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You are encouraged to solve this task according to the task description, using any language you may know.

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

O(n logn) sorts

O(n log2n) sorts
Shell Sort

Sort an array of positive integers using the Bead Sort Algorithm.

A   bead sort   is also known as a   gravity sort.

Algorithm has   O(S),   where   S   is the sum of the integers in the input set:   Each bead is moved individually.

This is the case when bead sort is implemented without a mechanism to assist in finding empty spaces below the beads, such as in software implementations.

## 11l

Translation of: Nim
```F bead_sort(&a)
V maxv = max(a)
V beads = [0] * (maxv * a.len)

L(i) 0 .< a.len
L(j) 0 .< a[i]
beads[i * maxv + j] = 1

L(j) 0 .< maxv
V sum = 0
L(i) 0 .< a.len
sum += beads[i * maxv + j]
beads[i * maxv + j] = 0

L(i) a.len - sum .< a.len
beads[i * maxv + j] = 1

L(i) 0 .< a.len
V j = 0
L j < maxv & beads[i * maxv + j] > 0
j++
a[i] = j

V a = [5, 3, 1, 7, 4, 1, 1, 20]
print(a)```
Output:
```[1, 1, 1, 3, 4, 5, 7, 20]
```

## 360 Assembly

Translation of: ooRexx

For maximum compatibility, this program uses only the basic instruction set (S/360) and two ASSIST macros (XDECO,XPRNT) to keep it as short as possible.

```*        Bead Sort                 11/05/2016
SAVEAR   B      STM-SAVEAR(R15)    skip savearea
DC     17F'0'             savearea
STM      STM    R14,R12,12(R13)    prolog
ST     R13,4(R15)         "
ST     R15,8(R13)         "
LR     R13,R15            "
LA     R6,1               i=1
LOOPI1   CH     R6,=AL2(N)         do i=1 to hbound(z)
BH     ELOOPI1            leave i
LR     R1,R6                i
SLA    R1,1                 <<1
LH     R2,Z-2(R1)           z(i)
CH     R2,LO                if z(i)<lo
BNL    EIHO                 then
STH    R2,LO                  lo=z(i)
EIHLO    CH     R2,HI                if z(i)>hi
BNH    EIHHI                then
STH    R2,HI                  hi=z(i)
EIHHI    LA     R6,1(R6)           iterate i
B      LOOPI1             next i
ELOOPI1  LA     R9,1               1
SH     R9,LO              -lo+1
LA     R6,1               i=1
LOOPI2   CH     R6,=AL2(N)         do i=1 to hbound(z)
BH     ELOOPI2            leave i
LR     R1,R6                i
SLA    R1,1                 <<1
LH     R3,Z-2(R1)           z(i)
AR     R3,R9                z(i)+o
LA     R6,1(R6)           iterate i
B      LOOPI2             next i
ELOOPI2  SR     R8,R8              k=0
LH     R6,LO              i=lo
LOOPI3   CH     R6,HI              do i=lo to hi
BH     ELOOPI3            leave i
LA     R7,1                 j=1
SR     R10,R10              clear r10
LR     R1,R6                i
AR     R1,R9                i+o
LOOPJ3   CR     R7,R10               do j=1 to beads(i+o)
BH     ELOOPJ3              leave j
LA     R8,1(R8)               k=k+1
LR     R1,R8                  k
SLA    R1,1                   <<1
STH    R6,S-2(R1)             s(k)=i
LA     R7,1(R7)             iterate j
B      LOOPJ3               next j
ELOOPJ3  AH     R6,=H'1'           iterate i
B      LOOPI3             next i
ELOOPI3  LA     R7,1               j=1
LOOPJ4   CH     R7,=H'2'           do j=1 to 2
BH     ELOOPJ4            leave j
CH     R7,=H'1'             if j<>1
BE     ONE                  then
MVC    PG(7),=C'sorted:'      zap
ONE      LA     R10,PG+7             pgi=@pg+7
LA     R6,1                 i=1
LOOPI4   CH     R6,=AL2(N)           do i=1 to hbound(z)
BH     ELOOPI4              leave i
CH     R7,=H'1'               if j=1
BNE    TWO                    then
LR     R1,R6                    i
SLA    R1,1                     <<1
LH     R11,Z-2(R1)              zs=z(i)
B      XDECO                  else
TWO      LR     R1,R6                    i
SLA    R1,1                     <<1
LH     R11,S-2(R1)              zs=s(i)
XDECO    XDECO  R11,XDEC               edit zs
MVC    0(6,R10),XDEC+6        output zs
LA     R10,6(R10)             pgi=pgi+6
LA     R6,1(R6)             iterate i
B      LOOPI4               next i
ELOOPI4  XPRNT  PG,80                print buffer
LA     R7,1(R7)             iterate j
B      LOOPJ4             next j
ELOOPJ4  L      R13,4(0,R13)       epilog
LM     R14,R12,12(R13)    "
XR     R15,R15            "
BR     R14                "
LTORG                     literal table
N        EQU    (S-Z)/2            number of items
Z        DC     H'5',H'3',H'1',H'7',H'-1',H'4',H'9',H'-12'
DC     H'2001',H'-2010',H'17',H'0'
S        DS     (N)H               s same size as z
LO       DC     H'32767'           2**31-1
HI       DC     H'-32768'          -2**31
PG       DC     CL80'   raw:'      buffer
XDEC     DS     CL12               temp
YREGS
Output:
```   raw:     5     3     1     7    -1     4     9   -12  2001 -2010    17     0
sorted: -2010   -12    -1     0     1     3     4     5     7     9    17  2001
```

