;
      e2 = e;
    }
    #endregion
  }

  #region Insertion Sort
  static class InsertionSort<T> where T : IComparable {
    public static void Sort(T[] entries, Int32 first, Int32 last) {
      for (var next = first + 1; next <= last; next++)
        insert(entries, first, next);
    }

    /// <summary>Bubble next entry up to its sorted location, assuming entries[first:next - 1] are already sorted.</summary>
    private static void insert(T[] entries, Int32 first, Int32 next) {
      var entry = entries[next];
      while (next > first && entries[next - 1].CompareTo(entry) > 0)
        entries[next] = entries[--next];
      entries[next] = entry;
    }
  }
  #endregion
}

Example:

  using Sort;
  using System;

  class Program {
    static void Main(String[] args) {
      var entries = new Int32[] { 1, 3, 5, 7, 9, 8, 6, 4, 2 };
      var sorter = new QuickSort<Int32>();
      sorter.Sort(entries);
      Console.WriteLine(String.Join(" ", entries));
    }
  }
Output:
1 2 3 4 5 6 7 8 9

A very inefficient way to do qsort in C# to prove C# code can be just as compact and readable as any dynamic code

using System;
using System.Collections.Generic;
using System.Linq;

namespace QSort
{
    class QSorter
    {
        private static IEnumerable<IComparable> empty = new List<IComparable>();

        public static IEnumerable<IComparable> QSort(IEnumerable<IComparable> iEnumerable)
        {
            if(iEnumerable.Any())
            {
                var pivot = iEnumerable.First();
                return QSort(iEnumerable.Where((anItem) => pivot.CompareTo(anItem) > 0)).
                    Concat(iEnumerable.Where((anItem) => pivot.CompareTo(anItem) == 0)).
                    Concat(QSort(iEnumerable.Where((anItem) => pivot.CompareTo(anItem) < 0)));
            }
            return empty;
        }
    }
}

CafeOBJ

There is no builtin list type in CafeOBJ, so a user written list module is included.

mod! SIMPLE-LIST(X :: TRIV){
[NeList < List ]
op [] : -> List
op [_] : Elt -> List 
op (_:_) : Elt List -> NeList  -- consr
op _++_ : List List -> List {assoc}  -- concatenate
var E : Elt
vars L L' : List
eq [ E ] = E : [] .
eq [] ++ L = L .
eq (E : L) ++ L' = E : (L ++ L') .
}

mod! QUICKSORT{
pr(SIMPLE-LIST(NAT))
op qsort_ : List -> List 
op smaller__ : List  Nat -> List
op larger__ : List Nat -> List

vars x y : Nat
vars xs ys : List

eq qsort []  = [] .
eq qsort (x : xs) = (qsort (smaller xs x)) ++ [ x ]  ++ (qsort (larger xs x)) .

eq smaller []  x = [] .
eq smaller (x : xs) y = if x <= y then  (x : (smaller xs y)) else (smaller xs y) fi .
eq larger []  x  = [] .
eq larger (x : xs) y = if x <= y then (larger xs  y) else (x : (larger xs y)) fi   .

}
open  QUICKSORT .
red qsort(5 : 4 : 3 : 2 : 1 : 0 : []) .
red qsort(5 : 5 : 4 : 3 : 5 : 2 : 1 : 1 : 0 : []) .
eof

C++

The following implements quicksort with a median-of-three pivot. As idiomatic in C++, the argument last is a one-past-end iterator. Note that this code takes advantage of std::partition, which is O(n). Also note that it needs a random-access iterator for efficient calculation of the median-of-three pivot (more exactly, for O(1) calculation of the iterator mid).

#include <iterator>
#include <algorithm> // for std::partition
#include <functional> // for std::less

// helper function for median of three
template<typename T>
 T median(T t1, T t2, T t3)
{
  if (t1 < t2)
  {
    if (t2 < t3)
      return t2;
    else if (t1 < t3)
      return t3;
    else
      return t1;
  }
  else
  {
    if (t1 < t3)
      return t1;
    else if (t2 < t3)
      return t3;
    else
      return t2;
  }
}

// helper object to get <= from <
template<typename Order> struct non_strict_op:
  public std::binary_function<typename Order::second_argument_type,
                              typename Order::first_argument_type,
                              bool>
{
  non_strict_op(Order o): order(o) {}
  bool operator()(typename Order::second_argument_type arg1,
                  typename Order::first_argument_type arg2) const
  {
    return !order(arg2, arg1);
  }
private:
  Order order;
};

template<typename Order> non_strict_op<Order> non_strict(Order o)
{
  return non_strict_op<Order>(o);
}

template<typename RandomAccessIterator,
         typename Order>
 void quicksort(RandomAccessIterator first, RandomAccessIterator last, Order order)
{
  if (first != last && first+1 != last)
  {
    typedef typename std::iterator_traits<RandomAccessIterator>::value_type value_type;
    RandomAccessIterator mid = first + (last - first)/2;
    value_type pivot = median(*first, *mid, *(last-1));
    RandomAccessIterator split1 = std::partition(first, last, std::bind2nd(order, pivot));
    RandomAccessIterator split2 = std::partition(split1, last, std::bind2nd(non_strict(order), pivot));
    quicksort(first, split1, order);
    quicksort(split2, last, order);
  }
}

template<typename RandomAccessIterator>
 void quicksort(RandomAccessIterator first, RandomAccessIterator last)
{
  quicksort(first, last, std::less<typename std::iterator_traits<RandomAccessIterator>::value_type>());
}

A simpler version of the above that just uses the first element as the pivot and only does one "partition".

#include <iterator>
#include <algorithm> // for std::partition
#include <functional> // for std::less

template<typename RandomAccessIterator,
         typename Order>
 void quicksort(RandomAccessIterator first, RandomAccessIterator last, Order order)
{
  if (last - first > 1)
  {
    RandomAccessIterator split = std::partition(first+1, last, std::bind2nd(order, *first));
    std::iter_swap(first, split-1);
    quicksort(first, split-1, order);
    quicksort(split, last, order);
  }
}

template<typename RandomAccessIterator>
 void quicksort(RandomAccessIterator first, RandomAccessIterator last)
{
  quicksort(first, last, std::less<typename std::iterator_traits<RandomAccessIterator>::value_type>());
}

Clojure

A very Haskell-like solution using list comprehensions and lazy evaluation.

(defn qsort [L]
  (if (empty? L) 
      '()
      (let [[pivot & L2] L]
           (lazy-cat (qsort (for [y L2 :when (<  y pivot)] y))
                     (list pivot)
                     (qsort (for [y L2 :when (>= y pivot)] y))))))

Another short version (using quasiquote):

(defn qsort [[pvt & rs]]
  (if pvt
    `(~@(qsort (filter #(<  % pvt) rs))
      ~pvt 
      ~@(qsort (filter #(>= % pvt) rs)))))

Another, more readable version (no macros):

(defn qsort [[pivot & xs]]
  (when pivot
    (let [smaller #(< % pivot)]
      (lazy-cat (qsort (filter smaller xs))
		[pivot]
		(qsort (remove smaller xs))))))

A 3-group quicksort (fast when many values are equal):

(defn qsort3 [[pvt :as coll]]
  (when pvt
    (let [{left -1 mid 0 right 1} (group-by #(compare % pvt) coll)]
      (lazy-cat (qsort3 left) mid (qsort3 right)))))

A lazier version of above (unlike group-by, filter returns (and reads) a lazy sequence)

(defn qsort3 [[pivot :as coll]]
  (when pivot
    (lazy-cat (qsort (filter #(< % pivot) coll))
              (filter #{pivot} coll)
              (qsort (filter #(> % pivot) coll)))))

COBOL

Works with: Visual COBOL
       IDENTIFICATION DIVISION.
       PROGRAM-ID. quicksort RECURSIVE.
       
       DATA DIVISION.
       LOCAL-STORAGE SECTION.
       01  temp                   PIC S9(8).
       
       01  pivot                  PIC S9(8).
       
       01  left-most-idx          PIC 9(5).
       01  right-most-idx         PIC 9(5).
       
       01  left-idx               PIC 9(5).
       01  right-idx              PIC 9(5).
       
       LINKAGE SECTION.
       78  Arr-Length             VALUE 50.
       
       01  arr-area.
           03  arr                PIC S9(8) OCCURS Arr-Length TIMES.
           
       01  left-val               PIC 9(5).
       01  right-val              PIC 9(5).  
       
       PROCEDURE DIVISION USING REFERENCE arr-area, OPTIONAL left-val,
               OPTIONAL right-val.
           IF left-val IS OMITTED OR right-val IS OMITTED
               MOVE 1 TO left-most-idx, left-idx
               MOVE Arr-Length TO right-most-idx, right-idx
           ELSE
               MOVE left-val TO left-most-idx, left-idx
               MOVE right-val TO right-most-idx, right-idx
           END-IF
           
           IF right-most-idx - left-most-idx < 1
               GOBACK
           END-IF
       
           COMPUTE pivot = arr ((left-most-idx + right-most-idx) / 2)
       
           PERFORM UNTIL left-idx > right-idx
               PERFORM VARYING left-idx FROM left-idx BY 1
                   UNTIL arr (left-idx) >= pivot
               END-PERFORM
               
               PERFORM VARYING right-idx FROM right-idx BY -1
                   UNTIL arr (right-idx) <= pivot
               END-PERFORM
               
               IF left-idx <= right-idx
                   MOVE arr (left-idx) TO temp
                   MOVE arr (right-idx) TO arr (left-idx)
                   MOVE temp TO arr (right-idx)
                   
                   ADD 1 TO left-idx
                   SUBTRACT 1 FROM right-idx
               END-IF
           END-PERFORM
       
           CALL "quicksort" USING REFERENCE arr-area,
               CONTENT left-most-idx, right-idx
           CALL "quicksort" USING REFERENCE arr-area, CONTENT left-idx,
               right-most-idx
               
           GOBACK
           .

CoffeeScript

quicksort = ([x, xs...]) ->
  return [] unless x?
  smallerOrEqual = (a for a in xs when a <= x)
  larger = (a for a in xs when a > x)
  (quicksort smallerOrEqual).concat(x).concat(quicksort larger)

Common Lisp

The functional programming way

(defun quicksort (list &aux (pivot (car list)) )
  (if (cdr list)
      (nconc (quicksort (remove-if-not #'(lambda (x) (< x pivot)) list))
             (remove-if-not #'(lambda (x) (= x pivot)) list)
             (quicksort (remove-if-not #'(lambda (x) (> x pivot)) list)))
      list))

With flet

(defun qs (list)
  (if (cdr list)
      (flet ((pivot (test)
               (remove (car list) list :test-not test)))
        (nconc (qs (pivot #'>)) (pivot #'=) (qs (pivot #'<))))
      list))

In-place non-functional

(defun quicksort (sequence)
  (labels ((swap (a b) (rotatef (elt sequence a) (elt sequence b)))
           (sub-sort (left right)
             (when (< left right)
               (let ((pivot (elt sequence right))
                     (index left))
                 (loop for i from left below right
                       when (<= (elt sequence i) pivot)
                         do (swap i (prog1 index (incf index))))
                 (swap right index)
                 (sub-sort left (1- index))
                 (sub-sort (1+ index) right)))))
    (sub-sort 0 (1- (length sequence)))
    sequence))

Functional with destructuring

(defun quicksort (list)
  (when list
    (destructuring-bind (x . xs) list
      (nconc (quicksort (remove-if (lambda (a) (> a x)) xs))
	     `(,x)
	     (quicksort (remove-if (lambda (a) (<= a x)) xs))))))

Cowgol

include "cowgol.coh";

# Comparator interface, on the model of C, i.e:
# foo < bar => -1, foo == bar => 0, foo > bar => 1
typedef CompRslt is int(-1, 1);
interface Comparator(foo: intptr, bar: intptr): (rslt: CompRslt);

# Quicksort an array of pointer-sized integers given a comparator function
# (This is the closest you can get to polymorphism in Cowgol).
# Because Cowgol does not support recursion, a pointer to free memory
# for a stack must also be given.
sub qsort(A: [intptr], len: intptr, comp: Comparator, stack: [intptr]) is 
    # The partition function can be taken almost verbatim from Wikipedia
    sub partition(lo: intptr, hi: intptr): (p: intptr) is
        # This is not quite as bad as it looks: /2 compiles into a single shift
        # and "@bytesof intptr" is always power of 2 so compiles into shift(s).
        var pivot := [A + (hi/2 + lo/2) * @bytesof intptr];
        var i := lo - 1;
        var j := hi + 1;
        loop
            loop    
                i := i + 1;
                if comp([A + i*@bytesof intptr], pivot) != -1 then
                    break;
                end if;
            end loop;
            loop
                j := j - 1;
                if comp([A + j*@bytesof intptr], pivot) != 1 then
                    break;
                end if;
            end loop;
            if i >= j then
                p := j;
                return;
            end if;
            var ii := i * @bytesof intptr;
            var jj := j * @bytesof intptr;
            var t := [A+ii];
            [A+ii] := [A+jj];
            [A+jj] := t;
        end loop;
    end sub;
    
    # Cowgol lacks recursion, so we'll have to solve it by implementing
    # the stack ourselves.
    var sp: intptr := 0; # stack index
    sub push(n: intptr) is
        sp := sp + 1;
        [stack] := n;
        stack := @next stack;
    end sub;
    sub pop(): (n: intptr) is
        sp := sp - 1;
        stack := @prev stack;
        n := [stack];
    end sub;
    
    # start by sorting [0..length-1]
    push(len-1); 
    push(0);
    while sp != 0 loop
        var lo := pop();
        var hi := pop();
        if lo < hi then
            var p := partition(lo, hi);
            push(hi);   # note the order - we need to push the high pair
            push(p+1);  # first for it to be done last
            push(p);
            push(lo);
        end if;
    end loop;
end sub;

# Test: sort a list of numbers
sub NumComp implements Comparator is
    # Compare the inputs as numbers
    if foo < bar then rslt := -1;
    elseif foo > bar then rslt := 1;
    else rslt := 0;
    end if;
end sub;

# Numbers
var numbers: intptr[] := {
    65,13,4,84,29,5,96,73,5,11,17,76,38,26,44,20,36,12,44,51,79,8,99,7,19,95,26
};

# Room for the stack
var stackbuf: intptr[256];

# Sort the numbers in place
qsort(&numbers as [intptr], @sizeof numbers, NumComp, &stackbuf as [intptr]);

# Print the numbers (hopefully in order)
var i: @indexof numbers := 0;
while i < @sizeof numbers loop
    print_i32(numbers[i] as uint32);
    print_char(' ');
    i := i + 1;
end loop;
print_nl();
Output:
4 5 5 7 8 11 12 13 17 19 20 26 26 29 36 38 44 44 51 65 73 76 79 84 95 96 99

Crystal

Translation of: Ruby
def quick_sort(a : Array(Int32)) : Array(Int32)
  return a if a.size <= 1
  p = a[0]
  lt, rt = a[1 .. -1].partition { |x| x < p }
  return quick_sort(lt) + [p] + quick_sort(rt)
end

a = [7, 6, 5, 9, 8, 4, 3, 1, 2, 0]
puts quick_sort(a) # => [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

Curry

Copied from Curry: Example Programs.

-- quicksort using higher-order functions:

qsort :: [Int] -> [Int] 
qsort []     = []
qsort (x:l)  = qsort (filter (<x) l) ++ x : qsort (filter (>=x) l)

goal = qsort [2,3,1,0]

D

A Functional version

import std.stdio : writefln, writeln;
import std.algorithm: filter;
import std.array;

T[] quickSort(T)(T[] xs) => 
  xs.length == 0 ? [] :  
    xs[1 .. $].filter!(x => x< xs[0]).array.quickSort ~  
    xs[0 .. 1] ~  
    xs[1 .. $].filter!(x => x>=xs[0]).array.quickSort; 

void main() =>
  [4, 65, 2, -31, 0, 99, 2, 83, 782, 1].quickSort.writeln;
Output:
[-31, 0, 1, 2, 2, 4, 65, 83, 99, 782]

A simple high-level version (same output):

import std.stdio, std.array;

T[] quickSort(T)(T[] items) pure nothrow {
    if (items.empty)
        return items;
    T[] less, notLess;
    foreach (x; items[1 .. $])
        (x < items[0] ? less : notLess) ~= x;
    return less.quickSort ~ items[0] ~ notLess.quickSort;
}

void main() {
    [4, 65, 2, -31, 0, 99, 2, 83, 782, 1].quickSort.writeln;
}

Often short functional sieves are not a true implementations of the Sieve of Eratosthenes: http://www.cs.hmc.edu/~oneill/papers/Sieve-JFP.pdf

Similarly, one could argue that a true QuickSort is in-place, as this more efficient version (same output):

import std.stdio, std.algorithm;

void quickSort(T)(T[] items) pure nothrow @safe @nogc {
    if (items.length >= 2) {
        auto parts = partition3(items, items[$ / 2]);
        parts[0].quickSort;
        parts[2].quickSort;
    }
}

void main() {
    auto items = [4, 65, 2, -31, 0, 99, 2, 83, 782, 1];
    items.quickSort;
    items.writeln;
}

Dart

quickSort(List a) {
  if (a.length <= 1) {
    return a;
  }
  
  var pivot = a[0];
  var less = [];
  var more = [];
  var pivotList = [];
  
  // Partition
  a.forEach((var i){    
    if (i.compareTo(pivot) < 0) {
      less.add(i);
    } else if (i.compareTo(pivot) > 0) {
      more.add(i);
    } else {
      pivotList.add(i);
    }
  });
  
  // Recursively sort sublists
  less = quickSort(less);
  more = quickSort(more);
  
  // Concatenate results
  less.addAll(pivotList);
  less.addAll(more);
  return less;
}

void main() {
  var arr=[1,5,2,7,3,9,4,6,8];
  print("Before sort");
  arr.forEach((var i)=>print("$i"));
  arr = quickSort(arr);
  print("After sort");
  arr.forEach((var i)=>print("$i"));
}

E

def quicksort := {

    def swap(container, ixA, ixB) {
        def temp := container[ixA]
        container[ixA] := container[ixB]
        container[ixB] := temp
    }

    def partition(array, var first :int, var last :int) {
        if (last <= first) { return }
  
        # Choose a pivot
        def pivot := array[def pivotIndex := (first + last) // 2]
  
        # Move pivot to end temporarily
        swap(array, pivotIndex, last)
  
        var swapWith := first
  
        # Scan array except for pivot, and...
        for i in first..!last {
            if (array[i] <= pivot) {   # items ≤ the pivot
                swap(array, i, swapWith) # are moved to consecutive positions on the left
                swapWith += 1
            }
        }
  
        # Swap pivot into between-partition position.
        # Because of the swapping we know that everything before swapWith is less
        # than or equal to the pivot, and the item at swapWith (since it was not
        # swapped) is greater than the pivot, so inserting the pivot at swapWith
        # will preserve the partition.
        swap(array, swapWith, last)
        return swapWith
    }

    def quicksortR(array, first :int, last :int) {
        if (last <= first) { return }
        def pivot := partition(array, first, last)
        quicksortR(array, first, pivot - 1)
        quicksortR(array, pivot + 1, last)
    }

    def quicksort(array) { # returned from block
        quicksortR(array, 0, array.size() - 1)
    }
}

EasyLang

data[] = [ 29 4 72 44 55 26 27 77 92 5 ]
# 
func qsort left right . .
  while left < right
    swap data[(left + right) / 2] data[left]
    mid = left
    for i = left + 1 to right
      if data[i] < data[left]
        mid += 1
        swap data[i] data[mid]
      .
    .
    swap data[left] data[mid]
    call qsort left mid - 1
    left = mid + 1
  .
.
# 
call qsort 0 len data[] - 1
print data[]

EchoLisp

(lib 'list) ;; list-partition

(define compare 0) ;; counter

(define (quicksort L compare-predicate: proc aux:  (part null))
(if  (<= (length L) 1) L
     (begin
     ;; counting the number of comparisons
     (set! compare (+ compare (length (rest L))))
      ;; pivot = first element of list
     (set! part (list-partition (rest L) proc (first L)))
     (append (quicksort (first part) proc )
            (list (first L)) 
            (quicksort (second part) proc)))))
Output:
(shuffle (iota 15))
     (10 0 14 11 13 9 2 5 4 8 1 7 12 3 6)
(quicksort (shuffle (iota 15)) <)
     (0 1 2 3 4 5 6 7 8 9 10 11 12 13 14)

;; random list of numbers in [0 .. n[
;; count number of comparisons
(define (qtest (n 10000))
	(set! compare 0)
	(quicksort (shuffle (iota n)) >)
	(writeln 'n n 'compare# compare ))
	
(qtest 1000)
  n     1000       compare#     12764    
(qtest 10000)
  n     10000      compare#     277868    
(qtest 100000)
  n     100000     compare#     6198601

Eero

Translated from Objective-C example on this page.

