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{{task|Sorting Algorithms}} {{Sorting Algorithm}} {{Wikipedia|Counting sort}}
;Task: Implement the [[wp:Counting sort|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''. (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''.)
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
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.
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;
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
{{trans|C}}
{{works with|ALGOL 68|Standard - no extensions to language used}}
{{works with|ALGOL 68G|Any - tested with release mk15-0.8b.fc9.i386}}
{{works with|ELLA ALGOL 68|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
AutoHotkey
contributed by Laszlo on the ahk [http://www.autohotkey.com/forum/post-276465.html#276465 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++
#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" ); } //------------------------------------------------------------------------------
{{out}}
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
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; } } }
Common Lisp
Straightforward implementation of counting sort. By using [http://www.lispworks.com/documentation/HyperSpec/Body/f_map.htm map] and [http://www.lispworks.com/documentation/HyperSpec/Body/f_map_in.htm 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)); }
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()
```
## Eiffel
```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:
```Eiffel
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
```
{{out}}
```txt
unsorted:
-7 4 2 6 1 3
sorted:
-7 1 2 3 4 6
```
## Elena
ELENA 4.x :
```elena
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.eval(10)).toArray();
console.printLine("before:", list.asEnumerable());
console.printLine("after :", list.countingSort().asEnumerable())
}
```
{{out}}
```txt
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|1.1}}
```elixir
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])
```
{{out}}
```txt
[-5, -3, -2, 1, 1, 2, 4, 5, 5, 5, 9]
```
## Fortran
{{works with|Fortran|95 and later}}
```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
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:
```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
```
## FreeBASIC
```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
```
{{out}}
```txt
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.
```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() {
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.
```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() {
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:
```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()
}
```
Test:
```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])
```
Output:
```txt
[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.
```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
```
## Io
{{trans|Java}}
```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)
```
A more functional-like version:
```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)
```
=={{header|Icon}} and {{header|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).
```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
```
Note: This example relies on [[Sorting_algorithms/Bubble_sort#Icon| the supporting procedures 'display sort', and 'writex' from Bubble Sort]].
Sample output:
```txt
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)
```
=={{header|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
{{eff note|J|/:~}}
```j
csort =: monad define
min =. <./y
cnt =. 0 $~ 1+(>./y)-min
for_a. y do.
cnt =. cnt >:@{`[`]}~ a-min
end.
cnt # min+i.#cnt
)
```
Alternative implementation:
```j
csort=: (+/@(=/) # ]) >./ (] + 1 i.@+ -) <./
```
'''Example:'''
```j
] a =. _3 + 20 ?@$ 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
```
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:
```j
csrt=:2 :0
(m+i.n-m) (+/@(=/)~ # [) ]
)
```
or
```j
csrt=:2 :0
(+/@(=/) # ])&(m+i.n-m)
)
```
Example:
```j
(_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|1.5+}}
```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]--;
}
}
}
```
## JavaScript
```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:
```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] + "
");
}
```
## jq
{{works with | jq|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.
```jq
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''':
```jq
[1,2,1,4,0,10] | countingSort(0;10)
```
{{out}}
```sh
$ jq -M -c -n -f counting_sort.jq
[0,1,1,2,4,10]
```
## Julia
{{works with|Julia|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.
```julia
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))")
```
{{out}}
```txt
# 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
```scala
// 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) {
val array = intArrayOf(4, 65, 2, -31, 0, 99, 2, 83, 782, 1)
println("Original : ${array.asList()}")
countingSort(array)
println("Sorted : ${array.asList()}")
}
```
{{out}}
```txt
Original : [4, 65, 2, -31, 0, 99, 2, 83, 782, 1]
Sorted : [-31, 0, 1, 2, 2, 4, 65, 83, 99, 782]
```
## Langur
```Langur
val .countingSort = f(.array) {
val (.min, .max) = (min(.array), max(.array))
var .count = arr(.max-.min+1, 0)
for .i in .array {
.count[.i-.min+1] += 1
}
var .result = []
for .i of .count {
for of .count[.i] {
.result ~= [.i+.min-1]
}
}
return .result
}
val .data = [7, 234, -234, 9, 43, 123, 14]
writeln "Original: ", .data
writeln "Sorted : ", .countingSort(.data)
```
{{out}}
```txt
Original: [7, 234, -234, 9, 43, 123, 14]
Sorted : [-234, 7, 9, 14, 43, 123, 234]
```
## Lua
```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
```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
```Mathematica
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;]
];
]
```
```txt
countingSort@{2, 3, 1, 5, 7, 6}
->{1, 2, 3, 5, 6, 7}
```
=={{header|MATLAB}} / {{header|Octave}}==
This is a direct translation of the pseudo-code, except to compensate for MATLAB using 1 based arrays.
