Sorting algorithms/Counting sort: Difference between revisions
m (made the last sentence in the task's prologue to be a counterexample for the note.) |
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show(`a')</lang> |
show(`a')</lang> |
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=={{header|Mathematica}}== |
=={{header|Mathematica}}/{{header|Wolfram Language}}== |
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<lang Mathematica>countingSort[list_] := Module[{minElem, maxElem, count, z, number}, |
<lang Mathematica>countingSort[list_] := Module[{minElem, maxElem, count, z, number}, |
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minElem = Min[list]; maxElem = Max[list]; |
minElem = Min[list]; maxElem = Max[list]; |
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]; |
]; |
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]</lang> |
]</lang> |
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<pre>countingSort@{2, 3, 1, 5, 7, 6} |
<pre>countingSort@{2, 3, 1, 5, 7, 6} |
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->{1, 2, 3, 5, 6, 7}</pre> |
->{1, 2, 3, 5, 6, 7}</pre> |
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Revision as of 09:11, 17 August 2021
You are encouraged to solve this task according to the task description, using any language you may know.
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
Heap sort | Merge sort | Patience sort | Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
| This page uses content from Wikipedia. The original article was at Counting sort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance) |
- Task
Implement the Counting sort. This is a way of sorting integers when the minimum and maximum value are known.
- Pseudocode
function countingSort(array, min, max):
count: array of (max - min + 1) elements
initialize count with 0
for each number in array do
count[number - min] := count[number - min] + 1
done
z := 0
for i from min to max do
while ( count[i - min] > 0 ) do
array[z] := i
z := z+1
count[i - min] := count[i - min] - 1
done
done
The min and max can be computed apart, or be known a priori.
Note: we know that, given an array of integers, its maximum and minimum values can be always found; but if we imagine the worst case for an array that can hold up to 32 bit integers, we see that in order to hold the counts, an array of up to 232 elements may be needed. I.E.: we need to hold a count value up to 232-1, which is a little over 4.2 Gbytes. So the counting sort is more practical when the range is (very) limited, and minimum and maximum values are known a priori. (However, as a counterexample, the use of sparse arrays minimizes the impact of the memory usage, as well as removing the need of having to know the minimum and maximum values a priori.)
11l
<lang 11l>F countingSort(a, min, max)
V cnt = [0] * (max - min + 1)
L(x) a
cnt[x - min]++
[Int] result
L(n) cnt
result [+]= [L.index + min] * n
R result
V data = [9, 7, 10, 2, 9, 7, 4, 3, 10, 2, 7, 10, 2, 1, 3, 8, 7, 3, 9, 5, 8, 5, 1, 6, 3, 7, 5, 4, 6, 9, 9, 6, 6, 10, 2, 4, 5, 2, 8, 2, 2, 5, 2, 9, 3, 3, 5, 7, 8, 4] print(countingSort(data, min(data), max(data)) == sorted(data))</lang>
- Output:
1B
360 Assembly
<lang 360asm>* Counting sort - 18/04/2020 COUNTS CSECT
USING COUNTS,R13 base register
B 72(R15) skip savearea
DC 17F'0' savearea
SAVE (14,12) save previous context
ST R13,4(R15) link backward
ST R15,8(R13) link forward
LR R13,R15 set addressability
LA R6,A i=1
DO WHILE=(C,R6,LE,=A(N)) do i=1 to hbound(a)
L R8,0(R6) a(i)
S R8,MIN k=a(i)-min
LR R1,R8 k
SLA R1,2 ~
L R3,COUNT(R1) count(k+1)
LA R3,1(R3) +1
ST R3,COUNT(R1) count(k+1)+=1
LA R6,4(R6) i++
ENDDO , enddo i
LA R7,A j=1
L R6,MIN i=min
DO WHILE=(C,R6,LE,MAX) do i=min to max
LR R8,R6 i
S R8,MIN k=i-min
WHILEC LR R1,R8 while k
SLA R1,2 ..... ~
L R2,COUNT(R1) ..... count(k+1)
LTR R2,R2 ..... test
BNP WHENDC ..... count(k+1)>0
ST R6,0(R7) a(j)=i
LA R7,4(R7) j++
LR R1,R8 k
SLA R1,2 ~
L R3,COUNT(R1) count(k+1)
BCTR R3,0 -1
ST R3,COUNT(R1) count(k+1)-=1
B WHILEC end while
WHENDC AH R6,=H'1' i++
ENDDO , enddo i
LA R9,PG @buffer
LA R6,A i=1
DO WHILE=(C,R6,LE,=A(N)) do i=1 to hbound(a)
L R2,0(R6) a(i)
XDECO R2,XDEC edit a(i)
MVC 0(3,R9),XDEC+9 output a(i)
LA R9,3(R9) @buffer++
LA R6,4(R6) i++
ENDDO , enddo i
XPRNT PG,L'PG print buffer
L R13,4(0,R13) restore previous savearea pointer
RETURN (14,12),RC=0 restore registers from calling save
MIN DC F'-9' min MAX DC F'99' max A DC F'98',F'35',F'15',F'46',F'6',F'64',F'92',F'44'
DC F'53',F'21',F'56',F'74',F'13',F'11',F'92',F'70'
DC F'43',F'2',F'-7',F'89',F'22',F'82',F'41',F'91'