#import <Foundation/Foundation.h>

void quicksortInPlace(MutableArray array, const long first, const long last)
  if first >= last
    return
  Value pivot = array[(first + last) / 2]
  left := first
  right := last
  while left <= right
    while array[left] < pivot
      left++
    while array[right] > pivot
      right--
    if left <= right
      array.exchangeObjectAtIndex: left++, withObjectAtIndex: right--

  quicksortInPlace(array, first, right)
  quicksortInPlace(array, left, last)

Array quicksort(Array unsorted)
  a := []
  a.addObjectsFromArray: unsorted
  quicksortInPlace(a, 0, a.count - 1)
  return a


int main(int argc, const char * argv[])
  autoreleasepool
    a := [1, 3, 5, 7, 9, 8, 6, 4, 2]
    Log( 'Unsorted: %@', a)
    Log( 'Sorted: %@', quicksort(a) )
    b := ['Emil', 'Peg', 'Helen', 'Juergen', 'David', 'Rick', 'Barb', 'Mike', 'Tom']
    Log( 'Unsorted: %@', b)
    Log( 'Sorted: %@', quicksort(b) )

  return 0

Alternative implementation (not necessarily as efficient, but very readable)

#import <Foundation/Foundation.h>

implementation Array (Quicksort)

  plus: Array array, return Array = 
    self.arrayByAddingObjectsFromArray: array

  filter: BOOL (^)(id) predicate, return Array
    array := []
    for id item in self
      if predicate(item)
        array.addObject: item
    return array.copy

  quicksort, return Array = self
    if self.count > 1      
      id x = self[self.count / 2]
      lesser := self.filter: (id y | return y < x)
      greater := self.filter: (id y | return y > x)
      return lesser.quicksort + [x] + greater.quicksort

end

int main()
  autoreleasepool
    a := [1, 3, 5, 7, 9, 8, 6, 4, 2]
    Log( 'Unsorted: %@', a)
    Log( 'Sorted: %@', a.quicksort )
    b := ['Emil', 'Peg', 'Helen', 'Juergen', 'David', 'Rick', 'Barb', 'Mike', 'Tom']
    Log( 'Unsorted: %@', b)
    Log( 'Sorted: %@', b.quicksort )

  return 0
Output:
2013-09-04 16:54:31.780 a.out[2201:507] Unsorted: (
    1,
    3,
    5,
    7,
    9,
    8,
    6,
    4,
    2
)
2013-09-04 16:54:31.781 a.out[2201:507] Sorted: (
    1,
    2,
    3,
    4,
    5,
    6,
    7,
    8,
    9
)
2013-09-04 16:54:31.781 a.out[2201:507] Unsorted: (
    Emil,
    Peg,
    Helen,
    Juergen,
    David,
    Rick,
    Barb,
    Mike,
    Tom
)
2013-09-04 16:54:31.782 a.out[2201:507] Sorted: (
    Barb,
    David,
    Emil,
    Helen,
    Juergen,
    Mike,
    Peg,
    Rick,
    Tom
)

Eiffel

The
QUICKSORT
class:
class
	QUICKSORT [G -> COMPARABLE]

create
	make

feature {NONE} --Implementation

	is_sorted (list: ARRAY [G]): BOOLEAN
		require
			not_void: list /= Void
		local
			i: INTEGER
		do
			Result := True
			from
				i := list.lower + 1
			invariant
				i >= list.lower + 1 and i <= list.upper + 1
			until
				i > list.upper
			loop
				Result := Result and list [i - 1] <= list [i]
				i := i + 1
			variant
				list.upper + 1 - i
			end
		end

	concatenate_array (a: ARRAY [G] b: ARRAY [G]): ARRAY [G]
		require
			not_void: a /= Void and b /= Void
		do
			create Result.make_from_array (a)
			across
				b as t
			loop
				Result.force (t.item, Result.upper + 1)
			end
		ensure
			same_size: a.count + b.count = Result.count
		end

	quicksort_array (list: ARRAY [G]): ARRAY [G]
		require
			not_void: list /= Void
		local
			less_a: ARRAY [G]
			equal_a: ARRAY [G]
			more_a: ARRAY [G]
			pivot: G
		do
			create less_a.make_empty
			create more_a.make_empty
			create equal_a.make_empty
			create Result.make_empty
			if list.count <= 1 then
				Result := list
			else
				pivot := list [list.lower]
				across
					list as li
				invariant
					less_a.count + equal_a.count + more_a.count <= list.count
				loop
					if li.item < pivot then
						less_a.force (li.item, less_a.upper + 1)
					elseif li.item = pivot then
						equal_a.force (li.item, equal_a.upper + 1)
					elseif li.item > pivot then
						more_a.force (li.item, more_a.upper + 1)
					end
				end
				Result := concatenate_array (Result, quicksort_array (less_a))
				Result := concatenate_array (Result, equal_a)
				Result := concatenate_array (Result, quicksort_array (more_a))
			end
		ensure
			same_size: list.count = Result.count
			sorted: is_sorted (Result)
		end

feature -- Initialization

	make
		do
		end

	quicksort (a: ARRAY [G]): ARRAY [G]
		do
			Result := quicksort_array (a)
		end

end

A test application:

class
	APPLICATION

create
	make

feature {NONE} -- Initialization

	make
			-- Run application.
		local
			test: ARRAY [INTEGER]
			sorted: ARRAY [INTEGER]
			sorter: QUICKSORT [INTEGER]
		do
			create sorter.make
			test := <<1, 3, 2, 4, 5, 5, 7, -1>>
			sorted := sorter.quicksort (test)
			across
				sorted as s
			loop
				print (s.item)
				print (" ")
			end
			print ("%N")
		end

end

Elena

ELENA 5.0 :

import extensions;
import system'routines;
import system'collections;
 
extension op
{
    quickSort()
    {
        if (self.isEmpty()) { ^ self };
 
        var pivot := self[0];
 
        auto less := new ArrayList();
        auto pivotList := new ArrayList();
        auto more := new ArrayList();
 
        self.forEach:(item)
        {
            if (item < pivot)
            {
                less.append(item)
            }
            else if (item > pivot) 
            {
                more.append(item)
            }
            else
            {
                pivotList.append(item)
            }
        };
 
        less := less.quickSort();
        more := more.quickSort();
 
        less.appendRange(pivotList);
        less.appendRange(more);
 
        ^ less
    }
}
 
public program()
{
    var list := new int[]{3, 14, 1, 5, 9, 2, 6, 3};
 
    console.printLine("before:", list.asEnumerable());
    console.printLine("after :", list.quickSort().asEnumerable());
}
Output:
before:3,14,1,5,9,2,6,3
after :1,2,3,3,5,6,9,14

Elixir

defmodule Sort do
  def qsort([]), do: []
  def qsort([h | t]) do
    {lesser, greater} = Enum.split_with(t, &(&1 < h))
    qsort(lesser) ++ [h] ++ qsort(greater)
  end
end

Erlang

like haskell. Used by Measure_relative_performance_of_sorting_algorithms_implementations. If changed keep the interface or change Measure_relative_performance_of_sorting_algorithms_implementations

-module( quicksort ).

-export( [qsort/1] ).

qsort([]) -> [];
qsort([X|Xs]) ->
   qsort([ Y || Y <- Xs, Y < X]) ++ [X] ++ qsort([ Y || Y <- Xs, Y >= X]).

multi-process implementation (number processes = number of processor cores):

quick_sort(L) -> qs(L, trunc(math:log2(erlang:system_info(schedulers)))).

qs([],_) -> [];
qs([H|T], N) when N > 0  -> 
    {Parent, Ref} = {self(), make_ref()},
    spawn(fun()-> Parent ! {l1, Ref, qs([E||E<-T, E<H], N-1)} end), 
    spawn(fun()-> Parent ! {l2, Ref, qs([E||E<-T, H =< E], N-1)} end), 
    {L1, L2} = receive_results(Ref, undefined, undefined), 
    L1 ++ [H] ++ L2;
qs([H|T],_) ->
    qs([E||E<-T, E<H],0) ++ [H] ++ qs([E||E<-T, H =< E],0).

receive_results(Ref, L1, L2) ->
    receive
        {l1, Ref, L1R} when L2 == undefined -> receive_results(Ref, L1R, L2);
        {l2, Ref, L2R} when L1 == undefined -> receive_results(Ref, L1, L2R);
        {l1, Ref, L1R} -> {L1R, L2};
        {l2, Ref, L2R} -> {L1, L2R}
    after 5000 -> receive_results(Ref, L1, L2)
    end.

Emacs Lisp

Unoptimized

Library: seq.el
(require 'seq)

(defun quicksort (xs)
  (if (null xs)
      ()
    (let* ((head (car xs))
           (tail (cdr xs))
           (lower-part (quicksort (seq-filter (lambda (x) (<= x head)) tail)))
           (higher-part (quicksort (seq-filter (lambda (x) (> x head)) tail))))
      (append lower-part (list head) higher-part))))

ERRE

PROGRAM QUICKSORT_DEMO

DIM ARRAY[21]

!$DYNAMIC
DIM QSTACK[0]

!$INCLUDE="PC.LIB"

PROCEDURE QSORT(ARRAY[],START,NUM)
  FIRST=START               ! initialize work variables
  LAST=START+NUM-1
  LOOP
    REPEAT
      TEMP=ARRAY[(LAST+FIRST) DIV 2]  ! seek midpoint
      I=FIRST
      J=LAST
      REPEAT     ! reverse both < and > below to sort descending
      WHILE ARRAY[I]<TEMP DO
        I=I+1
        END WHILE
        WHILE ARRAY[J]>TEMP DO
          J=J-1
        END WHILE
        EXIT IF I>J
        IF I<J THEN SWAP(ARRAY[I],ARRAY[J]) END IF
        I=I+1
        J=J-1
      UNTIL NOT(I<=J)
      IF I<LAST THEN             ! Done
         QSTACK[SP]=I            ! Push I
         QSTACK[SP+1]=LAST       ! Push Last
         SP=SP+2
      END IF
      LAST=J
    UNTIL NOT(FIRST<LAST)

    EXIT IF SP=0
    SP=SP-2
    FIRST=QSTACK[SP]            ! Pop First
    LAST=QSTACK[SP+1]           ! Pop Last
  END LOOP
END PROCEDURE

BEGIN
   RANDOMIZE(TIMER)              ! generate a new series each run

                                 ! create an array
   FOR X=1 TO 21 DO              ! fill with random numbers
       ARRAY[X]=RND(1)*500       ! between 0 and 500
   END FOR
   PRIMO=6                       ! sort starting here
   NUM=10                        ! sort this many elements
   CLS
   PRINT("Before Sorting:";TAB(31);"After sorting:")
   PRINT("===============";TAB(31);"==============")
   FOR X=1 TO 21 DO              ! show them before sorting
      IF X>=PRIMO AND X<=PRIMO+NUM-1 THEN
         PRINT("==>";)
      END IF
      PRINT(TAB(5);)
      WRITE("###.##";ARRAY[X])
   END FOR

! create a stack
!$DIM QSTACK[INT(NUM/5)+10]
   QSORT(ARRAY[],PRIMO,NUM)
!$ERASE QSTACK

   LOCATE(2,1)
   FOR X=1 TO 21 DO                ! print them after sorting
      LOCATE(2+X,30)
      IF X>=PRIMO AND X<=PRIMO+NUM-1 THEN
         PRINT("==>";)             ! point to sorted items
      END IF
      LOCATE(2+X,35)
      WRITE("###.##";ARRAY[X])
   END FOR
END PROGRAM

F#

let rec qsort = function
    hd :: tl ->
        let less, greater = List.partition ((>=) hd) tl
        List.concat [qsort less; [hd]; qsort greater]
    | _ -> []

Factor

: qsort ( seq -- seq )
    dup empty? [ 
      unclip [ [ < ] curry partition [ qsort ] bi@ ] keep
      prefix append
    ] unless ;

Fexl

# (sort xs) is the ordered list of all elements in list xs.
# This version preserves duplicates.
\sort== 
    (\xs
    xs [] \x\xs
    append (sort; filter (gt x) xs);   # all the items less than x
    cons x; append (filter (eq x) xs); # all the items equal to x
    sort; filter (lt x) xs             # all the items greater than x
    )

# (unique xs) is the ordered list of unique elements in list xs.
\unique==
    (\xs
    xs [] \x\xs
    append (unique; filter (gt x) xs); # all the items less than x
    cons x;                            # x itself
    unique; filter (lt x) xs           # all the items greater than x
    )

Forth

: mid ( l r -- mid ) over - 2/ -cell and + ;

: exch ( addr1 addr2 -- ) dup @ >r over @ swap ! r> swap ! ;

: partition ( l r -- l r r2 l2 )
  2dup mid @ >r ( r: pivot )
  2dup begin
    swap begin dup @  r@ < while cell+ repeat
    swap begin r@ over @ < while cell- repeat
    2dup <= if 2dup exch >r cell+ r> cell- then
  2dup > until  r> drop ;

: qsort ( l r -- )
  partition  swap rot
  \ 2over 2over - + < if 2swap then
  2dup < if recurse else 2drop then
  2dup < if recurse else 2drop then ;

: sort ( array len -- )
  dup 2 < if 2drop exit then
  1- cells over + qsort ;

Fortran

Works with: Fortran version 90 and later
MODULE qsort_mod

  IMPLICIT NONE

  TYPE group
     INTEGER :: order    ! original order of unsorted data
     REAL    :: VALUE    ! values to be sorted by
  END TYPE group

CONTAINS

  RECURSIVE SUBROUTINE QSort(a,na)

    ! DUMMY ARGUMENTS
    INTEGER, INTENT(in) :: nA
    TYPE (group), DIMENSION(nA), INTENT(in out) :: A

    ! LOCAL VARIABLES
    INTEGER :: left, right
    REAL :: random
    REAL :: pivot
    TYPE (group) :: temp
    INTEGER :: marker

    IF (nA > 1) THEN

       CALL random_NUMBER(random)
       pivot = A(INT(random*REAL(nA-1))+1)%VALUE   ! Choice a random pivot (not best performance, but avoids worst-case)
       left = 1
       right = nA
       ! Partition loop
       DO
          IF (left >= right) EXIT
          DO
             IF (A(right)%VALUE <= pivot) EXIT
             right = right - 1
          END DO
          DO
             IF (A(left)%VALUE >= pivot) EXIT
             left = left + 1
          END DO
          IF (left < right) THEN
             temp = A(left)
             A(left) = A(right)
             A(right) = temp
          END IF
       END DO

       IF (left == right) THEN
          marker = left + 1
       ELSE
          marker = left
       END IF

       CALL QSort(A(:marker-1),marker-1)
       CALL QSort(A(marker:),nA-marker+1)

    END IF

  END SUBROUTINE QSort

END MODULE qsort_mod
     
! Test Qsort Module
PROGRAM qsort_test
  USE qsort_mod
  IMPLICIT NONE

  INTEGER, PARAMETER :: nl = 10, nc = 5, l = nc*nl, ns=33
  TYPE (group), DIMENSION(l) :: A
  INTEGER, DIMENSION(ns) :: seed
  INTEGER :: i
  REAL :: random
  CHARACTER(LEN=80) :: fmt1, fmt2
  ! Using the Fibonacci sequence to initialize seed:
  seed(1) = 1 ; seed(2) = 1
  DO i = 3,ns
     seed(i) = seed(i-1)+seed(i-2)
  END DO
  ! Formats of the outputs
  WRITE(fmt1,'(A,I2,A)') '(', nc, '(I5,2X,F6.2))'
  WRITE(fmt2,'(A,I2,A)') '(3x', nc, '("Ord.  Num.",3x))' 
  PRINT *, "Unsorted Values:"
  PRINT fmt2,
  CALL random_SEED(put = seed)
  DO i = 1, l
     CALL random_NUMBER(random)
     A(i)%VALUE = NINT(1000*random)/10.0
     A(i)%order = i
     IF (MOD(i,nc) == 0) WRITE (*,fmt1) A(i-nc+1:i)
  END DO
  PRINT *
  CALL QSort(A,l)
  PRINT *, "Sorted Values:"
  PRINT fmt2,
  DO i = nc, l, nc
     IF (MOD(i,nc) == 0) WRITE (*,fmt1) A(i-nc+1:i)
  END DO
  STOP
END PROGRAM qsort_test
Output:
Compiled with GNU Fortran 9.3.0 
 Unsorted Values:
   Ord.  Num.   Ord.  Num.   Ord.  Num.   Ord.  Num.   Ord.  Num.
    1   47.10    2   11.70    3   35.80    4   35.20    5   55.30
    6   74.60    7   28.40    8   30.10    9   70.60   10   66.90
   11   15.90   12   71.70   13   49.80   14    2.60   15   12.80
   16   93.00   17   45.20   18   21.50   19   20.70   20   39.50
   21    9.20   22   21.60   23   18.60   24   22.80   25   98.50
   26   97.50   27   43.90   28    8.30   29   84.10   30   88.80
   31   10.30   32   30.50   33   79.30   34   24.40   35   45.00
   36   48.30   37   69.80   38   86.00   39   68.40   40   22.90
   41    7.50   42   18.50   43   80.40   44   29.60   45   43.60
   46   11.20   47   36.20   48   23.20   49   45.30   50   12.30

 Sorted Values:
   Ord.  Num.   Ord.  Num.   Ord.  Num.   Ord.  Num.   Ord.  Num.
   14    2.60   41    7.50   28    8.30   21    9.20   31   10.30
   46   11.20    2   11.70   50   12.30   15   12.80   11   15.90
   42   18.50   23   18.60   19   20.70   18   21.50   22   21.60
   24   22.80   40   22.90   48   23.20   34   24.40    7   28.40
   44   29.60    8   30.10   32   30.50    4   35.20    3   35.80
   47   36.20   20   39.50   45   43.60   27   43.90   35   45.00
   17   45.20   49   45.30    1   47.10   36   48.30   13   49.80
    5   55.30   10   66.90   39   68.40   37   69.80    9   70.60
   12   71.70    6   74.60   33   79.30   43   80.40   29   84.10
   38   86.00   30   88.80   16   93.00   26   97.50   25   98.50

A discussion about Quicksort pivot options, free source code for an optimized quicksort using insertion sort as a finisher, and an OpenMP multi-threaded quicksort is found at balfortran.org

FreeBASIC

' version 23-10-2016
' compile with: fbc -s console

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

Sub quicksort(qs() As Long, l As Long, r As Long)

    Dim As ULong size = r - l +1
    If size < 2 Then Exit Sub

    Dim As Long i = l, j = r
    Dim As Long pivot = qs(l + size \ 2)

    Do
        While qs(i) < pivot
            i += 1
        Wend
        While pivot < qs(j)
            j -= 1
        Wend
        If i <= j Then
            Swap qs(i), qs(j)
            i += 1
            j -= 1
        End If
    Loop Until i > j

    If l < j Then quicksort(qs(), l, j)
    If i < r Then quicksort(qs(), i, r)

End Sub

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

Dim As Long i, array(-7 To 7)
Dim As Long a = LBound(array), b = UBound(array)

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

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

quicksort(array(), LBound(array), UBound(array))

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

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

FunL

def
  qsort( [] )    =  []
  qsort( p:xs )  =  qsort( xs.filter((< p)) ) + [p] + qsort( xs.filter((>= p)) )

Here is a more efficient version using the partition function.

def
  qsort( [] )    =  []
  qsort( x:xs )  =
    val (ys, zs) = xs.partition( (< x) )
    qsort( ys ) + (x : qsort( zs ))

println( qsort([4, 2, 1, 3, 0, 2]) )
println( qsort(["Juan", "Daniel", "Miguel", "William", "Liam", "Ethan", "Jacob"]) )
Output:
[0, 1, 2, 2, 3, 4]
[Daniel, Ethan, Jacob, Juan, Liam, Miguel, William]


FutureBasic

include "NSLog.incl"

local fn Quicksort( qs as CFMutableArrayRef, l as NSInteger, r as NSInteger )
  UInt64 size = r - l + 1
  
  if size < 2 then exit fn
  
  NSinteger i = l, j = r
  NSinteger pivot = fn NumberIntegerValue( qs[l+size / 2] )
  
  do
    while fn NumberIntegerValue( qs[i] ) < pivot
      i++
    wend
    while pivot < fn NumberIntegerValue( qs[j] )
      j--
    wend
    if ( i <= j )
      MutableArrayExchangeObjects( qs, i, j )
      i++
      j--
    end if
  until i > j
  
  if l < j then fn Quicksort( qs, l, j )
  if i < r then fn Quicksort( qs, i, r )
end fn

CFMutableArrayRef qs
CFArrayRef        unsorted
NSUInteger        i, amount

qs = fn MutableArrayWithCapacity(0)

for i = 0 to 25
  if i mod 2 == 0 then amount = 100 else amount = 10000
  MutableArrayInsertObjectAtIndex( qs, fn NumberWithInteger( rnd(amount) ), i )
next

unsorted = fn ArrayWithArray( qs )

fn QuickSort( qs, 0, len(qs) - 1  )

NSLog( @"\n-----------------\nUnsorted : Sorted\n-----------------" )
for i = 0 to 25
  NSLog( @"%8ld : %-8ld", fn NumberIntegerValue( unsorted[i] ), fn NumberIntegerValue( qs[i] ) )
next

randomize

HandleEvents
Output:
-----------------
Unsorted : Sorted
-----------------
      97 : 5       
    6168 : 30      
      61 : 34      
    8847 : 40      
      55 : 46      
    2570 : 49      
      40 : 55      
    4676 : 61      
      94 : 62      
     693 : 67      
      62 : 79      
    3419 : 94      
      30 : 97      
     936 : 693     
       5 : 733     
    9910 : 936     
      67 : 1395    
    8460 : 1796    
      79 : 2570    
    9352 : 3419    
      49 : 4676    
    1395 : 6168    
      34 : 8460    
     733 : 8847    
      46 : 9352    
    1796 : 9910    

Go

Note that Go's sort.Sort function is a Quicksort so in practice it would be just be used. It's actually a combination of quick sort, heap sort, and insertion sort. It starts with a quick sort, after a depth of 2*ceil(lg(n+1)) it switches to heap sort, or once a partition becomes small (less than eight items) it switches to insertion sort.


Old school, following Hoare's 1962 paper.

As a nod to the task request to work for all types with weak strict ordering, code below uses the < operator when comparing key values. The three points are noted in the code below.

Actually supporting arbitrary types would then require at a minimum a user supplied less-than function, and values referenced from an array of interface{} types. More efficient and flexible though is the sort interface of the Go sort package. Replicating that here seemed beyond the scope of the task so code was left written to sort an array of ints.

Go has no language support for indexing with discrete types other than integer types, so this was not coded.

