Sorting algorithms/Counting sort

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

Sorting Algorithm
This is a sorting algorithm.   It may be applied to a set of data in order to sort it.     For comparing various sorts, see compare sorts.   For other sorting algorithms,   see sorting algorithms,   or:

O(n logn) sorts

Heap sort | Merge sort | Patience sort | Quick sort

O(n log²n) sorts
Shell Sort

O(n²) sorts
Bubble sort | Cocktail sort | Cocktail sort with shifting bounds | Comb sort | Cycle sort | Gnome sort | Insertion sort | Selection sort | Strand sort

other sorts
Bead sort | Bogo sort | Common sorted list | Composite structures sort | Custom comparator sort | Counting sort | Disjoint sublist sort | External sort | Jort sort | Lexicographical sort | Natural sorting | Order by pair comparisons | Order disjoint list items | Order two numerical lists | Object identifier (OID) sort | Pancake sort | Quickselect | Permutation sort | Radix sort | Ranking methods | Remove duplicate elements | Sleep sort | Stooge sort | [Sort letters of a string] | Three variable sort | Topological sort | Tree sort

This page uses content from Wikipedia. The original article was at Counting sort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)

Task

Implement the Counting sort.   This is a way of sorting integers when the minimum and maximum value are known.

Pseudocode

function countingSort(array, min, max):
    count: array of (max - min + 1) elements
    initialize count with 0
    for each number in array do
        count[number - min] := count[number - min] + 1
    done
    z := 0
    for i from min to max do
        while ( count[i - min] > 0 ) do
            array[z] := i
            z := z+1
            count[i - min] := count[i - min] - 1
        done
    done

The min and max can be computed apart, or be known a priori.

Note:   we know that, given an array of integers,   its maximum and minimum values can be always found;   but if we imagine the worst case for an array that can hold up to 32 bit integers,   we see that in order to hold the counts,   an array of up to 2³² elements may be needed.   I.E.:   we need to hold a count value up to 2³²-1,   which is a little over 4.2 Gbytes.   So the counting sort is more practical when the range is (very) limited,   and minimum and maximum values are known   a priori.     (However, as a counterexample,   the use of   sparse arrays   minimizes the impact of the memory usage,   as well as removing the need of having to know the minimum and maximum values   a priori.)

11l

Translation of: Python

F countingSort(a, min, max)
   V cnt = [0] * (max - min + 1)
   L(x) a
      cnt[x - min]++

   [Int] result
   L(n) cnt
      result [+]= [L.index + min] * n
   R result

V data = [9, 7, 10, 2, 9, 7, 4, 3, 10, 2, 7, 10, 2, 1, 3, 8, 7, 3, 9, 5, 8, 5, 1, 6, 3, 7, 5, 4, 6, 9, 9, 6, 6, 10, 2, 4, 5, 2, 8, 2, 2, 5, 2, 9, 3, 3, 5, 7, 8, 4]
print(countingSort(data, min(data), max(data)) == sorted(data))

Output:

1B

360 Assembly

*        Counting sort             - 18/04/2020
COUNTS   CSECT
         USING  COUNTS,R13         base register
         B      72(R15)            skip savearea
         DC     17F'0'             savearea
         SAVE   (14,12)            save previous context
         ST     R13,4(R15)         link backward
         ST     R15,8(R13)         link forward
         LR     R13,R15            set addressability
         LA     R6,A               i=1
       DO WHILE=(C,R6,LE,=A(N))    do i=1 to hbound(a)
         L      R8,0(R6)             a(i)
         S      R8,MIN               k=a(i)-min
         LR     R1,R8                k
         SLA    R1,2                 ~
         L      R3,COUNT(R1)         count(k+1)
         LA     R3,1(R3)             +1
         ST     R3,COUNT(R1)         count(k+1)+=1
         LA     R6,4(R6)             i++
       ENDDO    ,                  enddo i
         LA     R7,A               j=1
         L      R6,MIN             i=min 
       DO WHILE=(C,R6,LE,MAX)      do i=min to max
         LR     R8,R6                i
         S      R8,MIN               k=i-min
WHILEC   LR     R1,R8                while k
         SLA    R1,2                 ..... ~
         L      R2,COUNT(R1)         ..... count(k+1)
         LTR    R2,R2                ..... test
         BNP    WHENDC               ..... count(k+1)>0 
         ST     R6,0(R7)               a(j)=i
         LA     R7,4(R7)               j++ 
         LR     R1,R8                  k
         SLA    R1,2                   ~
         L      R3,COUNT(R1)           count(k+1)
         BCTR   R3,0                   -1
         ST     R3,COUNT(R1)           count(k+1)-=1
         B      WHILEC               end while
WHENDC   AH     R6,=H'1'             i++ 
       ENDDO    ,                  enddo i
         LA     R9,PG              @buffer
         LA     R6,A               i=1 
       DO WHILE=(C,R6,LE,=A(N))    do i=1 to hbound(a)
         L      R2,0(R6)             a(i)
         XDECO  R2,XDEC              edit a(i)
         MVC    0(3,R9),XDEC+9       output a(i)
         LA     R9,3(R9)             @buffer++
         LA     R6,4(R6)             i++
       ENDDO    ,                  enddo i
         XPRNT  PG,L'PG            print buffer
         L      R13,4(0,R13)       restore previous savearea pointer
         RETURN (14,12),RC=0       restore registers from calling save
MIN      DC     F'-9'              min
MAX      DC     F'99'              max
A        DC     F'98',F'35',F'15',F'46',F'6',F'64',F'92',F'44'
         DC     F'53',F'21',F'56',F'74',F'13',F'11',F'92',F'70'
         DC     F'43',F'2',F'-7',F'89',F'22',F'82',F'41',F'91'
         DC     F'28',F'51',F'0',F'39',F'29',F'34',F'15',F'26'
N        DC     A((N-A)/L'A)       hbound(a)
PG       DC     CL96' '            buffer
XDEC     DS     CL12               temp fo xdeco
COUNT    DC     200F'0'            count
         REGEQU
         END    COUNTS

Output:

 -7  0  2  6 11 13 15 15 21 22 26 28 29 32 34 35 39 41 43 44 46 51 53 56 64 70 74 82 89 91 92 92

AArch64 Assembly

Works with: as version Raspberry Pi 3B version Buster 64 bits

/* ARM assembly AARCH64 Raspberry PI 3B */
/*  program countSort64.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
#Caution : number strictly positive and not too big
TableNumber:      .quad   1,3,6,2,5,9,10,8,4,5
//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,NBELEMENTS                              // number of élements 
    bl searchMinMax
    mov x3,NBELEMENTS
    bl countSort
    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 table address  r1 return min  r2 return max */
searchMinMax:
    stp x3,lr,[sp,-16]!              // save  registers
    stp x3,x4,[sp,-16]!              // save  registers
    mov x3,x1                        // save size
    mov x1,1<<62                     // min
    mov x2,0                         // max
    mov x4,0                         // index
1:
    ldr x5,[x0,x4,lsl 3]
    cmp x5,x1
    csel x1,x5,x1,lt
    cmp x5,x2
    csel x2,x5,x2,gt
    add x4,x4,1
    cmp x4,x3
    blt 1b
100:
    ldp x4,x5,[sp],16                // restaur  2 registers
    ldp x3,lr,[sp],16                // restaur  2 registers
    ret                              // return to address lr x30
/******************************************************************/
/*     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
/******************************************************************/
/*         count sort                                             */ 
/******************************************************************/
/* x0 contains the address of table */
/* x1 contains the minimum          */
/* x2 contains the maximum          */
/* x3 contains area size            */ 
/* caution : the count area is in the stack. if max is very large, risk of error */ 
countSort:
    stp x1,lr,[sp,-16]!        // save  registers
    stp x2,x3,[sp,-16]!        // save  registers
    stp x4,x5,[sp,-16]!        // save  registers
    stp x6,x7,[sp,-16]!        // save  registers
    stp x8,x9,[sp,-16]!        // save  registers
    sub x3,x3,1                // compute endidx = n - 1
    sub x5,x2,x1               // compute max - min
    add x5,x5,1                // + 1
    lsl x9,x5,3                // 8 bytes by number
    sub sp,sp,x9               // reserve count area in stack
    mov fp,sp                  // frame pointer = stack
    mov x6,0
    mov x4,0
1:                             // loop init stack area 
    str x6,[fp,x4, lsl 3]
    add x4,x4,#1
    cmp x4,x5
    blt 1b
    mov x4,#0                  // indice
2:                             // start loop 2
    ldr x5,[x0,x4,lsl 3]       // load value A[j]
    sub x5,x5,x1               // - min
    ldr x6,[fp,x5,lsl 3]       // load count of value
    add x6,x6,1                // increment counter
    str x6,[fp,x5,lsl 3]       // and store 
    add x4,x4,1                // increment indice
    cmp x4,x3                  // end ?
    ble 2b                     // no -> loop 2
    
    mov x7,0                   // z
    mov x4,x1                  // index = min
3:                             // start loop 3
    sub x6,x4,x1               // compute index - min
    ldr x5,[fp,x6,lsl 3]       // load count
4:                             // start loop 4
    cmp x5,0                   // count <> zéro
    beq 5f
    str x4,[x0,x7,lsl 3]       // store value A[j]
    add x7,x7,1                // increment z
    sub x5,x5,1                // decrement count  
    b  4b

5:
    add x4,x4,1                // increment index
    cmp x4,x2                  // max ?
    ble 3b                     // no -> loop 3
    
    add sp,sp,x9               // stack alignement
 
100:
    ldp x8,x9,[sp],16          // restaur  2 registers
    ldp x6,x7,[sp],16          // restaur  2 registers
    ldp x4,x5,[sp],16          // restaur  2 registers
    ldp x2,x3,[sp],16          // restaur  2 registers
    ldp x1,lr,[sp],16          // restaur  2 registers
    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                       // table address
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"

Action!

DEFINE MAXSIZE="100"

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 CountingSort(INT ARRAY a INT size,min,max)
  INT ARRAY count(MAXSIZE)
  INT n,i,num,z

  n=max-min+1
  FOR i=0 TO n-1
  DO count(i)=0 OD

  FOR i=0 TO size-1
  DO
    num=a(i)
    count(num-min)==+1
  OD

  z=0
  FOR i=min TO max
  DO
    WHILE count(i-min)>0
    DO
      a(z)=i
      z==+1
      count(i-min)==-1
    OD
  OD
RETURN

PROC Test(INT ARRAY a INT size,min,max)
  PrintE("Array before sort:")
  PrintArray(a,size)
  CountingSort(a,size,min,max)
  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,-6,20)
  Test(b,21,-10,10)
  Test(c,8,101,108)
  Test(d,12,-1,1)
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

function countingSort(array:Array, min:int, max:int)
{
	var count:Array = new Array(array.length);
	for(var i:int = 0; i < count.length;i++)count[i]=0;
	for(i = 0; i < array.length; i++)
	{
		count[array[i]-min] ++;
	}
	var j:uint = 0;
	for(i = min; i <= max; i++)
	{
		for(; count[i-min] > 0; count[i-min]--)
			array[j++] = i;
	}
	return array;
}

Ada

with Ada.Text_Io;                 use Ada.Text_Io;
with Ada.Numerics;                use Ada.Numerics;
with Ada.Numerics.Float_Random;   use Ada.Numerics.Float_Random;

procedure Counting_Sort is
   type Data is array (Integer range <>) of Natural;
   procedure Sort(Item : in out Data) is
      minValue, maxValue: Natural;
   begin
      minValue := Item(Item'First); maxValue := Item(Item'First);
      for I in Item'Range loop
         if Item(I) < minValue then minValue := Item(I); end if;
         if Item(I) > maxValue then maxValue := Item(I); end if;
      end loop;
      declare
         Count    : Data(minValue .. maxValue);
         itemPos  : Integer range Item'First - 1 .. Item'Last;
      begin
         for I in Count'Range loop
            Count(I) := 0;
         end loop;
         for I in Item'Range loop
            Count(Item(I)) := Count(Item(I)) + 1;
         end loop;
         itemPos := 0;
         for I in Count'Range loop
            for J in 1..Count(I) loop
               itemPos := itemPos + 1;
               Item(itemPos) := I;
            end loop;
         end loop;
      end;
   end Sort;
   Stuff : Data(1..30);
   Seed  : Generator;
begin
   Put("Before: ");
   for I in Stuff'Range loop
      Stuff(I) := Integer( Float'Truncation( Random( seed ) * 100.0 ) );
      Put(Natural'Image(Stuff(I)));
   end loop;
   New_Line;
   Sort(Stuff);
   Put("After : ");
   for I in Stuff'range loop
      Put(Natural'Image(Stuff(I)));
   end loop;
   New_Line;
end Counting_Sort;

Output:

Before:  45 3 47 5 56 24 95 7 40 65 54 19 63 59 77 99 48 24 12 49 57 86 98 99 97 13 74 44 11 4
After :  3 4 5 7 11 12 13 19 24 24 40 44 45 47 48 49 54 56 57 59 63 65 74 77 86 95 97 98 99 99

ALGOL 68

Translation of: C

Works with: ALGOL 68 version Standard - no extensions to language used

Works with: ALGOL 68G version Any - tested with release mk15-0.8b.fc9.i386

Works with: ELLA ALGOL 68 version Any (with appropriate job cards) - tested with release 1.8.8d.fc9.i386

PROC counting sort mm = (REF[]INT array, INT min, max)VOID:
(
  INT z := LWB array - 1;
  [min:max]INT count;

  FOR i FROM LWB count TO UPB count DO count[i] := 0 OD;
  FOR i TO UPB array DO count[ array[i] ]+:=1 OD;

  FOR i FROM LWB count TO UPB count DO
    FOR j TO count[i] DO array[z+:=1] := i OD
  OD
);

PROC counting sort = (REF[]INT array)VOID:
(
  INT min, max;
  min := max := array[LWB array];

  FOR i FROM LWB array + 1 TO UPB array DO
    IF array[i] < min THEN
      min := array[i]
    ELIF array[i] > max THEN
      max := array[i]
    FI
  OD
);

# Testing (we suppose the oldest human being is less than 140 years old). #

INT n = 100;
INT min age = 0, max age = 140;
main:
(
  [n]INT ages;

  FOR i TO UPB ages DO ages[i] := ENTIER (random * ( max age + 1 ) ) OD;
  counting sort mm(ages, min age, max age);
  FOR i TO UPB ages DO print((" ", whole(ages[i],0))) OD;
  print(new line)
)

Sample output:

0 1 2 3 3 4 4 5 6 7 8 9 9 10 11 12 15 18 18 19 21 21 22 27 33 35 36 38 38 38 38 39 40 40 41 43 44 53 54 55 57 57 58 59 59 60 60 60 60 61 62 64 65 66 67 68 70 71 78 79 82 83 84 84 87 87 88 88 88 89 89 92 93 93 97 98 99 99 100 107 109 114 115 115 118 122 126 127 127 129 129 130 131 133 134 136 136 137 139 139

ARM Assembly

Works with: as version Raspberry Pi

/* ARM assembly Raspberry PI  */
/*  program countSort.s  */
 
 /* REMARK 1 : this program use routines in a include file 
   see task Include a file language arm assembly 
   for the routine affichageMess conversion10 
   see at end of this program the instruction include */
/* for constantes see task include a file in arm assembly */
/************************************/
/* Constantes                       */
/************************************/
.include "../constantes.inc"

.include "../../ficmacros.s"
/*********************************/
/* Initialized data              */
/*********************************/
.data
szMessSortOk:       .asciz "Table sorted.\n"
szMessSortNok:      .asciz "Table not sorted !!!!!.\n"
sMessResult:        .asciz "Value  : @ \n"
szCarriageReturn:   .asciz "\n"
 
.align 4
#Caution : number stritcly positive and not too big
#TableNumber:      .int   1,3,6,2,5,9,10,8,5,7       @ for test 2 sames values
TableNumber:       .int   10,9,8,7,6,5,4,3,2,1
                   .equ NBELEMENTS, (. - TableNumber) / 4
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss
sZoneConv:            .skip 24
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main 
main:                                              @ entry of program 
    ldr r0,iAdrTableNumber                         @ address number table
    mov r1,#NBELEMENTS                             @ number of élements 
    bl searchMinMax                                @ r1=min r2=max
    mov r3,#NBELEMENTS                             @ number of élements 
    bl countSort
    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
 
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 éléments number  */
/* r0 return address r1 return min  r2 return max */
searchMinMax:
    push {r3-r5,lr}                @ save registers
    mov r3,r1                      @ save size
    mov r1,#1<<30                  @ min
    mov r2,#0                      @ max
    mov r4,#0                      @ index
1:
    ldr r5,[r0,r4, lsl #2]         @ load value
    cmp r5,r1                      @ if < min
    movlt r1,r5
    cmp r5,r2                      @ if > max
    movgt r2,r5
    add r4,r4,#1                   @ increment index
    cmp r4,r3                      @ end ?
    blt 1b                         @ no -> loop
100:
    pop {r3-r5,lr}
    bx lr                                              @ return 
/******************************************************************/
/*     control sorted table                                   */ 
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the number of elements  > 0  */
/* r0 return 0  if not sorted   1  if sorted */
isSorted:
    push {r2-r4,lr}                                    @ save registers
    mov r2,#0
    ldr r4,[r0,r2,lsl #2]
1:
    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 
/******************************************************************/
/*         count Sort                                          */ 
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the minimum    */
/* r2 contains the maximun */
/* r3 contains elements number */
/* caution : the count area is in the stack. if max is very large, risk of error */ 
countSort:
    push {r1-r9,lr}           @ save registers
    sub r3,r3,#1              @ compute end index
    sub r5,r2,r1              @ compute max - min
    add r5,r5,#1              @ + 1
    lsl r9,r5,#2              @ 4 bytes by number
    sub sp,sp,r9              @ reserve area on stack 
    mov fp,sp                 @ frame pointer = stack address
    mov r6,#0
    mov r4,#0
1:                            @ loop init stack area 
    str r6,[fp,r4, lsl #2]
    add r4,r4,#1
    cmp r4,r5
    blt 1b
    mov r4,#0                 @ indice
2:                            @ start loop 2
    ldr r5,[r0,r4,lsl #2]     @ load value A[j]
    sub r5,r5,r1              @ - min
    ldr r6,[fp,r5,lsl #2]     @ load count of value
    add r6,r6,#1              @ increment counter
    str r6,[fp,r5,lsl #2]     @ and store 
    add r4,#1                 @ increment indice
    cmp r4,r3                 @ end ?
    ble 2b                    @ no -> loop 2

    mov r7,#0                 @ z
    mov r4,r1                 @ indice = min
    //bl displayTable
3:                            @ loop 3
    sub r6,r4,r1              @ compute index - min
    ldr r5,[fp,r6,lsl #2]     @ load count
4:                            @ loop 4
    cmp r5,#0                 @ cont <> zero
    beq 5f
    str r4,[r0,r7,lsl #2]     @ store value
    add r7,r7,#1              @ increment z
    sub r5,r5,#1              @ decrement count
    b 4b
5:
    add r4,r4,#1              @ decrement indice
    cmp r4,r2                 @ max ?
    ble 3b                    @ no -> loop 3
    
    add sp,sp,r9              @ stack alignement
100:
    pop {r1-r9,lr}
    bx lr                                                  @ return 
 
/******************************************************************/
/*      Display table elements                                */ 
/******************************************************************/
/* r0 contains the address of table */
displayTable:
    push {r0-r3,lr}                                    @ save registers
    mov r2,r0                                          @ table address
    mov r3,#0
1:                                                     @ loop display table
    ldr r0,[r2,r3,lsl #2]
    ldr r1,iAdrsZoneConv                               @ 
    bl conversion10S                                    @ décimal conversion 
    ldr r0,iAdrsMessResult
    ldr r1,iAdrsZoneConv                               @ insert conversion
    bl strInsertAtCharInc
    bl affichageMess                                   @ display message
    add r3,#1
    cmp r3,#NBELEMENTS - 1
    ble 1b
    ldr r0,iAdrszCarriageReturn
    bl affichageMess
    mov r0,r2
100:
    pop {r0-r3,lr}
    bx lr
iAdrsZoneConv:           .int sZoneConv
/***************************************************/
/*      ROUTINES INCLUDE                           */
/***************************************************/
.include "../affichage.inc"

Arturo

countingSort: function [items, minimum, maximum][
    a: new items
    rng: inc maximum - minimum
    cnt: array.of: rng 0 
    z: 0

    loop 0..dec size a 'i [
        mm: a\[i]-minimum
        cnt\[mm]: cnt\[mm] + 1
    ]

    loop minimum..maximum 'i [
        loop 0..dec cnt\[i-minimum] 'j [
            a\[z]: i
            z: z + 1
        ]
    ]
    return a
]

print countingSort [3 1 2 8 5 7 9 4 6] 1 9

Output:

1 2 3 4 5 6 7 8 9

ATS

#include "share/atspre_staload.hats"

(* My ATS solution to the radix sort task includes a counting sort for
   values in 0..255. Here, I will write an implementation that works
   with a given range of keys. *)

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

exception counting_sort_exception of (string)

extern fn {a  : t@ype}
          {tk : tkind}
counting_sort
          {n      : int}
          {keymin, keymax : int | keymin <= keymax}
          (arr    : &array (a, n) >> _,
           n      : size_t n,
           keymin : g1int (tk, keymin),
           keymax : g1int (tk, keymax))
    :<!exn,!wrt> void

extern fn {a  : t@ype}
          {tk : tkind}
counting_sort$key : a -<> g1int tk

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

fn {a  : t@ype}
   {tk : tkind}
count_entries
          {n        : int}
          {keymin, keymax : int | keymin <= keymax}
          (arr      : &array (a, n),
           n        : size_t n,
           keymin   : g1int (tk, keymin),
           keymax   : g1int (tk, keymax),
           bins     : &array (size_t, keymax - keymin + 1))
    :<!exn,!wrt> void =
  $effmask_ntm                (* The for-loop obviously terminates. *)
    begin
      let
        prval () = lemma_array_param arr
        var i : [i : nat | i <= n] size_t i
      in
        for (i := i2sz 0; i <> n; i := succ i)
          let
            val key = counting_sort$key<a> arr[i]
          in
            if key < keymin then
              $raise counting_sort_exception ("key too low")
            else if keymax < key then
              $raise counting_sort_exception ("key too high")
            else
              bins[key - keymin] := succ bins[key - keymin]
          end
      end
    end

fn {}
bin_sizes_to_indices
          {num_bins : int}
          (bins     : &array (size_t, num_bins) >> _,
           num_bins : size_t num_bins)
    :<!wrt> void =
  let
    fun
    loop {i     : nat | i <= num_bins}
         {accum : int}         
         .<num_bins - i>.
         (bins  : &array (size_t, num_bins) >> _,
          i     : size_t i,
          accum : size_t accum)
        :<!wrt> void =
      if i <> num_bins then
        let
          prval () = lemma_g1uint_param i
          val elem = g1ofg0 bins[i]
        in
          if elem = i2sz 0 then
            loop (bins, succ i, accum)
          else
            begin
              bins[i] := accum;
              loop (bins, succ i, accum + elem)
            end
        end

    prval () = lemma_array_param bins
  in
    loop (bins, i2sz 0, i2sz 0)
  end

fn {a  : t@ype}
   {tk : tkind}
rearrange {n : int}
          {keymin, keymax : int | keymin <= keymax}
          (arr    : &array (a, n) >> _,
           temp   : &array (a, n),
           n      : size_t n,
           keymin : g1int (tk, keymin),
           keymax : g1int (tk, keymax),
           bins   : &array (size_t, keymax - keymin + 1))
    :<!wrt> void =
  let
    prval () = lemma_array_param arr

    fun
    loop {i : nat | i <= n}
         .<n - i>.
         (arr  : &array (a, n) >> _,
          temp : &array (a, n),
          bins : &array (size_t, keymax - keymin + 1),
          i    : size_t i)
        :<!wrt> void =
      if i <> n then
        let
          val key = counting_sort$key<a><tk> temp[i]
          val () = $effmask_exn assertloc (keymin <= key)
          val () = $effmask_exn assertloc (key <= keymax)
          val index = g1ofg0 bins[key - keymin]
          prval () = lemma_g1uint_param index
          val () = $effmask_exn assertloc (index < n)
          val () = arr[index] := temp[i]
          val () = bins[key - keymin] := succ index
        in
          loop (arr, temp, bins, succ i)
        end
  in
    loop (arr, temp, bins, i2sz 0)
  end

implement {a} {tk}
counting_sort {n} {keymin, keymax} (arr, n, keymin, keymax) =
  if n <> i2sz 0 then
    let
      stadef num_bins = keymax - keymin + 1
      val num_bins : size_t num_bins = succ (g1i2u (keymax - keymin))

      val @(pf_bins, pfgc_bins | p_bins) =
        array_ptr_alloc<size_t> num_bins
      macdef bins = !p_bins
      val () = array_initize_elt<size_t> (bins, num_bins, i2sz 0)

      val () = count_entries<a><tk> (arr, n, keymin, keymax, bins)
      val () = bin_sizes_to_indices<> (bins, num_bins)

      val @(pf_temp, pfgc_temp | p_temp) = array_ptr_alloc<a> n
      macdef temp = !p_temp
      val () = array_copy<a> (temp, arr, n)
      val () = rearrange<a><tk> (arr, temp, n, keymin, keymax, bins)
      val () = array_ptr_free (pf_temp, pfgc_temp | p_temp)

      val () = array_ptr_free (pf_bins, pfgc_bins | p_bins)
    in
    end

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

typedef record = [i : int | 1 <= i; i <= 9] '(int i, string)

implement
counting_sort$key<record><intknd> entry =
  entry.0

implement
main0 () =
  let
    val data =
      $list{record}
        ('(8, "eight001"),
         '(6, "six00001"),
         '(6, "six00002"),
         '(8, "eight002"),
         '(1, "one00001"),
         '(4, "four0001"),
         '(2, "two00001"),
         '(8, "eight003"))
    var arr : @[record][8]
    val () = array_initize_list<record> (arr, 8, data)
    val () = counting_sort<record> (arr, i2sz 8, 1, 9)

    var i : [i : nat | i <= 8] int i
  in
    for (i := 0; i <> 8; i := succ i)
      println! (arr[i].0, " -> ", arr[i].1)
  end