## AArch64 Assembly

Works with: as version Raspberry Pi 3B version Buster 64 bits
```/* ARM assembly AARCH64 Raspberry PI 3B */
/* En français tri par gravité ou tri par bille (ne pas confondre
avec tri par bulle (bubble sort)) */

/*******************************************/
/* 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
.equ NBELEMENTS, (. - TableNumber) / 8
//.equ NBELEMENTS, 4 // for others tests
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss
sZoneConv:            .skip 24
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main
main:                         // entry of program

1:
mov x1,#NBELEMENTS        // number of élements
mov x1,#NBELEMENTS        // number of élements
bl displayTable

mov x1,#NBELEMENTS        // number of élements
bl isSorted               // control sort
cmp x0,#1                 // sorted ?
beq 2f
ldr x0,qAdrszMessSortNok  // no !! error sort
bl affichageMess
b 100f
2:                            // yes
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

/******************************************************************/
/*     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]        // load A[0]
1:
cmp x2,x1                    // end ?
bge 99f
ldr x3,[x0,x2, lsl #3]       // load A[i]
cmp x3,x4                    // compare A[i],A[i-1]
blt 98f                      // smaller -> error -> return
mov x4,x3                    // no -> A[i-1] = A[i]
b 1b                         // and loop
98:
mov x0,#0                    // error
b 100f
99:
mov x0,#1                    // ok -> return
100:
ldp x2,x3,[sp],16            // restaur  2 registers
ldp x1,lr,[sp],16            // restaur  2 registers
/******************************************************************/
/******************************************************************/
/* x0 contains the address of table */
/* x1 contains the number of element */
/* Caution registers x2-x12 are not saved */
stp x1,lr,[sp,-16]!       // save  registers
mov x12,x1                // save elements number
//search max
ldr x10,[x0]              // load value A[0] in max
mov x4,#1
1:                            // loop search max
cmp x4,x12                // end ?
bge 21f                   // yes
ldr x2,[x0,x4,lsl #3]     // load value A[i]
cmp x2,x10                // compare with max
csel x10,x2,x10,gt        // if greather
b 1b                      // loop
21:
mul x5,x10,x12            // max * elements number
lsl x5,x5,#3              // 8 bytes for each number
sub sp,sp,x5              // allocate on the stack
mov fp,sp                 // frame pointer = stack address
mov x3,x0                 // save table address
mov x0,#0                 // start index x
2:
mov x1,#0                 // index y
ldr x8,[x3,x0,lsl #3]     // load A[x]
mul x6,x0,x10             // compute bead x
3:
mov x4,#1                 // value to store
str x4,[fp,x9,lsl #3]     // store to stack area
cmp x1,x8
blt 3b
31:                           // init to zéro the bead end
cmp x1,x10                // max ?
bge 32f
mov x4,#0
str x4,[fp,x9,lsl #3]
b 31b
32:
cmp x0,x12                // end ?
blt 2b
mov x1,#0                 // y
4:
mov x0,#0                 // start index x
mov x8,#0                 // sum
5:
mul x6,x0,x10             // compute bead x
ldr x4,[fp,x9,lsl #3]
mov x4,#0
str x4,[fp,x9,lsl #3]     // raz bead
cmp x0,x12
blt 5b
sub x0,x12,x8             // compute end - sum
6:
mul x6,x0,x10             // compute bead x
mov x4,#1
str x4,[fp,x9,lsl #3]     // store new bead at end
cmp x0,x12
blt 6b

cmp x1,x10
blt 4b

// final compute
mov x0,#0                 // start index x
7:
mov x1,#0                 // start index y
mul x6,x0,x10             // compute bead x
8:
add x1,x1,#1              // add to x1 before str (index start at zéro)
cmp x4,#1
bne 9f
str x1,[x3,x0, lsl #3]    // store A[x]
9:
cmp x1,x10                // compare max
blt 8b
cmp x0,x12                // end ?
blt 7b

mov x0,#0
100:
ldp x1,lr,[sp],16         // restaur  2 registers
/******************************************************************/
/*      Display table elements                                */
/******************************************************************/
/* x0 contains the address of table */
/* x1 contains elements number  */
displayTable:
stp x1,lr,[sp,-16]!          // save  registers
stp x2,x3,[sp,-16]!          // save  registers
mov x4,x1                    // elements number
mov x3,#0
1:                               // loop display table
ldr x0,[x2,x3,lsl #3]
bl conversion10              // décimal conversion
bl strInsertAtCharInc
bl affichageMess             // display message
cmp x3,x4                    // end ?
blt 1b                       // no -> loop
bl affichageMess
100:
ldp x2,x3,[sp],16            // restaur  2 registers
ldp x1,lr,[sp],16            // restaur  2 registers

/********************************************************/
/*        File Include fonctions                        */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"```

## ARM Assembly

Works with: as version Raspberry Pi
```/* ARM assembly Raspberry PI  */
/* En français tri par gravité ou tri par bille (ne pas confondre
avec tri par bulle (bubble sort) */

/* 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"

/*********************************/
/* Initialized data              */
/*********************************/
.data
szMessSortOk:       .asciz "Table sorted.\n"
szMessSortNok:      .asciz "Table not sorted !!!!!.\n"
sMessResult:        .asciz "Value  : @ \n"
szCarriageReturn:   .asciz "\n"

.align 4
TableNumber:      .int   1,3,6,2,5,9,10,8,4,7
#TableNumber:     .int   10,9,8,7,6,5,4,3,2,1
.equ NBELEMENTS, (. - TableNumber) / 4
@.equ NBELEMENTS, 4 @ for others tests
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss
sZoneConv:            .skip 24
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main
main:                         @ entry of program

1:
mov r1,#NBELEMENTS        @ number of élements
mov r1,#NBELEMENTS        @ number of élements
bl displayTable

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
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

/******************************************************************/
/*     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]        @ load A[0]
1:
cmp r2,r1                    @ end ?
movge r0,#1                  @ yes -> ok -> return
bge 100f
ldr r3,[r0,r2, lsl #2]       @ load A[i]
cmp r3,r4                    @ compare A[i],A[i-1]
movlt r0,#0                  @ smaller ?
blt 100f                     @ yes -> error -> return
mov r4,r3                    @ no -> A[i-1] = A[i]
b 1b                         @ and loop
100:
pop {r2-r4,lr}
bx lr                        @ return
/******************************************************************/
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the number of element */
push {r1-r12,lr}          @ save registers
mov r12,r1                @ save elements number
@search max
ldr r10,[r0]              @ load value A[0] in max
mov r4,#1
1:                            @ loop search max
cmp r4,r12                @ end ?
bge 21f                   @ yes
ldr r2,[r0,r4,lsl #2]     @ load value A[i]
cmp r2,r10                @ compare with max
movgt r10,r2              @ if greather
b 1b                      @ loop
21:
mul r5,r10,r12            @ max * elements number
lsl r5,r5,#2              @ 4 bytes for each number
sub sp,sp,r5              @ allocate on the stack
mov fp,sp                 @ frame pointer = stack address
mov r3,r0                 @ save table address
mov r0,#0                 @ start index x
2:
mov r1,#0                 @ index y
ldr r7,[r3,r0,lsl #2]     @ load A[x]
mul r6,r0,r10             @ compute bead x
3:
mov r4,#1                 @ value to store
str r4,[fp,r9,lsl #2]     @ store to stack area
cmp r1,r7
blt 3b
31:                           @ init to zéro the bead end
cmp r1,r10                @ max ?
bge 32f
mov r4,#0
str r4,[fp,r9,lsl #2]
b 31b
32:
cmp r0,r12                @ end ?
blt 2b
mov r1,#0                 @ y
4:
mov r0,#0                 @ start index x
mov r8,#0                 @ sum
5:
mul r6,r0,r10             @ compute bead x
ldr r4,[fp,r9,lsl #2]
mov r4,#0
str r4,[fp,r9,lsl #2]
cmp r0,r12
blt 5b
sub r0,r12,r8
6:
mul r6,r0,r10             @ compute bead x
mov r4,#1
str r4,[fp,r9,lsl #2]
cmp r0,r12
blt 6b

cmp r1,r10
blt 4b

@ suite
mov r0,#0                 @ start index
7:
mov r1,#0
mul r6,r0,r10             @ compute bead x
8:
ldr r4,[fp,r9,lsl #2]
add r1,r1,#1              @ add to r1 before str (index start at zéro)
cmp r4,#1
streq r1,[r3,r0, lsl #2]  @ store A[i]
cmp r1,r10                @ compare max
blt 8b
cmp r0,r12                @ end ?
blt 7b

mov r0,#0
100:
pop {r1-r12,lr}
bx lr                     @ return
/******************************************************************/
/*      Display table elements                                */
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains elements number  */
displayTable:
push {r0-r4,lr}              @ save registers
mov r4,r1                    @ elements number
mov r3,#0
1:                               @ loop display table
ldr r0,[r2,r3,lsl #2]
bl conversion10              @ décimal conversion
bl strInsertAtCharInc
bl affichageMess             @ display message
cmp r3,r4                    @ end ?
blt 1b                       @ no -> loop
bl affichageMess
100:
pop {r0-r4,lr}
bx lr
/***************************************************/
/*      ROUTINES INCLUDE                           */
/***************************************************/
.include "../affichage.inc"```