Finally, the choice of a recursive closure over passing slices to a recursive function is really just a very small optimization. Slices are cheap because they do not copy the underlying array, but there's still a tiny bit of overhead in constructing the slice object. Passing just the two numbers is in the interest of avoiding that overhead.

package main

import "fmt"

func main() {
    list := []int{31, 41, 59, 26, 53, 58, 97, 93, 23, 84}
    fmt.Println("unsorted:", list)

    quicksort(list)
    fmt.Println("sorted!  ", list)
}

func quicksort(a []int) {
    var pex func(int, int)
    pex = func(lower, upper int) {
        for {
            switch upper - lower {
            case -1, 0: // 0 or 1 item in segment.  nothing to do here!
                return
            case 1: // 2 items in segment
                // < operator respects strict weak order
                if a[upper] < a[lower] {
                    // a quick exchange and we're done.
                    a[upper], a[lower] = a[lower], a[upper]
                }
                return
            // Hoare suggests optimized sort-3 or sort-4 algorithms here,
            // but does not provide an algorithm.
            }

            // Hoare stresses picking a bound in a way to avoid worst case
            // behavior, but offers no suggestions other than picking a
            // random element.  A function call to get a random number is
            // relatively expensive, so the method used here is to simply
            // choose the middle element.  This at least avoids worst case
            // behavior for the obvious common case of an already sorted list.
            bx := (upper + lower) / 2
            b := a[bx]  // b = Hoare's "bound" (aka "pivot")
            lp := lower // lp = Hoare's "lower pointer"
            up := upper // up = Hoare's "upper pointer"
        outer:
            for {
                // use < operator to respect strict weak order
                for lp < upper && !(b < a[lp]) {
                    lp++
                }
                for {
                    if lp > up {
                        // "pointers crossed!"
                        break outer
                    }
                    // < operator for strict weak order
                    if a[up] < b {
                        break // inner
                    }
                    up--
                }
                // exchange
                a[lp], a[up] = a[up], a[lp]
                lp++
                up--
            }
            // segment boundary is between up and lp, but lp-up might be
            // 1 or 2, so just call segment boundary between lp-1 and lp.
            if bx < lp {
                // bound was in lower segment
                if bx < lp-1 {
                    // exchange bx with lp-1
                    a[bx], a[lp-1] = a[lp-1], b
                }
                up = lp - 2
            } else {
                // bound was in upper segment
                if bx > lp {
                    // exchange
                    a[bx], a[lp] = a[lp], b
                }
                up = lp - 1
                lp++
            }
            // "postpone the larger of the two segments" = recurse on
            // the smaller segment, then iterate on the remaining one.
            if up-lower < upper-lp {
                pex(lower, up)
                lower = lp
            } else {
                pex(lp, upper)
                upper = up
            }
        }
    }
    pex(0, len(a)-1)
}
Output:
unsorted: [31 41 59 26 53 58 97 93 23 84]
sorted!   [23 26 31 41 53 58 59 84 93 97]

More traditional version of quicksort. It work generically with any container that conforms to sort.Interface.

package main

import (
    "fmt"
    "sort"
    "math/rand"
)

func partition(a sort.Interface, first int, last int, pivotIndex int) int {
    a.Swap(first, pivotIndex) // move it to beginning
    left := first+1
    right := last
    for left <= right {
        for left <= last && a.Less(left, first) {
            left++
        }
        for right >= first && a.Less(first, right) {
            right--
        }
        if left <= right {
            a.Swap(left, right)
            left++
            right--
        }
    }
    a.Swap(first, right) // swap into right place
    return right    
}

func quicksortHelper(a sort.Interface, first int, last int) {
    if first >= last {
        return
    }
    pivotIndex := partition(a, first, last, rand.Intn(last - first + 1) + first)
    quicksortHelper(a, first, pivotIndex-1)
    quicksortHelper(a, pivotIndex+1, last)
}

func quicksort(a sort.Interface) {
    quicksortHelper(a, 0, a.Len()-1)
}

func main() {
    a := []int{1, 3, 5, 7, 9, 8, 6, 4, 2}
    fmt.Printf("Unsorted: %v\n", a)
    quicksort(sort.IntSlice(a))
    fmt.Printf("Sorted: %v\n", a)
    b := []string{"Emil", "Peg", "Helen", "Juergen", "David", "Rick", "Barb", "Mike", "Tom"}
    fmt.Printf("Unsorted: %v\n", b)
    quicksort(sort.StringSlice(b))
    fmt.Printf("Sorted: %v\n", b)
}
Output:
Unsorted: [1 3 5 7 9 8 6 4 2]
Sorted: [1 2 3 4 5 6 7 8 9]
Unsorted: [Emil Peg Helen Juergen David Rick Barb Mike Tom]
Sorted: [Barb David Emil Helen Juergen Mike Peg Rick Tom]

Haskell

The famous two-liner, reflecting the underlying algorithm directly:

qsort [] = []
qsort (x:xs) = qsort [y | y <- xs, y < x] ++ [x] ++ qsort [y | y <- xs, y >= x]

A more efficient version, doing only one comparison per element:

import Data.List (partition)

qsort :: Ord a => [a] -> [a]
qsort [] = []
qsort (x:xs) = qsort ys ++ [x] ++ qsort zs where
    (ys, zs) = partition (< x) xs

Icon and Unicon

procedure main()                     #: demonstrate various ways to sort a list and string 
   demosort(quicksort,[3, 14, 1, 5, 9, 2, 6, 3],"qwerty")
end

procedure quicksort(X,op,lower,upper)                      #: return sorted list
local pivot,x 

   if /lower := 1 then {                                   # top level call setup
      upper := *X   
      op := sortop(op,X)                                   # select how and what we sort
      }

   if upper - lower > 0 then {
      every x := quickpartition(X,op,lower,upper) do       # find a pivot and sort ...
          /pivot | X := x                                  # ... how to return 2 values w/o a structure
      X := quicksort(X,op,lower,pivot-1)                   # ... left            
      X := quicksort(X,op,pivot,upper)                     # ... right
      }

   return X                                             
end

procedure quickpartition(X,op,lower,upper)                 #: quicksort partitioner helper
local   pivot
static  pivotL
initial pivotL := list(3)

   pivotL[1] := X[lower]                                   # endpoints
   pivotL[2] := X[upper]                                   # ... and
   pivotL[3] := X[lower+?(upper-lower)]                    # ... random midpoint
   if op(pivotL[2],pivotL[1]) then pivotL[2] :=: pivotL[1] # mini-
   if op(pivotL[3],pivotL[2]) then pivotL[3] :=: pivotL[2] # ... sort
   pivot := pivotL[2]                                      # median is pivot

   lower -:= 1
   upper +:= 1
   while lower < upper do {                                # find values on wrong side of pivot ...
      while op(pivot,X[upper -:= 1])                       # ... rightmost 
      while op(X[lower +:=1],pivot)                        # ... leftmost
      if lower < upper then                                # not crossed yet
         X[lower] :=: X[upper]                             # ... swap 
      }

   suspend lower                                           # 1st return pivot point
   suspend X                                               # 2nd return modified X (in case immutable)
end

Implementation notes:

  • Since this transparently sorts both string and list arguments the result must 'return' to bypass call by value (strings)
  • The partition procedure must "return" two values - 'suspend' is used to accomplish this

Algorithm notes:

  • The use of a type specific sorting operator meant that a general pivot choice need to be made. The median of the ends and random middle seemed reasonable. It turns out to have been suggested by Sedgewick.
  • Sedgewick's suggestions for tail calling to recurse into the larger side and using insertion sort below a certain size were not implemented. (Q: does Icon/Unicon has tail calling optimizations?)


Note: This example relies on the supporting procedures 'sortop', and 'demosort' in Bubble Sort. The full demosort exercises the named sort of a list with op = "numeric", "string", ">>" (lexically gt, descending),">" (numerically gt, descending), a custom comparator, and also a string.

Output:
Abbreviated
Sorting Demo using procedure quicksort
  on list : [ 3 14 1 5 9 2 6 3 ]
    with op = &null:         [ 1 2 3 3 5 6 9 14 ]   (0 ms)
  ...
  on string : "qwerty"
    with op = &null:         "eqrtwy"   (0 ms)

IDL

IDL has a powerful optimized sort() built-in. The following is thus merely for demonstration.

function qs, arr
  if (count = n_elements(arr)) lt 2 then return,arr
  pivot = total(arr) / count ; use the average for want of a better choice
  return,[qs(arr[where(arr le pivot)]),qs(arr[where(arr gt pivot)])]
 end

Example:

IDL> print,qs([3,17,-5,12,99])
     -5       3      12      17      99

Idris

quicksort : Ord elem => List elem -> List elem
quicksort [] = []
quicksort (x :: xs) =
  let lesser = filter (< x) xs
      greater = filter(>= x) xs in
        (quicksort lesser) ++ [x] ++ (quicksort greater)

Example:

*quicksort> quicksort [1, 3, 7, 2, 5, 4, 9, 6, 8, 0]
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9] : List Integer

Io

List do(
    quickSort := method(
        if(size > 1) then(
            pivot := at(size / 2 floor)
            return select(x, x < pivot) quickSort appendSeq(
                select(x, x == pivot) appendSeq(select(x, x > pivot) quickSort)
            )
        ) else(return self)
    )

    quickSortInPlace := method(
        copy(quickSort)
    )
)

lst := list(5, -1, -4, 2, 9)
lst quickSort println # ==> list(-4, -1, 2, 5, 9)
lst quickSortInPlace println # ==> list(-4, -1, 2, 5, 9)

Another more low-level Quicksort implementation can be found in Io's [github ] repository.

Isabelle

theory Quicksort
imports Main
begin

fun quicksort :: "('a :: linorder) list ⇒ 'a list" where
  "quicksort [] = []"
| "quicksort (x#xs) = (quicksort [y←xs. y<x]) @ [x] @ (quicksort [y←xs. y>x])"

lemma "quicksort [4::int, 2, 7, 1] = [1, 2, 4, 7]"
  by(code_simp)

lemma set_first_second_partition:
  fixes x :: "'a :: linorder"
  shows "{y ∈ ys. y < x} ∪ {x} ∪ {y ∈ ys. x < y} =
         insert x ys"
  by fastforce

lemma set_quicksort: "set (quicksort xs) = set xs"
  by(induction xs rule: quicksort.induct)
    (simp add: set_first_second_partition[simplified])+


theorem "sorted (quicksort xs)" 
proof(induction xs rule: quicksort.induct)
  case 1
  show "sorted (quicksort [])" by simp
next
  case (2 x xs)
  assume IH_less:    "sorted (quicksort [y←xs. y<x])"
  assume IH_greater: "sorted (quicksort [y←xs. y>x])"
  have pivot_geq_first_partition:
    "∀z∈set (quicksort [y←xs. y<x]). z ≤ x"
    by (simp add: set_quicksort less_imp_le)
  have pivot_leq_second_partition:
    "∀z ∈ (set (quicksort [y←xs. y>x])). (x ≤ z)"
    by (simp add: set_quicksort less_imp_le)
  have first_partition_leq_second_partition:
    "∀p∈set (quicksort [y←xs. y<x]).
        ∀z ∈ (set (quicksort [y←xs. y>x])). (p ≤ z)"
    by (auto simp add: set_quicksort)
    
  from IH_less IH_greater
       pivot_geq_first_partition pivot_leq_second_partition
       first_partition_leq_second_partition
  show "sorted (quicksort (x # xs))"  by(simp add: sorted_append)
qed


text
The specification on rosettacode says
  All elements less than the pivot must be in the first partition.
  All elements greater than the pivot must be in the second partition.
Since this specification neither says "less than or equal" nor
"greater or equal", this quicksort implementation removes duplicate elements.

lemma "quicksort [1::int, 1, 1, 2, 2, 3] = [1, 2, 3]"
  by(code_simp)

textIf we try the following, we automatically get a counterexample
lemma "length (quicksort xs) = length xs"
(*
  Auto Quickcheck found a counterexample:
    xs = [a⇩1, a⇩1]
  Evaluated terms:
    length (quicksort xs) = 1
    length xs = 2
*)
  oops
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.
sel=: 1 : 'u # ['

quicksort=: 3 : 0
 if.
  1 >: #y
 do.
  y
 else.
  e=. y{~?#y
  (quicksort y <sel e),(y =sel e),quicksort y >sel e
 end.
)

See the Quicksort essay in the J Wiki for additional explanations and examples.

Java

Imperative

Works with: Java version 1.5+

Translation of: Python
public static <E extends Comparable<? super E>> List<E> quickSort(List<E> arr) {
    if (arr.isEmpty())
        return arr;
    else {
        E pivot = arr.get(0);

        List<E> less = new LinkedList<E>();
        List<E> pivotList = new LinkedList<E>();
        List<E> more = new LinkedList<E>();

        // Partition
        for (E i: arr) {
            if (i.compareTo(pivot) < 0)
                less.add(i);
            else if (i.compareTo(pivot) > 0)
                more.add(i);
            else
                pivotList.add(i);
        }

        // Recursively sort sublists
        less = quickSort(less);
        more = quickSort(more);

        // Concatenate results
        less.addAll(pivotList);
        less.addAll(more);
        return less;
    }
}

Functional

Works with: Java version 1.8
public static <E extends Comparable<E>> List<E> sort(List<E> col) {
    if (col == null || col.isEmpty())
        return Collections.emptyList();
    else {
        E pivot = col.get(0);
        Map<Integer, List<E>> grouped = col.stream()
                .collect(Collectors.groupingBy(pivot::compareTo));
        return Stream.of(sort(grouped.get(1)), grouped.get(0), sort(grouped.get(-1)))
                .flatMap(Collection::stream).collect(Collectors.toList());
    }
}

JavaScript

Imperative

function sort(array, less) {

  function swap(i, j) {
    var t = array[i];
    array[i] = array[j];
    array[j] = t;
  }

  function quicksort(left, right) {

    if (left < right) {
      var pivot = array[left + Math.floor((right - left) / 2)],
          left_new = left,
          right_new = right;

      do {
        while (less(array[left_new], pivot)) {
          left_new += 1;
        }
        while (less(pivot, array[right_new])) {
          right_new -= 1;
        }
        if (left_new <= right_new) {
          swap(left_new, right_new);
          left_new += 1;
          right_new -= 1;
        }
      } while (left_new <= right_new);

      quicksort(left, right_new);
      quicksort(left_new, right);

    }
  }

  quicksort(0, array.length - 1);

  return array;
}
Example:
var test_array = [10, 3, 11, 15, 19, 1];
var sorted_array = sort(test_array, function(a,b) { return a<b; });
Output:
[ 1, 3, 10, 11, 15, 19 ]

Functional

ES6

Using destructuring and satisfying immutability we can propose a single expresion solution (from https://github.com/ddcovery/expressive_sort)

const qsort = ([pivot, ...others]) => 
  pivot === void 0 ? [] : [
    ...qsort(others.filter(n => n < pivot)),
    pivot,
    ...qsort(others.filter(n => n >= pivot))
  ];

qsort( [ 11.8, 14.1, 21.3, 8.5, 16.7, 5.7 ] )
Output:
[ 5.7, 8.5, 11.8, 14.1, 16.7, 21.3 ]

ES5

Unlike what happens with ES6, there are no destructuring nor lambdas, but we can ensure immutability and propose a single expression solution with standard anonymous functions

function qsort( xs ){
  return xs.length === 0 ? [] : [].concat(
    qsort( xs.slice(1).filter(function(x){ return x< xs[0] })),
    xs[0],
    qsort( xs.slice(1).filter(function(x){ return x>= xs[0] }))
  )
}
qsort( [ 11.8, 14.1, 21.3, 8.5, 16.7, 5.7 ] )
Output:
[5.7, 8.5, 11.8, 14.1, 16.7, 21.3]

Joy

DEFINE qsort ==
  [small]            # termination condition: 0 or 1 element
  []                 # do nothing
  [uncons [>] split] # pivot and two lists
  [enconcat]         # insert the pivot after the recursion
  binrec.            # recursion on the two lists

jq

jq's built-in sort currently (version 1.4) uses the standard C qsort, a quicksort. sort can be used on any valid JSON array.

Example:
[1, 1.1, [1,2], true, false, null, {"a":1}, null] | sort
Output:
[null,null,false,true,1,1.1,[1,2],{"a":1}]
Here is an implementation in jq of the pseudo-code (and comments :-) given at the head of this article:
def quicksort:
  if length < 2 then .                            # it is already sorted
  else .[0] as $pivot
       | reduce .[] as $x
         # state: [less, equal, greater]
           ( [ [], [], [] ];                      # three empty arrays:
             if   $x  < $pivot then .[0] += [$x]  # add x to less
             elif $x == $pivot then .[1] += [$x]  # add x to equal
             else                   .[2] += [$x]  # add x to greater
             end
         )
       | (.[0] | quicksort ) + .[1] + (.[2] | quicksort )
  end ;
Fortunately, the example input used above produces the same output,

and so both are omitted here.

Julia

Built-in function for in-place sorting via quicksort (the code from the standard library is quite readable):

sort!(A, alg=QuickSort)

A simple polymorphic implementation of an in-place recursive quicksort (based on the pseudocode above):

function quicksort!(A,i=1,j=length(A))
    if j > i
        pivot = A[rand(i:j)] # random element of A
        left, right = i, j
        while left <= right
            while A[left] < pivot
                left += 1
            end
            while A[right] > pivot
                right -= 1
            end
            if left <= right
                A[left], A[right] = A[right], A[left]
                left += 1
                right -= 1
            end
        end
        quicksort!(A,i,right)
        quicksort!(A,left,j)
    end
    return A
end

A one-line (but rather inefficient) implementation based on the Haskell version, which operates out-of-place and allocates temporary arrays:

qsort(L) = isempty(L) ? L : vcat(qsort(filter(x -> x < L[1], L[2:end])), L[1:1], qsort(filter(x -> x >= L[1], L[2:end])))
Output:
julia> A = [84,77,20,60,47,20,18,97,41,49,31,39,73,68,65,52,1,92,15,9]

julia> qsort(A)
[1,9,15,18,20,20,31,39,41,47,49,52,60,65,68,73,77,84,92,97]

julia> quicksort!(copy(A))
[1,9,15,18,20,20,31,39,41,47,49,52,60,65,68,73,77,84,92,97]

julia> qsort(A) == quicksort!(copy(A)) == sort(A) == sort(A, alg=QuickSort)
true

K

quicksort:{f:*x@1?#x;:[0=#x;x;,/(_f x@&x<f;x@&x=f;_f x@&x>f)]}

Example:

    quicksort 1 3 5 7 9 8 6 4 2
Output:
1 2 3 4 5 6 7 8 9


Explanation:

  _f()

is the current function called recursively.

   :[....]

generally means :[condition1;then1;condition2;then2;....;else]. Though here it is used as :[if;then;else].

This construct

   f:*x@1?#x

assigns a random element in x (the argument) to f, as the pivot value.

And here is the full if/then/else clause:

    :[
        0=#x;           / if length of x is zero 
        x;              / then return x
                        / else
        ,/(             / join the results of: 
          _f x@&x<f         / sort (recursively) elements less than f (pivot)
          x@&x=f            / element equal to f 
          _f x@&x>f)        / sort (recursively) elements greater than f 
     ]

Though - as with APL and J - for larger arrays it's much faster to sort using "<" (grade up) which gives the indices of the list sorted ascending, i.e.

   t@<t:1 3 5 7 9 8 6 4 2

Koka

Haskell-like solution

fun qsort( xs : list<int> ) : div list<int> {
  match(xs) {
    Cons(x,xx) -> {
      val ys = xx.filter fn(el) { el < x }
      val zs = xx.filter fn(el) { el >= x }
      qsort(ys) + [x] + qsort(zs)
    }
    Nil -> Nil
  }
}

or using standard partition function

fun qsort( xs : list<int> ) : div list<int> {
  match(xs) {
    Cons(x,xx) -> {
      val (ys, zs) = xx.partition fn(el) { el < x }
      qsort(ys) + [x] + qsort(zs)
    }
    Nil -> Nil
  }
}

Example:

fun main() {
  val arr = [24,63,77,26,84,64,56,80,85,17]
  println(arr.qsort.show)
}
Output:
[17,24,26,56,63,64,77,80,84,85]

Kotlin

A version that reflects the algorithm directly:

fun <E : Comparable<E>> List<E>.qsort(): List<E> =
        if (size < 2) this
        else filter { it < first() }.qsort() +
                filter { it == first() } +
                filter { it > first() }.qsort()

A more efficient version that does only one comparison per element:

fun <E : Comparable<E>> List<E>.qsort(): List<E> =
        if (size < 2) this
        else {
            val (less, high) = subList(1, size).partition { it < first() }
            less.qsort() + first() + high.qsort()
        }

Lambdatalk

We create a binary tree from a random array, then we walk the canopy.