Output:

$ patscc -DATS_MEMALLOC_GCBDW -O3 counting_sort_task.dats -lgc && ./a.out
1 -> one00001
2 -> two00001
4 -> four0001
6 -> six00001
6 -> six00002
8 -> eight001
8 -> eight002
8 -> eight003

AutoHotkey

contributed by Laszlo on the ahk forum

MsgBox % CountingSort("-1,1,1,0,-1",-1,1)

CountingSort(ints,min,max) {
   Loop % max-min+1
      i := A_Index-1, a%i% := 0
   Loop Parse, ints, `, %A_Space%%A_Tab%
      i := A_LoopField-min, a%i%++
   Loop % max-min+1 {
      i := A_Index-1, v := i+min
      Loop % a%i%
         t .= "," v
   }
   Return SubStr(t,2)
}

BASIC256

# counting sort

n = 10

dim test(n)
test = {4, 65, 2, -31, 0, 99, 2, 83, 782, 1}

mn = -31
mx = 782

dim cnt(mx - mn + 1)  # count is a reserved string function name

# seems initialized as 0
# for i = 1 to n
#   print cnt[i]
# next i

# sort
for i = 0 to n-1
  cnt[test[i] - mn] = cnt[test[i] - mn] + 1
next i

# output
print "original"
for i = 0 to n-1
  print test[i] + " ";
next i
print
print "ordered"
for i = 0 to mx - mn
  if 0 < cnt[i] then  # for i = k to 0  causes error
    for k = 1 to cnt[i]
      print i + mn + " ";
    next k
  endif
next i
print

BBC BASIC

      DIM test%(9)
      test%() = 4, 65, 2, -31, 0, 99, 2, 83, 782, 1
      PROCcountingsort(test%(), -31, 782)
      FOR i% = 0 TO 9
        PRINT test%(i%) ;
      NEXT
      PRINT
      END
      
      DEF PROCcountingsort(a%(), l%, h%)
      LOCAL i%, z%, c%()
      DIM c%(h% - l%)
      FOR i% = 0 TO DIM(a%(),1)
        c%(a%(i%) - l%) += 1
      NEXT
      FOR i% = l% TO h%
        WHILE c%(i% - l%)
          a%(z%) = i%
          z% += 1
          c%(i% - l%) -= 1
        ENDWHILE
      NEXT
      ENDPROC

Output:

       -31         0         1         2         2         4        65        83        99       782

C

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

void counting_sort_mm(int *array, int n, int min, int max)
{
  int i, j, z;

  int range = max - min + 1;
  int *count = malloc(range * sizeof(*array));

  for(i = 0; i < range; i++) count[i] = 0;
  for(i = 0; i < n; i++) count[ array[i] - min ]++;

  for(i = min, z = 0; i <= max; i++) {
    for(j = 0; j < count[i - min]; j++) {
      array[z++] = i;
    }
  } 

  free(count);
}

void min_max(int *array, int n, int *min, int *max)
{
  int i;
  
  *min = *max = array[0];
  for(i=1; i < n; i++) {
    if ( array[i] < *min ) {
      *min = array[i];
    } else if ( array[i] > *max ) {
      *max = array[i];
    }
  }
}

Testing (we suppose the oldest human being is less than 140 years old).

#define N 100
#define MAX_AGE 140
int main()
{
  int ages[N], i;

  for(i=0; i < N; i++) ages[i] = rand()%MAX_AGE;
  counting_sort_mm(ages, N, 0, MAX_AGE);
  for(i=0; i < N; i++) printf("%d\n", ages[i]);
  return EXIT_SUCCESS;
}

C#

using System;
using System.Linq;

namespace CountingSort
{
    class Program
    {
        static void Main(string[] args)
        {
            Random rand = new Random();                                   // Just for creating a test array
            int[] arr = new int[100];                                     // of random numbers
            for (int i = 0; i < 100; i++) { arr[i] = rand.Next(0, 100); } // ...

            int[] newarr = countingSort(arr, arr.Min(), arr.Max());
        }

        private static int[] countingSort(int[] arr, int min, int max)
        {
            int[] count = new int[max - min + 1];
            int z = 0;

            for (int i = 0; i < count.Length; i++) { count[i] = 0; }
            for (int i = 0; i < arr.Length; i++) { count[arr[i] - min]++; }           

            for (int i = min; i <= max; i++)
            {
                while (count[i - min]-- > 0)
                {
                    arr[z] = i;
                    z++;                    
                }
            }
            return arr;
        }
    }
}

C++

#include <iostream>
#include <time.h>
 
//------------------------------------------------------------------------------
using namespace std;
 
//------------------------------------------------------------------------------
const int MAX = 30;
 
//------------------------------------------------------------------------------
class cSort
{
public:
    void sort( int* arr, int len )
    {
	int mi, mx, z = 0; findMinMax( arr, len, mi, mx );
	int nlen = ( mx - mi ) + 1; int* temp = new int[nlen];
	memset( temp, 0, nlen * sizeof( int ) );
 
	for( int i = 0; i < len; i++ ) temp[arr[i] - mi]++;
 
	for( int i = mi; i <= mx; i++ )
	{
	    while( temp[i - mi] )
	    {
		arr[z++] = i;
		temp[i - mi]--;
	    }
	}
 
	delete [] temp;
    }
 
private:
    void findMinMax( int* arr, int len, int& mi, int& mx )
    {
	mi = INT_MAX; mx = 0;
	for( int i = 0; i < len; i++ )
	{
	    if( arr[i] > mx ) mx = arr[i];
	    if( arr[i] < mi ) mi = arr[i];
	}
    }
};
//------------------------------------------------------------------------------
int main( int argc, char* argv[] )
{
    srand( time( NULL ) ); int arr[MAX];
    for( int i = 0; i < MAX; i++ )
	arr[i] = rand() % 140 - rand() % 40 + 1;
 
    for( int i = 0; i < MAX; i++ )
	cout << arr[i] << ", ";
    cout << endl << endl;
 
    cSort s; s.sort( arr, MAX );
 
    for( int i = 0; i < MAX; i++ )
	cout << arr[i] << ", ";
    cout << endl << endl;
 
    return system( "pause" );
}
//------------------------------------------------------------------------------

Output:

105, -21, 20, 5, 3, 25, 101, 116, 82, 5, 88, 80, -9, 26, 62, 118, 131, -31, 3, 3
8, 40, -6, 46, 90, 7, 59, 104, 76, 12, 79,

-31, -21, -9, -6, 3, 3, 5, 5, 7, 12, 20, 25, 26, 38, 40, 46, 59, 62, 76, 79, 80,
 82, 88, 90, 101, 104, 105, 116, 118, 131,

Alternate version

Uses C++11. Compile with

g++ -std=c++11 counting.cpp

#include <algorithm>
#include <iterator>
#include <iostream>
#include <vector>

template<typename ForwardIterator> void counting_sort(ForwardIterator begin,
                                                      ForwardIterator end) {
  auto min_max = std::minmax_element(begin, end);
  if (min_max.first == min_max.second) {  // empty range
    return;
  }
  auto min = *min_max.first;
  auto max = *min_max.second;
  std::vector<unsigned> count((max - min) + 1, 0u);
  for (auto i = begin; i != end; ++i) {
    ++count[*i - min];
  }
  for (auto i = min; i <= max; ++i) {
    for (auto j = 0; j < count[i - min]; ++j) {
      *begin++ = i;
    }
  }
}

int main() {
  int a[] = {100, 2, 56, 200, -52, 3, 99, 33, 177, -199};
  counting_sort(std::begin(a), std::end(a));
  copy(std::begin(a), std::end(a), std::ostream_iterator<int>(std::cout, " "));
  std::cout << "\n";
}

Output:

-199 -52 2 3 33 56 99 100 177 200

Common Lisp

Straightforward implementation of counting sort. By using map and map-into, counting sort can work efficiently on both lists and vectors. The closure given as the second argument to map-into returns the sorted elements of sequence. Because map-into will only call the function as many times as necessary to re-populate sequence, there is no need for bounds checking. counts is declared to have dynamic-extent and so a compiler might stack allocate it.

(defun counting-sort (sequence &optional (min (reduce #'min sequence))
                                         (max (reduce #'max sequence)))
  (let ((i 0)
        (counts (make-array (1+ (- max min)) :initial-element 0
                                             :element-type `(integer 0 ,(length sequence)))))
    (declare (dynamic-extent counts))
    (map nil (lambda (n) (incf (aref counts (- n min)))) sequence)
    (map-into sequence (lambda ()
                         (do () ((plusp (aref counts i)))
                           (incf i))
                         (decf (aref counts i))
                         (+ i min)))))

D

import std.stdio, std.algorithm;

void countingSort(int[] array, in size_t min, in size_t max)
pure nothrow {
    auto count = new int[max - min + 1];
    foreach (number; array)
        count[number - min]++;

    size_t z = 0;
    foreach (i; min .. max + 1)
        while (count[i - min] > 0) {
            array[z] = i;
            z++;
            count[i - min]--;
        }
}

void main() {
    auto data = [9, 7, 10, 2, 9, 7, 4, 3, 10, 2, 7, 10, 2, 1, 3, 8,
                 7, 3, 9, 5, 8, 5, 1, 6, 3, 7, 5, 4, 6, 9, 9, 6, 6,
                 10, 2, 4, 5, 2, 8, 2, 2, 5, 2, 9, 3, 3, 5, 7, 8, 4];

    int dataMin = reduce!min(data);
    int dataMax = reduce!max(data);
    countingSort(data, dataMin, dataMax);
    assert(isSorted(data));
}

Delphi

See Pascal.

E

Straightforward implementation, no particularly interesting characteristics.

def countingSort(array, min, max) {
    def counts := ([0] * (max - min + 1)).diverge()
    for elem in array {
        counts[elem - min] += 1
    }
    var i := -1
    for offset => count in counts {
        def elem := min + offset
        for _ in 1..count {
            array[i += 1] := elem
        }
    }
}

? def arr := [34,6,8,7,4,3,56,7,8,4,3,5,7,8,6,4,4,67,9,0,0,76,467,453,34,435,37,4,34,234,435,3,2,7,4,634,534,735,5,4,6,78,4].diverge()
# value: [34, 6, 8, 7, 4, 3, 56, 7, 8, 4, 3, 5, 7, 8, 6, 4, 4, 67, 9, 0, 0, 76, 467, 453, 34, 435, 37, 4, 34, 234, 435, 3, 2, 7, 4, 634, 534, 735, 5, 4, 6, 78, 4].diverge()

? countingSort(arr, 0, 735)
? arr
# value: [0, 0, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 34, 34, 34, 37, 56, 67, 76, 78, 234, 435, 435, 453, 467, 534, 634, 735].diverge()

EasyLang

proc countsort min max . d[] .
   len count[] max - min + 1
   for n in d[]
      count[n - min + 1] += 1
   .
   z = 1
   for i = min to max
      while count[i - min + 1] > 0
         d[z] = i
         z += 1
         count[i - min + 1] -= 1
      .
   .
.
for i = 1 to 100
   d[] &= randint 1000
.
countsort 1 1000 d[]
print d[]