## Arturo

```beadSort: function [items][
a: new items
m: neg infinity
s: 0

loop a 'x [
if x > m -> m: x
]

beads: array.of: m * size a 0

loop 0..dec size a 'i [
loop 0..dec a\[i] 'j ->
beads\[j + i * m]: 1
]

loop 0..dec m 'j [
s: 0
loop 0..dec size a 'i [
s: s + beads\[j + i*m]
]

loop ((size a)-s)..dec size a 'i ->
]

loop 0..dec size a 'i [
j: 0
while [and? [j < m] [beads\[j + i*m] > 0]] -> j: j + 1
a\[i]: j
]

return a
]

print beadSort [3 1 2 8 5 7 9 4 6]
```
Output:
`1 2 3 4 5 6 7 8 9`

## AutoHotkey

```BeadSort(data){
Pole:=[]	, TempObj:=[], Result:=[]
for, i, v in data {
Row := i
loop, % v
MaxPole := MaxPole>A_Index?MaxPole:A_Index	, Pole[A_Index, row] := 1
}

for i , obj in Pole {
TempVar:=0	,	c := A_Index
for n, v in obj
TempVar += v
loop, % TempVar
TempObj[c, A_Index] := 1
}

loop, % Row {
TempVar:=0	,	c := A_Index
Loop, % MaxPole
TempVar += TempObj[A_Index,c]
Result[c] := TempVar
}
return Result
}
```

Examples:

```for i, val in BeadSort([54,12,87,56,36])
res := val (res?",":"") res
MsgBox % res
```
Output:
`12,36,54,56,87`

## BCPL

```get "libhdr"

let max(A, len) = valof
\$(  let x = 0
for i=0 to len-1
if x<A!i do x := A!i
resultis x
\$)

\$(  let size = max(A, len)
let tvec = getvec(size-1)
for i=0 to size-1 do tvec!i := 0
for i=0 to len-1
for j=0 to A!i-1 do tvec!j := tvec!j + 1
for i=len-1 to 0 by -1
\$(  let n = 0
for j=0 to size-1
if tvec!j > 0
\$(  tvec!j := tvec!j - 1
n := n + 1
\$)
A!i := n
\$)
freevec(tvec)
\$)

let write(s, A, len) be
\$(  writes(s)
for i=0 to len-1 do writed(A!i, 4)
wrch('*N')
\$)

let start() be
\$(  let array = table 10,1,5,5,9,2,20,6,8,4
let length = 10
write("Before: ", array, length)
write("After:  ", array, length)
\$)```
Output:
```Before:   10   1   5   5   9   2  20   6   8   4
After:     1   2   4   5   5   6   8   9  10  20```

## C

A rather straightforward implementation; since we do not use dynamic matrix, we have to know the maximum value in the array in advance. Requires (max * length) bytes for beads; if memory is of concern, bytes can be replaced by bits.

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

{
int i, j, max, sum;

for (i = 1, max = a[0]; i < len; i++)
if (a[i] > max) max = a[i];

beads = calloc(1, max * len);

for (i = 0; i < len; i++)
for (j = 0; j < a[i]; j++)

for (j = 0; j < max; j++) {
/* count how many beads are on each post */
for (sum = i = 0; i < len; i++) {
}
/* mark bottom sum beads */
for (i = len - sum; i < len; i++) BEAD(i, j) = 1;
}

for (i = 0; i < len; i++) {
for (j = 0; j < max && BEAD(i, j); j++);
a[i] = j;
}
}

int main()
{
int i, x[] = {5, 3, 1, 7, 4, 1, 1, 20};
int len = sizeof(x)/sizeof(x[0]);

for (i = 0; i < len; i++)
printf("%d\n", x[i]);

return 0;
}
```

## C++

```//this algorithm only works with positive, whole numbers.
//O(2n) time complexity where n is the summation of the whole list to be sorted.
//O(3n) space complexity.

#include <iostream>
#include <vector>

using std::cout;
using std::vector;

void distribute(int dist, vector<int> &List) {
if (dist > List.size() )
List.resize(dist); //resize if too big for current vector

for (int i=0; i < dist; i++)
List[i]++;
}

vector<int> beadSort(int *myints, int n) {
vector<int> list, list2, fifth (myints, myints + n);

cout << "#1 Beads falling down: ";
for (int i=0; i < fifth.size(); i++)
distribute (fifth[i], list);
cout << '\n';

cout << "\nBeads on their sides: ";
for (int i=0; i < list.size(); i++)
cout << " " << list[i];
cout << '\n';

//second part

cout << "#2 Beads right side up: ";
for (int i=0; i < list.size(); i++)
distribute (list[i], list2);
cout << '\n';

return list2;
}

int main() {
int myints[] = {734,3,1,24,324,324,32,432,42,3,4,1,1};
cout << "Sorted list/array: ";
for(unsigned int i=0; i<sorted.size(); i++)
cout << sorted[i] << ' ';
}
```

## Clojure

```(defn transpose [xs]
(loop [ret [], remain xs]
(if (empty? remain)
ret
(recur (conj ret (map first remain))
(filter not-empty (map rest remain))))))

(->> xs
(map #(repeat % 1))
transpose
transpose
(map #(reduce + %))))

;; This algorithm does not work if collection has zero
(-> [5 2 4 1 3 3 9] bead-sort println)
```
Output:
`(9 5 4 3 3 2 1)`

## COBOL

Works with: GnuCOBOL
```        >>SOURCE FORMAT FREE
*> This code is dedicated to the public domain
*> This is GNUCOBOL 2.0
identification division.
environment division.
configuration section.
repository. function all intrinsic.
data division.
working-storage section.
01  filler.
03  row occurs 9 pic x(9).
03  r pic 99.
03  r1 pic 99.
03  r2 pic 99.
03  pole pic 99.
03  a-lim pic 99 value 9.
03  a pic 99.
03  array occurs 9 pic 9.
01  NL pic x value x'0A'.
procedure division.