DC F'28',F'51',F'0',F'39',F'29',F'34',F'15',F'26'
N DC A((N-A)/L'A) hbound(a) PG DC CL96' ' buffer XDEC DS CL12 temp fo xdeco COUNT DC 200F'0' count
REGEQU
END COUNTS </lang>
- Output:
-7 0 2 6 11 13 15 15 21 22 26 28 29 32 34 35 39 41 43 44 46 51 53 56 64 70 74 82 89 91 92 92
AArch64 Assembly
<lang AArch64 Assembly> /* ARM assembly AARCH64 Raspberry PI 3B */ /* program countSort64.s */
/*******************************************/ /* Constantes file */ /*******************************************/ /* for this file see task include a file in language AArch64 assembly */ .include "../includeConstantesARM64.inc"
/*********************************/ /* Initialized data */ /*********************************/ .data szMessSortOk: .asciz "Table sorted.\n" szMessSortNok: .asciz "Table not sorted !!!!!.\n" sMessResult: .asciz "Value : @ \n" szCarriageReturn: .asciz "\n"
.align 4
- Caution : number strictly positive and not too big
TableNumber: .quad 1,3,6,2,5,9,10,8,4,5 //TableNumber: .quad 10,9,8,7,6,5,4,3,2,1
.equ NBELEMENTS, (. - TableNumber) / 8
/*********************************/ /* UnInitialized data */ /*********************************/ .bss sZoneConv: .skip 24 /*********************************/ /* code section */ /*********************************/ .text .global main main: // entry of program
ldr x0,qAdrTableNumber // address number table mov x1,NBELEMENTS // number of élements bl searchMinMax mov x3,NBELEMENTS bl countSort ldr x0,qAdrTableNumber // address number table bl displayTable ldr x0,qAdrTableNumber // address number table mov x1,NBELEMENTS // number of élements bl isSorted // control sort cmp x0,1 // sorted ? beq 1f ldr x0,qAdrszMessSortNok // no !! error sort bl affichageMess b 100f
1: // yes
ldr x0,qAdrszMessSortOk bl affichageMess
100: // standard end of the program
mov x0,0 // return code mov x8,EXIT // request to exit program svc 0 // perform the system call
qAdrsZoneConv: .quad sZoneConv qAdrszCarriageReturn: .quad szCarriageReturn qAdrsMessResult: .quad sMessResult qAdrTableNumber: .quad TableNumber qAdrszMessSortOk: .quad szMessSortOk qAdrszMessSortNok: .quad szMessSortNok /******************************************************************/ /* control sorted table */ /******************************************************************/ /* x0 contains the address of table */ /* x1 contains the number of elements > 0 */ /* x0 return table address r1 return min r2 return max */ searchMinMax:
stp x3,lr,[sp,-16]! // save registers stp x3,x4,[sp,-16]! // save registers mov x3,x1 // save size mov x1,1<<62 // min mov x2,0 // max mov x4,0 // index
1:
ldr x5,[x0,x4,lsl 3] cmp x5,x1 csel x1,x5,x1,lt cmp x5,x2 csel x2,x5,x2,gt add x4,x4,1 cmp x4,x3 blt 1b
100:
ldp x4,x5,[sp],16 // restaur 2 registers ldp x3,lr,[sp],16 // restaur 2 registers ret // return to address lr x30
/******************************************************************/ /* control sorted table */ /******************************************************************/ /* x0 contains the address of table */ /* x1 contains the number of elements > 0 */ /* x0 return 0 if not sorted 1 if sorted */ isSorted:
stp x2,lr,[sp,-16]! // save registers stp x3,x4,[sp,-16]! // save registers mov x2,0 ldr x4,[x0,x2,lsl 3]
1:
add x2,x2,1 cmp x2,x1 bge 99f ldr x3,[x0,x2, lsl 3] cmp x3,x4 blt 98f mov x4,x3 b 1b
98:
mov x0,0 // not sorted b 100f
99:
mov x0,1 // sorted
100:
ldp x3,x4,[sp],16 // restaur 2 registers ldp x2,lr,[sp],16 // restaur 2 registers ret // return to address lr x30
/******************************************************************/ /* count sort */ /******************************************************************/ /* x0 contains the address of table */ /* x1 contains the minimum */ /* x2 contains the maximum */ /* x3 contains area size */ /* caution : the count area is in the stack. if max is very large, risk of error */ countSort:
stp x1,lr,[sp,-16]! // save registers stp x2,x3,[sp,-16]! // save registers stp x4,x5,[sp,-16]! // save registers stp x6,x7,[sp,-16]! // save registers stp x8,x9,[sp,-16]! // save registers sub x3,x3,1 // compute endidx = n - 1 sub x5,x2,x1 // compute max - min add x5,x5,1 // + 1 lsl x9,x5,3 // 8 bytes by number sub sp,sp,x9 // reserve count area in stack mov fp,sp // frame pointer = stack mov x6,0 mov x4,0
1: // loop init stack area
str x6,[fp,x4, lsl 3] add x4,x4,#1 cmp x4,x5 blt 1b mov x4,#0 // indice
2: // start loop 2
ldr x5,[x0,x4,lsl 3] // load value A[j] sub x5,x5,x1 // - min ldr x6,[fp,x5,lsl 3] // load count of value add x6,x6,1 // increment counter str x6,[fp,x5,lsl 3] // and store add x4,x4,1 // increment indice cmp x4,x3 // end ? ble 2b // no -> loop 2 mov x7,0 // z mov x4,x1 // index = min