Eiffel

class
	COUNTING_SORT

feature

	sort (ar: ARRAY [INTEGER]; min, max: INTEGER): ARRAY [INTEGER]
			-- Sorted Array in ascending order.
		require
			ar_not_void: ar /= Void
			lowest_index_zero: ar.lower = 0
		local
			count: ARRAY [INTEGER]
			i, j, z: INTEGER
		do
			create Result.make_empty
			Result.deep_copy (ar)
			create count.make_filled (0, 0, max - min)
			from
				i := 0
			until
				i = Result.count
			loop
				count [Result [i] - min] := count [Result [i] - min] + 1
				i := i + 1
			end
			z := 0
			from
				i := min
			until
				i > max
			loop
				from
					j := 0
				until
					j = count [i - min]
				loop
					Result [z] := i
					z := z + 1
					j := j + 1
				end
				i := i + 1
			end
		ensure
			Result_is_sorted: is_sorted (Result)
		end

feature {NONE}

	is_sorted (ar: ARRAY [INTEGER]): BOOLEAN
			--- Is 'ar' sorted in ascending order?
		require
			ar_not_empty: ar.is_empty = False
		local
			i: INTEGER
		do
			Result := True
			from
				i := ar.lower
			until
				i = ar.upper
			loop
				if ar [i] > ar [i + 1] then
					Result := False
				end
				i := i + 1
			end
		end

end

TEST:

class
	APPLICATION

create
	make

feature

	make
		do
			create test.make_filled (0, 0, 5)
			test [0] := -7
			test [1] := 4
			test [2] := 2
			test [3] := 6
			test [4] := 1
			test [5] := 3
			io.put_string ("unsorted:%N")
			across
				test as t
			loop
				io.put_string (t.item.out + "%T")
			end
			io.new_line
			io.put_string ("sorted:%N")
			create count
			test := count.sort (test, -7, 6)
			across
				test as ar
			loop
				io.put_string (ar.item.out + "%T")
			end
		end

	count: COUNTING_SORT

	test: ARRAY [INTEGER]

end

Output:

unsorted:
-7 4 2 6 1 3
sorted:
-7 1 2 3 4 6

Elena

ELENA 6.x :

import extensions;
import system'routines;
 
extension op
{
    countingSort()
        = self.clone().countingSort(self.MinimalMember, self.MaximalMember);
 
    countingSort(int min, int max)
    {
        int[] count := new int[](max - min + 1);
        int z := 0;
 
        count.populate::(int i => 0);
 
        for(int i := 0; i < self.Length; i += 1) { count[self[i] - min] := count[self[i] - min] + 1 };
 
        for(int i := min; i <= max; i += 1)
        {
            while (count[i - min] > 0)
            {
                self[z] := i;
                z += 1;
 
                count[i - min] := count[i - min] - 1
            }
        }
    }
}
 
public program()
{
    var list := new Range(0, 10).selectBy::(i => randomGenerator.nextInt(10)).toArray();
 
    console.printLine("before:", list.asEnumerable());
    console.printLine("after :", list.countingSort().asEnumerable())
}

Output:

before:6,5,3,1,0,0,7,7,8,2
after :0,0,1,2,3,5,6,7,7,8

Elixir

Works with: Elixir version 1.1

defmodule Sort do
  def counting_sort([]), do: []
  def counting_sort(list) do
    {min, max} = Enum.min_max(list)
    count = Tuple.duplicate(0, max - min + 1)
    counted = Enum.reduce(list, count, fn x,acc ->
      i = x - min
      put_elem(acc, i, elem(acc, i) + 1)
    end)
    Enum.flat_map(min..max, &List.duplicate(&1, elem(counted, &1 - min)))
  end
end

IO.inspect Sort.counting_sort([1,-2,-3,2,1,-5,5,5,4,5,9])

Output:

[-5, -3, -2, 1, 1, 2, 4, 5, 5, 5, 9]

Fortran

Works with: Fortran version 95 and later

module CountingSort
  implicit none

  interface counting_sort
     module procedure counting_sort_mm, counting_sort_a
  end interface

contains

  subroutine counting_sort_a(array)
    integer, dimension(:), intent(inout) :: array

    call counting_sort_mm(array, minval(array), maxval(array))

  end subroutine counting_sort_a

  subroutine counting_sort_mm(array, tmin, tmax)
    integer, dimension(:), intent(inout) :: array
    integer, intent(in) :: tmin, tmax

    integer, dimension(tmin:tmax) :: cnt
    integer :: i, z

    cnt = 0                   ! Initialize to zero to prevent false counts
    FORALL (I=1:size(array))  ! Not sure that this gives any benefit over a DO loop.
        cnt(array(i)) = cnt(array(i))+1
    END FORALL
!
!   ok - cnt contains the frequency of every value
!   let's unwind them into the original array
!
    z = 1
    do i = tmin, tmax
       do while ( cnt(i) > 0 )
          array(z) = i
          z = z + 1
          cnt(i) = cnt(i) - 1
       end do
    end do

  end subroutine counting_sort_mm

end module CountingSort

Testing:

program test
  use CountingSort
  implicit none

  integer, parameter :: n = 100, max_age = 140

  real, dimension(n) :: t
  integer, dimension(n) :: ages

  call random_number(t)
  ages = floor(t * max_age)

  call counting_sort(ages, 0, max_age)

  write(*,'(I4)') ages

end program test

FreeBASIC

' FB 1.05.0 Win64

Function findMax(array() As Integer) As Integer
  Dim length As Integer = UBound(array) - LBound(array) + 1
  If length = 0 Then Return 0 '' say
  If length = 1 Then Return array(LBound(array))
  Dim max As Integer = LBound(array)
  For i As Integer = LBound(array) + 1 To UBound(array) 
    If array(i) > max Then max = array(i)
  Next
  Return max
End Function

Function findMin(array() As Integer) As Integer
  Dim length As Integer = UBound(array) - LBound(array) + 1
  If length = 0 Then Return 0 '' say
  If length = 1 Then Return array(LBound(array))
  Dim min As Integer = LBound(array)
  For i As Integer = LBound(array) + 1 To UBound(array) 
    If array(i) < min Then min = array(i)
  Next
  Return min
End Function

Sub countingSort(array() As Integer, min As Integer, max As Integer)
  Dim count(0 To max - min) As Integer '' all zero by default
  Dim As Integer number, z
  For i As Integer = LBound(array) To UBound(array)
    number = array(i)
    count(number - min) += 1
  Next
  z = LBound(array)
  For i As Integer = min To max
    While count(i - min) > 0
      array(z) = i
      z += 1
      count(i - min) -= 1  
    Wend
  Next
End Sub

Sub printArray(array() As Integer)
  For i As Integer = LBound(array) To UBound(array)
    Print Using "####"; array(i);
  Next
  Print
End Sub

Dim array(1 To 10) As Integer = {4, 65, 2, -31, 0, 99, 2, 83, 782, 1} '' using BBC BASIC example array
Print "Unsorted : ";
printArray(array())
Dim max As Integer = findMax(array())
Dim min As Integer = findMin(array())
countingSort array(), min, max
Print "Sorted   : ";
printArray(array())
Print
Print "Press any key to quit"
Sleep

Output:

Unsorted :    4  65   2 -31   0  99   2  83 782   1
Sorted   :  -31   0   1   2   2   4  65  83  99 782

Go

This version follows the task pseudocode above, with one more optimization.

package main

import (
    "fmt"
    "runtime"
    "strings"
)

var a = []int{170, 45, 75, -90, -802, 24, 2, 66}
var aMin, aMax = -1000, 1000

func main() {
    fmt.Println("before:", a)
    countingSort(a, aMin, aMax)
    fmt.Println("after: ", a)
}

func countingSort(a []int, aMin, aMax int) {
    defer func() {
        if x := recover(); x != nil {
            // one error we'll handle and print a little nicer message
            if _, ok := x.(runtime.Error); ok &&
                strings.HasSuffix(x.(error).Error(), "index out of range") {
                fmt.Printf("data value out of range (%d..%d)\n", aMin, aMax)
                return
            }
            // anything else, we re-panic
            panic(x)
        }
    }()

    count := make([]int, aMax-aMin+1)
    for _, x := range a {
        count[x-aMin]++
    }
    z := 0
    // optimization over task pseudocode:   variable c is used instead of
    // count[i-min].  This saves some unneccessary calculations.
    for i, c := range count {
        for ; c > 0; c-- {
            a[z] = i + aMin
            z++
        }
    }
}

This version follows the WP pseudocode. It can be adapted to sort items other than integers.

package main

import (
    "fmt"
    "runtime"
    "strings"
)

var a = []int{170, 45, 75, -90, -802, 24, 2, 66}
var aMin, aMax = -1000, 1000

func main() {
    fmt.Println("before:", a)
    countingSort(a, aMin, aMax)
    fmt.Println("after: ", a)
}

func countingSort(a []int, aMin, aMax int) {
    defer func() {
        if x := recover(); x != nil {
            // one error we'll handle and print a little nicer message
            if _, ok := x.(runtime.Error); ok &&
                strings.HasSuffix(x.(error).Error(), "index out of range") {
                fmt.Printf("data value out of range (%d..%d)\n", aMin, aMax)
                return
            }
            // anything else, we re-panic
            panic(x)
        }
    }()

    // WP algorithm
    k := aMax - aMin // k is maximum key value. keys range 0..k
    count := make([]int, k+1)
    key := func(v int) int { return v - aMin }
    for _, x := range a {
        count[key(x)]++
    }
    total := 0
    for i, c := range count {
        count[i] = total
        total += c
    }
    output := make([]int, len(a))
    for _, x := range a {
        output[count[key(x)]] = x
        count[key(x)]++
    }
    copy(a, output)
}

Groovy

Solution:

def countingSort = { array ->
    def max = array.max()
    def min = array.min()
    // this list size allows use of Groovy's natural negative indexing
    def count = [0] * (max + 1 + [0, -min].max())
    array.each { count[it] ++ }
    (min..max).findAll{ count[it] }.collect{ [it]*count[it] }.flatten()
}

Test:

println countingSort([23,76,99,58,97,57,35,89,51,38,95,92,24,46,31,24,14,12,57,78,4])
println countingSort([88,18,31,44,4,0,8,81,14,78,20,76,84,33,73,75,82,5,62,70,12,7,1])

println countingSort([15,-3,0,-1,5,4,5,20,-8])
println countingSort([34,6,8,7,4,3,56,7,8,4,3,5,7,8,6,4,4,67,9,0,0,76,467,453,34,435,37,4,34,234,435,3,2,7,4,634,534,-735,5,4,6,78,4])
// slo-o-o-o-ow due to unnecessarily large counting array
println countingSort([10000033,10000006,10000008,10000009,10000013,10000031,10000013,10000032,10000023,10000023,10000011,10000012,10000021])

Output:

[4, 12, 14, 23, 24, 24, 31, 35, 38, 46, 51, 57, 57, 58, 76, 78, 89, 92, 95, 97, 99]
[0, 1, 4, 5, 7, 8, 12, 14, 18, 20, 31, 33, 44, 62, 70, 73, 75, 76, 78, 81, 82, 84, 88]
[-8, -3, -1, 0, 4, 5, 5, 15, 20]
[-735, 0, 0, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 34, 34, 34, 37, 56, 67, 76, 78, 234, 435, 435, 453, 467, 534, 634]
[10000006, 10000008, 10000009, 10000011, 10000012, 10000013, 10000013, 10000021, 10000023, 10000023, 10000031, 10000032, 10000033]

Haskell

We use lists for input and output rather than arrays, since lists are used more often in Haskell.

import Data.Array
 
countingSort :: (Ix n) => [n] -> n -> n -> [n]
countingSort l lo hi = concatMap (uncurry $ flip replicate) count
  where count = assocs . accumArray (+) 0 (lo, hi) . map (\i -> (i, 1)) $ l

Haxe

Translation of: C

class CountingSort {
  public static function sort(arr:Array<Int>) {
    var min = arr[0], max = arr[0];
    for (i in 1...arr.length) {
      if (arr[i] < min)
        min = arr[i];
      else if (arr[i] > max)
        max = arr[i];
    }

    var range = max - min + 1;
    var count = new Array<Int>();
    count.resize(range * arr.length);

    for (i in 0...range) count[i] = 0;
    for (i in 0...arr.length) count[arr[i] - min]++;

    var z = 0;
    for (i in min...(max + 1)) {
      for (j in 0...count[i - min])
        arr[z++] = i;
    }
  }
}

class Main {
  static function main() {
    var integerArray = [1, 10, 2, 5, -1, 5, -19, 4, 23, 0];
    Sys.println('Unsorted Integers: ' + integerArray);
    CountingSort.sort(integerArray);
    Sys.println('Sorted Integers:   ' + integerArray);
  }
}

Output:

Unsorted Integers: [1,10,2,5,-1,5,-19,4,23,0]
Sorted Integers:   [-19,-1,0,1,2,4,5,5,10,23]

Icon and Unicon

The following example is hopefully in the spirit of a counting sort using a hash table as a substituted for a sparse array. Simply translating the pseudo-code would be very un-Iconish (as opposed to Uniconish).

procedure main()                                         #: demonstrate various ways to sort a list and string 
   write("Sorting Demo using ",image(countingsort))                
   writes("  on list : ")
   writex(UL)
   displaysort(countingsort,copy(UL))           
end

procedure countingsort(X)                                #: return sorted list (integers only)
local T,lower,upper

   T := table(0)                                         # hash table as sparse array
   lower := upper := X[1]

   every x := !X do {
      if not ( integer(x) = x ) then runerr(x,101)       # must be integer
      lower >:= x                                        # minimum
      upper <:= x                                        # maximum
      T[x] +:= 1                                         # record x's and duplicates
      }

   every put(X := [],( 1 to T[i := lower to upper], i) ) # reconstitute with correct order and count
   return X
end

Note: This example relies on the supporting procedures 'display sort', and 'writex' from Bubble Sort.