1) three functions for readability:         
 
{def BT.data  {lambda {:t} {A.get 0 :t}}} -> BT.data
{def BT.left  {lambda {:t} {A.get 1 :t}}} -> BT.left
{def BT.right {lambda {:t} {A.get 2 :t}}} -> BT.right

2) adding a leaf to the tree: 

{def BT.add {lambda {:x :t}
 {if {A.empty? :t}
  then {A.new :x {A.new} {A.new}}
  else {if   {= :x {BT.data :t}}
        then :t
        else {if {< :x {BT.data :t}}
              then {A.new {BT.data :t} 
                          {BT.add :x {BT.left :t}}
                          {BT.right :t}}
              else {A.new {BT.data :t} 
                          {BT.left :t}
                          {BT.add :x {BT.right :t}} }}}}}}
-> BT.add

3) creating the tree from an array of numbers:

{def BT.create           
 {def BT.create.rec
  {lambda {:l :t}
   {if {A.empty? :l}
    then :t
    else {BT.create.rec {A.rest :l}
                        {BT.add {A.first :l} :t}} }}}
 {lambda {:l}
  {BT.create.rec :l {A.new}} }}
-> BT.create

4) walking the canopy -> sorting in increasing order:

{def BT.sort
 {lambda {:t}
  {if {A.empty? :t}
   then else {BT.sort {BT.left :t}}
             {BT.data :t}
             {BT.sort {BT.right :t}} }}}   
-> BT.sort

Testing

1) generating random numbers:

{def L {A.new 
 {S.map {lambda {:n} {floor {* {random} 100000}}} {S.serie 1 100}}}} 
-> L =  [1850,7963,50540,92667,72892,47361,19018,40640,10126,80235,48407,51623,63597,71675,27814,63478,18985,88032,46585,85209,
74053,95005,27592,9575,22162,35904,70467,38527,89715,36594,54309,39950,89345,72224,7772,65756,68766,43942,52422,85144,
66010,38961,21647,53194,72166,33545,49037,23218,27969,83566,19382,53120,55291,77374,27502,66648,99637,37322,9815,432,90565,
37831,26503,99232,87024,65625,75155,55382,30120,58117,70031,13011,81375,10490,39786,1926,71311,4213,55183,2583,22075,90411,
92928,61120,94259,433,93332,88423,64119,40850,94318,27816,84818,90632,5094,36696,94705,50602,45818,61365]

2) creating the tree is the main work:

{def T {BT.create {L}}} 
-> T = [1850,[432,],[433,],]]],[7963,[7772,[1926,],[4213,[2583,],]],[5094,],]]]],]],[50540,[47361,[19018,[10126,[9575,],
[9815,],]]],[18985,[13011,[10490,],]],]],]]],[40640,[27814,[27592,[22162,[21647,[19382,],]],[22075,],]]],[23218,],
[27502,[26503,],]],]]]],]],[35904,[33545,[27969,[27816,],]],[30120,],]]],]],[38527,[36594,],[37322,[36696,],]],[37831,],]]]],
[39950,[38961,],[39786,],]]],]]]]],[46585,[43942,[40850,],]],[45818,],]]],]]]],[48407,],[49037,],]]]],[92667,[72892,
[51623,[50602,],]],[63597,[63478,[54309,[52422,],[53194,[53120,],]],]]],[55291,[55183,],]],[55382,],[58117,],[61120,],[61365,],]]]]]]],]],[71675,[70467,[65756,[65625,[64119,],]],]],[68766,[66010,],[66648,],]]],[70031,],]]]],[71311,],]]],
[72224,[72166,],]],]]]]],[80235,[74053,],[77374,[75155,],]],]]],[88032,[85209,[85144,[83566,[81375,],]],[84818,],]]],]],
[87024,],]]],[89715,[89345,[88423,],]],]],[90565,[90411,],]],[90632,],]]]]]]],[95005,[92928,],[94259,[93332,],]],[94318,],
[94705,],]]]]],[99637,[99232,],]],]]]]]]]

3) walking the canopy is fast:   

{BT.sort {T}}
->  432 433 1850 1926 2583 4213 5094 7772 7963 9575 9815 10126 10490 13011 18985 19018 19382 21647 22075 22162 23218 26503
 27502 27592 27814 27816 27969 30120 33545 35904 36594 36696 37322 37831 38527 38961 39786 39950 40640 40850 43942 45818
 46585 47361 48407 49037 50540 50602 51623 52422 53120 53194 54309 55183 55291 55382 58117 61120 61365 63478 63597 64119
 65625 65756 66010 66648 68766 70031 70467 71311 71675 72166 72224 72892 74053 75155 77374 80235 81375 83566 84818 85144
 85209 87024 88032 88423 89345 89715 90411 90565 90632 92667 92928 93332 94259 94318 94705 95005 99232 99637     

4) walking with new leaves is fast:

{BT.sort {BT.add -1 {T}}}
->  -1 432 433 1850 1926 2583 4213 5094 7772 7963 9575 9815 10126 10490 13011 18985 19018 19382 21647 22075 22162 23218 26503
 27502 27592 27814 27816 27969 30120 33545 35904 36594 36696 37322 37831 38527 38961 39786 39950 40640 40850 43942 45818 46585
 47361 48407 49037 50540 50602 51623 52422 53120 53194 54309 55183 55291 55382 58117 61120 61365 63478 63597 64119 65625 65756
 66010 66648 68766 70031 70467 71311 71675 72166 72224 72892 74053 75155 77374 80235 81375 83566 84818 85144 85209 87024 88032
 88423 89345 89715 90411 90565 90632 92667 92928 93332 94259 94318 94705 95005 99232 99637

{BT.sort {BT.add 50000 {T}}}
->  432 433 1850 1926 2583 4213 5094 7772 7963 9575 9815 10126 10490 13011 18985 19018 19382 21647 22075 22162 23218 26503
 27502 27592 27814 27816 27969 30120 33545 35904 36594 36696 37322 37831 38527 38961 39786 39950 40640 40850 43942 45818 46585
 47361 48407 49037 50000 50540 50602 51623 52422 53120 53194 54309 55183 55291 55382 58117 61120 61365 63478 63597 64119 65625
 65756 66010 66648 68766 70031 70467 71311 71675 72166 72224 72892 74053 75155 77374 80235 81375 83566 84818 85144 85209 87024
 88032 88423 89345 89715 90411 90565 90632 92667 92928 93332 94259 94318 94705 95005 99232 99637

{BT.sort {BT.add 100000 {T}}}
->  432 433 1850 1926 2583 4213 5094 7772 7963 9575 9815 10126 10490 13011 18985 19018 19382 21647 22075 22162 23218 26503
 27502 27592 27814 27816 27969 30120 33545 35904 36594 36696 37322 37831 38527 38961 39786 39950 40640 40850 43942 45818 46585
 47361 48407 49037 50540 50602 51623 52422 53120 53194 54309 55183 55291 55382 58117 61120 61365 63478 63597 64119 65625 65756
 66010 66648 68766 70031 70467 71311 71675 72166 72224 72892 74053 75155 77374 80235 81375 83566 84818 85144 85209 87024 88032
 88423 89345 89715 90411 90565 90632 92667 92928 93332 94259 94318 94705 95005 99232 99637 100000


Lobster

include "std.lobster"

def quicksort(xs, lt):
    if xs.length <= 1:
        xs
    else:
        pivot := xs[0]
        tail := xs.slice(1, -1)
        f1 := filter tail:  lt(_, pivot)
        f2 := filter tail: !lt(_, pivot)
        append(append(quicksort(f1, lt), [ pivot ]),
                      quicksort(f2, lt))

sorted := [ 3, 9, 5, 4, 1, 3, 9, 5, 4, 1 ].quicksort(): _a < _b
print sorted

; quicksort (lists, functional)

to small? :list
  output or [empty? :list] [empty? butfirst :list]
end
to quicksort :list
  if small? :list [output :list]
  localmake "pivot first :list
  output (sentence
    quicksort filter [? < :pivot] butfirst :list
              filter [? = :pivot]          :list
    quicksort filter [? > :pivot] butfirst :list
  )
end

show quicksort [1 3 5 7 9 8 6 4 2]
; quicksort (arrays, in-place)

to incr :name
  make :name (thing :name) + 1
end
to decr :name
  make :name (thing :name) - 1
end
to swap :i :j :a
  localmake "t item :i :a
  setitem :i :a item :j :a
  setitem :j :a :t
end

to quick :a :low :high
  if :high <= :low [stop]
  localmake "l :low
  localmake "h :high
  localmake "pivot item ashift (:l + :h) -1  :a
  do.while [
    while [(item :l :a) < :pivot] [incr "l]
    while [(item :h :a) > :pivot] [decr "h]
    if :l <= :h [swap :l :h :a  incr "l  decr "h]
  ] [:l <= :h]
  quick :a :low :h
  quick :a :l :high
end
to sort :a
  quick :a first :a count :a
end

make "test {1 3 5 7 9 8 6 4 2}
sort :test
show :test

Logtalk

quicksort(List, Sorted) :-
    quicksort(List, [], Sorted).

quicksort([], Sorted, Sorted).
quicksort([Pivot| Rest], Acc, Sorted) :- 
    partition(Rest, Pivot, Smaller0, Bigger0),
    quicksort(Smaller0, [Pivot| Bigger], Sorted),
    quicksort(Bigger0, Acc, Bigger).

partition([], _, [], []).
partition([X| Xs], Pivot, Smalls, Bigs) :-
    (   X @< Pivot ->
        Smalls = [X| Rest],
        partition(Xs, Pivot, Rest, Bigs)
    ;   Bigs = [X| Rest],
        partition(Xs, Pivot, Smalls, Rest)
    ).

Lua

NOTE: If you want to use quicksort in a Lua script, you don't need to implement it yourself. Just do:
table.sort(tableName)

in-place

--in-place quicksort
function quicksort(t, start, endi)
  start, endi = start or 1, endi or #t
  --partition w.r.t. first element
  if(endi - start < 1) then return t end
  local pivot = start
  for i = start + 1, endi do
    if t[i] <= t[pivot] then
      if i == pivot + 1 then
        t[pivot],t[pivot+1] = t[pivot+1],t[pivot]
      else
        t[pivot],t[pivot+1],t[i] = t[i],t[pivot],t[pivot+1]
      end
      pivot = pivot + 1
    end
  end
  t = quicksort(t, start, pivot - 1)
  return quicksort(t, pivot + 1, endi)
end

--example
print(unpack(quicksort{5, 2, 7, 3, 4, 7, 1}))

non in-place

function quicksort(t)
  if #t<2 then return t end
  local pivot=t[1]
  local a,b,c={},{},{}
  for _,v in ipairs(t) do
    if     v<pivot then a[#a+1]=v
    elseif v>pivot then c[#c+1]=v
    else                b[#b+1]=v
    end
  end
  a=quicksort(a)
  c=quicksort(c)
  for _,v in ipairs(b) do a[#a+1]=v end
  for _,v in ipairs(c) do a[#a+1]=v end
  return a
end

Lucid

[1]

qsort(a) = if eof(first a) then a else follow(qsort(b0),qsort(b1)) fi
 where
    p = first a < a;
    b0 = a whenever p;
    b1 = a whenever not p;
    follow(x,y) = if xdone then y upon xdone else x fi
                    where
                       xdone = iseod x fby xdone or iseod x; 
                    end;
 end

M2000 Interpreter

Recursive calling Functions

Module Checkit1 {
      Group Quick {
      Private:
            Function partition {
                     Read &A(), p, r
                     x = A(r)
                     i = p-1
                     For j=p to r-1 {
                         If .LE(A(j), x) Then {
                                i++
                                Swap A(i),A(j)
                             }
                      }
                      Swap A(i+1),A(r)
                     = i+1
                  }
      Public:
            LE=Lambda->Number<=Number
            Function quicksort {
                 Read &A(), p, r
                 If p < r Then {
                   q = .partition(&A(), p, r)
                   Call .quicksort(&A(), p, q - 1)
                   Call .quicksort(&A(), q + 1, r)
                }
            }
      }
      Dim A(10)<<Random(50, 100)
      Print A()
      Call Quick.quicksort(&A(), 0, Len(A())-1)
      Print A()
}
Checkit1

Recursive calling Subs

Variables p, r, q removed from quicksort function. we use stack for values. Also Partition push to stack now. Works for string arrays too.

Module Checkit2 {
      Class Quick {
      Private:
            partition=lambda-> {
                  Read &A(), p, r : i = p-1 : x=A(r)
                  For j=p to r-1 {If .LE(A(j), x) Then i++:Swap A(i),A(j)
                  } : Swap A(i+1), A(r) :  Push i+1
            }
      Public:
            LE=Lambda->Number<=Number
            Module ForStrings {
                  .partition<=lambda-> {
                        Read &A$(), p, r : i = p-1 : x$=A$(r)
                        For j=p to r-1 {If A$(j)<= x$ Then i++:Swap A$(i),A$(j)
                        } : Swap A$(i+1), A$(r) : Push i+1
                  }
            }
            Function quicksort (ref$) {
                  myQuick()
                  sub myQuick()
                        If Stackitem() >= stackitem(2) Then drop 2 : Exit Sub
                        Over 2, 2 : Call .partition(ref$) : Over : Shiftback  3, 2
                        myQuick(number,  number - 1)
                        myQuick( number + 1, number)
                  End Sub
             } 
      }
      Quick=Quick()
      Dim A(10)
      A(0):=57, 83, 74, 98, 51, 73, 85, 76, 65, 92
      Print A()
      Call Quick.quicksort(&A(), 0, Len(A())-1)
      Print A()
      Quick=Quick()
      Quick.ForStrings
      Dim A$()
      A$()=("one","two", "three","four", "five")
      Print A$()
      Call Quick.quicksort(&A$(), 0, Len(A$())-1)
      Print A$()
}
Checkit2

Non Recursive

Partition function return two values (where we want q, and use it as q-1 an q+1 now Partition() return final q-1 and q+1_ Example include numeric array, array of arrays (we provide a lambda for comparison) and string array.

Module Checkit3 {
      Class Quick {
      Private:
            partition=lambda-> {
                  Read &A(), p, r : i = p-1 : x=A(r)
                  For j=p to r-1 {If .LE(A(j), x) Then i++:Swap A(i),A(j)
                  } : Swap A(i+1), A(r) :  Push  i+2, i 
            }
      Public:
            LE=Lambda->Number<=Number
            Module ForStrings {
                  .partition<=lambda-> {
                        Read &A$(), p, r : i = p-1 : x$=A$(r)
                        For j=p to r-1 {If A$(j)<= x$ Then i++:Swap A$(i),A$(j)
                        } : Swap A$(i+1), A$(r) : Push i+2, i
                  }
            }
            Function quicksort {
                 Read ref$
                 {
                         loop : If Stackitem() >= Stackitem(2) Then Drop 2 : if  empty then {Break} else continue
                         over 2,2 : call .partition(ref$) :shift 3 
                 }
            }
      }
      Quick=Quick()
      Dim A(10)<<Random(50, 100)
      Print A()
      Call Quick.quicksort(&A(), 0, Len(A())-1)
      Print A()
      Quick=Quick()
      Function join$(a$()) {
            n=each(a$(), 1, -2)
            k$=""
            while n {
                  overwrite k$, ".", n^:=array$(n)
            }
            =k$
      }
      Stack New {
                  Data "1.3.6.1.4.1.11.2.17.19.3.4.0.4" , "1.3.6.1.4.1.11.2.17.19.3.4.0.1", "1.3.6.1.4.1.11150.3.4.0.1"
                  Data "1.3.6.1.4.1.11.2.17.19.3.4.0.10", "1.3.6.1.4.1.11.2.17.5.2.0.79", "1.3.6.1.4.1.11150.3.4.0"
                  Dim Base 0, arr(Stack.Size)
                  Link arr() to arr$()
                  i=0 : While not Empty {arr$(i)=piece$(letter$+".", ".") : i++ }
      }
      \\ change comparison function
      Quick.LE=lambda (a, b)->{
            Link a, b to a$(), b$()
             def i=-1
             do {
                   i++
             } until a$(i)="" or b$(i)="" or a$(i)<>b$(i)
             if b$(i)="" then =a$(i)="":exit
             if a$(i)="" then =true:exit
             =val(a$(i))<=val(b$(i))
      }
      Call Quick.quicksort(&arr(), 0, Len(arr())-1)
      For i=0 to len(arr())-1 {
            Print join$(arr(i))
      }
      \\ Fresh load
      Quick=Quick()
      Quick.ForStrings
      Dim A$()
      A$()=("one","two", "three","four", "five")
      Print A$()
      Call Quick.quicksort(&A$(), 0, Len(A$())-1)
      Print A$()
}
Checkit3

M4

dnl  return the first element of a list when called in the funny way seen below
define(`arg1', `$1')dnl
dnl
dnl  append lists 1 and 2
define(`append',
   `ifelse(`$1',`()',
      `$2',
      `ifelse(`$2',`()',
         `$1',
         `substr($1,0,decr(len($1))),substr($2,1)')')')dnl
dnl
dnl  separate list 2 based on pivot 1, appending to left 3 and right 4,
dnl  until 2 is empty, and then combine the sort of left with pivot with
dnl  sort of right
define(`sep',
   `ifelse(`$2', `()',
      `append(append(quicksort($3),($1)),quicksort($4))',
      `ifelse(eval(arg1$2<=$1),1,
         `sep($1,(shift$2),append($3,(arg1$2)),$4)',
         `sep($1,(shift$2),$3,append($4,(arg1$2)))')')')dnl
dnl
dnl  pick first element of list 1 as pivot and separate based on that
define(`quicksort',
   `ifelse(`$1', `()',
      `()',
      `sep(arg1$1,(shift$1),`()',`()')')')dnl
dnl
quicksort((3,1,4,1,5,9))
Output:
(1,1,3,4,5,9)

Maclisp

;; While not strictly required, it simplifies the
;; implementation considerably to use filter. MACLisp
;; Doesn't have one out of the box, so we bring our own
(DEFUN FILTER (F LIST)
        (COND
         ((EQ LIST NIL) NIL)
         ((FUNCALL F (CAR LIST))
          (CONS (CAR LIST) (FILTER F (CDR LIST))))
         (T
          (FILTER F (CDR LIST)))))

;; And then, quicksort.
(DEFUN QUICKSORT (LIST)
    (COND
     ((OR (EQ LIST ())
          (EQ (CDR LIST) ()))
      LIST)
     (T
      (LET
        ((PIVOT (CAR LIST))
         (REST (CDR LIST)))
        (APPEND
            (QUICKSORT (FILTER #'(LAMBDA (X) (<= X PIVOT)) REST))
            (LIST PIVOT)
            (QUICKSORT (FILTER #'(LAMBDA (X) (> X PIVOT)) REST)))))))

Maple

swap := proc(arr, a, b)
	local temp := arr[a]:
	arr[a] := arr[b]:
	arr[b] := temp:
end proc:
quicksort := proc(arr, low, high)
	local pi:
	if (low < high) then
		pi := qpart(arr,low,high):
		quicksort(arr, low, pi-1):
		quicksort(arr, pi+1, high):
	end if:
end proc:
qpart := proc(arr, low, high)
	local i,j,pivot;
	pivot := arr[high]:
	i := low-1:
	for j from low to high-1 by 1 do
		if (arr[j] <= pivot) then
			i++:
			swap(arr, i, j):
		end if;
	end do;
	swap(arr, i+1, high):
	return (i+1):
end proc:
a:=Array([12,4,2,1,0]);
quicksort(a,1,5);
a;
Output:
[0, 1, 2, 4, 12]

Mathematica/Wolfram Language

QuickSort[x_List] := Module[{pivot},
  If[Length@x <= 1, Return[x]];
  pivot = RandomChoice@x;
  Flatten@{QuickSort[Cases[x, j_ /; j < pivot]], Cases[x, j_ /; j == pivot], QuickSort[Cases[x, j_ /; j > pivot]]}
  ]
qsort[{}] = {};
qsort[{x_, xs___}] := Join[qsort@Select[{xs}, # <= x &], {x}, qsort@Select[{xs}, # > x &]];
QuickSort[{}] := {}
QuickSort[list: {__}] := With[{pivot=RandomChoice[list]},
	Join[ <|1->{}, -1->{}|>, GroupBy[list,Order[#,pivot]&] ] // Catenate[ {QuickSort@#[1], #[0], QuickSort@#[-1]} ]&
]

MATLAB

This implements the pseudo-code in the specification. The input can be either a row or column vector, but the returned vector will always be a row vector. This can be modified to operate on any built-in primitive or user defined class by replacing the "<=" and ">" comparisons with "le" and "gt" functions respectively. This is because operators can not be overloaded, but the functions that are equivalent to the operators can be overloaded in class definitions.

This should be placed in a file named quickSort.m.

function sortedArray = quickSort(array)

    if numel(array) <= 1 %If the array has 1 element then it can't be sorted       
        sortedArray = array;
        return
    end
    
    pivot = array(end);
    array(end) = [];
        
    %Create two new arrays which contain the elements that are less than or
    %equal to the pivot called "less" and greater than the pivot called
    %"greater"
    less = array( array <= pivot );
    greater = array( array > pivot );
    
    %The sorted array is the concatenation of the sorted "less" array, the
    %pivot and the sorted "greater" array in that order
    sortedArray = [quickSort(less) pivot quickSort(greater)];
    
end

A slightly more vectorized version of the above code that removes the need for the less and greater arrays:

function sortedArray = quickSort(array)

    if numel(array) <= 1 %If the array has 1 element then it can't be sorted       
        sortedArray = array;
        return
    end
    
    pivot = array(end);
    array(end) = [];
    
    sortedArray = [quickSort( array(array <= pivot) ) pivot quickSort( array(array > pivot) )];
    
end

Sample usage:

quickSort([4,3,7,-2,9,1])

ans =

    -2     1     3     4     7     9

MAXScript

fn quickSort arr =
(
    less = #()
    pivotList = #()
    more = #()
    if arr.count <= 1 then
    (
        arr
    )
    else
    (
        pivot = arr[arr.count/2]
        for i in arr do
        (
            case of
            (
                (i < pivot):	(append less i)
                (i == pivot):	(append pivotList i)
                (i > pivot):	(append more i)
            )
        )
        less = quickSort less
        more = quickSort more
        less + pivotList + more
    )
)
a = #(4, 89, -3, 42, 5, 0, 2, 889)
a = quickSort a

Mercury

A quicksort that works on linked lists

Works with: Mercury version 22.01.1


%%%-------------------------------------------------------------------

:- module quicksort_task_for_lists.

:- interface.
:- import_module io.
:- pred main(io, io).
:- mode main(di, uo) is det.

:- implementation.
:- import_module int.
:- import_module list.

%%%-------------------------------------------------------------------
%%%
%%% Partitioning a list into three:
%%%
%%%    Left         elements less than the pivot
%%%    Middle       elements equal to the pivot
%%%    Right        elements greater than the pivot
%%%
%%% The implementation is tail-recursive.
%%%

:- pred partition(comparison_func(T), T, list(T),
                  list(T), list(T), list(T)).
:- mode partition(in, in, in, out, out, out) is det.
partition(Compare, Pivot, Lst, Left, Middle, Right) :-
  partition(Compare, Pivot, Lst, [], Left, [], Middle, [], Right).