*> fill the array
compute a = random(seconds-past-midnight)
perform varying a from 1 by 1 until a > a-lim
compute array(a) = random() * 10
end-perform

perform display-array
display space 'initial array'

perform varying r from 1 by 1 until r > a-lim
move all '.' to row(r)
perform varying pole from 1 by 1 until pole > array(r)
move 'o' to row(r)(pole:1)
end-perform
end-perform

perform varying pole from 1 by 1 until pole > a-lim
move a-lim to r2
perform find-opening
compute r1 = r2 - 1
perform until r1 = 0 *> no bead or no opening
move '.' to row(r1)(pole:1)
move 'o' to row(r2)(pole:1)
*> continue up the pole
compute r2 = r2 - 1
perform find-opening
compute r1 = r2 - 1
end-perform
end-perform

*> count the beads in each row
perform varying r from 1 by 1 until r > a-lim
move 0 to array(r)
inspect row(r) tallying array(r)
for all 'o' before initial '.'
end-perform

perform display-array
display space 'sorted array'

stop run
.
find-opening.
perform varying r2 from r2 by -1
until r2 = 1 or row(r2)(pole:1) = '.'
continue
end-perform
.
perform varying r1 from r1 by -1
until r1 = 0 or row(r1)(pole:1) = 'o'
continue
end-perform
.
display-array.
display space
perform varying a from 1 by 1 until a > a-lim
display space array(a) with no advancing
end-perform
.
perform varying r from 1 by 1 until r > a-lim
display row(r)
end-perform
.
```
Output:
```prompt\$ cobc -xj beadsort.cob

3 2 1 6 1 6 4 9 7 initial array

ooo......
oo.......
o........
oooooo...
o........
oooooo...
oooo.....
ooooooooo
ooooooo..

o........
o........
oo.......
ooo......
oooo.....
oooooo...
oooooo...
ooooooo..
ooooooooo

1 1 2 3 4 6 6 7 9 sorted array```

## Common Lisp

Translation of: Clojure
```(defun transpose (remain &optional (ret '()))
(if (null remain)
ret
(transpose (remove-if #'null (mapcar #'cdr remain))
(append ret (list (mapcar #'car remain))))))

(mapcar #'length (transpose (transpose (mapcar (lambda (x) (make-list x :initial-element 1)) xs)))))

(bead-sort '(5 2 4 1 3 3 9))
```
Output:
`(9 5 4 3 3 2 1)`

## D

A functional-style solution.

```import std.stdio, std.algorithm, std.range, std.array, std.functional;

alias repeat0 = curry!(repeat, 0);

// Currenty std.range.transposed doesn't work.
auto columns(R)(R m) pure /*nothrow*/ @safe /*@nogc*/ {
return m
.map!walkLength
.reduce!max
.iota
.map!(i => m.filter!(s => s.length > i).walkLength.repeat0);
}

auto beadSort(in uint[] data) pure /*nothrow @nogc*/ {
return data.map!repeat0.columns.columns.map!walkLength;
}

void main() {
[5, 3, 1, 7, 4, 1, 1].beadSort.writeln;
}
```
Output:
`[7, 5, 4, 3, 1, 1, 1]`

## Delphi

Translation of: C
```program BeadSortTest;

{\$APPTYPE CONSOLE}

uses
SysUtils;

procedure BeadSort(var a : array of integer);
var
i, j, max, sum : integer;
beads : array of array of integer;
begin
max := a[Low(a)];
for i := Low(a) + 1 to High(a) do
if a[i] > max then
max := a[i];

SetLength(beads, High(a) - Low(a) + 1, max);

for i := Low(a) to High(a) do
for j := 0 to a[i] - 1 do

for j := 0 to max - 1 do
begin
// count how many beads are on each post
sum := 0;
for i := Low(a) to High(a) do
begin
sum := sum + beads[i, j];
end;
for i := High(a) + 1 - sum to High(a) do
end;

for i := Low(a) to High(a) do
begin
j := 0;
while (j < max) and (beads[i, j] <> 0) do
inc(j);
a[i] := j;
end;

end;

const
N = 8;
var
i : integer;
x : array[1..N] of integer = (5, 3, 1, 7, 4, 1, 1, 20);
begin
for i := 1 to N do
writeln(Format('x[%d] = %d', [i, x[i]]));

for i := 1 to N do
writeln(Format('x[%d] = %d', [i, x[i]]));

end.
```

--DavidIzadaR 18:12, 7 August 2011 (UTC)

## Eiffel

```class

feature

bead_sort (ar: ARRAY [INTEGER]): ARRAY [INTEGER]
-- Sorted array in descending order.
require
only_positive_integers: across ar as a all a.item > 0 end
local
max, count, i, j, k: INTEGER
do
max := max_item (ar)
create Result.make_filled (0, 1, ar.count)
from
i := 1
until
i > max
loop
count := 0
from
k := 1
until
k > ar.count
loop
if ar.item (k) >= i then
count := count + 1
end
k := k + 1
end
from
j := 1
until
j > count
loop
Result [j] := i
j := j + 1
end
i := i + 1
end
ensure
array_is_sorted: is_sorted (Result)
end

feature {NONE}

max_item (ar: ARRAY [INTEGER]): INTEGER
-- Max item of 'ar'.
require
ar_not_void: ar /= Void
do
across
ar as a
loop
if a.item > Result then
Result := a.item
end
end
ensure
Result_is_max: across ar as a all a.item <= Result end
end

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

end
```

Test:

```class
APPLICATION

create
make

feature

make
do
test := <<1, 5, 99, 2, 95, 7, 7>>
io.put_string ("unsorted:" + "%N")
across
test as ar
loop
io.put_string (ar.item.out + "%T")
end
io.put_string ("%N" + "sorted:" + "%N")
across
test as ar
loop
io.put_string (ar.item.out + "%T")
end
end

test: ARRAY [INTEGER]

end
```
Output:
```unsorted:
1 5 99 2 95 7 7
sorted:
99 95 7 7 5 2 1
```

## Elixir

Translation of: Erlang
```defmodule Sort do
def bead_sort(list) when is_list(list), do: dist(dist(list))

defp dist(list), do: List.foldl(list, [], fn(n, acc) when n>0 -> dist(acc, n, []) end)

defp dist([],    0, acc), do: Enum.reverse(acc)
defp dist([h|t], 0, acc), do: dist(t,    0, [h  |acc])
defp dist([],    n, acc), do: dist([], n-1, [1  |acc])
defp dist([h|t], n, acc), do: dist(t,  n-1, [h+1|acc])
end
```

Example:

```iex(20)> Sort.bead_sort([5,3,9,4,1,6,8,2,7])
[9, 8, 7, 6, 5, 4, 3, 2, 1]
```

## Erlang

```-module(beadsort).

-export([sort/1]).

sort(L) ->
dist(dist(L)).

dist(L) when is_list(L) ->
lists:foldl(fun (N, Acc) -> dist(Acc, N, []) end, [], L).

dist([H | T], N, Acc) when N > 0 ->
dist(T, N - 1, [H + 1 | Acc]);
dist([], N, Acc) when N > 0 ->
dist([], N - 1, [1 | Acc]);
dist([H | T], 0, Acc) ->
dist(T, 0, [H | Acc]);
dist([], 0, Acc) ->
lists:reverse(Acc).
```

Example;

```1> beadsort:sort([1,734,24,3,324,324,32,432,42,3,4,1,1]).
[734,432,324,324,42,32,24,4,3,3,1,1,1]
```

## F#

```open System

let removeEmptyLists lists = lists |> List.filter (not << List.isEmpty)
let flip f x y = f y x

let rec transpose = function
| []    -> []
| lists -> (List.map List.head lists) :: transpose(removeEmptyLists (List.map List.tail lists))

// Using the backward composition operator "<<" (equivalent to Haskells ".") ...
let beadSort = List.map List.sum << transpose << transpose << List.map (flip List.replicate 1)

// Using the forward composition operator ">>" ...
let beadSort2 = List.map (flip List.replicate 1) >> transpose >> transpose >> List.map List.sum
```