3: // start loop 3
sub x6,x4,x1 // compute index - min ldr x5,[fp,x6,lsl 3] // load count
4: // start loop 4
cmp x5,0 // count <> zéro beq 5f str x4,[x0,x7,lsl 3] // store value A[j] add x7,x7,1 // increment z sub x5,x5,1 // decrement count b 4b
5:
add x4,x4,1 // increment index cmp x4,x2 // max ? ble 3b // no -> loop 3 add sp,sp,x9 // stack alignement
100:
ldp x8,x9,[sp],16 // restaur 2 registers ldp x6,x7,[sp],16 // restaur 2 registers ldp x4,x5,[sp],16 // restaur 2 registers ldp x2,x3,[sp],16 // restaur 2 registers ldp x1,lr,[sp],16 // restaur 2 registers ret // return to address lr x30
/******************************************************************/ /* Display table elements */ /******************************************************************/ /* x0 contains the address of table */ displayTable:
stp x1,lr,[sp,-16]! // save registers stp x2,x3,[sp,-16]! // save registers mov x2,x0 // table address mov x3,0
1: // loop display table
ldr x0,[x2,x3,lsl 3] ldr x1,qAdrsZoneConv bl conversion10S // décimal conversion ldr x0,qAdrsMessResult ldr x1,qAdrsZoneConv bl strInsertAtCharInc // insert result at @ character bl affichageMess // display message add x3,x3,1 cmp x3,NBELEMENTS - 1 ble 1b ldr x0,qAdrszCarriageReturn bl affichageMess mov x0,x2 // table address
100:
ldp x2,x3,[sp],16 // restaur 2 registers ldp x1,lr,[sp],16 // restaur 2 registers ret // return to address lr x30
/********************************************************/ /* File Include fonctions */ /********************************************************/ /* for this file see task include a file in language AArch64 assembly */ .include "../includeARM64.inc" </lang>
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
<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
);
- 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
ARM Assembly
<lang ARM Assembly> /* ARM assembly Raspberry PI */ /* program countSort.s */
/* REMARK 1 : this program use routines in a include file see task Include a file language arm assembly for the routine affichageMess conversion10 see at end of this program the instruction include */
/* for constantes see task include a file in arm assembly */ /************************************/ /* Constantes */ /************************************/ .include "../constantes.inc"
.include "../../ficmacros.s" /*********************************/ /* Initialized data */ /*********************************/ .data szMessSortOk: .asciz "Table sorted.\n" szMessSortNok: .asciz "Table not sorted !!!!!.\n" sMessResult: .asciz "Value : @ \n" szCarriageReturn: .asciz "\n"
.align 4
- Caution : number stritcly positive and not too big
- TableNumber: .int 1,3,6,2,5,9,10,8,5,7 @ for test 2 sames values
TableNumber: .int 10,9,8,7,6,5,4,3,2,1
.equ NBELEMENTS, (. - TableNumber) / 4
/*********************************/ /* UnInitialized data */ /*********************************/ .bss sZoneConv: .skip 24 /*********************************/ /* code section */ /*********************************/ .text .global main main: @ entry of program
ldr r0,iAdrTableNumber @ address number table mov r1,#NBELEMENTS @ number of élements bl searchMinMax @ r1=min r2=max mov r3,#NBELEMENTS @ number of élements bl countSort ldr r0,iAdrTableNumber @ address number table bl displayTable ldr r0,iAdrTableNumber @ address number table mov r1,#NBELEMENTS @ number of élements bl isSorted @ control sort cmp r0,#1 @ sorted ? beq 2f ldr r0,iAdrszMessSortNok @ no !! error sort bl affichageMess b 100f
2: @ yes
ldr r0,iAdrszMessSortOk bl affichageMess
100: @ standard end of the program
mov r0, #0 @ return code mov r7, #EXIT @ request to exit program svc #0 @ perform the system call
iAdrszCarriageReturn: .int szCarriageReturn iAdrsMessResult: .int sMessResult iAdrTableNumber: .int TableNumber iAdrszMessSortOk: .int szMessSortOk iAdrszMessSortNok: .int szMessSortNok /******************************************************************/ /* control sorted table */ /******************************************************************/ /* r0 contains the address of table */ /* r1 contains the éléments number */ /* r0 return address r1 return min r2 return max */ searchMinMax:
push {r3-r5,lr} @ save registers
mov r3,r1 @ save size
mov r1,#1<<30 @ min
mov r2,#0 @ max
mov r4,#0 @ index
1:
ldr r5,[r0,r4, lsl #2] @ load value cmp r5,r1 @ if < min movlt r1,r5 cmp r5,r2 @ if > max movgt r2,r5 add r4,r4,#1 @ increment index cmp r4,r3 @ end ? blt 1b @ no -> loop
100:
pop {r3-r5,lr}
bx lr @ return