:- pred partition(comparison_func(T), T, list(T),
                  list(T), list(T),
                  list(T), list(T),
                  list(T), list(T)).
:- mode partition(in, in, in,
                  in, out,
                  in, out,
                  in, out) is det.
partition(_, _, [], Left0, Left, Middle0, Middle, Right0, Right) :-
  Left = Left0,
  Middle = Middle0,
  Right = Right0.
partition(Compare, Pivot, [Head | Tail], Left0, Left,
          Middle0, Middle, Right0, Right) :-
  Compare(Head, Pivot) = Cmp,
  (if (Cmp = (<))
   then partition(Compare, Pivot, Tail,
                  [Head | Left0], Left,
                  Middle0, Middle,
                  Right0, Right)
   else if (Cmp = (=))
   then partition(Compare, Pivot, Tail,
                  Left0, Left,
                  [Head | Middle0], Middle,
                  Right0, Right)
   else partition(Compare, Pivot, Tail,
                  Left0, Left,
                  Middle0, Middle,
                  [Head | Right0], Right)).

%%%-------------------------------------------------------------------
%%%
%%% Quicksort using the first element as pivot.
%%%
%%% This is not the world's best choice of pivot, but it is the
%%% easiest one to get from a linked list.
%%%
%%% This implementation is *not* tail-recursive--as most quicksort
%%% implementations also are not. (However, do an online search on
%%% "quicksort fortran 77" and you will find some "tail-recursive"
%%% implementations, with the tail recursions expressed as gotos.)
%%%

:- func quicksort(comparison_func(T), list(T)) = list(T).
quicksort(_, []) = [].
quicksort(Compare, [Pivot | Tail]) = Sorted_Lst :-
  partition(Compare, Pivot, Tail, Left, Middle, Right),
  quicksort(Compare, Left) = Sorted_Left,
  quicksort(Compare, Right) = Sorted_Right,
  Sorted_Left ++ [Pivot | Middle] ++ Sorted_Right = Sorted_Lst.

%%%-------------------------------------------------------------------

:- func example_numbers = list(int).
example_numbers = [1, 3, 9, 5, 8, 6, 5, 1, 7, 9, 8, 6, 4, 2].

:- func int_compare(int, int) = comparison_result.
int_compare(I, J) = Cmp :-
  if (I < J) then (Cmp = (<))
  else if (I = J) then (Cmp = (=))
  else (Cmp = (>)).

main(!IO) :-
  quicksort(int_compare, example_numbers) = Sorted_Numbers,
  print("unsorted: ", !IO),
  print_line(example_numbers, !IO),
  print("sorted:   ", !IO),
  print_line(Sorted_Numbers, !IO).

%%%-------------------------------------------------------------------
%%% local variables:
%%% mode: mercury
%%% prolog-indent-width: 2
%%% end:
Output:
$ mmc quicksort_task_for_lists.m && ./quicksort_task_for_lists
unsorted: [1, 3, 9, 5, 8, 6, 5, 1, 7, 9, 8, 6, 4, 2]
sorted:   [1, 1, 2, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9]

A quicksort that works on arrays

Works with: Mercury version 22.01.1


The in-place partitioning algorithm here is similar to but not quite the same as that of the task pseudocode. I wrote it by referring to some Fortran code I wrote several months ago for a quickselect. (That quickselect had a random pivot, however.)

%%%-------------------------------------------------------------------

:- module quicksort_task_for_arrays.

:- interface.
:- import_module io.
:- pred main(io, io).
:- mode main(di, uo) is det.

:- implementation.
:- import_module array.
:- import_module int.
:- import_module list.

%%%-------------------------------------------------------------------
%%%
%%% Partitioning a subarray into two halves: one with elements less
%%% than or equal to a pivot, the other with elements greater than or
%%% equal to a pivot.
%%%
%%% The implementation is tail-recursive.
%%%

:- pred partition(pred(T, T), T, int, int, array(T), array(T), int).
:- mode partition(pred(in, in) is semidet, in, in, in,
                  array_di, array_uo, out).
partition(Less_than, Pivot, I_first, I_last, Arr0, Arr, I_pivot) :-
  I = I_first - 1,
  J = I_last + 1,
  partition_loop(Less_than, Pivot, I, J, Arr0, Arr, I_pivot).

:- pred partition_loop(pred(T, T), T, int, int,
                       array(T), array(T), int).
:- mode partition_loop(pred(in, in) is semidet, in, in, in,
                       array_di, array_uo, out).
partition_loop(Less_than, Pivot, I, J, Arr0, Arr, Pivot_index) :-
  if (I = J) then (Arr = Arr0,
                   Pivot_index = I)
  else (I1 = I + 1,
        I2 = search_right(Less_than, Pivot, I1, J, Arr0),
        (if (I2 = J) then (Arr = Arr0,
                           Pivot_index = J)
         else (J1 = J - 1,
               J2 = search_left(Less_than, Pivot, I2, J1, Arr0),
               swap(I2, J2, Arr0, Arr1),
               partition_loop(Less_than, Pivot, I2, J2, Arr1, Arr,
                              Pivot_index)))).

:- func search_right(pred(T, T), T, int, int, array(T)) = int.
:- mode search_right(pred(in, in) is semidet,
                     in, in, in, in) = out is det.
search_right(Less_than, Pivot, I, J, Arr0) = K :-
  if (I = J) then (I = K)
  else if Less_than(Pivot, Arr0^elem(I)) then (I = K)
  else (search_right(Less_than, Pivot, I + 1, J, Arr0) = K).

:- func search_left(pred(T, T), T, int, int, array(T)) = int.
:- mode search_left(pred(in, in) is semidet,
                    in, in, in, in) = out is det.
search_left(Less_than, Pivot, I, J, Arr0) = K :-
  if (I = J) then (J = K)
  else if Less_than(Arr0^elem(J), Pivot) then (J = K)
  else (search_left(Less_than, Pivot, I, J - 1, Arr0) = K).

%%%-------------------------------------------------------------------
%%%
%%% Quicksort with median of three as pivot.
%%%
%%% Like most quicksort implementations, this one is *not*
%%% tail-recursive.
%%%

%% quicksort/3 sorts an entire array.
:- pred quicksort(pred(T, T), array(T), array(T)).
:- mode quicksort(pred(in, in) is semidet, array_di, array_uo) is det.
quicksort(Less_than, Arr0, Arr) :-
  bounds(Arr0, I_first, I_last),
  quicksort(Less_than, I_first, I_last, Arr0, Arr).

%% quicksort/5 sorts a subarray.
:- pred quicksort(pred(T, T), int, int, array(T), array(T)).
:- mode quicksort(pred(in, in) is semidet, in, in,
                  array_di, array_uo) is det.
quicksort(Less_than, I_first, I_last, Arr0, Arr) :-
  if (I_last - I_first >= 2)
  then (median_of_three(Less_than, I_first, I_last,
                        Arr0, Arr1, Pivot),

        %% Partition only from I_first to I_last - 1.
        partition(Less_than, Pivot, I_first, I_last - 1,
                  Arr1, Arr2, K),

        %% Now everything that is less than the pivot is to the
        %% left of K.

        %% Put the pivot at K, moving the element that had been there
        %% to the end. If K = I_last, then this element is actually
        %% garbage and will be overwritten with the pivot, which turns
        %% out to be the greatest element. Otherwise, the moved
        %% element is not less than the pivot and so the partitioning
        %% is preserved.
        Arr2^elem(K) = Elem_to_move,
        (Arr2^elem(I_last) := Elem_to_move) = Arr3,
        (Arr3^elem(K) := Pivot) = Arr4,

        %% Sort the subarray on either side of the pivot.
        quicksort(Less_than, I_first, K - 1, Arr4, Arr5),
        quicksort(Less_than, K + 1, I_last, Arr5, Arr))

  else if (I_last - I_first = 1) % Two elements.
  then (Elem_first = Arr0^elem(I_first),
        Elem_last = Arr0^elem(I_last),
        (if Less_than(Elem_first, Elem_last)
         then (Arr = Arr0)
         else ((Arr0^elem(I_first) := Elem_last) = Arr1,
               (Arr1^elem(I_last) := Elem_first) = Arr)))

  else (Arr = Arr0).            % Zero or one element.

%% median_of_three/6 both chooses a pivot and rearranges the array
%% elements so one may partition them from I_first to I_last - 1,
%% leaving the pivot element out of the array.
:- pred median_of_three(pred(T, T), int, int, array(T), array(T), T).
:- mode median_of_three(pred(in, in) is semidet, in, in,
                        array_di, array_uo, out) is det.
median_of_three(Less_than, I_first, I_last, Arr0, Arr, Pivot) :-
  I_middle = I_first + ((I_last - I_first) // 2),
  Elem_first = Arr0^elem(I_first),
  Elem_middle = Arr0^elem(I_middle),
  Elem_last = Arr0^elem(I_last),
  (if pred_xor(Less_than, Less_than,
               Elem_middle, Elem_first,
               Elem_last, Elem_first)
   then (Pivot = Elem_first,
         (if Less_than(Elem_middle, Elem_last)
          then (Arr1 = (Arr0^elem(I_first) := Elem_middle),
                Arr = (Arr1^elem(I_middle) := Elem_last))
          else (Arr = (Arr0^elem(I_first) := Elem_last))))
   else if pred_xor(Less_than, Less_than,
                    Elem_middle, Elem_first,
                    Elem_middle, Elem_last)
   then (Pivot = Elem_middle,
         (if Less_than(Elem_first, Elem_last)
          then (Arr = (Arr0^elem(I_middle) := Elem_last))
          else (Arr1 = (Arr0^elem(I_first) := Elem_last),
                Arr = (Arr1^elem(I_middle) := Elem_first))))
   else (Pivot = Elem_last,
         (if Less_than(Elem_first, Elem_middle)
          then (Arr = Arr0)
          else (Arr1 = (Arr0^elem(I_first) := Elem_middle),
                Arr = (Arr1^elem(I_middle) := Elem_first))))).

:- pred pred_xor(pred(T, T), pred(T, T), T, T, T, T).
:- mode pred_xor(pred(in, in) is semidet,
                 pred(in, in) is semidet,
                 in, in, in, in) is semidet.
pred_xor(P, Q, W, X, Y, Z) :-
  if P(W, X) then (not Q(Y, Z)) else Q(Y, Z).

%%%-------------------------------------------------------------------

:- func example_numbers = list(int).
example_numbers = [1, 3, 9, 5, 8, 6, 5, 0, 1, 7, 9, 8, 6, 4, 2, -28,
                   30, 31, 1, 3, 9, 5, 8, 6, 5, 1, 6, 4, 2, -28, 30,
                   -50, 500, -1234, 1234, 12].

main(!IO) :-
  (array.from_list(example_numbers, Arr0)),
  print_line("", !IO),
  print_line(Arr0, !IO),
  print_line("", !IO),
  print_line("                                               |", !IO),
  print_line("                                               V", !IO),
  print_line("", !IO),
  quicksort(<, Arr0, Arr1),
  print_line(Arr1, !IO),
  print_line("", !IO).

%%%-------------------------------------------------------------------
%%% local variables:
%%% mode: mercury
%%% prolog-indent-width: 2
%%% end:
Output:
$ mmc quicksort_task_for_arrays.m && ./quicksort_task_for_arrays

array([1, 3, 9, 5, 8, 6, 5, 0, 1, 7, 9, 8, 6, 4, 2, -28, 30, 31, 1, 3, 9, 5, 8, 6, 5, 1, 6, 4, 2, -28, 30, -50, 500, -1234, 1234, 12])

                                               |
                                               V

array([-1234, -50, -28, -28, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 8, 8, 8, 9, 9, 9, 12, 30, 30, 31, 500, 1234])

Modula-2

The definition module exposes the interface. This one uses the procedure variable feature to pass a caller defined compare callback function so that it can sort various simple and structured record types.

This Quicksort assumes that you are working with an an array of pointers to an arbitrary type and are not moving the record data itself but only the pointers. The M2 type "ADDRESS" is considered compatible with any pointer type.

The use of type ADDRESS here to achieve genericity is something of a chink the the normal strongly typed flavor of Modula-2. Unlike the other language types, "system" types such as ADDRESS or WORD must be imported explicity from the SYSTEM MODULE. The ISO standard for the "Generic Modula-2" language extension provides genericity without the chink, but most compilers have not implemented this extension.

(*#####################*)
 DEFINITION MODULE QSORT; 
(*#####################*)      

FROM SYSTEM IMPORT ADDRESS;

TYPE CmpFuncPtrs = PROCEDURE(ADDRESS, ADDRESS):INTEGER;

 PROCEDURE QuickSortPtrs(VAR Array:ARRAY OF ADDRESS; N:CARDINAL;
                         Compare:CmpFuncPtrs);
END QSORT.

The implementation module is not visible to clients, so it may be changed without worry so long as it still implements the definition.

Sedgewick suggests that faster sorting will be achieved if you drop back to an insertion sort once the partitions get small.

(*##########################*)
 IMPLEMENTATION MODULE QSORT; 
(*##########################*)

FROM SYSTEM    IMPORT ADDRESS;

CONST SmallPartition  = 9;

(*
NOTE
        1.Reference on QuickSort: "Implementing Quicksort Programs", Robert
          Sedgewick, Communications of the ACM, Oct 78, v21 #10.
*)

(*==============================================================*)
 PROCEDURE QuickSortPtrs(VAR Array:ARRAY OF ADDRESS; N:CARDINAL;
                         Compare:CmpFuncPtrs);
(*==============================================================*)

         (*-----------------------------*)
          PROCEDURE Swap(VAR A,B:ADDRESS);
         (*-----------------------------*)

         VAR  temp :ADDRESS;

         BEGIN

         temp := A; A := B; B := temp;

         END Swap;

         (*-------------------------------*)
          PROCEDURE TstSwap(VAR A,B:ADDRESS);
         (*-------------------------------*)

         VAR  temp   :ADDRESS;

         BEGIN

         IF Compare(A,B) > 0 THEN
            temp := A; A := B; B := temp;
         END;

         END TstSwap;

         (*--------------*)
          PROCEDURE Isort;
         (*--------------*)
         (*
                 Insertion sort.
         *)

         VAR  i,j    :CARDINAL;
              temp   :ADDRESS;

         BEGIN

         IF N < 2 THEN RETURN END;

         FOR i := N-2 TO 0 BY -1 DO
            IF Compare(Array[i],Array[i+1]) > 0 THEN
               temp := Array[i];
               j := i+1;
               REPEAT
                  Array[j-1] := Array[j];
                  INC(j);
               UNTIL (j = N) OR (Compare(Array[j],temp) >= 0);
               Array[j-1] := temp;
            END;
         END;

         END Isort;

         (*----------------------------------*)
          PROCEDURE Quick(left,right:CARDINAL);
         (*----------------------------------*)

         VAR
              i,j,
              second     :CARDINAL;
              Partition  :ADDRESS;

         BEGIN

         IF right > left THEN
            i := left; j := right;

            Swap(Array[left],Array[(left+right) DIV 2]);

            second := left+1;                          (* insure 2nd element is in   *)
            TstSwap(Array[second], Array[right]);      (* the lower part, last elem  *)
            TstSwap(Array[left], Array[right]);        (* in the upper part          *)
            TstSwap(Array[second], Array[left]);       (* THUS, only one test is     *)
                                                       (* needed in repeat loops     *)
            Partition := Array[left];

            LOOP
               REPEAT INC(i) UNTIL Compare(Array[i],Partition) >= 0;
               REPEAT DEC(j) UNTIL Compare(Array[j],Partition) <= 0;
               IF j < i THEN
                  EXIT
               END;
               Swap(Array[i],Array[j]);
            END; (*loop*)
            Swap(Array[left],Array[j]);

            IF (j > 0) AND (j-1-left >= SmallPartition) THEN
               Quick(left,j-1);
            END;
            IF right-i >= SmallPartition THEN
               Quick(i,right);
            END;
         END;

         END Quick;

 BEGIN (* QuickSortPtrs --------------------------------------------------*)

IF N > SmallPartition THEN              (* won't work for 2 elements *)
   Quick(0,N-1);
END;

Isort;

END QuickSortPtrs;

END QSORT.

Modula-3

This code is taken from libm3, which is basically Modula-3's "standard library". Note that this code uses Insertion sort when the array is less than 9 elements long.

GENERIC INTERFACE ArraySort(Elem);

PROCEDURE Sort(VAR a: ARRAY OF Elem.T; cmp := Elem.Compare);

END ArraySort.
GENERIC MODULE ArraySort (Elem);

PROCEDURE Sort (VAR a: ARRAY OF Elem.T;  cmp := Elem.Compare) =
  BEGIN
    QuickSort (a, 0, NUMBER (a), cmp);
    InsertionSort (a, 0, NUMBER (a), cmp);
  END Sort;

PROCEDURE QuickSort (VAR a: ARRAY OF Elem.T;  lo, hi: INTEGER;
                     cmp := Elem.Compare) =
  CONST CutOff = 9;
  VAR i, j: INTEGER;  key, tmp: Elem.T;
  BEGIN
    WHILE (hi - lo > CutOff) DO (* sort a[lo..hi) *)

      (* use median-of-3 to select a key *)
      i := (hi + lo) DIV 2;
      IF cmp (a[lo], a[i]) < 0 THEN
        IF cmp (a[i], a[hi-1]) < 0 THEN
          key := a[i];
        ELSIF cmp (a[lo], a[hi-1]) < 0 THEN
          key := a[hi-1];  a[hi-1] := a[i];  a[i] := key;
        ELSE
          key := a[lo];  a[lo] := a[hi-1];  a[hi-1] := a[i];  a[i] := key;
        END;
      ELSE (* a[lo] >= a[i] *)
        IF cmp (a[hi-1], a[i]) < 0 THEN
          key := a[i];  tmp := a[hi-1];  a[hi-1] := a[lo];  a[lo] := tmp;
        ELSIF cmp (a[lo], a[hi-1]) < 0 THEN
          key := a[lo];  a[lo] := a[i];  a[i] := key;
        ELSE
          key := a[hi-1];  a[hi-1] := a[lo];  a[lo] := a[i];  a[i] := key;
        END;
      END;

      (* partition the array *)
      i := lo+1;  j := hi-2;

      (* find the first hole *)
      WHILE cmp (a[j], key) > 0 DO DEC (j) END;
      tmp := a[j];
      DEC (j);

      LOOP
        IF (i > j) THEN EXIT END;

        WHILE i < hi AND cmp (a[i], key) < 0 DO INC (i) END;
        IF (i > j) THEN EXIT END;
        a[j+1] := a[i];
        INC (i);

        WHILE j > lo AND cmp (a[j], key) > 0 DO DEC (j) END;
        IF (i > j) THEN  IF (j = i-1) THEN  DEC (j)  END;  EXIT  END;
        a[i-1] := a[j];
        DEC (j);
      END;

      (* fill in the last hole *)
      a[j+1] := tmp;
      i := j+2;

      (* then, recursively sort the smaller subfile *)
      IF (i - lo < hi - i)
        THEN  QuickSort (a, lo, i-1, cmp);   lo := i;
        ELSE  QuickSort (a, i, hi, cmp);     hi := i-1;
      END;

    END; (* WHILE (hi-lo > CutOff) *)
  END QuickSort;

PROCEDURE InsertionSort (VAR a: ARRAY OF Elem.T;  lo, hi: INTEGER;
                         cmp := Elem.Compare) =
  VAR j: INTEGER;  key: Elem.T;
  BEGIN
    FOR i := lo+1 TO hi-1 DO
      key := a[i];
      j := i-1;
      WHILE (j >= lo) AND cmp (key, a[j]) < 0 DO
        a[j+1] := a[j];
        DEC (j);
      END;
      a[j+1] := key;
    END;
  END InsertionSort;

BEGIN
END ArraySort.

To use this generic code to sort an array of text, we create two files called TextSort.i3 and TextSort.m3, respectively.

INTERFACE TextSort = ArraySort(Text) END TextSort.
MODULE TextSort = ArraySort(Text) END TextSort.

Then, as an example:

MODULE Main;

IMPORT IO, TextSort;

VAR arr := ARRAY [1..10] OF TEXT {"Foo", "bar", "!ooF", "Modula-3", "hickup", 
                                 "baz", "quuz", "Zeepf", "woo", "Rosetta Code"};

BEGIN
  TextSort.Sort(arr);
  FOR i := FIRST(arr) TO LAST(arr) DO
    IO.Put(arr[i] & "\n");
  END;
END Main.