Output:
```  val it : int list = [4; 3; 3; 2; 1]
```

## Factor

```USING: kernel math math.order math.vectors sequences ;
: fill ( seq len -- newseq ) [ dup length ] dip swap - 0 <repetition> append ;

: bead ( seq -- newseq )
dup 0 [ max ] reduce
[ swap 1 <repetition> swap fill ] curry map
[ ] [ v+ ] map-reduce ;

```
```( scratchpad ) { 5 2 4 1 3 3 9 } beadsort .
{ 9 5 4 3 3 2 1 }
```

## Fortran

Works with: Fortran version 2003
Works with: Fortran version 95

removing the iso_fortran_env as explained in code

This implementation suffers the same problems of the C implementation: if the maximum value in the array to be sorted is very huge, likely there will be not enough free memory to complete the task. Nonetheless, if the Fortran implementation would use "silently" sparse arrays and a compact representation for "sequences" of equal values in an array, then this very same code would run fine even with large integers.

```program BeadSortTest
use iso_fortran_env
! for ERROR_UNIT; to make this a F95 code,
! remove prev. line and declare ERROR_UNIT as an
! integer parameter matching the unit associated with
! standard error

integer, dimension(7) :: a = (/ 7, 3, 5, 1, 2, 1, 20 /)

print *, a

contains

integer, dimension(:), intent(inout) :: a

integer, dimension(maxval(a), maxval(a)) :: t
integer, dimension(maxval(a)) :: s
integer :: i, m

m = maxval(a)

if ( any(a < 0) ) then
write(ERROR_UNIT,*) "can't sort"
return
end if

t = 0
forall(i=1:size(a)) t(i, 1:a(i)) = 1  ! set up abacus
s(i) = sum(t(:, i))    ! moving them one by one, we just
t(:, i) = 0            ! count how many should be at bottom,
t(1:s(i), i) = 1       ! and then "reset" and set only those
end forall

forall(i=1:size(a)) a(i) = sum(t(i,:))

```

## FreeBASIC

```#define MAXNUM 100

Dim As Long i, j = 1, lb = Lbound(bs), ub = Ubound(bs)
Dim As Long poles(MAXNUM)

For i = 1 To ub
For j = 1 To bs(i)
poles(j) += 1
Next j
Next i
For j = 1 To ub
bs(j) = 0
Next j
For i = 1 To Ubound(poles)
For j = 1 To poles(i)
bs(j) += 1
Next j
Next i
End Sub

'--- Programa Principal ---
Dim As Long i
Dim As Ulong array(1 To 8) => {5, 3, 1, 7, 4, 1, 1, 20}
Dim As Long a = Lbound(array), b = Ubound(array)

Randomize Timer

Print "unsort ";
For i = a To b : Print Using "####"; array(i); : Next i

Print !"\n  sort ";
For i = a To b : Print Using "####"; array(i); : Next i

Sleep```
Output:
```unsort    5   3   1   7   4   1   1  20
sort   20   7   5   4   3   1   1   1```

## Go

Sorts non-negative integers only. The extension to negative values seemed a distraction from this fun task.

```package main

import (
"fmt"
"sync"
)

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

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

// All space in the abacus = aMax poles x len(a) rows.
all := make([]byte, aMax*len(a))
// Slice up space by pole.  (The space could be sliced by row instead,
// but slicing by pole seemed a more intuitive model of a physical abacus.)
abacus := make([][]byte, aMax)
for pole, space := 0, all; pole < aMax; pole++ {
abacus[pole] = space[:len(a)]
space = space[len(a):]
}
// Use a sync.Waitgroup as the checkpoint mechanism.
var wg sync.WaitGroup
// "snapped on" to the middle of a pole without disturbing neighboring
// beads.)  Also note 'row' here is a row of the abacus.
for row, n := range a {
go func(row, n int) {
for pole := 0; pole < n; pole++ {
}
wg.Done()
}(row, n)
}
wg.Wait()
// Now tip the abacus, letting beads fall on each pole concurrently.
for _, pole := range abacus {
go func(pole []byte) {
// Track the top of the stack of beads that have already fallen.
top := 0
for row, space := range pole {
// Move each bead individually, but move it from its
// starting row to the top of stack in a single operation.
// (More physical simulation such as discovering the top
// of stack by inspection, or modeling gravity, are
// possible, but didn't seem called for by the task.
pole[row] = 0
top++
}
}
wg.Done()
}(pole)
}
wg.Wait()
// Read out sorted numbers by row.
for row := range a {
x := 0
for pole := 0; pole < aMax && abacus[pole][row] == bead; pole++ {
x++
}
a[len(a)-1-row] = x
}
}
```

## Groovy

Solution:

```def beadSort = { list ->
final nPoles = list.max()
list.collect {
print "."
([true] * it) + ([false] * (nPoles - it))
}.transpose().collect { pole ->
print "."
pole.findAll { ! it } + pole.findAll { it }
}
}
```

Annotated Solution (same solution really):

```def beadSortVerbose = { list ->
final nPoles = list.max()
// each row is a number tally-arrayed across the abacus
def beadTallies = list.collect { number ->
print "."
([true] * number) + ([false] * (nPoles - number))
}
// each row is an abacus pole
def abacusPolesDrop = abacusPoles.collect { pole ->
print "."
// beads drop to the BOTTOM of the pole
pole.findAll { ! it } + pole.findAll { it }
}
// each row is a number again
}
```

Test:

```println beadSort([23,76,99,58,97,57,35,89,51,38,95,92,24,46,31,24,14,12,57,78,4])
```
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]```

Individual dots shown here are "retallying dots". They are not equivalent to the "swap dots" shown in other Groovy sorting examples. Like the swap dots the retallying dots represent atomic operations that visually indicate the overall sorting effort. However, they are not equivalent to swaps, or even equivalent in actual effort between bead sorts.

The cost of transposition is not accounted for here because with clever indexing it can easily be optimized away. In fact, one could write a list class for Groovy that performs the transpose operation merely by setting a single boolean value that controls indexing calculations.

```import Data.List

beadSort = map sum. transpose. transpose. map (flip replicate 1)
```

Example;

```*Main> beadSort [2,4,1,3,3]
[4,3,3,2,1]
```

## Icon and Unicon

The program below handles integers and not just whole numbers. As are so many others, the solution is limited by the lack of sparse array or list compression.

```procedure main()                     #: demonstrate various ways to sort a list and string
writes("  on list : ")
writex(UL := [3, 14, 1, 5, 9, 2, 6, 3])
end

procedure beadsort(X)                           #: return sorted list ascending(or descending)
local base,i,j,x                                # handles negatives and zeros, may also reduce storage

poles := list(max!X-(base := min!X -1),0)    # set up poles, we will track sums not individual beads
every x := !X do {                           # each item in the list
if integer(x) ~= x then runerr(101,x)     # ... must be an integer
every poles[1 to x - base] +:= 1          # ... beads "fall" into the sum for that pole
}

every (X[j := *X to 1 by -1] := base) &
(i := 1 to *poles) do                   # read from the bottom of the poles
if poles[i] > 0 then {                     # if there's a bead on the pole ...
poles[i] -:= 1                          # ... remove it
X[j] +:= 1                          # ... and add it in place
}
return X
end
```

Note: This example relies on the supporting procedures 'writex' in Bubble Sort. Note: min and max are available in the Icon Programming Library (IPL).

