Sorting algorithms/Counting sort

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Task
Sorting algorithms/Counting sort
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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)

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 of 32 bit integers, we see that in order to hold the counts, we need an array of 232 elements, i.e., we need, to hold a count value up to 232-1, more or less 4 Gbytes. So the counting sort is more practical when the range is (very) limited and minimum and maximum values are known a priori. (Anyway sparse arrays may limit the impact of the memory usage)

ActionScript

<lang 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; }</lang>

Ada

Given that we know the range of data, the problem really reduces to initializing the array to the ordered range of values. The input order is irrelevant. <lang Ada>with Ada.Text_Io; use Ada.Text_Io;

procedure Counting_Sort is

  type Data is array (Integer range <>) of Natural;
  procedure Sort(Item : out Data) is
  begin
     for I in Item'range loop
        Item(I) := I;
     end loop;
  end Sort;
  Stuff : Data(1..140);

begin

  Sort(Stuff);
  for I in Stuff'range loop
     Put(Natural'Image(Stuff(I)));
  end loop;
  New_Line;

end Counting_Sort;</lang>

Output

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97
98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 
133 134 135 136 137 138 139 140

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

<lang algol68>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

);

  1. 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)

)</lang> 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

AutoHotkey

contributed by Laszlo on the ahk forum <lang AutoHotkey>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)

}</lang>

C

<lang c>#include <stdio.h>

  1. 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 counting_sort(int *array, int n) {

 int i, min, max;
 
 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];
   }
 }

}</lang>

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

<lang c>#define N 100

  1. 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;

}</lang>

C#

<lang csharp>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;
       }
   }

}</lang>

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.

<lang lisp>(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)))))</lang>

D

<lang d>import std.stdio, std.algorithm;

void countingSort(int[] array, in size_t min, in size_t max) {

   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));

}</lang>

E

Straightforward implementation, no particularly interesting characteristics.

<lang e>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
       }
   }

}</lang>

? 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()

Fortran

Works with: Fortran version 95 and later

<lang fortran>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
   forall(i=tmin:tmax)
      cnt(i) = count(array == i)
   end forall
   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</lang>

Testing:

<lang fortran>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</lang>

Go

<lang go>package main

import (

   "fmt"
   "runtime"
   "strings"

)

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

func main() {

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

}

func countingSort() {

   count := make([]int, aMax-aMin+1)
   for _, x := range a {
       count[x-aMin]++
   }
   z := 0
   for i, c := range count {
       for ; c > 0; c-- {
           a[z] = i + aMin
           z++
       }
   }

}</lang>

Groovy

Solution: <lang groovy>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()

}</lang>

Test: <lang groovy>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])</lang>

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.

<lang haskell>import Control.Monad.ST import Data.Array.ST

countingSort :: (Enum n, Ix n) => [n] -> n -> n -> [n] countingSort l lo hi = concatMap (uncurry $ flip replicate) count

 where count = runST $ do
           a <- myNewArray (lo, hi) 0
           let increment i = readArray a i >>= writeArray a i . (+1)
           mapM_ increment l
           getAssocs a
       myNewArray :: (Ix n) => (n,n) -> Int -> ST s (STArray s n Int)
       myNewArray = newArray</lang>

Io

Translation of: Java

<lang io>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)</lang>

A more functional-like version: <lang io>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)</lang>

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).

<lang Icon>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</lang>

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)

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.

<lang j>csort =: monad define

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

)</lang> Example: <lang j> ] 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</lang>

Java

Works with: Java version 1.5+

<lang java5>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]--; } } }</lang>

JavaScript

<lang 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;
       }
   }
   

}</lang>

Testing:

<lang javascript>// 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] + "
");

}</lang>

Lua

<lang 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</lang>

M4

<lang 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')</lang>

MATLAB

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

<lang MATLAB>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</lang>

Sample Usage: <lang MATLAB>>> countingSort([4 3 1 5 6 2])

ans =

    1     2     3     4     5     6</lang>

Modula-3

<lang modula3>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.</lang> Output:

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

Objeck

<lang 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;          
       };
     };      
   }
 }

} </lang>

OCaml

For arrays: <lang ocaml>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))</lang>

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) <lang octave>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</lang>

Testing:

<lang octave>ages = unidrnd(140, 100, 1); sorted = counting_sort(ages, 0, 140); disp(sorted);</lang>