Sample output:

Sorting Demo using procedure countingsort
  on list : [ 3 14 1 5 9 2 6 3 ]
    with op = &null:         [ 1 2 3 3 5 6 9 14 ]   (0 ms)

Io

Translation of: Java

List do(
    countingSort := method(min, max,
        count := list() setSize(max - min + 1) mapInPlace(0)
        foreach(x,
            count atPut(x - min, count at(x - min) + 1)
        )

        j := 0
        for(i, min, max,
            while(count at(i - min) > 0,
                atPut(j, i)
                count atPut(i - min, at(i - min) - 1)
                j = j + 1
            )
        )
    self)

    countingSortInPlace := method(
        countingSort(min, max)
    )
)

l := list(2, 3, -4, 5, 1)
l countingSortInPlace println # ==> list(-4, 1, 2, 3, 5)

A more functional-like version:

List do(
    fill := method(x, size,
        /* Resizes list to a given size and fills it with a given value. */
        setSize(size) mapInPlace(x)
    )

    countingSort := method(min, max,
        count := list() fill(0, max - min + 1)
        foreach(x,
            count atPut(x - min, count at(x - min) + 1)
        )

        return count map(i, x, list() fill(i + min, x)) \
            prepend(list()) reduce(xs, x, xs appendSeq(x))
    )

    countingSortInPlace := method(
        copy(countingSort(min, max))
    )
)

l := list(2, 3, -4, 5, 1)
l countingSortInPlace println # ==> list(-4, 1, 2, 3, 5)

IS-BASIC

100 PROGRAM "CountSrt.bas"
110 RANDOMIZE
120 NUMERIC ARRAY(5 TO 24)
130 CALL INIT(ARRAY)
140 CALL WRITE(ARRAY)
150 CALL COUNTINGSORT(ARRAY)
160 CALL WRITE(ARRAY)
170 DEF INIT(REF A)
180   FOR I=LBOUND(A) TO UBOUND(A)
190     LET A(I)=RND(98)+1
200   NEXT
210 END DEF
220 DEF WRITE(REF A)
230   FOR I=LBOUND(A) TO UBOUND(A)
240     PRINT A(I);
250   NEXT
260   PRINT
270 END DEF
280 DEF FMIN(REF A)
290   LET T=INF
300   FOR I=LBOUND(A) TO UBOUND(A)
310     LET T=MIN(A(I),T)
320   NEXT
330   LET FMIN=T
340 END DEF
350 DEF FMAX(REF A)
360   LET T=-INF
370   FOR I=LBOUND(A) TO UBOUND(A)
380     LET T=MAX(A(I),T)
390   NEXT 
400   LET FMAX=T
410 END DEF
420 DEF COUNTINGSORT(REF A)
430   LET MX=FMAX(A):LET MN=FMIN(A):LET Z=LBOUND(A)
440   NUMERIC COUNT(0 TO MX-MN)
450   FOR I=0 TO UBOUND(COUNT)
460     LET COUNT(I)=0
470   NEXT 
480   FOR I=Z TO UBOUND(A)
490     LET COUNT(A(I)-MN)=COUNT(A(I)-MN)+1
500   NEXT
510   FOR I=MN TO MX
520     DO WHILE COUNT(I-MN)>0
530       LET A(Z)=I:LET Z=Z+1:LET COUNT(I-MN)=COUNT(I-MN)-1
540     LOOP
550   NEXT
560 END DEF

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.

csort =: monad define
  min =. <./y
  cnt =. 0 $~ 1+(>./y)-min
  for_a. y do.
    cnt =. cnt >:@{`[`]}~ a-min
  end.
  cnt # min+i.#cnt
)

Alternative implementation:

csort=: (+/@(=/) # ]) >./ (] + 1 i.@+ -) <./

Example:

   ] a =. _3 + 20 ?@$ 10
_2 _2 6 _1 1 6 _1 4 4 1 4 4 5 _3 5 3 0 _1 3 4

   csort a
_3 _2 _2 _1 _1 _1 0 1 1 3 3 4 4 4 4 4 5 5 6 6

And note that this can be further simplified if the range is known in advance (which could easily be the case -- this sorting mechanism is practical when we have a small fixed range of values that we are sorting). Here, we do not need to inspect the data to find min and max values, since they are already known:

csrt=:2 :0
  (m+i.n-m) (+/@(=/)~ # [) ]
)

or

csrt=:2 :0
   (+/@(=/) # ])&(m+i.n-m)
)

Example:

   (_3 csrt 17) a
_3 _2 _2 _1 _1 _1 0 1 1 3 3 4 4 4 4 4 5 5 6 6

Java

Works with: Java version 1.5+

public static void countingSort(int[] array, int min, int max){
	int[] count= new int[max - min + 1];
	for(int number : array){
		count[number - min]++;
	}
	int z= 0;
	for(int i= min;i <= max;i++){
		while(count[i - min] > 0){
			array[z]= i;
			z++;
			count[i - min]--;
		}
	}
}

JavaScript

var countSort = function(arr, min, max) {
    var i, z = 0, count = [];
    
    for (i = min; i <= max; i++) {
        count[i] = 0;
    }
    
    for (i=0; i < arr.length; i++) {
        count[arr[i]]++;
    }
    
    for (i = min; i <= max; i++) {
        while (count[i]-- > 0) {
            arr[z++] = i;
        }
    }
    
}

Testing:

// Line breaks are in HTML

var i, ages = [];

for (i = 0; i < 100; i++) {
    ages.push(Math.floor(Math.random() * (141)));
}

countSort(ages, 0, 140);

for (i = 0; i < 100; i++) {
    document.write(ages[i] + "<br />");
}

jq

Works with: jq version 1.4

The task description points out the disadvantage of using an array to hold the counts, so in the following implementation, a JSON object is used instead. This ensures the space requirement is just O(length). In jq, this approach is both time and space efficient, except for the small cost of converting integers to strings, which is necessary because JSON keys must be strings.

def countingSort(min; max):
  . as $in
  | reduce range(0;length) as $i
      ( {};
        ($in[$i]|tostring) as $s | .[$s] += 1 # courtesy of the fact that in jq, (null+1) is 1
      )
  | . as $hash
  # now construct the answer:
  | reduce range(min; max+1) as $i
      ( [];
        ($i|tostring) as $s
        | if $hash[$s] == null then .
          else reduce range(0; $hash[$s]) as $j (.; . + [$i])
          end 
      );

Example:

 [1,2,1,4,0,10] | countingSort(0;10)

Output:

$ jq -M -c -n -f counting_sort.jq
[0,1,1,2,4,10]

Julia

Works with: Julia version 0.6

This is a translation of the pseudocode presented in the task description, accounting for the fact that Julia arrays start indexing at 1 rather than zero and taking care to return a result of the same type as the input. Note that cnt has the machine's standard integer type (typically Int64), which need not match that of the input.

function countsort(a::Vector{<:Integer})
    lo, hi = extrema(a)
    b   = zeros(a)
    cnt = zeros(eltype(a), hi - lo + 1)
    for i in a cnt[i-lo+1] += 1 end
    z = 1
    for i in lo:hi
        while cnt[i-lo+1] > 0
            b[z] = i
            z += 1
            cnt[i-lo+1] -= 1
        end
    end
    return b
end

v = rand(UInt8, 20)
println("# unsorted bytes: $v\n -> sorted bytes: $(countsort(v))")
v = rand(1:2 ^ 10, 20)
println("# unsorted integers: $v\n -> sorted integers: $(countsort(v))")

Output:

# unsorted bytes: UInt8[0xcc, 0x67, 0x64, 0xbd, 0x74, 0x18, 0xd2, 0xf8, 0xf1, 0x6c, 0x3e, 0x7c, 0x90, 0x07, 0x48, 0x99, 0xb3, 0xf8, 0x8f, 0x23]
 -> sorted bytes: UInt8[0x07, 0x18, 0x23, 0x3e, 0x48, 0x64, 0x67, 0x6c, 0x74, 0x7c, 0x8f, 0x90, 0x99, 0xb3, 0xbd, 0xcc, 0xd2, 0xf1, 0xf8, 0xf8]
# unsorted integers: [634, 332, 756, 206, 971, 496, 962, 994, 795, 411, 981, 69, 366, 136, 227, 442, 731, 245, 179, 33]
 -> sorted integers: [33, 69, 136, 179, 206, 227, 245, 332, 366, 411, 442, 496, 634, 731, 756, 795, 962, 971, 981, 994]

Kotlin

// version 1.1.0

fun countingSort(array: IntArray) {
    if (array.isEmpty()) return 
    val min = array.min()!!
    val max = array.max()!!
    val count = IntArray(max - min + 1)  // all elements zero by default
    for (number in array) count[number - min]++
    var z = 0
    for (i in min..max) 
        while (count[i - min] > 0) {
            array[z++] = i
            count[i - min]--
        }
}

fun main(args: Array<String>) {
    val array = intArrayOf(4, 65, 2, -31, 0, 99, 2, 83, 782, 1)
    println("Original : ${array.asList()}")
    countingSort(array)
    println("Sorted   : ${array.asList()}")
}

Output:

Original : [4, 65, 2, -31, 0, 99, 2, 83, 782, 1]
Sorted   : [-31, 0, 1, 2, 2, 4, 65, 83, 99, 782]

langur

val .countingSort = fn(.list) {
    val .min, .max = minmax(.list)
    var .count = [0] * (.max-.min+1)
    for .i in .list { .count[.i-.min+1] += 1 }
    for .i of .count { _for ~= .count[.i] * [.i+.min-1] }
}

val .data = [7, 234, -234, 9, 43, 123, 14]

writeln "Original: ", .data
writeln "Sorted  : ", .countingSort(.data)

Output:

Original: [7, 234, -234, 9, 43, 123, 14]
Sorted  : [-234, 7, 9, 14, 43, 123, 234]

Lua

function CountingSort( f )
    local min, max = math.min( unpack(f) ), math.max( unpack(f) )
    local count = {}
    for i = min, max do
        count[i] = 0
    end
    
    for i = 1, #f do
        count[ f[i] ] = count[ f[i] ] + 1
    end
    
    local z = 1
    for i = min, max do
        while count[i] > 0 do
            f[z] = i
            z = z + 1
            count[i] = count[i] - 1
        end
    end
    
end


f = { 15, -3, 0, -1, 5, 4, 5, 20, -8 }

CountingSort( f )

for i in next, f do
    print( f[i] )
end

M4

divert(-1)

define(`randSeed',141592653)
define(`setRand',
   `define(`randSeed',ifelse(eval($1<10000),1,`eval(20000-$1)',`$1'))')
define(`rand_t',`eval(randSeed^(randSeed>>13))')
define(`random',
   `define(`randSeed',eval((rand_t^(rand_t<<18))&0x7fffffff))randSeed')

define(`set',`define(`$1[$2]',`$3')')
define(`get',`defn(`$1[$2]')')
define(`new',`set($1,size,0)')
define(`append',
   `set($1,size,incr(get($1,size)))`'set($1,get($1,size),$2)')
define(`deck',
   `new($1)for(`x',1,$2,
         `append(`$1',eval(random%$3))')')
define(`for',
   `ifelse($#,0,``$0'',
   `ifelse(eval($2<=$3),1,
   `pushdef(`$1',$2)$4`'popdef(`$1')$0(`$1',incr($2),$3,`$4')')')')
define(`show',
   `for(`x',1,get($1,size),`get($1,x) ')')

define(`countingsort',
   `for(`x',$2,$3,`set(count,x,0)')`'for(`x',1,get($1,size),
      `set(count,get($1,x),incr(get(count,get($1,x))))')`'define(`z',
      1)`'for(`x',$2,$3,
         `for(`y',1,get(count,x),
            `set($1,z,x)`'define(`z',incr(z))')')')

divert
deck(`a',10,100)
show(`a')
countingsort(`a',0,99)
show(`a')

Mathematica/Wolfram Language

countingSort[list_] := Module[{minElem, maxElem, count, z, number},
  minElem = Min[list]; maxElem = Max[list];
  count = ConstantArray[0, (maxElem - minElem + 1)];
  For[number = 1, number < Length[list], number++, 
   count[[number - minElem + 1]] = count[[number - minElem + 1]] + 1;] ;
  z = 1;
  For[i = minElem, i < maxElem, i++, 
   While[count[[i - minElem + 1]] > 0,
    list[[z]] = i; z++;
    count[[i - minElem + 1]] = count[[i - minElem + 1]] - 1;]
   ];   
  ]

countingSort@{2, 3, 1, 5, 7, 6}
->{1, 2, 3, 5, 6, 7}

MATLAB / Octave

This is a direct translation of the pseudo-code, except to compensate for MATLAB using 1 based arrays.