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

## J

Generally, this task should be accomplished in J using `\:~`. Here we take an approach that's more comparable with the other examples on this page.
```bead=: [: +/ #"0&1
```

Example use:

```   bead bead 2 4 1 3 3
4 3 3 2 1
7 5 4 3 1 1 1
```

Extending to deal with sequences of arbitrary integers:

```bball=: ] (] + [: bead^:2 -) <./ - 1:
```

Example use:

```   bball 2 0 _1 3 1 _2 _3 0
3 2 1 0 0 _1 _2 _3
```

## Java

```public class BeadSort
{
public static void main(String[] args)
{
int[] arr=new int[(int)(Math.random()*11)+5];
for(int i=0;i<arr.length;i++)
arr[i]=(int)(Math.random()*10);
System.out.print("Unsorted: ");
now.display1D(arr);

System.out.print("Sorted: ");
now.display1D(sort);
}
{
int max=a[0];
for(int i=1;i<arr.length;i++)
if(arr[i]>max)
max=arr[i];

//Set up abacus
char[][] grid=new char[arr.length][max];
int[] levelcount=new int[max];
for(int i=0;i<max;i++)
{
levelcount[i]=0;
for(int j=0;j<arr.length;j++)
grid[j][i]='_';
}
/*
display1D(arr);
display1D(levelcount);
display2D(grid);
*/

for(int i=0;i<arr.length;i++)
{
int num=arr[i];
for(int j=0;num>0;j++)
{
grid[levelcount[j]++][j]='*';
num--;
}
}
System.out.println();
display2D(grid);
int[] sorted=new int[arr.length];
for(int i=0;i<arr.length;i++)
{
int putt=0;
for(int j=0;j<max&&grid[arr.length-1-i][j]=='*';j++)
putt++;
sorted[i]=putt;
}

return sorted;
}
void display1D(int[] arr)
{
for(int i=0;i<arr.length;i++)
System.out.print(arr[i]+" ");
System.out.println();
}
void display1D(char[] arr)
{
for(int i=0;i<arr.length;i++)
System.out.print(arr[i]+" ");
System.out.println();
}
void display2D(char[][] arr)
{
for(int i=0;i<arr.length;i++)
display1D(arr[i]);
System.out.println();
}
}
```
Output:
```Unsorted: 9 4 7 0 4 3 0 5 3 8 7 9 8 7 0

* * * * * * * * *
* * * * * * * * *
* * * * * * * * _
* * * * * * * * _
* * * * * * * _ _
* * * * * * * _ _
* * * * * * * _ _
* * * * * _ _ _ _
* * * * _ _ _ _ _
* * * * _ _ _ _ _
* * * _ _ _ _ _ _
* * * _ _ _ _ _ _
_ _ _ _ _ _ _ _ _
_ _ _ _ _ _ _ _ _
_ _ _ _ _ _ _ _ _

Sorted: 0 0 0 3 3 4 4 5 7 7 7 8 8 9 9
```

## jq

Part 1: The abacus This implementation uses an "abacus" as described in the Wikipedia article. However, rather than representing each row as a set of n beads, it suffices to use the integer n instead. Thus the initial state of our abacus is simply the array of numbers to be sorted. (A better approach would be to normalize the integers by subtracting their minimum value minus 1; that would also allow sorting arrays of integers without restriction.)

Part 2: Gravity

```# ncols is the number of columns (i.e. vertical poles)
def column_sums(ncols):
. as \$abacus
| reduce range(0; ncols) as \$col
([];
. + [reduce \$abacus[] as \$row
(0; if \$row > \$col then .+1 else . end)]) ;```

```# Generic function to count the number of items in a stream:
def count(stream): reduce stream as \$i (0; .+1);

. as \$sums
| .[0] as \$n
| reduce range(0;\$n) as \$i
([]; . + [count( \$sums[] | select( . > \$i) )]);```

`def bead_sort: column_sums(max) | readout;`

Example:

`[734,3,1,24,324,324,32,432,42,3,4,1,1] | bead_sort`
Output:
```\$ jq -n -c -f bead_sort.jq
[734,432,324,324,42,32,24,4,3,3,1,1,1]
```

## Julia

Works with: Julia version 0.6

Implement `beadsort` on a `BitArray` abacus. The function should work for any integer type. It throws a `DomainError` if the input array contains a non-positive integer.

```function beadsort(a::Vector{<:Integer})
lo, hi = extrema(a)
if lo < 1 throw(DomainError()) end
len = length(a)
abacus = falses(len, hi)
for (i, v) in enumerate(a)
abacus[i, 1:v] = true
end
for i in 1:hi
v = sum(abacus[:, i])
if v < len
abacus[1:end-v, i] = false
abacus[end-v+1:end, i] = true
end
end
return collect(eltype(a), sum(abacus[i,:]) for i in 1:len)
end

v = rand(UInt8, 20)
println("# unsorted bytes: \$v\n -> sorted bytes: \$(beadsort(v))")
v = rand(1:2 ^ 10, 20)
println("# unsorted integers: \$v\n -> sorted integers: \$(beadsort(v))")
```
Output:
```# unsorted bytes: UInt8[0xff, 0x52, 0xdd, 0x72, 0xe2, 0x13, 0xb5, 0xd3, 0x7f, 0xea, 0x3b, 0x46, 0x4b, 0x78, 0xfb, 0xbe, 0xd8, 0x2e, 0xa9, 0x7a]
-> sorted bytes: UInt8[0x13, 0x2e, 0x3b, 0x46, 0x4b, 0x52, 0x72, 0x78, 0x7a, 0x7f, 0xa9, 0xb5, 0xbe, 0xd3, 0xd8, 0xdd, 0xe2, 0xea, 0xfb, 0xff]
# unsorted integers: [1012, 861, 798, 949, 481, 889, 78, 699, 718, 195, 426, 922, 762, 360, 1017, 208, 304, 13, 910, 854]
-> sorted integers: [13, 78, 195, 208, 304, 360, 426, 481, 699, 718, 762, 798, 854, 861, 889, 910, 922, 949, 1012, 1017]```

## Kotlin

Translation of: C
```// version 1.1.2

val n = a.size
if (n < 2) return
var max = a.max()!!
val beads = ByteArray(max * n)
for (i in 0 until n)
for (j in 0 until a[i])
beads[i * max + j] = 1

for (j in 0 until max) {
/* count how many beads are on each post */
var sum = 0
for (i in 0 until n) {
sum += beads[i * max + j]
beads[i * max + j] = 0
}
/* mark bottom sum beads */
for (i in n - sum until n) beads[i * max + j] = 1
}

for (i in 0 until n) {
var j = 0
while (j < max && beads[i * max + j] == 1.toByte()) j++
a[i] = j
}
}

fun main(args: Array<String>) {
val a  = intArrayOf(5, 3, 1, 7, 4, 1, 1, 20)
println("Before sorting : \${a.contentToString()}")
println("After sorting  : \${a.contentToString()}")
}
```
Output:
```Before sorting : [5, 3, 1, 7, 4, 1, 1, 20]
After sorting  : [1, 1, 1, 3, 4, 5, 7, 20]
```

## Lua