/******************************************************************/ /* control sorted table */ /******************************************************************/ /* r0 contains the address of table */ /* r1 contains the number of elements > 0 */ /* r0 return 0 if not sorted 1 if sorted */ isSorted:
push {r2-r4,lr} @ save registers
mov r2,#0
ldr r4,[r0,r2,lsl #2]
1:
add r2,#1 cmp r2,r1 movge r0,#1 bge 100f ldr r3,[r0,r2, lsl #2] cmp r3,r4 movlt r0,#0 blt 100f mov r4,r3 b 1b
100:
pop {r2-r4,lr}
bx lr @ return
/******************************************************************/ /* count Sort */ /******************************************************************/ /* r0 contains the address of table */ /* r1 contains the minimum */ /* r2 contains the maximun */ /* r3 contains elements number */ /* caution : the count area is in the stack. if max is very large, risk of error */ countSort:
push {r1-r9,lr} @ save registers
sub r3,r3,#1 @ compute end index
sub r5,r2,r1 @ compute max - min
add r5,r5,#1 @ + 1
lsl r9,r5,#2 @ 4 bytes by number
sub sp,sp,r9 @ reserve area on stack
mov fp,sp @ frame pointer = stack address
mov r6,#0
mov r4,#0
1: @ loop init stack area
str r6,[fp,r4, lsl #2] add r4,r4,#1 cmp r4,r5 blt 1b mov r4,#0 @ indice
2: @ start loop 2
ldr r5,[r0,r4,lsl #2] @ load value A[j] sub r5,r5,r1 @ - min ldr r6,[fp,r5,lsl #2] @ load count of value add r6,r6,#1 @ increment counter str r6,[fp,r5,lsl #2] @ and store add r4,#1 @ increment indice cmp r4,r3 @ end ? ble 2b @ no -> loop 2
mov r7,#0 @ z mov r4,r1 @ indice = min //bl displayTable
3: @ loop 3
sub r6,r4,r1 @ compute index - min ldr r5,[fp,r6,lsl #2] @ load count
4: @ loop 4
cmp r5,#0 @ cont <> zero beq 5f str r4,[r0,r7,lsl #2] @ store value add r7,r7,#1 @ increment z sub r5,r5,#1 @ decrement count b 4b
5:
add r4,r4,#1 @ decrement indice cmp r4,r2 @ max ? ble 3b @ no -> loop 3 add sp,sp,r9 @ stack alignement
100:
pop {r1-r9,lr}
bx lr @ return
/******************************************************************/ /* Display table elements */ /******************************************************************/ /* r0 contains the address of table */ displayTable:
push {r0-r3,lr} @ save registers
mov r2,r0 @ table address
mov r3,#0
1: @ loop display table
ldr r0,[r2,r3,lsl #2] ldr r1,iAdrsZoneConv @ bl conversion10S @ décimal conversion ldr r0,iAdrsMessResult ldr r1,iAdrsZoneConv @ insert conversion bl strInsertAtCharInc bl affichageMess @ display message add r3,#1 cmp r3,#NBELEMENTS - 1 ble 1b ldr r0,iAdrszCarriageReturn bl affichageMess mov r0,r2
100:
pop {r0-r3,lr}
bx lr
iAdrsZoneConv: .int sZoneConv /***************************************************/ /* ROUTINES INCLUDE */ /***************************************************/ .include "../affichage.inc" </lang>
Arturo
<lang rebol>countingSort: function [items, minimum, maximum][
a: new items rng: inc maximum - minimum cnt: array.of: rng 0 z: 0
loop 0..dec size a 'i [
mm: a\[i]-minimum
cnt\[mm]: cnt\[mm] + 1
]
loop minimum..maximum 'i [
loop 0..dec cnt\[i-minimum] 'j [
a\[z]: i
z: z + 1
]
]
return a
]
print countingSort [3 1 2 8 5 7 9 4 6] 1 9</lang>
- Output:
1 2 3 4 5 6 7 8 9
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>
BASIC256
<lang 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 </lang>
BBC BASIC
<lang bbcbasic> 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</lang>
Output:
-31 0 1 2 2 4 65 83 99 782
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 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];
}
}
}</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>
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>
C++
<lang cpp>
- 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" );
} //------------------------------------------------------------------------------ </lang>
- Output:
105, -21, 20, 5, 3, 25, 101, 116, 82, 5, 88, 80, -9, 26, 62, 118, 131, -31, 3, 3 8, 40, -6, 46, 90, 7, 59, 104, 76, 12, 79, -31, -21, -9, -6, 3, 3, 5, 5, 7, 12, 20, 25, 26, 38, 40, 46, 59, 62, 76, 79, 80, 82, 88, 90, 101, 104, 105, 116, 118, 131,
Alternate version
Uses C++11. Compile with
g++ -std=c++11 counting.cpp
<lang 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";
}</lang> Output:
-199 -52 2 3 33 56 99 100 177 200
Common Lisp
Straightforward implementation of counting sort. By using map and map-into, counting sort can work efficiently on both lists and vectors. The closure given as the second argument to map-into returns the sorted elements of sequence. Because map-into will only call the function as many times as necessary to re-populate sequence, there is no need for bounds checking. counts is declared to have dynamic-extent and so a compiler might stack allocate it.