function list = countingSort(list)

    minElem = min(list);
    maxElem = max(list);
    
    count = zeros((maxElem-minElem+1),1);
    
    for number = list
        count(number - minElem + 1) = count(number - minElem + 1) + 1;
    end
    
    z = 1;
    
    for i = (minElem:maxElem)     
        while( count(i-minElem +1) > 0)
            list(z) = i;
            z = z+1;
            count(i - minElem + 1) = count(i - minElem + 1) - 1;
        end
    end
    
end %countingSort

Sample Usage:

>> countingSort([4 3 1 5 6 2])

ans =

     1     2     3     4     5     6

MAXScript

fn countingSort arr =
(
	if arr.count < 2 do return arr
	local minVal = amin arr
	local maxVal = amax arr
	local count = for i in 1 to (maxVal-minVal+1) collect 0
	for i in arr do
	(
		count[i-minVal+1] = count[i-minVal+1] + 1
	)
	local z = 1
	for i = minVal to maxVal do
	(
		while (count[i-minVal+1]>0) do
		(
			arr[z] = i
			z += 1
			count[i-minVal+1] = count[i-minVal+1] - 1
		)
		
	)
	return arr
)

Output:

a = for i in 1 to 15 collect random 1 30
#(7, 1, 6, 16, 27, 11, 24, 16, 25, 11, 22, 7, 28, 15, 17)
countingSort a
#(1, 6, 7, 7, 11, 11, 15, 16, 16, 17, 22, 24, 25, 27, 28)

Modula-3

MODULE Counting EXPORTS Main;

IMPORT IO, Fmt;

VAR test := ARRAY [1..8] OF INTEGER {80, 10, 40, 60, 50, 30, 20, 70};

PROCEDURE Sort(VAR a: ARRAY OF INTEGER; min, max: INTEGER) =
  VAR range := max - min + 1;
      count := NEW(REF ARRAY OF INTEGER, range);
      z := 0;
  BEGIN
    FOR i := FIRST(count^) TO LAST(count^) DO
      count[i] := 0;
    END;

    FOR i := FIRST(a) TO LAST(a) DO
      INC(count[a[i] - min]);
    END;

    FOR i := min TO max DO
      WHILE (count[i - min] > 0) DO
        a[z] := i;
        INC(z);
        DEC(count[i - min]);
      END;
    END;
  END Sort;

BEGIN
  IO.Put("Unsorted: ");
  FOR i := FIRST(test) TO LAST(test) DO
    IO.Put(Fmt.Int(test[i]) & " ");
  END;
  IO.Put("\n");
  Sort(test, 10, 80);
  IO.Put("Sorted: ");
  FOR i := FIRST(test) TO LAST(test) DO
    IO.Put(Fmt.Int(test[i]) & " ");
  END;
  IO.Put("\n");
END Counting.

Output:

Unsorted: 80 10 40 60 50 30 20 70 
Sorted: 10 20 30 40 50 60 70 80 

Nanoquery

Translation of: Java

def countingSort(array, min, max)
        count = {0} * (max - min + 1)

        for number in array
                count[number - min] += 1
        end

        z = 0
        for i in range(min, max)
                while count[i - min] > 0
                        array[z] = i
                        z += 1
                        count[i - min] -= 1;
                end
        end
end

NetRexx

Version 1

An almost direct implementation of the pseudocode.

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

import java.util.List

icounts = [int -
      1,   3,   6,   2,   7,  13,  20,  12,  21,  11 -
  ,  22,  10,  23,   9,  24,   8,  25,  43,  62,  42 - 
  ,  63,  41,  18,  42,  17,  43,  16,  44,  15,  45 -
  ,  14,  46,  79, 113,  78, 114,  77,  39,  78,  38 -
]
scounts = int[icounts.length]

System.arraycopy(icounts, 0, scounts, 0, icounts.length)
lists = [ -
     icounts -
  ,  countingSort(scounts) -
]

loop ln = 0 to lists.length - 1
  cl = lists[ln]
  rep = Rexx('')
  loop ct = 0 to cl.length - 1
    rep = rep cl[ct]
    end ct
    say '['rep.strip.changestr(' ', ',')']'
  end ln

return

method getMin(array = int[]) public constant binary returns int

  amin = Integer.MAX_VALUE
  loop x_ = 0 to array.length - 1
    if array[x_] < amin then
      amin = array[x_]
    end x_

  return amin

method getMax(array = int[]) public constant binary returns int

  amax = Integer.MIN_VALUE
  loop x_ = 0 to array.length - 1
    if array[x_] > amax then
      amax = array[x_]
    end x_

  return amax

method countingSort(array = int[], amin = getMin(array), amax = getMax(array)) public constant binary returns int[]

  count = int[amax - amin + 1]
  loop nr = 0 to array.length - 1
    numbr = array[nr]
    count[numbr - amin] = count[numbr - amin] + 1
    end nr

  z_ = 0

  loop i_ = amin to amax
    loop label count while count[i_ - amin] > 0
      array[z_] = i_
      z_ = z_ + 1
      count[i_ - amin] = count[i_ - amin] - 1
      end count
    end i_

  return array

Output:

[1,3,6,2,7,13,20,12,21,11,22,10,23,9,24,8,25,43,62,42,63,41,18,42,17,43,16,44,15,45,14,46,79,113,78,114,77,39,78,38]
[1,2,3,6,7,8,9,10,11,12,13,14,15,16,17,18,20,21,22,23,24,25,38,39,41,42,42,43,43,44,45,46,62,63,77,78,78,79,113,114]

Version 2

A more Rexx-like (and shorter) version. Due to NetRexx's built in indexed string capability, negative values are also easily supported.

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

runSample(arg)
return

-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method countingSort(icounts) public constant

  parse getMinMax(icounts) amin amax
  array = 0
  loop ix = 1 to icounts.words
    iw = icounts.word(ix) + 0
    array[iw] = array[iw] + 1
    end ix
  ocounts = ''
  loop ix = amin to amax
    if array[ix] = 0 then iterate ix
    loop for array[ix]
      ocounts = ocounts ix
      end
    end ix
  return ocounts.space

-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method getMinMax(icounts) public constant

  amin = Long.MAX_VALUE
  amax = Long.MIN_VALUE
  loop x_ = 1 to icounts.words
    amin = icounts.word(x_).min(amin)
    amax = icounts.word(x_).max(amax)
    end x_

  return amin amax

-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method runSample(arg) public static
parse arg icounts
if icounts = '' then -
  icounts = - 
    ' 1   3   6   2   7  13  20  12  21  11  22  10  23   9  24   8  25  43  62  42' - 
    '63  41  18  42  17  43  16  44  15  45  14  46  79 113  78 114  77  39  78  38' -
    '0  -200 -6  -10 -0' -
    ''

say icounts.space
say countingSort(icounts)

return

Output:

1 3 6 2 7 13 20 12 21 11 22 10 23 9 24 8 25 43 62 42 63 41 18 42 17 43 16 44 15 45 14 46 79 113 78 114 77 39 78 38 0 -200 -6 -10 -0
-200 -10 -6 0 0 1 2 3 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21 22 23 24 25 38 39 41 42 42 43 43 44 45 46 62 63 77 78 78 79 113 114

Nim

proc countingSort[T](a: var openarray[T]; min, max: int) =
  let range = max - min + 1
  var count = newSeq[T](range)
  var z = 0

  for i in 0 ..< a.len: inc count[a[i] - min]

  for i in min .. max:
    for j in 0 ..< count[i - min]:
      a[z] = i
      inc z

var a = @[5, 3, 1, 7, 4, 1, 1, 20]
countingSort(a, 1, 20)
echo a

Output:

@[1, 1, 1, 3, 4, 5, 7, 20]

Oberon-2

Translation of: Modula-3

MODULE CS;

IMPORT Out;

VAR
  A:ARRAY 8 OF INTEGER;
  I:LONGINT;

PROCEDURE Init(VAR A:ARRAY OF INTEGER);
BEGIN
  A[0] := 80; A[1] := 10; A[2] := 40; A[3] := 60;
  A[4] := 50; A[5] := 30; A[6] := 20; A[7] := 70;
END Init;

PROCEDURE CountingSort(VAR A:ARRAY OF INTEGER; Min,Max:INTEGER);
VAR
  I,Z,Range:LONGINT;
  Count:POINTER TO ARRAY OF INTEGER; 
BEGIN
  Range := Max - Min + 1;
  NEW(Count, Range);
  Z := 0;
  FOR I := 0 TO LEN(A)-1 DO
    INC(Count[A[I] - Min]);
  END;
  FOR I := Min TO Max DO
    WHILE(Count[I - Min] > 0) DO
      A[Z] := SHORT(I);
      INC(Z);
      DEC(Count[I - Min]);
    END;
  END;
END CountingSort;

BEGIN
  Init(A);
  CountingSort(A, 10, 80);
  FOR I := 0 TO LEN(A)-1 DO
    Out.Int(A[I],0); Out.String(" ");
  END;
  Out.Ln;
END CS.

Objeck

bundle Default {
  class Cocktail {
    function : Main(args : String[]) ~ Nil {
      values := [9, 7, 10, 2, 9, 7, 4, 3, 10, 2, 7, 10];
      CountingSort(values, 2, 10);
      each(i : values) {
        values[i]->PrintLine();
      };
    }
      
    function : CountingSort(array : Int[], min : Int, max : Int) ~ Nil {
      count := Int->New[max - min + 1];
      each(i : array) {
        number := array[i];
        v := count[number - min];
        count[number - min] := v + 1;
      };
  
      z := 0;
      for(i := min; i <= max; i += 1;) {
        while(count[i - min] > 0) {  
          array[z] := i;
          z += 1;
          v := count[i - min]
          count[i - min] := v - 1;          
        };
      };      
    }
  }
}

OCaml

For arrays:

let counting_sort_array arr lo hi =
  let count = Array.make (hi-lo+1) 0 in
    Array.iter (fun i -> count.(i-lo) <- count.(i-lo) + 1) arr;
    Array.concat (Array.to_list (Array.mapi (fun i x -> Array.make x (lo+i)) count))

Octave

This implements the same algorithm but in a more compact way (using the same loop to count and to update the sorted vector). This implementation is elegant (and possible since the sort is not done "in place"), but not so efficient on machines that can't parallelize some operations (the vector arr is scanned for every value between minval and maxval)

function r = counting_sort(arr, minval, maxval)
  r = arr;
  z = 1;
  for i = minval:maxval
    cnt = sum(arr == i);
    while( cnt-- > 0 )
      r(z++) = i;
    endwhile
  endfor
endfunction

Testing:

ages = unidrnd(140, 100, 1);
sorted = counting_sort(ages, 0, 140);
disp(sorted);

Oz

Using arrays as in the original algorithm. The implementation is slightly simpler because arrays can start with an arbitrary index in Oz.

declare
  proc {CountingSort Arr Min Max}
     Count = {Array.new Min Max 0}
     Z = {NewCell {Array.low Arr}}
  in
     %% fill frequency array
     for J in {Array.low Arr}..{Array.high Arr} do
        Number = Arr.J
     in
        Count.Number := Count.Number + 1
     end
     %% recreate array from frequencies
     for I in Min..Max do
        for C in 1..Count.I do
  	 Arr.(@Z) := I
  	 Z := @Z + 1
        end
     end
  end

  A = {Tuple.toArray unit(3 1 4 1 5 9 2 6 5)}
in
  {CountingSort A 1 9}
  {Show {Array.toRecord unit A}}

Using lists for input and output and a dictionary as a sparse array:

declare
  fun {CountingSort Xs}
     Count = {Dictionary.new}
  in
     for X in Xs do
        Count.X := {CondSelect Count X 0} + 1
     end
     {Concat {Map {Dictionary.entries Count} Repeat}}
  end

  fun {Repeat Val#Count}
     if Count == 0 then nil
     else Val|{Repeat Val#Count-1}
     end
  end

  fun {Concat Xs}
     {FoldR Xs Append nil}
  end
in
  {Show {CountingSort [3 1 4 1 5 9 2 6 5]}}

PARI/GP

countingSort(v,mn,mx)={
  my(u=vector(#v),i=0);
  for(n=mn,mx,
    for(j=1,#v,if(v[j]==n,u[i++]=n))
  );
  u
};

Pascal

program CountingSort;

procedure counting_sort(var arr : Array of Integer; n, min, max : Integer);
var
   count   : Array of Integer;
   i, j, z : Integer;
begin
   SetLength(count, max-min);
   for i := 0 to (max-min) do
      count[i] := 0;
   for i := 0 to (n-1) do
      count[ arr[i] - min ] := count[ arr[i] - min ] + 1;
   z := 0;
   for i := min to max do
      for j := 0 to (count[i - min] - 1) do begin
	 arr[z] := i;
	 z := z + 1
      end
end;

var
   ages	: Array[0..99] of Integer;
   i	: Integer;
   
begin 
   { testing }
   for i := 0 to 99 do
      ages[i] := 139 - i;
   counting_sort(ages, 100, 0, 140);
   for i := 0 to 99 do
      writeln(ages[i]);
end.