```-- Display message followed by all values of a table in one line
function show (msg, t)
io.write(msg .. ":\t")
for _, v in pairs(t) do io.write(v .. " ") end
print()
end

-- Return a table of random numbers
function randList (length, lo, hi)
local t = {}
for i = 1, length do table.insert(t, math.random(lo, hi)) end
return t
end

-- Count instances of numbers that appear in counting to each list value
function tally (list)
local tal = {}
for k, v in pairs(list) do
for i = 1, v do
if tal[i] then tal[i] = tal[i] + 1 else tal[i] = 1 end
end
end
return tal
end

-- Sort a table of positive integers into descending order
show("Before sort", numList)
local abacus = tally(numList)
show("Tally list", abacus)
local sorted = tally(abacus)
show("After sort", sorted)
end

-- Main procedure
math.randomseed(os.time())
```
Output:
```Before sort:    9 5 3 9 4 1 3 8 1 2
Tally list:     10 8 7 5 4 3 3 3 2
After sort:     9 9 8 5 4 3 3 2 1 1```

## Mathematica/Wolfram Language

```beadsort[ a ] := Module[ { m, sorted, s ,t },
sorted = a; m = Max[a]; t=ConstantArray[0, {m,m} ];
If[ Min[a] < 0, Print["can't sort"]];
For[ i = 1, i < Length[a], i++,  t[[i,1;;a[[i]]]]=1 ]
For[ i = 1 ,i <= m, i++, s = Total[t[[;;,i]]];
t[[ ;; , i]] = 0; t[[1 ;; s , i]] = 1; ]
For[ i=1,i<=Length[a],i++, sorted[[i]] = Total[t[[i,;;]]]; ]
Print[sorted];
]
```
Output:
`{6,3,2,1,0}`

## NetRexx

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

runSample(arg)
return

-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method bead_sort(harry = Rexx[]) public static binary returns Rexx[]
MIN_ = 'MIN'
MAX_ = 'MAX'

loop val over harry
-- collect occurences of beads in indexed string indexed on value
if val < beads[MIN_] then beads[MIN_] = val -- keep track of min value
if val > beads[MAX_] then beads[MAX_] = val -- keep track of max value
end val

harry_sorted = Rexx[harry.length]
bi = 0
-- extract beads in value order and insert in result array
if beads[xx] == 0 then iterate xx
harry_sorted[bi] = xx
bi = bi + 1
end
end xx

return harry_sorted

-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method runSample(arg) public static
unsorted = [734, 3, 1, 24, 324, -1024, -666, -1, 0, 324, 32, 0, 432, 42, 3, 4, 1, 1]
say arrayToString(unsorted)
say arrayToString(sorted)
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method arrayToString(harry = Rexx[]) private static
list = Rexx ''
loop vv over harry
list = list vv
end vv
return '['list.space(1, ',')']'```
Output:
```[734,3,1,24,324,-1024,-666,-1,0,324,32,0,432,42,3,4,1,1]
[-1024,-666,-1,0,0,1,1,1,3,3,4,24,32,42,324,324,432,734]
```

## Nim

```proc beadSort[T](a: var openarray[T]) =
var max = low(T)
var sum = 0

for x in a:
if x > max: max = x

var beads = newSeq[int](max * a.len)

for i in 0 ..< a.len:
for j in 0 ..< a[i]:
beads[i * max + j] = 1

for j in 0 ..< max:
sum = 0
for i in 0 ..< a.len:
sum += beads[i * max + j]
beads[i * max + j] = 0

for i in a.len - sum ..< a.len:
beads[i * max + j] = 1

for i in 0 ..< a.len:
var j = 0
while j < max and beads[i * max + j] > 0: inc j
a[i] = j

var a = @[5, 3, 1, 7, 4, 1, 1, 20]
echo a
```
Output:
`@[1, 1, 1, 3, 4, 5, 7, 20]`

## OCaml

```let rec columns l =
match List.filter ((<>) []) l with
[] -> []
| l -> List.map List.hd l :: columns (List.map List.tl l)

let replicate n x = Array.to_list (Array.make n x)

List.map List.length (columns (columns (List.map (fun e -> replicate e 1) l)))
```

usage

```# bead_sort [5;3;1;7;4;1;1];;
- : int list = [7; 5; 4; 3; 1; 1; 1]
```

## Octave

Translation of: Fortran
```function sorted = beadsort(a)
sorted = a;
m = max(a);
if ( any(a < 0) )
error("can't sort");
endif
t = zeros(m, m);
for i = 1:numel(a)
t(i, 1:a(i)) = 1;
endfor
for i = 1:m
s = sum(t(:, i));
t(:, i) = 0;
t(1:s, i) = 1;
endfor
for i = 1:numel(a)
sorted(i) = sum(t(i, :));
endfor
endfunction

beadsort([5, 7, 1, 3, 1, 1, 20])
```

## ooRexx

### version 1

```in='10 -12 1 0 999 8 2 2 4 4'
Do i=1 To words(in)
z.i=word(in,i)
End
n=i-1
init=0
Call minmax

Do i=1 To words(in)
z=z.i
End
j=0
Do i=lo To hi
j+=1
s.j=i
End;
End;
Call show ' Input:',z.,n
Call show 'Sorted:',s.,n
Exit

minmax:
Do i=1 To n
If init=0 Then Do
init=1
lo=z.i
hi=z.i
End
Else Do
lo=min(lo,z.i)
hi=max(hi,z.i)
End
End
Return

show: Procedure Expose n
Use Arg txt,a.
ol=txtg>
Do i=1 To n
ol=ol format(a.i,3)
End
Say ol
Return```
Output:
``` Input:  10 -12   1   0 999   8   2   2   4   4
Sorted: -12   0   1   2   2   4   4   8  10 999```