<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) 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));
}</lang>
Delphi
See Pascal.
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()
Eiffel
<lang 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 </lang> TEST: <lang 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
</lang>
- Output:
unsorted: -7 4 2 6 1 3 sorted: -7 1 2 3 4 6
Elena
ELENA 4.x : <lang 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())
}</lang>
- Output:
before:6,5,3,1,0,0,7,7,8,2 after :0,0,1,2,3,5,6,7,7,8
Elixir
<lang 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])</lang>
- Output:
[-5, -3, -2, 1, 1, 2, 4, 5, 5, 5, 9]
Fortran
<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
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</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>
FreeBASIC
<lang 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</lang>
- Output:
Unsorted : 4 65 2 -31 0 99 2 83 782 1 Sorted : -31 0 1 2 2 4 65 83 99 782
Go
This version follows the task pseudocode above, with one more optimization. <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() {
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++
}
}
}</lang> This version follows the WP pseudocode. It can be adapted to sort items other than integers. <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() {
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)
}</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 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</lang>
Haxe
<lang haxe>class CountingSort {
public static function sort(arr:Array<Int>) {
var min = arr[0], max = arr[0];
for (i in 1...arr.length) {
if (arr[i] < min)
min = arr[i];
else if (arr[i] > max)
max = arr[i];
}
var range = max - min + 1; var count = new Array<Int>(); count.resize(range * arr.length);
for (i in 0...range) count[i] = 0; for (i in 0...arr.length) count[arr[i] - min]++;
var z = 0;
for (i in min...(max + 1)) {
for (j in 0...count[i - min])
arr[z++] = i;
}
}
}
class Main {
static function main() {
var integerArray = [1, 10, 2, 5, -1, 5, -19, 4, 23, 0];
Sys.println('Unsorted Integers: ' + integerArray);
CountingSort.sort(integerArray);
Sys.println('Sorted Integers: ' + integerArray);
}
}</lang>
- Output:
Unsorted Integers: [1,10,2,5,-1,5,-19,4,23,0] Sorted Integers: [-19,-1,0,1,2,4,5,5,10,23]
Icon and Unicon
The following example is hopefully in the spirit of a counting sort using a hash table as a substituted for a sparse array. Simply translating the pseudo-code would be very un-Iconish (as opposed to Uniconish).
<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)
Io
<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>
IS-BASIC
<lang 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</lang>
J
<lang j>csort =: monad define
min =. <./y
cnt =. 0 $~ 1+(>./y)-min
for_a. y do.
cnt =. cnt >:@{`[`]}~ a-min
end.
cnt # min+i.#cnt
)</lang>
Alternative implementation:
<lang j>csort=: (+/@(=/) # ]) >./ (] + 1 i.@+ -) <./</lang>
Example:
<lang j> ] a =. _3 + 20 ?@$ 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>
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:
<lang j>csrt=:2 :0
(m+i.n-m) (+/@(=/)~ # [) ]
)</lang>
or
<lang j>csrt=:2 :0
(+/@(=/) # ])&(m+i.n-m)
)</lang>
Example:
<lang 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</lang>
Java
<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>
jq
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. <lang 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
);</lang>
Example: <lang jq> [1,2,1,4,0,10] | countingSort(0;10)</lang>
- Output:
<lang sh> $ jq -M -c -n -f counting_sort.jq [0,1,1,2,4,10]</lang>
Julia
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.