Perl

#! /usr/bin/perl
use strict;

sub counting_sort
{
    my ($a, $min, $max) = @_;
 
    my @cnt = (0) x ($max - $min + 1);
    $cnt[$_ - $min]++ foreach @$a;
 
    my $i = $min;
    @$a = map {($i++) x $_} @cnt;
}

Testing:

my @ages = map {int(rand(140))} 1 .. 100;
 
counting_sort(\@ages, 0, 140);
print join("\n", @ages), "\n";

Phix

with javascript_semantics

function countingSort(sequence array, integer mina, maxa)
    sequence count = repeat(0,maxa-mina+1)
    array = deep_copy(array)
    for i=1 to length(array) do
        count[array[i]-mina+1] += 1
    end for
    integer z = 1
    for i=mina to maxa do
        for j=1 to count[i-mina+1] do
            array[z] := i
            z += 1
        end for
    end for
    return array
end function
 
sequence s = {5, 3, 1, 7, 4, 1, 1, 20}
?countingSort(s,min(s),max(s))

Output:

{1,1,1,3,4,5,7,20}

PHP

<?php

function counting_sort(&$arr, $min, $max)
{
  $count = array();
  for($i = $min; $i <= $max; $i++)
  {
    $count[$i] = 0;
  }

  foreach($arr as $number)
  {
    $count[$number]++; 
  }
  $z = 0;
  for($i = $min; $i <= $max; $i++) {
    while( $count[$i]-- > 0 ) {
      $arr[$z++] = $i;
    }
  }
}

Testing:

$ages = array();
for($i=0; $i < 100; $i++) {
  array_push($ages, rand(0, 140));
}
counting_sort($ages, 0, 140);

for($i=0; $i < 100; $i++) {
  echo $ages[$i] . "\n";
}
?>

PicoLisp

(de countingSort (Lst Min Max)
   (let Count (need (- Max Min -1) 0)
      (for N Lst
         (inc (nth Count (- N Min -1))) )
      (make
         (map
            '((C I)
               (do (car C) (link (car I))) )
            Count
            (range Min Max) ) ) ) )

Output:

: (countingSort (5 3 1 7 4 1 1 20) 1 20)
-> (1 1 1 3 4 5 7 20)

PL/I

count_sort: procedure (A);
   declare A(*) fixed;
   declare (min, max) fixed;
   declare i fixed binary;

   max, min = A(lbound(A,1));
   do i = 1 to hbound(A,1);
       if max < A(i) then max = A(i);
       if min > A(i) then min = A(i);
   end;

   begin;
      declare t(min:max) fixed;
      declare (i, j, k) fixed binary (31);
      t = 0;
      do i = 1 to hbound(A,1);
         j = A(i);
         t(j) = t(j) + 1;
      end;
      k = lbound(A,1);
      do i = min to max;
         if t(i) ^= 0 then
            do j = 1 to t(i);
               A(k) = i;
               k = k + 1;
            end;
      end;
   end;
end count_sort;

PowerShell

function countingSort($array) {
    $minmax = $array | Measure-Object -Minimum -Maximum 
    $min, $max = $minmax.Minimum, $minmax.Maximum
    $count = @(0) * ($max - $min  + 1)
    foreach ($number in $array) {
        $count[$number - $min] = $count[$number - $min] + 1
    }
    $z = 0
    foreach ($i in $min..$max) {
        while (0 -lt $count[$i - $min]) {
            $array[$z] = $i
            $z = $z+1
            $count[$i - $min] = $count[$i - $min] - 1
        }
    }
    $array
}

$array = foreach ($i in 1..50) {Get-Random -Minimum 0 -Maximum 26}
"$array"
"$(countingSort $array)"

Output:

13 18 8 6 3 7 22 20 10 7 18 10 25 13 9 21 8 19 24 24 18 6 23 23 24 7 15 25 24 25 11 23 19 5 4 8 9 7 1 19 10 24 13 1 9 0 9 10 19 16
0 1 1 3 4 5 6 6 7 7 7 7 8 8 8 9 9 9 9 10 10 10 10 11 13 13 13 15 16 18 18 18 19 19 19 19 20 21 22 23 23 23 24 24 24 24 24 25 25 25

PureBasic

Procedure Counting_sort(Array data_array(1), min, max)
  Define i, j
  Dim c(max - min)

  For i = 0 To ArraySize(data_array())
    c(data_array(i) - min) + 1
  Next

  For i = 0 To ArraySize(c())
    While c(i)
      data_array(j) = i + min
      j + 1
      c(i) - 1
    Wend
  Next
EndProcedure

Python

Follows the spirit of the counting sort but uses Pythons defaultdict(int) to initialize array accesses to zero, and list concatenation:

>>> from collections import defaultdict
>>> def countingSort(array, mn, mx):
	count = defaultdict(int)
	for i in array:
		count[i] += 1
	result = []
	for j in range(mn,mx+1):
		result += [j]* count[j]
	return result

>>> data = [9, 7, 10, 2, 9, 7, 4, 3, 10, 2, 7, 10, 2, 1, 3, 8, 7, 3, 9, 5, 8, 5, 1, 6, 3, 7, 5, 4, 6, 9, 9, 6, 6, 10, 2, 4, 5, 2, 8, 2, 2, 5, 2, 9, 3, 3, 5, 7, 8, 4]
>>> mini,maxi = 1,10
>>> countingSort(data, mini, maxi) == sorted(data)
True

Using a list:

Works with: Python version 2.6

def countingSort(a, min, max):
    cnt = [0] * (max - min + 1)
    for x in a:
        cnt[x - min] += 1
 
    return [x for x, n in enumerate(cnt, start=min)
              for i in xrange(n)]

Quackery

  [ 2dup peek 1+
    unrot poke ]          is [1+]  (   [ n --> [ )
 
  [ 1+ dip tuck - 
    rot 0 swap of
    swap rot witheach
      [ over + 
        rot swap [1+] 
        swap ] 
    negate swap 
    [] swap witheach
      [ dip [ over i^ + ] 
        of join ]
     nip ]                is csort ( [ n n --> [ )
 
  [] 15 times 
    [ 10 random 10 + join ]
 
  dup say "Before: " echo cr
  10 19 csort
  say "After:  " echo

Output:

Before: [ 16 14 15 10 19 18 12 16 12 14 10 13 12 15 18 ]
After:  [ 10 10 12 12 12 13 14 14 15 15 16 16 18 18 19 ]

R

Translation of: Octave

counting_sort <- function(arr, minval, maxval) {
  r <- arr
  z <- 1
  for(i in minval:maxval) {
    cnt = sum(arr == i)
    while(cnt > 0) {
      r[z] = i
      z <- z + 1
      cnt <- cnt - 1
    }
  }
  r
}

# 140+1 instead of 140, since random numbers generated
# by runif are always less than the given maximum;
# floor(a number at most 140.9999...) is 140
ages <- floor(runif(100, 0, 140+1))
sorted <- counting_sort(ages, 0, 140)
print(sorted)

Racket

#lang racket

(define (counting-sort xs min max)
  (define ns (make-vector (+ max (- min) 1) 0))
  (for ([x xs])  (vector-set! ns (- x min) (+ (vector-ref ns (- x min)) 1)))
  (for/fold ([i 0]) ([n ns] [x (in-naturals)])
    (for ([j (in-range i (+ i n ))])
      (vector-set! xs j (+ x min)))
    (+ i n))
  xs)

(counting-sort (vector 0 9 3 8 1 -1 1 2 3 7 4) -1 10)

Output:

'#(-1 0 1 1 2 3 3 4 7 8 9)

Raku

(formerly Perl 6)

Works with: rakudo version 2018.03

sub counting-sort (@ints) {
    my $off = @ints.min;
    (my @counts)[$_ - $off]++ for @ints;
    flat @counts.kv.map: { ($^k + $off) xx ($^v // 0) }
}

# Testing:
constant @age-range = 2 .. 102;
my @ages = @age-range.roll(50);
say @ages.&counting-sort;
say @ages.sort;

say @ages.&counting-sort.join eq @ages.sort.join ?? 'ok' !! 'not ok';

Output:

(5 5 5 7 9 17 19 19 20 21 25 27 28 30 32 34 38 40 41 45 48 49 50 51 53 54 55 56 59 62 65 66 67 69 70 73 74 81 83 85 87 91 91 93 94 96 99 99 100 101)
(5 5 5 7 9 17 19 19 20 21 25 27 28 30 32 34 38 40 41 45 48 49 50 51 53 54 55 56 59 62 65 66 67 69 70 73 74 81 83 85 87 91 91 93 94 96 99 99 100 101)
ok

REXX

These REXX versions make use of sparse arrays.

Negative, zero, and positive integers are supported.

version 1

/*REXX pgm sorts an array of integers (can be negative) using the  count─sort algorithm.*/
$= '1 3 6 2 7 13 20 12 21 11 22 10 23 9 24 8 25 43 62 42 63 41 18 42 17 43 16 44 15 45 14 46 79 113 78 114 77 39 78 38'
#= words($);          w= length(#);     !.= 0    /* [↑]  a list of some Recaman numbers.*/
m= 1;                 LO= word($, #);   HI= LO   /*M: max width of any integer in $ list*/
      do j=1  for #;  z= word($, j)+0;  @.j= z;  m= max(m, length(z) ) /*get from $ list*/
      !.z= !.z + 1;   LO= min(LO, z);   HI= max(HI, z)                 /*find LO and HI.*/
      end   /*j*/
                                                 /*W:  max index width for the @. array.*/
call show 'before sort: ';   say copies('▓', 55) /*show the   before   array elements.  */
call countSort   #                               /*sort a number of entries of @. array.*/
call show ' after sort: '                        /*show the    after   array elements.  */
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
countSort: parse arg N;  x= 1;    do k=LO  to  HI;   do x=x  for !.k;  @.x= k;  end  /*x*/
                                  end   /*k*/
           return
/*──────────────────────────────────────────────────────────────────────────────────────*/
show: do s=1  for #;  say right("element",20) right(s,w) arg(1) right(@.s,m); end;  return

output   when using the default input:

(Shown at   ⁵/₆   size.)

             element  1 before sort:    1
             element  2 before sort:    3
             element  3 before sort:    6
             element  4 before sort:    2
             element  5 before sort:    7
             element  6 before sort:   13
             element  7 before sort:   20
             element  8 before sort:   12
             element  9 before sort:   21
             element 10 before sort:   11
             element 11 before sort:   22
             element 12 before sort:   10
             element 13 before sort:   23
             element 14 before sort:    9
             element 15 before sort:   24
             element 16 before sort:    8
             element 17 before sort:   25
             element 18 before sort:   43
             element 19 before sort:   62
             element 20 before sort:   42
             element 21 before sort:   63
             element 22 before sort:   41
             element 23 before sort:   18
             element 24 before sort:   42
             element 25 before sort:   17
             element 26 before sort:   43
             element 27 before sort:   16
             element 28 before sort:   44
             element 29 before sort:   15
             element 30 before sort:   45
             element 31 before sort:   14
             element 32 before sort:   46
             element 33 before sort:   79
             element 34 before sort:  113
             element 35 before sort:   78
             element 36 before sort:  114
             element 37 before sort:   77
             element 38 before sort:   39
             element 39 before sort:   78
             element 40 before sort:   38
▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
             element  1  after sort:    1
             element  2  after sort:    2
             element  3  after sort:    3
             element  4  after sort:    6
             element  5  after sort:    7
             element  6  after sort:    8
             element  7  after sort:    9
             element  8  after sort:   10
             element  9  after sort:   11
             element 10  after sort:   12
             element 11  after sort:   13
             element 12  after sort:   14
             element 13  after sort:   15
             element 14  after sort:   16
             element 15  after sort:   17
             element 16  after sort:   18
             element 17  after sort:   20
             element 18  after sort:   21
             element 19  after sort:   22
             element 20  after sort:   23
             element 21  after sort:   24
             element 22  after sort:   25
             element 23  after sort:   38
             element 24  after sort:   39
             element 25  after sort:   41
             element 26  after sort:   42
             element 27  after sort:   42
             element 28  after sort:   43
             element 29  after sort:   43
             element 30  after sort:   44
             element 31  after sort:   45
             element 32  after sort:   46
             element 33  after sort:   62
             element 34  after sort:   63
             element 35  after sort:   77
             element 36  after sort:   78
             element 37  after sort:   78
             element 38  after sort:   79
             element 39  after sort:  113
             element 40  after sort:  114

version 2

Translation of: PL/I

/* REXX ---------------------------------------------------------------
* 13.07.2014 Walter Pachl translated from PL/I
* 27.05.2023 Walter Pachl take care of bad lists
*--------------------------------------------------------------------*/
Parse Arg alist
If alist='*' Then
  alist='999 888 777 1 5 13 15 17 19 21 5'
Select
  When alist='' Then Call exit 'List is empty'
  When words(alist)=1 Then Call exit 'List has only one element:' alist
  Otherwise Nop
  End
Parse Var alist lo hi .
Do i=1 By 1 While alist<>''
  Parse Var alist a.i alist;
  lo=min(lo,a.i)
  hi=max(hi,a.i)
  End
a.0=i-1