Oz

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

Using lists for input and output and a dictionary as a sparse array: <lang oz>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]}}</lang>

PARI/GP

<lang parigp>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

};</lang>

Pascal

<lang 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.</lang>

Perl

<lang 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;

}</lang>

Testing:

<lang perl>my @ages = map {int(rand(140))} 1 .. 100;

counting_sort(\@ages, 0, 140); print join("\n", @ages), "\n";</lang>

Perl 6

<lang perl6>sub counting_sort ( @a ) {

   my ( $min, $max ) = .min, .max given @a.minmax;
   my @counts;
   @counts[ $_ - $min ]++ for @a;
   return @counts.kv.map: { $^k + $min xx $^v if $^v };

}

my @all_ages = 2 .. 102; my @ages = (^50).map: { @all_ages.pick }; say @ages.sort.Str eq @ages.&counting_sort.Str ?? 'ok' !! 'not ok'; </lang>

PHP

<lang 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;
   }
 }

}</lang>

Testing:

<lang php>$ages = array(); for($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";

} ?></lang>

PicoLisp

<lang 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) ) ) ) )</lang>

Output:

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

PL/I

<lang 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;</lang>

PureBasic

<lang 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</lang>

Python

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

Using a list:

Works with: Python version 2.6

<lang python>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)]</lang>

R

Translation of: Octave

<lang R>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

}

  1. 140+1 instead of 140, since random numbers generated
  2. by runif are always less than the given maximum;
  3. floor(a number at most 140.9999...) is 140

ages <- floor(runif(100, 0, 140+1)) sorted <- counting_sort(ages, 0, 140) print(sorted)</lang>

REXX

<lang rexx> /*REXX program sorts an array using the count-sort method. */

call gen@ /*generate array elements. */ call show@ 'before sort' /*show before array elements*/ call countSort highItem /*invoke the count sort. */ call show@ ' after sort' /*show after array elements*/ exit


/*─────────────────────────────────────countSORT subroutine────────*/ countSort: procedure expose @.; parse arg n h=@.1 L=h

    do m=2 to n
    L=min(L,@.m)
    h=max(h,@.m)
    end

_.=0

  do j=1 for n
  k=@.j
  _.k=_.k+1
  end
  1. =1
   do j=L to h
   if _.j\==0 then do #=# for _.j
                   @.#=j
                   end
   end

return



/*─────────────────────────────────────GEN@ subroutine─────────────*/ gen@: @.= /*assign default value. */

          /* get the first 40 Recaman numbers:  subtract if you can,   */
          /* otherwise add.     Another way:      Recaman(1) = 1,      */
          /*  Recaman(n) = Recaman(n-1)-n    if positive and new, else */
          /*  Recaman(n) = Recaman(n-1)+n                              */

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

 do highItem=1 while @.highItem\==  /*find how many entries.    */
 end

highItem=highItem-1 /*adjust highItem slightly. */ return


/*─────────────────────────────────────SHOW@ subroutine────────────*/ show@: widthH=length(highItem) /*maximum width of any line.*/

 do j=1 for highItem
 say 'element' right(j,widthH) arg(1)":" @.j
 end

say copies('─',80) /*show a seperator line. */ return </lang> Output:

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
────────────────────────────────────────────────────────────────────────────────

Ruby

<lang ruby>class Array

 def countingsort!
   do_countingsort!(min, max)
 end
 
 protected
 def do_countingsort!(min, max)
   count = Array.new(max - min + 1, 0)
   each {|number| count[number - min] += 1}
   z = 0
   min.upto(max) do |i|
     while count[i - min] > 0
       self[z] = i
       z += 1
       count[i - min] -= 1
     end
   end
   self
 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] ary.countingsort!.join(",")

  1. => "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"</lang>

Scala

<lang 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</lang>

Slate

<lang 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

].</lang>

Smalltalk

Works with: GNU Smalltalk

<lang 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. ] ]

   ]

].</lang>

Testing:

<lang smalltalk>|ages|

ages := OrderedCollection new.

1 to: 100 do: [ :n |

   ages add: (Random between: 0 and: 140)

].

ages countingSortWithMin: 0 andMax: 140. ages printNl.</lang>

Tcl

Works with: Tcl version 8.5

<lang tcl>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

}

  1. 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}]

}

  1. Demo code

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

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

VBScript

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

Implementation

<lang vb>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</lang>

Invocation

<lang vb>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, ", " )</lang>

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