<lang 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))")</lang>
- Output:
# unsorted bytes: UInt8[0xcc, 0x67, 0x64, 0xbd, 0x74, 0x18, 0xd2, 0xf8, 0xf1, 0x6c, 0x3e, 0x7c, 0x90, 0x07, 0x48, 0x99, 0xb3, 0xf8, 0x8f, 0x23] -> sorted bytes: UInt8[0x07, 0x18, 0x23, 0x3e, 0x48, 0x64, 0x67, 0x6c, 0x74, 0x7c, 0x8f, 0x90, 0x99, 0xb3, 0xbd, 0xcc, 0xd2, 0xf1, 0xf8, 0xf8] # unsorted integers: [634, 332, 756, 206, 971, 496, 962, 994, 795, 411, 981, 69, 366, 136, 227, 442, 731, 245, 179, 33] -> sorted integers: [33, 69, 136, 179, 206, 227, 245, 332, 366, 411, 442, 496, 634, 731, 756, 795, 962, 971, 981, 994]
Kotlin
<lang 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<String>) {
val array = intArrayOf(4, 65, 2, -31, 0, 99, 2, 83, 782, 1)
println("Original : ${array.asList()}")
countingSort(array)
println("Sorted : ${array.asList()}")
}</lang>
- Output:
Original : [4, 65, 2, -31, 0, 99, 2, 83, 782, 1] Sorted : [-31, 0, 1, 2, 2, 4, 65, 83, 99, 782]
langur
Prior to 0.10, multi-variable declaration/assignment would use parentheses around variable names and values.
<lang langur>val .countingSort = f(.array) {
val .min, .max = minmax(.array)
var .count = arr .max-.min+1, 0
for .i in .array { .count[.i-.min+1] += 1 }
for .i of .count { _for ~= arr .count[.i], .i+.min-1 }
}
val .data = [7, 234, -234, 9, 43, 123, 14]
writeln "Original: ", .data writeln "Sorted : ", .countingSort(.data)</lang>
- Output:
Original: [7, 234, -234, 9, 43, 123, 14] Sorted : [-234, 7, 9, 14, 43, 123, 234]
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>
Mathematica/Wolfram Language
<lang 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++, countnumber - minElem + 1 = countnumber - minElem + 1 + 1;] ; z = 1; For[i = minElem, i < maxElem, i++, While[counti - minElem + 1 > 0, listz = i; z++; counti - minElem + 1 = counti - minElem + 1 - 1;] ]; ]</lang>
countingSort@{2, 3, 1, 5, 7, 6}
->{1, 2, 3, 5, 6, 7}
MATLAB / Octave
This is a direct translation of the pseudo-code, except to compensate for MATLAB using 1 based arrays.
<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>
MAXScript
<lang 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 )</lang>
- Output:
<lang 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)
</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
Nanoquery
<lang nanoquery>def countingSort(array, min, max)
count = {0} * (max - min + 1)
for number in array
count[number - min] += 1
end
z = 0
for i in range(min, max)
while count[i - min] > 0
array[z] = i
z += 1
count[i - min] -= 1;
end
end
end</lang>
NetRexx
Version 1
An almost direct implementation of the pseudocode. <lang 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
</lang>
- Output:
[1,3,6,2,7,13,20,12,21,11,22,10,23,9,24,8,25,43,62,42,63,41,18,42,17,43,16,44,15,45,14,46,79,113,78,114,77,39,78,38] [1,2,3,6,7,8,9,10,11,12,13,14,15,16,17,18,20,21,22,23,24,25,38,39,41,42,42,43,43,44,45,46,62,63,77,78,78,79,113,114]
Version 2
A more Rexx-like (and shorter) version. Due to NetRexx's built in indexed string capability, negative values are also easily supported. <lang 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 </lang>
- Output:
1 3 6 2 7 13 20 12 21 11 22 10 23 9 24 8 25 43 62 42 63 41 18 42 17 43 16 44 15 45 14 46 79 113 78 114 77 39 78 38 0 -200 -6 -10 -0 -200 -10 -6 0 0 1 2 3 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21 22 23 24 25 38 39 41 42 42 43 43 44 45 46 62 63 77 78 78 79 113 114
Nim
<lang nim>proc countingSort[T](a: var openarray[T]; min, max: int) =
let range = max - min + 1 var count = newSeq[T](range) var z = 0