Mond

Implements the simple quicksort algorithm.

fun quicksort( arr, cmp )
{
    if( arr.length() < 2 )
        return arr;
    
    if( !cmp )
        cmp = ( a, b ) -> a - b;
    
    var a = [ ], b = [ ];
    var pivot = arr[0];
    var len = arr.length();
    
    for( var i = 1; i < len; ++i )
    {
        var item = arr[i];
        
        if( cmp( item, pivot ) < cmp( pivot, item ) )
            a.add( item );
        else
            b.add( item );
    }
    
    a = quicksort( a, cmp );
    b = quicksort( b, cmp );
    
    a.add( pivot );
    
    foreach( var item in b )
        a.add( item );
    
    return a;
}
Usage
var array = [ 532, 16, 153, 3, 63.60, 925, 0.214 ];
var sorted = quicksort( array );

printLn( sorted );
Output:
[
  0.214,
  3,
  16,
  63.6,
  153,
  532,
  925
]

MUMPS

Shows quicksort on a 16-element array.

main 
 new collection,size
 set size=16
 set collection=size for i=0:1:size-1 set collection(i)=$random(size)
 write "Collection to sort:",!!
 zwrite collection ; This will only work on Intersystem's flavor of MUMPS
 do quicksort(.collection,0,collection-1)
 write:$$isSorted(.collection) !,"Collection is sorted:",!!
 zwrite collection  ; This will only work on Intersystem's flavor of MUMPS
 q
quicksort(array,low,high)
 if low<high do  
 . set pivot=$$partition(.array,low,high)
 . do quicksort(.array,low,pivot-1)
 . do quicksort(.array,pivot+1,high)
 q
partition(A,p,r)
 set pivot=A(r)
 set i=p-1
 for j=p:1:r-1 do  
 . i A(j)<=pivot do  
 . . set i=i+1
 . . set helper=A(j)
 . . set A(j)=A(i)
 . . set A(i)=helper
 set helper=A(r)
 set A(r)=A(i+1)
 set A(i+1)=helper
 quit i+1
isSorted(array)
 set sorted=1
 for i=0:1:array-2 do  quit:sorted=0
 . for j=i+1:1:array-1 do  quit:sorted=0
 . . set:array(i)>array(j) sorted=0
 quit sorted
Usage
 do main()
Output:
Collection to sort:

collection=16
collection(0)=4
collection(1)=0
collection(2)=6
collection(3)=14
collection(4)=4
collection(5)=0
collection(6)=10
collection(7)=5
collection(8)=11
collection(9)=4
collection(10)=12
collection(11)=9
collection(12)=13
collection(13)=4
collection(14)=14
collection(15)=0

Collection is sorted:

collection=16
collection(0)=0
collection(1)=0
collection(2)=0
collection(3)=4
collection(4)=4
collection(5)=4
collection(6)=4
collection(7)=5
collection(8)=6
collection(9)=9
collection(10)=10
collection(11)=11
collection(12)=12
collection(13)=13
collection(14)=14
collection(15)=14

Nanoquery

Translation of: Python
def quickSort(arr)
	less = {}
	pivotList = {}
	more = {}
	if len(arr) <= 1
		return arr
	else
		pivot = arr[0]
		for i in arr
			if i < pivot
				less.append(i)
			else if i > pivot
				more.append(i)
			else
				pivotList.append(i)
			end
		end
		
		less = quickSort(less)
		more = quickSort(more)
		
		return less + pivotList + more
	end
end

Nemerle

Translation of: Haskell

A little less clean and concise than Haskell, but essentially the same.

using System;
using System.Console;
using Nemerle.Collections.NList;

module Quicksort
{
    Qsort[T] (x : list[T]) : list[T]
      where T : IComparable
    {
        |[]    => []
        |x::xs => Qsort($[y|y in xs, (y.CompareTo(x) < 0)]) + [x] + Qsort($[y|y in xs, (y.CompareTo(x) > 0)])
    }
    
    Main() : void
    {
        def empty = [];
        def single = [2];
        def several = [2, 6, 1, 7, 3, 9, 4];
        WriteLine(Qsort(empty));
        WriteLine(Qsort(single));
        WriteLine(Qsort(several));
    }
}

NetRexx

This sample implements both the simple and in place algorithms as described in the task's description:

/* NetRexx */
options replace format comments java crossref savelog symbols binary

import java.util.List

placesList = [String -
    "UK  London",     "US  New York",   "US  Boston",     "US  Washington" -
  , "UK  Washington", "US  Birmingham", "UK  Birmingham", "UK  Boston"     -
]
lists = [ -
    placesList -
  , quickSortSimple(String[] Arrays.copyOf(placesList, placesList.length)) -
  , quickSortInplace(String[] Arrays.copyOf(placesList, placesList.length)) -
]

loop ln = 0 to lists.length - 1
  cl = lists[ln]
  loop ct = 0 to cl.length - 1
    say cl[ct]
    end ct
    say
  end ln

return

method quickSortSimple(array = String[]) public constant binary returns String[]

  rl = String[array.length]
  al = List quickSortSimple(Arrays.asList(array))
  al.toArray(rl)

  return rl

method quickSortSimple(array = List) public constant binary returns ArrayList

  if array.size > 1 then do
    less    = ArrayList()
    equal   = ArrayList()
    greater = ArrayList()

    pivot = array.get(Random().nextInt(array.size - 1))
    loop x_ = 0 to array.size - 1
      if (Comparable array.get(x_)).compareTo(Comparable pivot) < 0 then less.add(array.get(x_))
      if (Comparable array.get(x_)).compareTo(Comparable pivot) = 0 then equal.add(array.get(x_))
      if (Comparable array.get(x_)).compareTo(Comparable pivot) > 0 then greater.add(array.get(x_))
      end x_
    less    = quickSortSimple(less)
    greater = quickSortSimple(greater)
    out = ArrayList(array.size)
    out.addAll(less)
    out.addAll(equal)
    out.addAll(greater)

    array = out
    end

  return ArrayList array

method quickSortInplace(array = String[]) public constant binary returns String[]

  rl = String[array.length]
  al = List quickSortInplace(Arrays.asList(array))
  al.toArray(rl)

  return rl

method quickSortInplace(array = List, ixL = int 0, ixR = int array.size - 1) public constant binary returns ArrayList

  if ixL < ixR then do
    ixP = int ixL + (ixR - ixL) % 2
    ixP = quickSortInplacePartition(array, ixL, ixR, ixP)
    quickSortInplace(array, ixL, ixP - 1)
    quickSortInplace(array, ixP + 1, ixR)
    end

  array = ArrayList(array)
  return ArrayList array

method quickSortInplacePartition(array = List, ixL = int, ixR = int, ixP = int) public constant binary returns int

  pivotValue = array.get(ixP)
  rValue     = array.get(ixR)
  array.set(ixP, rValue)
  array.set(ixR, pivotValue)
  ixStore = ixL
  loop i_ = ixL to ixR - 1
    iValue = array.get(i_)
    if (Comparable iValue).compareTo(Comparable pivotValue) < 0 then do
      storeValue = array.get(ixStore)
      array.set(i_, storeValue)
      array.set(ixStore, iValue)
      ixStore = ixStore + 1
      end
    end i_
  storeValue = array.get(ixStore)
  rValue     = array.get(ixR)
  array.set(ixStore, rValue)
  array.set(ixR, storeValue)

  return ixStore
Output:
UK  London
US  New York
US  Boston
US  Washington
UK  Washington
US  Birmingham
UK  Birmingham
UK  Boston

UK  Birmingham
UK  Boston
UK  London
UK  Washington
US  Birmingham
US  Boston
US  New York
US  Washington

UK  Birmingham
UK  Boston
UK  London
UK  Washington
US  Birmingham
US  Boston
US  New York
US  Washington

Nial

quicksort is fork [ >= [1 first,tally],
  pass,
  link [
      quicksort sublist [ < [pass, first], pass ],
      sublist [ match [pass,first],pass ],
      quicksort sublist [ > [pass,first], pass ]
  ]
]

Using it.

|quicksort [5, 8, 7, 4, 3]
=3 4 5 7 8

Nim

Procedural (in place) algorithm

proc quickSortImpl[T](a: var openarray[T], start, stop: int) =
  if stop - start > 0:
    let pivot = a[start]
    var left = start
    var right = stop
    while left <= right:
      while cmp(a[left], pivot) < 0:
        inc(left)
      while cmp(a[right], pivot) > 0:
        dec(right)
      if left <= right:
        swap(a[left], a[right])
        inc(left)
        dec(right)
    quickSortImpl(a, start, right)
    quickSortImpl(a, left, stop)

proc quickSort[T](a: var openarray[T]) =
  quickSortImpl(a, 0, a.len - 1)

var a = @[4, 65, 2, -31, 0, 99, 2, 83, 782]
a.quickSort()
echo a

Functional (inmmutability) algorithm

import sequtils,sugar

func sorted[T](xs:seq[T]): seq[T] =
  if xs.len==0: @[] else: concat(
    xs[1..^1].filter(x=>x<xs[0]).sorted,
    @[xs[0]],
    xs[1..^1].filter(x=>x>=xs[0]).sorted
  )

@[4, 65, 2, -31, 0, 99, 2, 83, 782].sorted.echo
Output:
@[-31, 0, 2, 2, 4, 65, 83, 99, 782]

Nix

let
  qs = l:
    if l == [] then []
    else
      with builtins;
      let x  = head l;
          xs = tail l;
          low  = filter (a: a < x)  xs;
          high = filter (a: a >= x) xs;
      in qs low ++ [x] ++ qs high;
in
  qs [4 65 2 (-31) 0 99 83 782]
Output:
[ -31 0 2 4 65 83 99 782 ]

Objeck

class QuickSort {
  function : Main(args : String[]) ~ Nil {
    array := [1, 3, 5, 7, 9, 8, 6, 4, 2];
    Sort(array);
    each(i : array) {
      array[i]->PrintLine();
    };
  }

  function : Sort(array : Int[]) ~ Nil {
    size := array->Size();
    if(size <= 1) {
      return;
    };
    Sort(array, 0, size - 1);
  }

  function : native : Sort(array : Int[], low : Int, high : Int) ~ Nil {
    i := low; j := high;
    pivot := array[low + (high-low)/2];

    while(i <= j) {
      while(array[i] < pivot) {
        i+=1;
      };

      while(array[j] > pivot) {
        j-=1;
      };

      if (i <= j) {
        temp := array[i];
        array[i] := array[j];
        array[j] := temp;
        i+=1; j-=1;
      };
    };

    if(low < j) {
      Sort(array, low, j);
    };

    if(i < high) {
      Sort(array, i, high);
    };
  }
}

Objective-C

The latest XCode compiler is assumed with ARC enabled.

void quicksortInPlace(NSMutableArray *array, NSInteger first, NSInteger last, NSComparator comparator) {
    if (first >= last) return;
    id pivot = array[(first + last) / 2];
    NSInteger left = first;
    NSInteger right = last;
    while (left <= right) {
        while (comparator(array[left], pivot) == NSOrderedAscending)
            left++;
        while (comparator(array[right], pivot) == NSOrderedDescending)
            right--;
        if (left <= right)
            [array exchangeObjectAtIndex:left++ withObjectAtIndex:right--];
    }
    quicksortInPlace(array, first, right, comparator);
    quicksortInPlace(array, left, last, comparator);
}

NSArray* quicksort(NSArray *unsorted, NSComparator comparator) {
    NSMutableArray *a = [NSMutableArray arrayWithArray:unsorted];
    quicksortInPlace(a, 0, a.count - 1, comparator);
    return a;
}

int main(int argc, const char * argv[]) {
    @autoreleasepool {
        NSArray *a = @[ @1, @3, @5, @7, @9, @8, @6, @4, @2 ];
        NSLog(@"Unsorted: %@", a);
        NSLog(@"Sorted: %@", quicksort(a, ^(id x, id y) { return [x compare:y]; }));
        NSArray *b = @[ @"Emil", @"Peg", @"Helen", @"Juergen", @"David", @"Rick", @"Barb", @"Mike", @"Tom" ];
        NSLog(@"Unsorted: %@", b);
        NSLog(@"Sorted: %@", quicksort(b, ^(id x, id y) { return [x compare:y]; }));
    }
    return 0;
}
Output:
Unsorted: (
    1,
    3,
    5,
    7,
    9,
    8,
    6,
    4,
    2
)
Sorted: (
    1,
    2,
    3,
    4,
    5,
    6,
    7,
    8,
    9
)
Unsorted: (
    Emil,
    Peg,
    Helen,
    Juergen,
    David,
    Rick,
    Barb,
    Mike,
    Tom
)
Sorted: (
    Barb,
    David,
    Emil,
    Helen,
    Juergen,
    Mike,
    Peg,
    Rick,
    Tom
)

OCaml

Declarative and purely functional

let rec quicksort gt = function
  | [] -> []
  | x::xs ->
      let ys, zs = List.partition (gt x) xs in
      (quicksort gt ys) @ (x :: (quicksort gt zs))
 
let _ =
  quicksort (>) [4; 65; 2; -31; 0; 99; 83; 782; 1]

The list based implementation is elegant and perspicuous, but inefficient in time (because partition and @ are linear) and in space (since it creates numerous new lists along the way).

Imperative and in place

Using aliased array slices from the Containers library.

  module Slice = CCArray_slice

  let quicksort : int Array.t -> unit = fun arr ->
    let rec quicksort' : int Slice.t -> unit = fun slice ->
      let len = Slice.length slice in

      if len > 1 then begin
        let pivot = Slice.get slice (len / 2)
        and i = ref 0
        and j = ref (len - 1)
        in
        while !i < !j do
          while Slice.get slice !i < pivot do incr i done;
          while Slice.get slice !j > pivot do decr j done;

          if !i < !j then begin
            let i_val = Slice.get slice !i in
            Slice.set slice !i (Slice.get slice !j);
            Slice.set slice !j i_val;

            incr i;
            decr j;
          end
        done;

        quicksort' (Slice.sub slice 0 !i);
        quicksort' (Slice.sub slice !i (len - !i));
      end
    in
    (* Take the array into an aliased array slice *)
    Slice.full arr |> quicksort'

Octave

Translation of: MATLAB
(The MATLAB version works as is in Octave, provided that the code is put in a file named quicksort.m, and everything below the return must be typed in the prompt of course)
function f=quicksort(v)                       % v must be a column vector
  f = v; n=length(v);
  if(n > 1)
     vl = min(f); vh = max(f);                  % min, max
     p  = (vl+vh)*0.5;                          % pivot
     ia = find(f < p); ib = find(f == p); ic=find(f > p);
     f  = [quicksort(f(ia)); f(ib); quicksort(f(ic))];
  end
endfunction
 
N=30; v=rand(N,1); tic,u=quicksort(v); toc
u

Oforth

Oforth built-in sort uses quick sort algorithm (see lang/collect/ListBuffer.of for implementation) :

[ 5, 8, 2, 3, 4, 1 ] sort

Ol

(define (quicksort l ??)
  (if (null? l)
      '()
      (append (quicksort (filter (lambda (x) (?? (car l) x)) (cdr l)) ??)
              (list (car l))
              (quicksort (filter (lambda (x) (not (?? (car l) x))) (cdr l)) ??))))
 
(print 
   (quicksort (list 1 3 5 9 8 6 4 3 2) >))
(print 
   (quicksort (iota 100) >))
(print 
   (quicksort (iota 100) <))
Output:
(1 2 3 3 4 5 6 8 9)
(0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99)
(99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0)

ooRexx

Translation of: Python
    a = .array~Of(4, 65, 2, -31, 0, 99, 83, 782, 1)
    say 'before:' a~toString( ,', ')
    a = quickSort(a)
    say ' after:' a~toString( ,', ')
    exit

::routine quickSort
    use arg arr -- the array to be sorted
    less = .array~new
    pivotList = .array~new
    more = .array~new
    if arr~items <= 1 then
        return arr
    else do
        pivot = arr[1]
        do i over arr
            if i < pivot then
                less~append(i)
            else if i > pivot then
                more~append(i)
            else
                pivotList~append(i)
        end
        less = quickSort(less)
        more = quickSort(more)
        return less~~appendAll(pivotList)~~appendAll(more)
    end
Output:
before: 4, 65, 2, -31, 0, 99, 83, 782, 1
 after: -31, 0, 1, 2, 4, 65, 83, 99, 782 

Oz

declare
  fun {QuickSort Xs}
     case Xs of nil then nil
     [] Pivot|Xr then
	fun {IsSmaller X} X < Pivot end
        Smaller Larger
     in
	{List.partition Xr IsSmaller ?Smaller ?Larger}
        {Append {QuickSort Smaller} Pivot|{QuickSort Larger}}
     end
  end
in
  {Show {QuickSort [3 1 4 1 5 9 2 6 5]}}

PARI/GP

quickSort(v)={
  if(#v<2, return(v));
  my(less=List(),more=List(),same=List(),pivot);
  pivot=median([v[random(#v)+1],v[random(#v)+1],v[random(#v)+1]]); \\ Middle-of-three
  for(i=1,#v,
    if(v[i]<pivot,
      listput(less, v[i]),
      if(v[i]==pivot, listput(same, v[i]), listput(more, v[i]))
    )
  );
  concat(quickSort(Vec(less)), concat(Vec(same), quickSort(Vec(more))))
};
median(v)={
  vecsort(v)[#v>>1]
};

Pascal

{ X is array of LongInt }
Procedure QuickSort ( Left, Right : LongInt );
Var 
  i, j,
  tmp, pivot : LongInt;         { tmp & pivot are the same type as the elements of array }
Begin
  i:=Left;
  j:=Right;
  pivot := X[(Left + Right) shr 1]; // pivot := X[(Left + Right) div 2] 
  Repeat
    While pivot > X[i] Do inc(i);   // i:=i+1;
    While pivot < X[j] Do dec(j);   // j:=j-1;
    If i<=j Then Begin
      tmp:=X[i];
      X[i]:=X[j];
      X[j]:=tmp;
      dec(j);   // j:=j-1;
      inc(i);   // i:=i+1;
    End;
  Until i>j;
  If Left<j Then QuickSort(Left,j);
  If i<Right Then QuickSort(i,Right);
End;

Perl

sub quick_sort {
    return @_ if @_ < 2;
    my $p = splice @_, int rand @_, 1;
    quick_sort(grep $_ < $p, @_), $p, quick_sort(grep $_ >= $p, @_);
}

my @a = (4, 65, 2, -31, 0, 99, 83, 782, 1);
@a = quick_sort @a;
print "@a\n";

Phix

with javascript_semantics

function quick_sort(sequence x)
--
-- put x into ascending order using recursive quick sort
--
    integer n = length(x)
    if n<2 then
        return x    -- already sorted (trivial case)
    end if
 
    integer mid = floor((n+1)/2),
            last = 1
    object midval = x[mid]
    x[mid] = x[1]
    for i=2 to n do
        object xi = x[i]
        if xi<midval then
            last += 1
            x[i] = x[last]
            x[last] = xi
        end if
    end for
 
    return quick_sort(x[2..last]) & {midval} & quick_sort(x[last+1..n])
end function
 
?quick_sort({5,"oranges","and",3,"apples"})
Output:
{3,5,"and","apples","oranges"}

PHP

function quicksort($arr){
	$lte = $gt = array();
	if(count($arr) < 2){
		return $arr;
	}
	$pivot_key = key($arr);
	$pivot = array_shift($arr);
	foreach($arr as $val){
		if($val <= $pivot){
			$lte[] = $val;
		} else {
			$gt[] = $val;
		}
	}
	return array_merge(quicksort($lte),array($pivot_key=>$pivot),quicksort($gt));
}

$arr = array(1, 3, 5, 7, 9, 8, 6, 4, 2);
$arr = quicksort($arr);
echo implode(',',$arr);
1,2,3,4,5,6,7,8,9
function quickSort(array $array) {
    // base case
    if (empty($array)) {
        return $array;
    }
    $head = array_shift($array);
    $tail = $array;
    $lesser = array_filter($tail, function ($item) use ($head) {
        return $item <= $head;
    });
    $bigger = array_filter($tail, function ($item) use ($head) {
        return $item > $head;
    });
    return array_merge(quickSort($lesser), [$head], quickSort($bigger));
}
$testCase = [1, 4, 8, 2, 8, 0, 2, 8];
$result = quickSort($testCase);
echo sprintf("[%s] ==> [%s]\n", implode(', ', $testCase), implode(', ', $result));
[1, 4, 8, 2, 8, 0, 2, 8] ==> [0, 1, 2, 2, 4, 8, 8, 8]

Picat

Function

qsort([])    = [].
qsort([H|T]) = qsort([E : E in T, E =< H]) 
               ++ [H] ++
               qsort([E : E in T, E > H]).

Recursion

Translation of: Prolog
qsort( [], [] ).
qsort( [H|U], S ) :-
  splitBy(H, U, L, R),
  qsort(L, SL),
  qsort(R, SR),
  append(SL, [H|SR], S).
 
% splitBy( H, U, LS, RS )
% True if LS = { L in U | L <= H }; RS = { R in U | R > H }
splitBy( _, [], [], []).
splitBy( H, [U|T], [U|LS], RS ) :- U =< H, splitBy(H, T, LS, RS).
splitBy( H, [U|T], LS, [U|RS] ) :- U  > H, splitBy(H, T, LS, RS).