```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
```
Sample Usage:
```MATLAB>>
countingSort([4 3 1 5 6 2])
ans =
1 2 3 4 5 6
```
## MAXScript
```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
)
```
{{out}}
```MAXScript
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)
```
=={{header|Modula-3}}==
```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.
```
Output:
```txt
Unsorted: 80 10 40 60 50 30 20 70
Sorted: 10 20 30 40 50 60 70 80
```
## NetRexx
### Version 1
An almost direct implementation of the pseudocode.
```NetRexx
/* 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
```
{{out}}
[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
/* 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
```
{{out}}
```txt
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
```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 .. 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:
```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))
```
## 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)
```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
```
Testing:
```octave
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.
```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:
```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]}}
```
## PARI/GP
```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
};
```
## Pascal
```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
```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:
```perl
my @ages = map {int(rand(140))} 1 .. 100;
counting_sort(\@ages, 0, 140);
print join("\n", @ages), "\n";
```
## Perl 6
{{Works with|rakudo|2018.03}}
```perl6
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';
```
{{out}}
```txt
(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
```
## Phix
```Phix
function countingSort(sequence array, integer mina, maxa)
sequence count = repeat(0,maxa-mina+1)
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))
```
{{out}}
```txt
{1,1,1,3,4,5,7,20}
```
## PHP
```php
0 ) {
$arr[$z++] = $i;
}
}
}
```
Testing:
```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";
}
?>
```
## PicoLisp
```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:
```txt
: (countingSort (5 3 1 7 4 1 1 20) 1 20)
-> (1 1 1 3 4 5 7 20)
```
## PL/I
```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
```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:
```txt
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
```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:
```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
```
Using a list:
{{works with|Python|2.6}}
```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)]
```
## R
{{trans|Octave}}
```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
}
# 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
```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:
```racket
'#(-1 0 1 1 2 3 3 4 7 8 9)
```
## REXX
These REXX versions make use of ''sparse'' arrays.
Negative, zero, and positive integers are supported.
### version 1
```rexx
/*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= 0; LO= word($, 1); HI= LO /*M: max width of any number in @. */
do i=1 for #; z= word($, i); @.i= z; m= max(m, length(z)) /*get from $ list. */
_.z= _.z + 1; LO= min(LO, z); HI= max(HI, z) /*find the LO & HI.*/
end /*i*/
/*W: max index width for the @. array*/
call show 'before sort: ' /*show the before array elements. */
say copies('▒', 55) /*show a separator line (before/after).*/
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
```
{{out|output|text= 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
{{trans|PL/I}}
```rexx
/* REXX ---------------------------------------------------------------
* 13.07.2014 Walter Pachl translated from PL/I
*--------------------------------------------------------------------*/
alist='999 888 777 1 5 13 15 17 19 21 5'
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
```
'''Output:'''
```txt
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
```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
```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
```rust
fn counting_sort(
mut data: Vec,
min: usize,
max: usize,
) -> Vec {
// create and fill counting bucket with 0
let mut count: Vec = 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));
}
```
{{out}}
```txt
[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
```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
```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.reverse.foldLeft(List[Int]()) {
case (lst, (cnt, ndx)) => List.fill(cnt)(ndx + min) ::: lst
}
```
## Sidef
```ruby
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
```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}}
```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:
```smalltalk
|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|8.5}}
```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]
```
```txt
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
{{trans|Phix}}
```vb
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
```
{{out}}
```txt
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==
```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
```
### ==Invocation==
```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, ", " )
```
### ==Output==
```txt
300, 1, -2, 3, -4, 5, -6, 7, -8, 100, 11
-8, -6, -4, -2, 1, 3, 5, 7, 11, 100, 300
```
## XPL0
```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, ^ )];
]
```
{{out}}
```txt
-5 1 1 2 3 4 4 5 6 9
```
## zkl
```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
}
```
```zkl
array:=List(4, 65, 2, -31, 0, 99, 2, 83, 182, 1);
countingSort(array,(0).min(array), (0).max(array)).println();
```
{{out}}
```txt
L(-31,0,1,2,2,4,65,83,99,182)
```
{{omit from|GUISS}}