for i in 0 ..< a.len: inc count[a[i] - min]
for i in min .. max:
for j in 0 ..< count[i - min]:
a[z] = i
inc z
var a = @[5, 3, 1, 7, 4, 1, 1, 20] countingSort(a, 1, 20) echo a</lang> Output:
@[1, 1, 1, 3, 4, 5, 7, 20]
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 $_} @cnt;
}</lang>
Testing:
<lang perl>my @ages = map {int(rand(140))} 1 .. 100;
counting_sort(\@ages, 0, 140); print join("\n", @ages), "\n";</lang>
Phix
with javascript_semantics function countingSort(sequence array, integer mina, maxa) sequence count = repeat(0,maxa-mina+1) array = deep_copy(array) for i=1 to length(array) do count[array[i]-mina+1] += 1 end for integer z = 1 for i=mina to maxa do for j=1 to count[i-mina+1] do array[z] := i z += 1 end for end for return array end function sequence s = {5, 3, 1, 7, 4, 1, 1, 20} ?countingSort(s,min(s),max(s))
- Output:
{1,1,1,3,4,5,7,20}
PHP
<lang php><?php
function counting_sort(&$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>
PowerShell
<lang 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)" </lang> Output:
13 18 8 6 3 7 22 20 10 7 18 10 25 13 9 21 8 19 24 24 18 6 23 23 24 7 15 25 24 25 11 23 19 5 4 8 9 7 1 19 10 24 13 1 9 0 9 10 19 16 0 1 1 3 4 5 6 6 7 7 7 7 8 8 8 9 9 9 9 10 10 10 10 11 13 13 13 15 16 18 18 18 19 19 19 19 20 21 22 23 23 23 24 24 24 24 24 25 25 25
PureBasic
<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:
<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>
Quackery
<lang Quackery> [ 2dup peek 1+
unrot poke ] is [1+] ( [ n --> [ )
[ 1+ dip tuck -
rot 0 swap of
swap rot witheach
[ over +
rot swap [1+]
swap ]
negate swap
[] swap witheach
[ dip [ over i^ + ]
of join ]
nip ] is csort ( [ n n --> [ )
[] 15 times
[ 10 random 10 + join ]
dup say "Before: " echo cr
10 19 csort
say "After: " echo</lang>
- Output:
Before: [ 16 14 15 10 19 18 12 16 12 14 10 13 12 15 18 ] After: [ 10 10 12 12 12 13 14 14 15 15 16 16 18 18 19 ]
R
<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
}
- 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)</lang>
Racket
<lang 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) </lang> Output: <lang racket> '#(-1 0 1 1 2 3 3 4 7 8 9) </lang>
Raku
(formerly Perl 6)
<lang 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';</lang>
- Output:
(5 5 5 7 9 17 19 19 20 21 25 27 28 30 32 34 38 40 41 45 48 49 50 51 53 54 55 56 59 62 65 66 67 69 70 73 74 81 83 85 87 91 91 93 94 96 99 99 100 101) (5 5 5 7 9 17 19 19 20 21 25 27 28 30 32 34 38 40 41 45 48 49 50 51 53 54 55 56 59 62 65 66 67 69 70 73 74 81 83 85 87 91 91 93 94 96 99 99 100 101) ok
REXX
These REXX versions make use of sparse arrays.
Negative, zero, and positive integers are supported.
version 1
<lang 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= 1; LO= word($, #); HI= LO /*M: max width of any integer in $ list*/
do j=1 for #; z= word($, j)+0; @.j= z; m= max(m, length(z) ) /*get from $ list*/
!.z= !.z + 1; LO= min(LO, z); HI= max(HI, z) /*find LO and HI.*/
end /*j*/
/*W: max index width for the @. array.*/
call show 'before sort: '; say copies('▓', 55) /*show the before array elements. */ call countSort # /*sort a number of entries of @. array.*/ call show ' after sort: ' /*show the after array elements. */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ countSort: parse arg N; x= 1; do k=LO to HI; do x=x for !.k; @.x= k; end /*x*/
end /*k*/
return
/*──────────────────────────────────────────────────────────────────────────────────────*/ show: do s=1 for #; say right("element",20) right(s,w) arg(1) right(@.s,m); end; return</lang>
- output when using the default input:
(Shown at 5/6 size.)
