Sorting algorithms/Counting sort

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

Pseudocode:

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

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 16 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)

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 algol>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)

)</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

C

<lang 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 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

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>

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>

<lang e>? 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()</lang>

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>

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>

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>

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

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>

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>

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>

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>

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

}

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]</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