PicoLisp

(de quicksort (L)
   (if (cdr L)
      (let Pivot (car L)
          (append (quicksort (filter '((A) (< A Pivot)) (cdr L)))
                             (filter '((A) (= A Pivot))      L )
                  (quicksort (filter '((A) (> A Pivot)) (cdr L)))) )
      L) )

PL/I

DCL (T(20)) FIXED BIN(31);   /* scratch space of length N */

QUICKSORT: PROCEDURE (A,AMIN,AMAX,N) RECURSIVE ;
   DECLARE (A(*))              FIXED BIN(31);
   DECLARE (N,AMIN,AMAX)       FIXED BIN(31) NONASGN;
   DECLARE (I,J,IA,IB,IC,PIV)  FIXED BIN(31);
   DECLARE (P,Q)               POINTER;
   DECLARE (AP(1))             FIXED BIN(31) BASED(P);
   
   IF(N <= 1)THEN RETURN;
   IA=0; IB=0; IC=N+1;
   PIV=(AMIN+AMAX)/2;
   DO I=1 TO N;
      IF(A(I) < PIV)THEN DO;
         IA+=1; A(IA)=A(I);
      END; ELSE IF(A(I) > PIV) THEN DO;
         IC-=1; T(IC)=A(I);
      END; ELSE DO;
         IB+=1; T(IB)=A(I);
      END;
   END;
   DO I=1  TO IB; A(I+IA)=T(I);   END;
   DO I=IC TO N;  A(I)=T(N+IC-I); END;
   P=ADDR(A(IC));
   IC=N+1-IC;
   IF(IA > 1) THEN CALL QUICKSORT(A, AMIN, PIV-1,IA);
   IF(IC > 1) THEN CALL QUICKSORT(AP,PIV+1,AMAX, IC);
   RETURN;
END QUICKSORT;
 MINMAX: PROC(A,AMIN,AMAX,N);
   DCL (AMIN,AMAX) FIXED BIN(31),
       (N,A(*))    FIXED BIN(31) NONASGN ;
   DCL (I,X,Y) FIXED BIN(31);
   
   AMIN=A(N); AMAX=AMIN;
   DO I=1 TO N-1;
      X=A(I); Y=A(I+1);
      IF (X < Y)THEN DO;
         IF (X < AMIN) THEN AMIN=X;
         IF (Y > AMAX) THEN AMAX=Y;
       END; ELSE DO;
          IF (X > AMAX) THEN AMAX=X;
          IF (Y < AMIN) THEN AMIN=Y;
       END;
   END;
   RETURN;
END MINMAX;
CALL MINMAX(A,AMIN,AMAX,N);
CALL QUICKSORT(A,AMIN,AMAX,N);

PowerShell

First solution

Function SortThree( [Array] $data )
{
	if( $data[ 0 ] -gt $data[ 1 ] )
	{
		if( $data[ 0 ] -lt $data[ 2 ] )
		{
			$data = $data[ 1, 0, 2 ]
		} elseif ( $data[ 1 ] -lt $data[ 2 ] ){
			$data = $data[ 1, 2, 0 ]
		} else {
			$data = $data[ 2, 1, 0 ]
		}
	} else {
		if( $data[ 0 ] -gt $data[ 2 ] )
		{
			$data = $data[ 2, 0, 1 ]
		} elseif( $data[ 1 ] -gt $data[ 2 ] ) {
			$data = $data[ 0, 2, 1 ]
		}
	}
	$data
}

Function QuickSort( [Array] $data, $rand = ( New-Object Random ) )
{
	$datal = $data.length
	if( $datal -gt 3 )
	{
		[void] $datal--
		$median = ( SortThree $data[ 0, ( $rand.Next( 1, $datal - 1 ) ), -1 ] )[ 1 ]
		$lt = @()
		$eq = @()
		$gt = @()
		$data | ForEach-Object { if( $_ -lt $median ) { $lt += $_ } elseif( $_ -eq $median ) { $eq += $_ } else { $gt += $_ } }
		$lt = ( QuickSort $lt $rand )
		$gt = ( QuickSort $gt $rand )
		$data = @($lt) + $eq + $gt
	} elseif( $datal -eq 3 ) {
		$data = SortThree( $data )
	} elseif( $datal -eq 2 ) {
		if( $data[ 0 ] -gt $data[ 1 ] )
		{
			$data = $data[ 1, 0 ]
		}
	}
	$data
}

QuickSort 5,3,1,2,4 
QuickSort 'e','c','a','b','d' 
QuickSort 0.5,0.3,0.1,0.2,0.4 
$l = 100; QuickSort ( 1..$l | ForEach-Object { $Rand = New-Object Random }{ $Rand.Next( 0, $l - 1 ) } )


Another solution

function quicksort($array) {
    $less, $equal, $greater = @(), @(), @()
    if( $array.Count -gt 1 ) { 
        $pivot = $array[0]
        foreach( $x in $array) {
            if($x -lt $pivot) { $less += @($x) }
            elseif ($x -eq $pivot) { $equal += @($x)}
            else { $greater += @($x) }
        }    
        $array = (@(quicksort $less) + @($equal) + @(quicksort $greater))
    }
    $array
}
$array = @(60, 21, 19, 36, 63, 8, 100, 80, 3, 87, 11)
"$(quicksort $array)"
The output is: 3 8 11 19 21 36 60 63 80 87 100


Yet another solution

function quicksort($in) {
    $n = $in.count
    switch ($n) {
        0 {}
        1 { $in[0] }
        2 { if ($in[0] -lt $in[1]) {$in[0], $in[1]} else {$in[1], $in[0]} }
        default {
            $pivot = $in | get-random
            $lt = $in | ? {$_ -lt $pivot}
            $eq = $in | ? {$_ -eq $pivot}
            $gt = $in | ? {$_ -gt $pivot}
            @(quicksort $lt) + @($eq) + @(quicksort $gt)
        }
    }
}

Prolog

qsort( [], [] ).
qsort( [H|U], S ) :- splitBy(H, U, L, R), qsort(L, SL), qsort(R, SR), append(SL, [H|SR], S).

% splitBy( H, U, LS, RS )
% True if LS = { L in U | L <= H }; RS = { R in U | R > H }
splitBy( _, [], [], []).
splitBy( H, [U|T], [U|LS], RS ) :- U =< H, splitBy(H, T, LS, RS).
splitBy( H, [U|T], LS, [U|RS] ) :- U  > H, splitBy(H, T, LS, RS).

PureBasic

Procedure qSort(Array a(1), firstIndex, lastIndex)
  Protected  low, high, pivotValue

  low = firstIndex
  high = lastIndex
  pivotValue = a((firstIndex + lastIndex) / 2)
  
  Repeat
    
    While a(low) < pivotValue
      low + 1
    Wend
    
    While a(high) > pivotValue
      high - 1
    Wend
    
    If low <= high
      Swap a(low), a(high)
      low + 1
      high - 1
    EndIf
    
  Until low > high
  
  If firstIndex < high
    qSort(a(), firstIndex, high)
  EndIf
  
  If low < lastIndex
    qSort(a(), low, lastIndex)
  EndIf
EndProcedure

Procedure quickSort(Array a(1))
  qSort(a(),0,ArraySize(a()))
EndProcedure

Python

def quickSort(arr):
    less = []
    pivotList = []
    more = []
    if len(arr) <= 1:
        return arr
    else:
        pivot = arr[0]
        for i in arr:
            if i < pivot:
                less.append(i)
            elif i > pivot:
                more.append(i)
            else:
                pivotList.append(i)
        less = quickSort(less)
        more = quickSort(more)
        return less + pivotList + more

a = [4, 65, 2, -31, 0, 99, 83, 782, 1]
a = quickSort(a)

In a Haskell fashion --

def qsort(L):
    return (qsort([y for y in L[1:] if y <  L[0]]) + 
            [L[0]] + 
            qsort([y for y in L[1:] if y >= L[0]])) if len(L) > 1 else L

More readable, but still using list comprehensions:

def qsort(list):
    if not list:
        return []
    else:
        pivot = list[0]
        less = [x for x in list[1:]   if x <  pivot]
        more = [x for x in list[1:] if x >= pivot]
        return qsort(less) + [pivot] + qsort(more)

More correctly in some tests:

from random import *

def qSort(a):
    if len(a) <= 1:
        return a
    else:
        q = choice(a)
        return qSort([elem for elem in a if elem < q]) + [q] * a.count(q) + qSort([elem for elem in a if elem > q])


def quickSort(a):
    if len(a) <= 1:
        return a
    else:
        less = []
        more = []
        pivot = choice(a)
        for i in a:
            if i < pivot:
                less.append(i)
            if i > pivot:
                more.append(i)
        less = quickSort(less)
        more = quickSort(more)
        return less + [pivot] * a.count(pivot) + more

Returning a new list:

def qsort(array):
    if len(array) < 2:
        return array
    head, *tail = array
    less = qsort([i for i in tail if i < head])
    more = qsort([i for i in tail if i >= head])
    return less + [head] + more

Sorting a list in place:

def quicksort(array):
    _quicksort(array, 0, len(array) - 1)

def _quicksort(array, start, stop):
    if stop - start > 0:
        pivot, left, right = array[start], start, stop
        while left <= right:
            while array[left] < pivot:
                left += 1
            while array[right] > pivot:
                right -= 1
            if left <= right:
                array[left], array[right] = array[right], array[left]
                left += 1
                right -= 1
        _quicksort(array, start, right)
        _quicksort(array, left, stop)

Qi

(define keep
  _    []       -> []
  Pred [A|Rest] -> [A | (keep Pred Rest)] where (Pred A)
  Pred [_|Rest] -> (keep Pred Rest))

(define quicksort
  []    -> []
  [A|R] -> (append (quicksort (keep (>= A) R))
                   [A]
                   (quicksort (keep (< A) R))))

(quicksort [6 8 5 9 3 2 2 1 4 7])

Quackery

Sort a nest of numbers.

[ stack ]                      is less      (     --> s )

[ stack ]                      is same      (     --> s )

[ stack ]                      is more      (     --> s )

[ - -1 1 clamp 1+ ]            is <=>       ( n n --> n )

[ tuck take join swap put ]    is append    ( x s -->   )

[ dup size 2 < if done
  [] less put
  [] same put
  [] more put
  behead swap witheach
    [ 2dup swap <=>
      [ table less same more ]
      append ]
  same append
  less take recurse
  same take join
  more take recurse join ]     is quicksort (   [ --> [ )

[] 10 times [ i^ join ] 3 of
dup       echo cr
quicksort echo cr

Output:

[ 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 ]
[ 0 0 0 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 ]

R

Translation of: Octave
qsort <- function(v) {
  if ( length(v) > 1 ) 
  {
    pivot <- (min(v) + max(v))/2.0                            # Could also use pivot <- median(v)
    c(qsort(v[v < pivot]), v[v == pivot], qsort(v[v > pivot])) 
  } else v
}

N <- 100
vs <- runif(N)
system.time(u <- qsort(vs))
print(u)

Racket

#lang racket
(define (quicksort < l)
  (match l
    ['() '()]
    [(cons x xs) 
     (let-values ([(xs-gte xs-lt) (partition (curry < x) xs)])
       (append (quicksort < xs-lt) 
               (list x) 
               (quicksort < xs-gte)))]))

Examples

(quicksort < '(8 7 3 6 4 5 2))
;returns '(2 3 4 5 6 7 8)
(quicksort string<? '("Mergesort" "Quicksort" "Bubblesort"))
;returns '("Bubblesort" "Mergesort" "Quicksort")

Raku

(formerly Perl 6)

# Empty list sorts to the empty list
 multi quicksort([]) { () }
 
 # Otherwise, extract first item as pivot...
 multi quicksort([$pivot, *@rest]) {
     # Partition.
     my $before := @rest.grep(* before $pivot);
     my $after  := @rest.grep(* !before $pivot);
 
     # Sort the partitions.
     flat quicksort($before), $pivot, quicksort($after)
 }

Note that $before and $after are bound to lazy lists, so the partitions can (at least in theory) be sorted in parallel.

Red

Red []

;;-------------------------------
;; we have to use function not func here, otherwise we'd have to define all "vars" as local...
qsort: function [list][
;;-------------------------------
  if 1 >= length? list [  return list ]
  left: copy [] 
  right: copy []
  eq:   copy []  ;; "equal"
  pivot: list/2 ;; simply choose second element as pivot element
  foreach ele list [
      case [
       ele < pivot [ append left ele ]
       ele > pivot [ append right ele ]
       true       [append eq ele ]
      ]
  ]
  ;; this is the last expression of the function, so coding "return" here is not necessary
  reduce [qsort left eq qsort right]
]


;; lets test the function with an array of 100k integers, range 1..1000  
list: []
loop 100000 [append list random 1000]
t0: now/time/precise  ;; start timestamp
qsort list ;; the return value (block) contains the sorted list, original list has not changed
print ["time1: "  now/time/precise   - t0]  ;; about 1.1 sec on my machine
t0: now/time/precise  
sort list  ;; just for fun time the builtin function also ( also implementation of quicksort ) 
print ["time2: " now/time/precise   - t0]

REXX

version 1

This REXX version doesn't use or modify the program stack.

It is over   400%   times faster then the 2nd REXX version   (using the exact same random numbers).

/*REXX program  sorts  a  stemmed array  using the   quicksort  algorithm.              */
call gen@                                        /*generate the elements for the array. */
call show@   'before sort'                       /*show  the  before   array elements.  */
call qSort       #                               /*invoke the  quicksort  subroutine.   */
call show@   ' after sort'                       /*show  the   after   array elements.  */
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
inOrder: parse arg n; do j=1  for n-1;  k= j+1;  if @.j>@.k  then return 0; end;  return 1
/*──────────────────────────────────────────────────────────────────────────────────────*/
qSort: procedure expose @.; a.1=1; parse arg b.1;  $= 1 /*access @.; get @. size; pivot.*/
       if inOrder(b.1)  then return                     /*Array already in order? Return*/
             do  while  $\==0;   L= a.$;    t= b.$;    $= $ - 1;    if t<2  then iterate
                  H= L + t - 1;    ?= L  +  t % 2
             if @.H<@.L  then if @.?<@.H  then do;  p= @.H;  @.H= @.L;  end
                                          else if @.?>@.L  then     p= @.L
                                                           else do; p= @.?; @.?= @.L;  end
                         else if @.?<@.L  then p=@.L
                                          else if @.?>@.H  then do; p= @.H; @.H= @.L;  end
                                                           else do; p= @.?; @.?= @.L;  end
             j= L+1;                            k= h
                    do forever
                        do j=j         while j<=k & @.j<=p;  end    /*a teeny─tiny loop.*/
                        do k=k  by -1  while j< k & @.k>=p;  end    /*another   "    "  */
                    if j>=k  then leave                             /*segment finished? */
                    _= @.j;   @.j= @.k;   @.k= _                    /*swap J&K elements.*/
                    end   /*forever*/
             $= $ + 1
             k= j - 1;   @.L= @.k;   @.k= p
             if j<=?  then do;  a.$= j;  b.$= H-j+1;  $= $+1;   a.$= L;   b.$= k-L;    end
                      else do;  a.$= L;  b.$= k-L;    $= $+1;   a.$= j;   b.$= H-j+1;  end
             end          /*while $¬==0*/
       return
/*──────────────────────────────────────────────────────────────────────────────────────*/
show@: w= length(#);       do j=1  for #;  say 'element'  right(j,w)  arg(1)":"  @.j;  end
       say copies('▒', maxL + w + 22)            /*display a separator (between outputs)*/
       return
/*──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────*/
gen@:  @.=;   maxL=0                                    /*assign a default value for the array.*/
       @.1  = " Rivers that form part of a (USA) state's border "                                   /*this value is adjusted later to include a prefix & suffix.*/
       @.2  = '='                                                                                   /*this value is expanded later.  */
       @.3  = "Perdido River                       Alabama, Florida"
       @.4  = "Chattahoochee River                 Alabama, Georgia"
       @.5  = "Tennessee River                     Alabama, Kentucky, Mississippi, Tennessee"
       @.6  = "Colorado River                      Arizona, California, Nevada, Baja California (Mexico)"
       @.7  = "Mississippi River                   Arkansas, Illinois, Iowa, Kentucky, Minnesota, Mississippi, Missouri, Tennessee, Louisiana, Wisconsin"
       @.8  = "St. Francis River                   Arkansas, Missouri"
       @.9  = "Poteau River                        Arkansas, Oklahoma"
       @.10 = "Arkansas River                      Arkansas, Oklahoma"
       @.11 = "Red River (Mississippi watershed)   Arkansas, Oklahoma, Texas"
       @.12 = "Byram River                         Connecticut, New York"
       @.13 = "Pawcatuck River                     Connecticut, Rhode Island and Providence Plantations"
       @.14 = "Delaware River                      Delaware, New Jersey, New York, Pennsylvania"
       @.15 = "Potomac River                       District of Columbia, Maryland, Virginia, West Virginia"
       @.16 = "St. Marys River                     Florida, Georgia"
       @.17 = "Chattooga River                     Georgia, South Carolina"
       @.18 = "Tugaloo River                       Georgia, South Carolina"
       @.19 = "Savannah River                      Georgia, South Carolina"
       @.20 = "Snake River                         Idaho, Oregon, Washington"
       @.21 = "Wabash River                        Illinois, Indiana"
       @.22 = "Ohio River                          Illinois, Indiana, Kentucky, Ohio, West Virginia"
       @.23 = "Great Miami River (mouth only)      Indiana, Ohio"
       @.24 = "Des Moines River                    Iowa, Missouri"
       @.25 = "Big Sioux River                     Iowa, South Dakota"
       @.26 = "Missouri River                      Kansas, Iowa, Missouri, Nebraska, South Dakota"
       @.27 = "Tug Fork River                      Kentucky, Virginia, West Virginia"
       @.28 = "Big Sandy River                     Kentucky, West Virginia"
       @.29 = "Pearl River                         Louisiana, Mississippi"
       @.30 = "Sabine River                        Louisiana, Texas"
       @.31 = "Monument Creek                      Maine, New Brunswick (Canada)"
       @.32 = "St. Croix River                     Maine, New Brunswick (Canada)"
       @.33 = "Piscataqua River                    Maine, New Hampshire"
       @.34 = "St. Francis River                   Maine, Quebec (Canada)"
       @.35 = "St. John River                      Maine, Quebec (Canada)"
       @.36 = "Pocomoke River                      Maryland, Virginia"
       @.37 = "Palmer River                        Massachusetts, Rhode Island and Providence Plantations"
       @.38 = "Runnins River                       Massachusetts, Rhode Island and Providence Plantations"
       @.39 = "Montreal River                      Michigan (upper peninsula), Wisconsin"
       @.40 = "Detroit River                       Michigan, Ontario (Canada)"
       @.41 = "St. Clair River                     Michigan, Ontario (Canada)"
       @.42 = "St. Marys River                     Michigan, Ontario (Canada)"
       @.43 = "Brule River                         Michigan, Wisconsin"
       @.44 = "Menominee River                     Michigan, Wisconsin"
       @.45 = "Red River of the North              Minnesota, North Dakota"
       @.46 = "Bois de Sioux River                 Minnesota, North Dakota, South Dakota"
       @.47 = "Pigeon River                        Minnesota, Ontario (Canada)"
       @.48 = "Rainy River                         Minnesota, Ontario (Canada)"
       @.49 = "St. Croix River                     Minnesota, Wisconsin"
       @.50 = "St. Louis River                     Minnesota, Wisconsin"
       @.51 = "Halls Stream                        New Hampshire, Canada"
       @.52 = "Salmon Falls River                  New Hampshire, Maine"
       @.53 = "Connecticut River                   New Hampshire, Vermont"
       @.54 = "Arthur Kill                         New Jersey, New York (tidal strait)"
       @.55 = "Kill Van Kull                       New Jersey, New York (tidal strait)"
       @.56 = "Hudson River (lower part only)      New Jersey, New York"
       @.57 = "Rio Grande                          New Mexico, Texas, Tamaulipas (Mexico), Nuevo Leon (Mexico), Coahuila de Zaragoza (Mexico), Chihuahua (Mexico)"
       @.58 = "Niagara River                       New York, Ontario (Canada)"
       @.59 = "St. Lawrence River                  New York, Ontario (Canada)"
       @.60 = "Poultney River                      New York, Vermont"
       @.61 = "Catawba River                       North Carolina, South Carolina"
       @.62 = "Blackwater River                    North Carolina, Virginia"
       @.63 = "Columbia River                      Oregon, Washington"
                       do #=1  until  @.#==''           /*find how many entries in array,  and */
                       maxL=max(maxL, length(@.#))      /*   also find the maximum width entry.*/
                       end   /*#*/;   #= #-1            /*adjust the highest element number.   */
       @.1= center(@.1, maxL, '-')                      /*   "    "  header information.       */
       @.2= copies(@.2, maxL)                           /*   "    "     "   separator.         */
       return
output   when using the internal default input:
element  1 before sort: ------------------------------------------------ Rivers that form part of a (USA) state's border -------------------------------------------------
element  2 before sort: ==================================================================================================================================================
element  3 before sort: Perdido River                       Alabama, Florida
element  4 before sort: Chattahoochee River                 Alabama, Georgia
element  5 before sort: Tennessee River                     Alabama, Kentucky, Mississippi, Tennessee
element  6 before sort: Colorado River                      Arizona, California, Nevada, Baja California (Mexico)
element  7 before sort: Mississippi River                   Arkansas, Illinois, Iowa, Kentucky, Minnesota, Mississippi, Missouri, Tennessee, Louisiana, Wisconsin
element  8 before sort: St. Francis River                   Arkansas, Missouri
element  9 before sort: Poteau River                        Arkansas, Oklahoma
element 10 before sort: Arkansas River                      Arkansas, Oklahoma
element 11 before sort: Red River (Mississippi watershed)   Arkansas, Oklahoma, Texas
element 12 before sort: Byram River                         Connecticut, New York
element 13 before sort: Pawcatuck River                     Connecticut, Rhode Island and Providence Plantations
element 14 before sort: Delaware River                      Delaware, New Jersey, New York, Pennsylvania
element 15 before sort: Potomac River                       District of Columbia, Maryland, Virginia, West Virginia
element 16 before sort: St. Marys River                     Florida, Georgia
element 17 before sort: Chattooga River                     Georgia, South Carolina
element 18 before sort: Tugaloo River                       Georgia, South Carolina
element 19 before sort: Savannah River                      Georgia, South Carolina
element 20 before sort: Snake River                         Idaho, Oregon, Washington
element 21 before sort: Wabash River                        Illinois, Indiana
element 22 before sort: Ohio River                          Illinois, Indiana, Kentucky, Ohio, West Virginia
element 23 before sort: Great Miami River (mouth only)      Indiana, Ohio
element 24 before sort: Des Moines River                    Iowa, Missouri
element 25 before sort: Big Sioux River                     Iowa, South Dakota
element 26 before sort: Missouri River                      Kansas, Iowa, Missouri, Nebraska, South Dakota
element 27 before sort: Tug Fork River                      Kentucky, Virginia, West Virginia
element 28 before sort: Big Sandy River                     Kentucky, West Virginia
element 29 before sort: Pearl River                         Louisiana, Mississippi
element 30 before sort: Sabine River                        Louisiana, Texas
element 31 before sort: Monument Creek                      Maine, New Brunswick (Canada)
element 32 before sort: St. Croix River                     Maine, New Brunswick (Canada)
element 33 before sort: Piscataqua River                    Maine, New Hampshire
element 34 before sort: St. Francis River                   Maine, Quebec (Canada)
element 35 before sort: St. John River                      Maine, Quebec (Canada)
element 36 before sort: Pocomoke River                      Maryland, Virginia
element 37 before sort: Palmer River                        Massachusetts, Rhode Island and Providence Plantations
element 38 before sort: Runnins River                       Massachusetts, Rhode Island and Providence Plantations
element 39 before sort: Montreal River                      Michigan (upper peninsula), Wisconsin
element 40 before sort: Detroit River                       Michigan, Ontario (Canada)
element 41 before sort: St. Clair River                     Michigan, Ontario (Canada)
element 42 before sort: St. Marys River                     Michigan, Ontario (Canada)
element 43 before sort: Brule River                         Michigan, Wisconsin
element 44 before sort: Menominee River                     Michigan, Wisconsin
element 45 before sort: Red River of the North              Minnesota, North Dakota
element 46 before sort: Bois de Sioux River                 Minnesota, North Dakota, South Dakota
element 47 before sort: Pigeon River                        Minnesota, Ontario (Canada)
element 48 before sort: Rainy River                         Minnesota, Ontario (Canada)
element 49 before sort: St. Croix River                     Minnesota, Wisconsin
element 50 before sort: St. Louis River                     Minnesota, Wisconsin
element 51 before sort: Halls Stream                        New Hampshire, Canada
element 52 before sort: Salmon Falls River                  New Hampshire, Maine
element 53 before sort: Connecticut River                   New Hampshire, Vermont
element 54 before sort: Arthur Kill                         New Jersey, New York (tidal strait)
element 55 before sort: Kill Van Kull                       New Jersey, New York (tidal strait)
element 56 before sort: Hudson River (lower part only)      New Jersey, New York
element 57 before sort: Rio Grande                          New Mexico, Texas, Tamaulipas (Mexico), Nuevo Leon (Mexico), Coahuila de Zaragoza (Mexico), Chihuahua (Mexico)
element 58 before sort: Niagara River                       New York, Ontario (Canada)
element 59 before sort: St. Lawrence River                  New York, Ontario (Canada)
element 60 before sort: Poultney River                      New York, Vermont
element 61 before sort: Catawba River                       North Carolina, South Carolina
element 62 before sort: Blackwater River                    North Carolina, Virginia
element 63 before sort: Columbia River                      Oregon, Washington
▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
element  1  after sort: ------------------------------------------------ Rivers that form part of a (USA) state's border -------------------------------------------------
element  2  after sort: ==================================================================================================================================================
element  3  after sort: Arkansas River                      Arkansas, Oklahoma
element  4  after sort: Arthur Kill                         New Jersey, New York (tidal strait)
element  5  after sort: Big Sandy River                     Kentucky, West Virginia
element  6  after sort: Big Sioux River                     Iowa, South Dakota
element  7  after sort: Blackwater River                    North Carolina, Virginia
element  8  after sort: Bois de Sioux River                 Minnesota, North Dakota, South Dakota
element  9  after sort: Brule River                         Michigan, Wisconsin
element 10  after sort: Byram River                         Connecticut, New York
element 11  after sort: Catawba River                       North Carolina, South Carolina
element 12  after sort: Chattahoochee River                 Alabama, Georgia
element 13  after sort: Chattooga River                     Georgia, South Carolina
element 14  after sort: Colorado River                      Arizona, California, Nevada, Baja California (Mexico)
element 15  after sort: Columbia River                      Oregon, Washington
element 16  after sort: Connecticut River                   New Hampshire, Vermont
element 17  after sort: Delaware River                      Delaware, New Jersey, New York, Pennsylvania
element 18  after sort: Des Moines River                    Iowa, Missouri
element 19  after sort: Detroit River                       Michigan, Ontario (Canada)
element 20  after sort: Great Miami River (mouth only)      Indiana, Ohio
element 21  after sort: Halls Stream                        New Hampshire, Canada
element 22  after sort: Hudson River (lower part only)      New Jersey, New York
element 23  after sort: Kill Van Kull                       New Jersey, New York (tidal strait)
element 24  after sort: Menominee River                     Michigan, Wisconsin
element 25  after sort: Mississippi River                   Arkansas, Illinois, Iowa, Kentucky, Minnesota, Mississippi, Missouri, Tennessee, Louisiana, Wisconsin
element 26  after sort: Missouri River                      Kansas, Iowa, Missouri, Nebraska, South Dakota
element 27  after sort: Montreal River                      Michigan (upper peninsula), Wisconsin
element 28  after sort: Monument Creek                      Maine, New Brunswick (Canada)
element 29  after sort: Niagara River                       New York, Ontario (Canada)
element 30  after sort: Ohio River                          Illinois, Indiana, Kentucky, Ohio, West Virginia
element 31  after sort: Palmer River                        Massachusetts, Rhode Island and Providence Plantations
element 32  after sort: Pawcatuck River                     Connecticut, Rhode Island and Providence Plantations
element 33  after sort: Pearl River                         Louisiana, Mississippi
element 34  after sort: Perdido River                       Alabama, Florida
element 35  after sort: Pigeon River                        Minnesota, Ontario (Canada)
element 36  after sort: Piscataqua River                    Maine, New Hampshire
element 37  after sort: Pocomoke River                      Maryland, Virginia
element 38  after sort: Poteau River                        Arkansas, Oklahoma
element 39  after sort: Potomac River                       District of Columbia, Maryland, Virginia, West Virginia
element 40  after sort: Poultney River                      New York, Vermont
element 41  after sort: Rainy River                         Minnesota, Ontario (Canada)
element 42  after sort: Red River (Mississippi watershed)   Arkansas, Oklahoma, Texas
element 43  after sort: Red River of the North              Minnesota, North Dakota
element 44  after sort: Rio Grande                          New Mexico, Texas, Tamaulipas (Mexico), Nuevo Leon (Mexico), Coahuila de Zaragoza (Mexico), Chihuahua (Mexico)
element 45  after sort: Runnins River                       Massachusetts, Rhode Island and Providence Plantations
element 46  after sort: Sabine River                        Louisiana, Texas
element 47  after sort: Salmon Falls River                  New Hampshire, Maine
element 48  after sort: Savannah River                      Georgia, South Carolina
element 49  after sort: Snake River                         Idaho, Oregon, Washington
element 50  after sort: St. Clair River                     Michigan, Ontario (Canada)
element 51  after sort: St. Croix River                     Maine, New Brunswick (Canada)
element 52  after sort: St. Croix River                     Minnesota, Wisconsin
element 53  after sort: St. Francis River                   Arkansas, Missouri
element 54  after sort: St. Francis River                   Maine, Quebec (Canada)
element 55  after sort: St. John River                      Maine, Quebec (Canada)
element 56  after sort: St. Lawrence River                  New York, Ontario (Canada)
element 57  after sort: St. Louis River                     Minnesota, Wisconsin
element 58  after sort: St. Marys River                     Florida, Georgia
element 59  after sort: St. Marys River                     Michigan, Ontario (Canada)
element 60  after sort: Tennessee River                     Alabama, Kentucky, Mississippi, Tennessee
element 61  after sort: Tug Fork River                      Kentucky, Virginia, West Virginia
element 62  after sort: Tugaloo River                       Georgia, South Carolina
element 63  after sort: Wabash River                        Illinois, Indiana
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version 2