element 1 before sort: 1
element 2 before sort: 3
element 3 before sort: 6
element 4 before sort: 2
element 5 before sort: 7
element 6 before sort: 13
element 7 before sort: 20
element 8 before sort: 12
element 9 before sort: 21
element 10 before sort: 11
element 11 before sort: 22
element 12 before sort: 10
element 13 before sort: 23
element 14 before sort: 9
element 15 before sort: 24
element 16 before sort: 8
element 17 before sort: 25
element 18 before sort: 43
element 19 before sort: 62
element 20 before sort: 42
element 21 before sort: 63
element 22 before sort: 41
element 23 before sort: 18
element 24 before sort: 42
element 25 before sort: 17
element 26 before sort: 43
element 27 before sort: 16
element 28 before sort: 44
element 29 before sort: 15
element 30 before sort: 45
element 31 before sort: 14
element 32 before sort: 46
element 33 before sort: 79
element 34 before sort: 113
element 35 before sort: 78
element 36 before sort: 114
element 37 before sort: 77
element 38 before sort: 39
element 39 before sort: 78
element 40 before sort: 38
▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
element 1 after sort: 1
element 2 after sort: 2
element 3 after sort: 3
element 4 after sort: 6
element 5 after sort: 7
element 6 after sort: 8
element 7 after sort: 9
element 8 after sort: 10
element 9 after sort: 11
element 10 after sort: 12
element 11 after sort: 13
element 12 after sort: 14
element 13 after sort: 15
element 14 after sort: 16
element 15 after sort: 17
element 16 after sort: 18
element 17 after sort: 20
element 18 after sort: 21
element 19 after sort: 22
element 20 after sort: 23
element 21 after sort: 24
element 22 after sort: 25
element 23 after sort: 38
element 24 after sort: 39
element 25 after sort: 41
element 26 after sort: 42
element 27 after sort: 42
element 28 after sort: 43
element 29 after sort: 43
element 30 after sort: 44
element 31 after sort: 45
element 32 after sort: 46
element 33 after sort: 62
element 34 after sort: 63
element 35 after sort: 77
element 36 after sort: 78
element 37 after sort: 78
element 38 after sort: 79
element 39 after sort: 113
element 40 after sort: 114
version 2
<lang 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</lang> Output:
before count_sort 999 888 777 1 5 13 15 17 19 21 5 after count_sort 1 5 5 13 15 17 19 21 777 888 999
Ring
<lang 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
</lang>
Ruby
<lang 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]</lang>
Rust
<lang rust>fn counting_sort(
mut data: Vec<usize>, min: usize, max: usize,
) -> Vec<usize> {
// create and fill counting bucket with 0 let mut count: Vec<usize> = Vec::with_capacity(data.len()); count.resize(data.len(), 0);
for num in &data {
count[num - min] = count[num - min] + 1;
}
let mut z: usize = 0;
for i in min..max+1 {
while count[i - min] > 0 {
data[z] = i;
z += 1;
count[i - min] = count[i - min] - 1;
}
}
data
}
fn main() {
let arr1 = vec![1, 0, 2, 9, 3, 8, 4, 7, 5, 6];
println!("{:?}", counting_sort(arr1, 0, 9));
let arr2 = vec![0, 1, 2, 3, 4, 5, 6, 7, 8, 9];
println!("{:?}", counting_sort(arr2, 0, 9));
let arr3 = vec![10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0];
println!("{:?}", counting_sort(arr3, 0, 10));
}</lang>
- Output:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9] [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
Scala
<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>
It's better (i.e. slightly faster) to reverse the frequencies list before processing it, instead of the whole result <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.reverse.foldLeft(List[Int]()) {
case (lst, (cnt, ndx)) => List.fill(cnt)(ndx + min) ::: lst
}</lang>
Sidef
<lang 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)</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
<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
<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
VBA
<lang 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</lang>
- Output:
1, 1, 1, 3, 4, 5, 7, 20
VBScript
All my other sort demos just pass in the array, thus the findMax and findMin
Implementation
<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
Vlang
<lang vlang>fn counting_sort(arr mut []int, min int, max int) { println('Input: ' + arr.str()) mut count := [0].repeat(max - min + 1) for i in 0 .. arr.len { nbr := arr[i] ndx1 := nbr - min count[ndx1] = count[ndx1] + 1 } mut z := 0 for i in min .. max { curr := i - min for count[curr] > 0 { arr[z] = i z++ count[curr]-- } } println('Output: ' + arr.str()) }
fn main() { mut arr := [6, 2, 1, 7, 6, 8] counting_sort(mut arr, 1, 8) }</lang>
- Output:
Input: [6, 2, 1, 7, 6, 8] Output: [1, 2, 6, 6, 7, 8]
Wren
<lang ecmascript>var countingSort = Fn.new { |a, min, max|
var count = List.filled(max - min + 1, 0)
for (n in a) count[n - min] = count[n - min] + 1
var z = 0
for (i in min..max) {
while (count[i - min] > 0) {
a[z] = i
z = z + 1
count[i - min] = count[i - min] - 1
}
}
}
var a = [4, 65, 2, -31, 0, 99, 2, 83, 782, 1] System.print("Unsorted: %(a)") var min = a.reduce { |min, i| (i < min) ? i : min } var max = a.reduce { |max, i| (i > max) ? i : max } countingSort.call(a, min, max) System.print("Sorted : %(a)")</lang>
- Output:
Unsorted: [4, 65, 2, -31, 0, 99, 2, 83, 782, 1] Sorted : [-31, 0, 1, 2, 2, 4, 65, 83, 99, 782]
XPL0
<lang 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, ^ )]; ]</lang>
- Output:
-5 1 1 2 3 4 4 5 6 9
zkl
<lang 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
}</lang> <lang zkl>array:=List(4, 65, 2, -31, 0, 99, 2, 83, 182, 1); countingSort(array,(0).min(array), (0).max(array)).println();</lang>
- Output:
L(-31,0,1,2,2,4,65,83,99,182)
- Programming Tasks
- Sorting Algorithms
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