Call show 'before count_sort'
Call count_sort
Call show 'after count_sort'
Exit

count_sort: procedure Expose a. lo hi
  t.=0
  do i=1 to a.0
    j=a.i
    t.j=t.j+1
    end
  k=1
  do i=lo to hi
    if t.i<>0 then Do
      do j=1 to t.i
        a.k=i
        k=k+1
        end
      end
    end
  Return

show: Procedure Expose a.
Parse Arg head
Say head
ol=''
Do i=1 To a.0
  ol=ol right(a.i,3)
  End
Say ol
Return

exit:
Say arg(1)

Output:

before count_sort
 999 888 777   1   5  13  15  17  19  21   5
after count_sort
   1   5   5  13  15  17  19  21 777 888 999

Ring

aList = [4, 65, 2, 99, 83, 782, 1]
see countingSort(aList, 1, 782)

func countingSort f, min, max
     count = list(max-min+1)
     for i = min to max 
         count[i] = 0
     next
 
     for i = 1 to len(f)
         count[ f[i] ] = count[ f[i] ] + 1
     next
 
     z = 1
     for i = min to max
         while count[i] > 0
               f[z] = i
               z = z + 1
               count[i] = count[i] - 1
         end
     next
     return f

Ruby

class Array
  def counting_sort!
    replace counting_sort
  end
  
  def counting_sort
    min, max = minmax
    count = Array.new(max - min + 1, 0)
    each {|number| count[number - min] += 1}
    (min..max).each_with_object([]) {|i, ary| ary.concat([i] * count[i - min])}
  end
end

ary = [9,7,10,2,9,7,4,3,10,2,7,10,2,1,3,8,7,3,9,5,8,5,1,6,3,7,5,4,6,9,9,6,6,10,2,4,5,2,8,2,2,5,2,9,3,3,5,7,8,4]
p ary.counting_sort.join(",")
# => "1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,6,6,7,7,7,7,7,7,8,8,8,8,9,9,9,9,9,9,10,10,10,10"

p ary = Array.new(20){rand(-10..10)}
# => [-3, -1, 9, -6, -8, -3, 5, -7, 4, 0, 5, 0, 2, -2, -6, 10, -10, -7, 5, -7]
p ary.counting_sort
# => [-10, -8, -7, -7, -7, -6, -6, -3, -3, -2, -1, 0, 0, 2, 4, 5, 5, 5, 9, 10]

Rust

fn counting_sort(
    mut data: Vec<usize>,
    min: usize,
    max: usize,
) -> Vec<usize> {
    // create and fill counting bucket with 0
    let mut count: Vec<usize> = Vec::with_capacity(data.len());
    count.resize(data.len(), 0);

    for num in &data {
        count[num - min] = count[num - min] + 1;
    }
    let mut z: usize = 0;
    for i in min..max+1 {
        while count[i - min] > 0 {
            data[z] = i;
            z += 1;
            count[i - min] = count[i - min] - 1;
        }
    }

    data
}

fn main() {
    let arr1 = vec![1, 0, 2, 9, 3, 8, 4, 7, 5, 6];
    println!("{:?}", counting_sort(arr1, 0, 9));

    let arr2 = vec![0, 1, 2, 3, 4, 5, 6, 7, 8, 9];
    println!("{:?}", counting_sort(arr2, 0, 9));

    let arr3 = vec![10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0];
    println!("{:?}", counting_sort(arr3, 0, 10));
}

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, 10]

Scala

def countSort(input: List[Int], min: Int, max: Int): List[Int] =
  input.foldLeft(Array.fill(max - min + 1)(0)) { (arr, n) => 
    arr(n - min) += 1
    arr
  }.zipWithIndex.foldLeft(List[Int]()) {
    case (lst, (cnt, ndx)) => List.fill(cnt)(ndx + min) ::: lst
  }.reverse

It's better (i.e. slightly faster) to reverse the frequencies list before processing it, instead of the whole result

def countSort(input: List[Int], min: Int, max: Int): List[Int] =
  input.foldLeft(Array.fill(max - min + 1)(0)) { (arr, n) => 
    arr(n - min) += 1
    arr
  }.zipWithIndex.reverse.foldLeft(List[Int]()) {
    case (lst, (cnt, ndx)) => List.fill(cnt)(ndx + min) ::: lst
  }

Sidef

func counting_sort(a, min, max) {
    var cnt = ([0] * (max - min + 1))
    a.each {|i| cnt[i-min]++ }
    cnt.map {|i| [min++] * i }.flat
}
 
var a = 100.of { 100.irand }
say counting_sort(a, 0, 100)

Slate

s@(Sequence traits) countingSort &min: min &max: max
[| counts index |
  min `defaultsTo: (s reduce: #min: `er).
  max `defaultsTo: (s reduce: #max: `er).
  counts: ((0 to: max - min) project: [| :_ | 0]).
  s do: [| :value | counts at: value - min infect: [| :count | count + 1]].
  index: 0.
  min to: max do: [| :value |
    [(counts at: value - min) isPositive]
      whileTrue:
        [s at: index put: value.
         index: index + 1.
         counts at: value - min infect: [| :val | val - 1]]
  ].
  s
].

Smalltalk

Works with: GNU Smalltalk

OrderedCollection extend [
    countingSortWithMin: min andMax: max [
	|oc z|
	oc := OrderedCollection new.
	1 to: (max - min + 1) do: [ :n| oc add: 0 ].
	self do: [ :v |
	    oc at: (v - min + 1) put: ( (oc at: (v - min + 1)) + 1)
	].
	z := 1.
	min to: max do: [ :i |
	    1 to: (oc at: (i - min + 1)) do: [ :k |
		self at: z put: i.
		z := z + 1.
	    ]
	]
    ]
].

Testing:

|ages|

ages := OrderedCollection new.

1 to: 100 do: [ :n |
    ages add: (Random between: 0 and: 140)
].

ages countingSortWithMin: 0 andMax: 140.
ages printNl.

Tcl

Works with: Tcl version 8.5

proc countingsort {a {min ""} {max ""}} {
    # If either of min or max weren't given, compute them now
    if {$min eq ""} {
        set min [::tcl::mathfunc::min $a]
    }
    if {$max eq ""} {
        set max [::tcl::mathfunc::max $a]
    }

    # Make the "array" of counters
    set count [lrepeat [expr {$max - $min + 1}] 0]

    # Count the values in the input list
    foreach n $a {
        set idx [expr {$n - $min}]
        lincr count $idx
    }

    # Build the output list
    set z 0
    for {set i $min} {$i <= $max} {incr i} {
        set idx [expr {$i - $min}]
        while {[lindex $count $idx] > 0} {
            lset a $z $i
            incr z
            lincr count $idx -1
        }
    }
    return $a
}

# Helper that will increment an existing element of a list
proc lincr {listname idx {value 1}} {
    upvar 1 $listname list
    lset list $idx [expr {[lindex $list $idx] + $value}]
}

# Demo code
for {set i 0} {$i < 50} {incr i} {lappend a [expr {1+ int(rand()*10)}]}
puts $a
puts [countingsort $a]

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

VBA

Translation of: Phix

Option Base 1
Private Function countingSort(array_ As Variant, mina As Long, maxa As Long) As Variant
    Dim count() As Integer
    ReDim count(maxa - mina + 1)
    For i = 1 To UBound(array_)
        count(array_(i) - mina + 1) = count(array_(i) - mina + 1) + 1
    Next i
    Dim z As Integer: z = 1
    For i = mina To maxa
        For j = 1 To count(i - mina + 1)
            array_(z) = i
            z = z + 1
        Next j
    Next i
    countingSort = array_
End Function
 
Public Sub main()
    s = [{5, 3, 1, 7, 4, 1, 1, 20}]
    Debug.Print Join(countingSort(s, WorksheetFunction.Min(s), WorksheetFunction.Max(s)), ", ")
End Sub

Output:

1, 1, 1, 3, 4, 5, 7, 20

VBScript

All my other sort demos just pass in the array, thus the findMax and findMin

Implementation

function findMax( a )
	dim num
	dim max
	max = 0
	for each num in a
		if num > max then max = num
	next
	findMax = max
end function

function findMin( a )
	dim num
	dim min
	min = 0
	for each num in a
		if num < min then min = num
	next
	findMin = min
end function

'the function returns the sorted array, but the fact is that VBScript passes the array by reference anyway
function countingSort( a )
	dim count()
	dim min, max
	min = findMin(a)
	max = findMax(a)
	redim count( max - min + 1 )
	dim i
	dim z
	for i = 0 to ubound( a )  
		count( a(i) - min ) = count( a( i ) - min ) + 1
	next
	z = 0
	for i = min to max
		while count( i - min) > 0
			a(z) = i
			z = z + 1
			count( i - min ) = count( i - min ) - 1
		wend
	next
	countingSort = a
end function

Invocation

dim a
a = array(300, 1, -2, 3, -4, 5, -6, 7, -8, 100, 11 )
wscript.echo join( a, ", " )
countingSort a
wscript.echo join( a, ", " )

Output

300, 1, -2, 3, -4, 5, -6, 7, -8, 100, 11
-8, -6, -4, -2, 1, 3, 5, 7, 11, 100, 300

V (Vlang)

fn counting_sort(mut arr []int, min int, max int) {
	println('Input: ' + arr.str())
	mut count := [0].repeat(max - min + 1)
	for i in 0 .. arr.len {
		nbr := arr[i]
		ndx1 := nbr - min
		count[ndx1] = count[ndx1] + 1
	}
	mut z := 0
	for i in min .. max {
		curr := i - min
		for count[curr] > 0 {
			arr[z] = i
			z++
			count[curr]--
		}
	}
	println('Output: ' + arr.str())
}

fn main() {
	mut arr := [6, 2, 1, 7, 6, 8]
	counting_sort(mut arr, 1, 8)
}

Output:

Input: [6, 2, 1, 7, 6, 8]
Output: [1, 2, 6, 6, 7, 8]

Wren

var countingSort = Fn.new { |a, min, max|
    var count = List.filled(max - min + 1, 0)
    for (n in a) count[n - min] = count[n - min] + 1
    var z = 0
    for (i in min..max) {
        while (count[i - min] > 0) {
            a[z] = i
            z = z + 1
            count[i - min] = count[i - min] - 1
        }
    }
}

var a = [4, 65, 2, -31, 0, 99, 2, 83, 782, 1]
System.print("Unsorted: %(a)")
var min = a.reduce { |min, i| (i < min) ? i : min }
var max = a.reduce { |max, i| (i > max) ? i : max }
countingSort.call(a, min, max)
System.print("Sorted  : %(a)")

Output:

Unsorted: [4, 65, 2, -31, 0, 99, 2, 83, 782, 1]
Sorted  : [-31, 0, 1, 2, 2, 4, 65, 83, 99, 782]

XPL0

include c:\cxpl\codes;

proc CountingSort(Array, Min, Max, Size); \Sort Array
int  Array, Min, Max, Size;     \minimum, maximum values, number of elements
int  Count, I, Z;
[Count:= Reserve((Max-Min+1)*4);         \Reserve Count with 4 bytes per integer
for I:= 0 to Max-Min do Count(I):= 0;    \initialize Count with 0
for I:= 0 to Size-1 do                   \for each number count its occurrences
    Count(Array(I)-Min):= Count(Array(I)-Min) + 1;
Z:= 0;
for I:= Min to Max do
    while Count(I-Min) > 0 do
        [Array(Z):= I;
        Z:= Z+1;
        Count(I-Min):= Count(I-Min) - 1;
        ];
];

int A, I;
[A:= [3, 1, 4, 1, -5, 9, 2, 6, 5, 4];
CountingSort(A, -5, 9, 10);
for I:= 0 to 10-1 do [IntOut(0, A(I));  ChOut(0, ^ )];
]

Output:

-5 1 1 2 3 4 4 5 6 9 

zkl

fcn countingSort(array, min, max){  // modifies array
   count:=(max - min + 1).pump(List().write,0); // array of (max - min + 1) zeros
   foreach number in (array){
      count[number - min] += 1;
   }
   z:=-1;
   foreach i in ([min .. max]){
      do(count[i - min]){ array[z += 1] = i }
   }
   array
}

array:=List(4, 65, 2, -31, 0, 99, 2, 83, 182, 1);
countingSort(array,(0).min(array), (0).max(array)).println();

Output:

L(-31,0,1,2,2,4,65,83,99,182)