Translation of: Python
The Python code translates very well to ooRexx but here is a way to implement it in classic REXX as well.

This REXX version doesn't handle numbers with leading/trailing/embedded blanks, or textual values that have blanks (or whitespace) in them.

 
/*REXX*/
    a = '4 65 2 -31 0 99 83 782 1'
    do i = 1 to words(a)
        queue word(a, i)
    end
    call quickSort
    parse pull item
    do queued()
        call charout ,item', '
        parse pull item
    end
    say item
    exit

quickSort: procedure
/* In classic Rexx, arguments are passed by value, not by reference so stems
    cannot be passed as arguments nor used as return values.  Putting their
    contents on the external data queue is a way to bypass this issue. */

    /* construct the input stem */
    arr.0 = queued()
    do i = 1 to arr.0
        parse pull arr.i
    end
    less.0 = 0
    pivotList.0 = 0
    more.0 = 0
    if arr.0 <= 1 then do
        if arr.0 = 1 then
            queue arr.1
        return
    end
    else do
        pivot = arr.1
        do i = 1 to arr.0
            item = arr.i
            select
                when item < pivot then do
                    j = less.0 + 1
                    less.j = item
                    less.0 = j
                end
                when item > pivot then do
                    j = more.0 + 1
                    more.j = item
                    more.0 = j
                end
                otherwise
                    j = pivotList.0 + 1
                    pivotList.j = item
                    pivotList.0 = j
            end
        end
    end
    /* recursive call to sort the less. stem */
    do i = 1 to less.0
        queue less.i
    end
    if queued() > 0 then do
        call quickSort
        less.0 = queued()
        do i = 1 to less.0
            parse pull less.i
        end
    end
    /* recursive call to sort the more. stem */
    do i = 1 to more.0
        queue more.i
    end
    if queued() > 0 then do
        call quickSort
        more.0 = queued()
        do i = 1 to more.0
            parse pull more.i
        end
    end
    /* put the contents of all 3 stems on the queue in order */
    do i = 1 to less.0
        queue less.i
    end
    do i = 1 to pivotList.0
        queue pivotList.i
    end
    do i = 1 to more.0
        queue more.i
    end
    return

Ring

# Project : Sorting algorithms/Quicksort

test = [4, 65, 2, -31, 0, 99, 2, 83, 782, 1]
see "before sort:" + nl
showarray(test)
quicksort(test, 1, 10)
see "after sort:" + nl
showarray(test)
 
func quicksort(a, s, n)
       if n < 2 
          return
       ok
       t = s + n - 1
       l = s
       r = t
       p = a[floor((l + r) / 2)]
       while l <= r
               while a[l] < p 
                       l = l + 1
               end
               while a[r] > p
                       r = r - 1
               end
               if l <= r
                  temp = a[l]
                  a[l] = a[r]
                  a[r] = temp
                  l = l + 1
                  r = r - 1
              ok
       end
       if s < r 
          quicksort(a, s, r - s + 1)
       ok
       if l < t 
         quicksort(a, l, t - l + 1 )
       ok

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

Output:

before sort:
4 65 2 -31 0 99 2 83 782 1
after sort:
-31 0 1 2 2 4 65 83 99 782

Ruby

class Array
  def quick_sort
    return self if length <= 1
    pivot = self[0]
    less, greatereq = self[1..-1].partition { |x| x < pivot }
    less.quick_sort + [pivot] + greatereq.quick_sort
  end
end

or

class Array
  def quick_sort
    return self if length <= 1
    pivot = sample
    group = group_by{ |x| x <=> pivot }
    group.default = []
    group[-1].quick_sort + group[0] + group[1].quick_sort
  end
end

or functionally

class Array
  def quick_sort
    h, *t = self
    h ? t.partition { |e| e < h }.inject { |l, r| l.quick_sort + [h] + r.quick_sort } : []
  end
end

Run BASIC

' -------------------------------
' quick sort
' -------------------------------
size = 50
dim s(size)			' array to sort
for i = 1 to size		' fill it with some random numbers
 s(i) = rnd(0) * 100
next i

lft  = 1
rht  = size

[qSort]
  lftHold = lft
  rhtHold = rht
  pivot   = s(lft)
  while lft < rht
    while (s(rht) >= pivot) and (lft < rht) : rht = rht - 1 :wend
    if lft <> rht then
      s(lft) = s(rht)
      lft    = lft + 1
    end if
    while (s(lft) <= pivot) and (lft < rht) : lft = lft + 1 :wend
    if lft <> rht then
      s(rht) = s(lft)
      rht    = rht - 1
    end if
  wend

  s(lft) = pivot
  pivot  = lft
  lft    = lftHold
  rht    = rhtHold
  if lft < pivot then
    rht = pivot - 1
    goto [qSort]
  end if 
 if rht > pivot then
    lft = pivot + 1
    goto [qSort]
 end if

for i = 1 to size
 print i;"-->";s(i)
next i

Rust

fn main() {
    println!("Sort numbers in descending order");
    let mut numbers = [4, 65, 2, -31, 0, 99, 2, 83, 782, 1];
    println!("Before: {:?}", numbers);

    quick_sort(&mut numbers, &|x,y| x > y);
    println!("After:  {:?}\n", numbers);

    println!("Sort strings alphabetically");
    let mut strings = ["beach", "hotel", "airplane", "car", "house", "art"];
    println!("Before: {:?}", strings);

    quick_sort(&mut strings, &|x,y| x < y);
    println!("After:  {:?}\n", strings);
    
    println!("Sort strings by length");
    println!("Before: {:?}", strings);

    quick_sort(&mut strings, &|x,y| x.len() < y.len());
    println!("After:  {:?}", strings);    
}

fn quick_sort<T,F>(v: &mut [T], f: &F) 
    where F: Fn(&T,&T) -> bool
{
    let len = v.len();
    if len >= 2 {
        let pivot_index = partition(v, f);
        quick_sort(&mut v[0..pivot_index], f);
        quick_sort(&mut v[pivot_index + 1..len], f);
    }
}

fn partition<T,F>(v: &mut [T], f: &F) -> usize 
    where F: Fn(&T,&T) -> bool
{
    let len = v.len();
    let pivot_index = len / 2;
    let last_index = len - 1;

    v.swap(pivot_index, last_index);

    let mut store_index = 0;
    for i in 0..last_index {
        if f(&v[i], &v[last_index]) {
            v.swap(i, store_index);
            store_index += 1;
        }
    }

    v.swap(store_index, len - 1);
    store_index
}
Output:
Sort numbers in descending order
Before: [4, 65, 2, -31, 0, 99, 2, 83, 782, 1]
After:  [782, 99, 83, 65, 4, 2, 2, 1, 0, -31]

Sort strings alphabetically
Before: ["beach", "hotel", "airplane", "car", "house", "art"]
After:  ["airplane", "art", "beach", "car", "hotel", "house"]

Sort strings by length
Before: ["airplane", "art", "beach", "car", "hotel", "house"]
After:  ["car", "art", "house", "hotel", "beach", "airplane"]

Or, using functional style (slower than the imperative style but faster than functional style in other languages):

fn main() {
    let numbers = [4, 65, 2, -31, 0, 99, 2, 83, 782, 1];
    println!("{:?}\n", quick_sort(numbers.iter()));
}

fn quick_sort<T, E>(mut v: T) -> Vec<E>
where
    T: Iterator<Item = E>,
    E: PartialOrd,
{
    match v.next() {
        None => Vec::new(),

        Some(pivot) => {
            let (lower, higher): (Vec<_>, Vec<_>) = v.partition(|it| it < &pivot);
            let lower = quick_sort(lower.into_iter());
            let higher = quick_sort(higher.into_iter());
            lower.into_iter()
                .chain(core::iter::once(pivot))
                .chain(higher.into_iter())
                .collect()
        }
    }
}

By the way this implementation needs only O(n) memory because the partition(...) call already "consumes" v. This means that the memory of v will be freed here, before the recursive calls to quick_sort(...). If we tried to use v later, we would get a compilation error.

SASL

Copied from SASL manual, Appendix II, solution (2)(b)

DEF || this rather nice solution is due to Silvio Meira
sort () = ()
sort (a : x) = sort {b <- x; b <= a } ++ a : sort { b <- x; b>a}
?

Sather

class SORT{T < $IS_LT{T}} is

  private afilter(a:ARRAY{T}, cmp:ROUT{T,T}:BOOL, p:T):ARRAY{T} is
    filtered ::= #ARRAY{T};
    loop v ::= a.elt!;
      if cmp.call(v, p) then
        filtered := filtered.append(|v|);
      end;
    end;
    return filtered;
  end;

  private mlt(a, b:T):BOOL is return a < b; end;
  private mgt(a, b:T):BOOL is return a > b; end;
  quick_sort(inout a:ARRAY{T}) is
    if a.size < 2 then return; end;
    pivot ::= a.median;
    left:ARRAY{T} := afilter(a, bind(mlt(_,_)), pivot);
    right:ARRAY{T} := afilter(a, bind(mgt(_,_)), pivot);
    quick_sort(inout left);
    quick_sort(inout right);
    res ::= #ARRAY{T};
    res := res.append(left, |pivot|,  right);
    a := res;
  end;
end;
class MAIN is
  main is
    a:ARRAY{INT} := |10, 9, 8, 7, 6, -10, 5, 4, 656, -11|;
    b ::= a.copy;
    SORT{INT}::quick_sort(inout a);
    #OUT + a + "\n" + b.sort + "\n";
  end;
end;

The ARRAY class has a builtin sorting method, which is quicksort (but under certain condition an insertion sort is used instead), exactly quicksort_range; this implementation is original.

Scala

What follows is a progression on genericity here.

First, a quick sort of a list of integers:

  def sort(xs: List[Int]): List[Int] = xs match {
    case Nil => Nil
    case head :: tail =>
      val (less, notLess) = tail.partition(_ < head) // Arbitrarily partition list in two
      sort(less) ++ (head :: sort(notLess))          // Sort each half
  }

Next, a quick sort of a list of some type T, given a lessThan function:

  def sort[T](xs: List[T], lessThan: (T, T) => Boolean): List[T] = xs match {
    case Nil => Nil
    case x :: xx =>
      val (lo, hi) = xx.partition(lessThan(_, x))
      sort(lo, lessThan) ++ (x :: sort(hi, lessThan))
  }

To take advantage of known orderings, a quick sort of a list of some type T, for which exists an implicit (or explicit) Ordering[T]:

  def sort[T](xs: List[T])(implicit ord: Ordering[T]): List[T] = xs match {
    case Nil => Nil
    case x :: xx =>
      val (lo, hi) = xx.partition(ord.lt(_, x))
      sort[T](lo) ++ (x :: sort[T](hi))
  }

That last one could have worked with Ordering, but Ordering is Java, and doesn't have the less than operator. Ordered is Scala-specific, and provides it.

  def sort[T <: Ordered[T]](xs: List[T]): List[T] = xs match {
    case Nil => Nil
    case x :: xx =>
      val (lo, hi) = xx.partition(_ < x)
      sort(lo) ++ (x :: sort(hi))
  }

What hasn't changed in all these examples is ordering a list. It is possible to write a generic quicksort in Scala, which will order any kind of collection. To do so, however, requires that the type of the collection, itself, be made a parameter to the function. Let's see it below, and then remark upon it:

  def sort[T, C[T] <: scala.collection.TraversableLike[T, C[T]]]
    (xs: C[T])
    (implicit ord: scala.math.Ordering[T],
      cbf: scala.collection.generic.CanBuildFrom[C[T], T, C[T]]): C[T] = {
    // Some collection types can't pattern match
    if (xs.isEmpty) {
      xs
    } else {
      val (lo, hi) = xs.tail.partition(ord.lt(_, xs.head))
      val b = cbf()
      b.sizeHint(xs.size)
      b ++= sort(lo)
      b += xs.head
      b ++= sort(hi)
      b.result()
    }
  }

The type of our collection is "C[T]", and, by providing C[T] as a type parameter to TraversableLike, we ensure C[T] is capable of returning instances of type C[T]. Traversable is the base type of all collections, and TraversableLike is a trait which contains the implementation of most Traversable methods.

We need another parameter, though, which is a factory capable of building a C[T] collection. That is being passed implicitly, so callers to this method do not need to provide them, as the collection they are using should already provide one as such implicitly. Because we need that implicitly, then we need to ask for the "T => Ordering[T]" as well, as the "T <: Ordered[T]" which provides it cannot be used in conjunction with implicit parameters.

The body of the function is from the list variant, since many of the Traversable collection types don't support pattern matching, "+:" or "::".

Scheme

List quicksort

(define (split-by l p k)
  (let loop ((low '())
             (high '())
             (l l))
    (cond ((null? l)
           (k low high))
          ((p (car l))
           (loop low (cons (car l) high) (cdr l)))
          (else
           (loop (cons (car l) low) high (cdr l))))))
 
(define (quicksort l gt?)
  (if (null? l)
      '()
      (split-by (cdr l) 
                (lambda (x) (gt? x (car l)))
                (lambda (low high)
                  (append (quicksort low gt?)
                          (list (car l))
                          (quicksort high gt?))))))

(quicksort '(1 3 5 7 9 8 6 4 2) >)

With srfi-1:

(define (quicksort l gt?)
  (if (null? l)
      '()
      (append (quicksort (filter (lambda (x) (gt? (car l) x)) (cdr l)) gt?)
              (list (car l))
              (quicksort (filter (lambda (x) (not (gt? (car l) x))) (cdr l)) gt?))))

(quicksort '(1 3 5 7 9 8 6 4 2) >)


Vector quicksort (in place)

Works with: Chibi Scheme
Works with: Gauche Scheme
Works with: CHICKEN Scheme version 5.3.0
For CHICKEN:
Library: r7rs


;;;-------------------------------------------------------------------
;;;
;;; Quicksort in R7RS Scheme, working in-place on vectors (that is,
;;; arrays). I closely follow the "better quicksort algorithm"
;;; pseudocode, and thus the code is more "procedural" than
;;; "functional".
;;;
;;; I use a random pivot. If you can generate a random number quickly,
;;; this is a good method, but for this demonstration I have taken a
;;; fast linear congruential generator and made it brutally slow. It's
;;; just a demonstration. :)
;;;

(import (scheme base))
(import (scheme case-lambda))
(import (scheme write))

;;;-------------------------------------------------------------------
;;;
;;; Add "while" loops to the language.
;;;

(define-syntax while
  (syntax-rules ()
    ((_ pred? body ...)
     (let loop ()
       (when pred?
         (begin body ...)
         (loop))))))

;;;-------------------------------------------------------------------
;;;
;;; In-place quicksort.
;;;

(define vector-quicksort!
  (case-lambda

    ;; Use a default pivot selector.
    ((<? vec)
     ;; Random pivot.
     (vector-quicksort! (lambda (vec i-first i-last)
                          (vector-ref vec (randint i-first i-last)))
                        <? vec))

    ;; Specify a pivot selector.
    ((pivot-select <? vec)
     ;;
     ;; The recursion:
     ;;
     (let quicksort! ((i-first 0)
                      (i-last (- (vector-length vec) 1)))
       (let ((n (- i-last i-first -1)))
         (when (> n 1)
           (let* ((pivot (pivot-select vec i-first i-last)))
             (let ((left i-first)
                   (right i-last))
               (while (<= left right)
                 (while (< (vector-ref vec left) pivot)
                   (set! left (+ left 1)))
                 (while (> (vector-ref vec right) pivot)
                   (set! right (- right 1)))
                 (when (<= left right)
                   (let ((lft (vector-ref vec left))
                         (rgt (vector-ref vec right)))
                     (vector-set! vec left rgt)
                     (vector-set! vec right lft)