### version 2

Translation of: REXX

Note: The only changes needed were to substitute _, ! and ? characters for the "deprecated" \$, # and @ characters within variable names; as per The REXX Language, Second Edition by M. F. Cowlishaw. (See a description here).

```/*REXX program sorts a list of integers using a bead sort. */

/*get some grassHopper numbers.                            */
grasshopper=,
1 4 10 12 22 26 30 46 54 62 66 78 94 110 126 134 138 158 162 186 190 222 254 270

/*GreeenGrocer numbers are also called hexagonal pyramidal */
/*             numbers.                                    */
greengrocer=,
0 4 16 40 80 140 224 336 480 660 880 1144 1456 1820 2240 2720 3264 3876 4560

/*get some Bernoulli numerator numbers.                    */
bernN='1 -1 1 0 -1 0 1 0 -1 0 5 0 -691 0 7 0 -3617 0 43867 0 -174611 0 854513'

/*Psi is also called the Reduced Totient function,  and    */
/*    is also called Carmichale lambda, or LAMBDA function.*/
psi=,
1 1 2 2 4 2 6 2 6 4 10 2 12 6 4 4 16 6 18 4 6 10 22 2 20 12 18 6 28 4 30 8 10 16

list=grasshopper greengrocer bernN psi /*combine the four lists into one*/

call showL 'before sort',list          /*show list before sorting. */
call showL ' after sort',!             /*show  after array elements*/
exit

parse arg z
!=''                                 /*this'll be the sorted list*/
low=999999999; high=-low             /*define the low and high #s*/
_.=0                                 /*define all beads to zero. */

do j=1 until z==''                   /*pick the meat off the bone*/
parse var z x z
if \datatype(x,'Whole') then
do
say
say '*** error! ***'
say
say 'element' j "in list isn't numeric:" x
say
exit 13
end

x=x/1                              /*normalize number, it could*/
/*be:  +4  007  5.  2e3 etc.*/
_.x=_.x+1                          /*indicate this bead has a #*/
low=min(low,x)                     /*keep track of the lowest #*/
high=max(high,x)                   /* "     "    "  "  highest#*/
end j

do m=low to high                     /*let them fall (to zero).  */
if _.m==0 then iterate             /*No bead here? Keep looking*/
do n=1 for _.m                     /*let the beads fall to  0. */
!=! m                            /*add it to the sorted list.*/
end n
end m

return !

/*─────────────────────────────────────SHOW@ subroutine────────────*/
showL:
widthH=length(words(arg(2)))         /*maximum width of the index*/

do j=1 for words(arg(2))
say 'element' right(j,widthH) arg(1)":" right(word(arg(2),j),10)
end j

say copies('─',80)                   /*show a separator line.    */
return```
Output:
```element   1 before sort:          1
element   2 before sort:          4
element   3 before sort:         10
element   4 before sort:         12
element   5 before sort:         22
element   6 before sort:         26
element   7 before sort:         30
element   8 before sort:         46
element   9 before sort:         54
element  10 before sort:         62
element  11 before sort:         66
element  12 before sort:         78
element  13 before sort:         94
element  14 before sort:        110
element  15 before sort:        126
element  16 before sort:        134
element  17 before sort:        138
element  18 before sort:        158
element  19 before sort:        162
element  20 before sort:        186
element  21 before sort:        190
element  22 before sort:        222
element  23 before sort:        254
element  24 before sort:        270
element  25 before sort:          0
element  26 before sort:          4
element  27 before sort:         16
element  28 before sort:         40
element  29 before sort:         80
element  30 before sort:        140
element  31 before sort:        224
element  32 before sort:        336
element  33 before sort:        480
element  34 before sort:        660
element  35 before sort:        880
element  36 before sort:       1144
element  37 before sort:       1456
element  38 before sort:       1820
element  39 before sort:       2240
element  40 before sort:       2720
element  41 before sort:       3264
element  42 before sort:       3876
element  43 before sort:       4560
element  44 before sort:          1
element  45 before sort:         -1
element  46 before sort:          1
element  47 before sort:          0
element  48 before sort:         -1
element  49 before sort:          0
element  50 before sort:          1
element  51 before sort:          0
element  52 before sort:         -1
element  53 before sort:          0
element  54 before sort:          5
element  55 before sort:          0
element  56 before sort:       -691
element  57 before sort:          0
element  58 before sort:          7
element  59 before sort:          0
element  60 before sort:      -3617
element  61 before sort:          0
element  62 before sort:      43867
element  63 before sort:          0
element  64 before sort:    -174611
element  65 before sort:          0
element  66 before sort:     854513
element  67 before sort:          1
element  68 before sort:          1
element  69 before sort:          2
element  70 before sort:          2
element  71 before sort:          4
element  72 before sort:          2
element  73 before sort:          6
element  74 before sort:          2
element  75 before sort:          6
element  76 before sort:          4
element  77 before sort:         10
element  78 before sort:          2
element  79 before sort:         12
element  80 before sort:          6
element  81 before sort:          4
element  82 before sort:          4
element  83 before sort:         16
element  84 before sort:          6
element  85 before sort:         18
element  86 before sort:          4
element  87 before sort:          6
element  88 before sort:         10
element  89 before sort:         22
element  90 before sort:          2
element  91 before sort:         20
element  92 before sort:         12
element  93 before sort:         18
element  94 before sort:          6
element  95 before sort:         28
element  96 before sort:          4
element  97 before sort:         30
element  98 before sort:          8
element  99 before sort:         10
element 100 before sort:         16
────────────────────────────────────────────────────────────────────────────────
element   1  after sort:    -174611
element   2  after sort:      -3617
element   3  after sort:       -691
element   4  after sort:         -1
element   5  after sort:         -1
element   6  after sort:         -1
element   7  after sort:          0
element   8  after sort:          0
element   9  after sort:          0
element  10  after sort:          0
element  11  after sort:          0
element  12  after sort:          0
element  13  after sort:          0
element  14  after sort:          0
element  15  after sort:          0
element  16  after sort:          0
element  17  after sort:          0
element  18  after sort:          1
element  19  after sort:          1
element  20  after sort:          1
element  21  after sort:          1
element  22  after sort:          1
element  23  after sort:          1
element  24  after sort:          2
element  25  after sort:          2
element  26  after sort:          2
element  27  after sort:          2
element  28  after sort:          2
element  29  after sort:          2
element  30  after sort:          4
element  31  after sort:          4
element  32  after sort:          4
element  33  after sort:          4
element  34  after sort:          4
element  35  after sort:          4
element  36  after sort:          4
element  37  after sort:          4
element  38  after sort:          5
element  39  after sort:          6
element  40  after sort:          6
element  41  after sort:          6
element  42  after sort:          6
element  43  after sort:          6
element  44  after sort:          6
element  45  after sort:          7
element  46  after sort:          8
element  47  after sort:         10
element  48  after sort:         10
element  49  after sort:         10
element  50  after sort:         10
element  51  after sort:         12
element  52  after sort:         12
element  53  after sort:         12
element  54  after sort:         16
element  55  after sort:         16
element  56  after sort:         16
element  57  after sort:         18
element  58  after sort:         18
element  59  after sort:         20
element  60  after sort:         22
element  61  after sort:         22
element  62  after sort:         26
element  63  after sort:         28
element  64  after sort:         30
element  65  after sort:         30
element  66  after sort:         40
element  67  after sort:         46
element  68  after sort:         54
element  69  after sort:         62
element  70  after sort:         66
element  71  after sort:         78
element  72  after sort:         80
element  73  after sort:         94
element  74  after sort:        110
element  75  after sort:        126
element  76  after sort:        134
element  77  after sort:        138
element  78  after sort:        140
element  79  after sort:        158
element  80  after sort:        162
element  81  after sort:        186
element  82  after sort:        190
element  83  after sort:        222
element  84  after sort:        224
element  85  after sort:        254
element  86  after sort:        270
element  87  after sort:        336
element  88  after sort:        480
element  89  after sort:        660
element  90  after sort:        880
element  91  after sort:       1144
element  92  after sort:       1456
element  93  after sort:       1820
element  94  after sort:       2240
element  95  after sort:       2720
element  96  after sort:       3264
element  97  after sort:       3876
element  98  after sort:       4560
element  99  after sort:      43867
element 100  after sort:     854513
────────────────────────────────────────────────────────────────────────────────
```

## OpenEdge/Progress

Sorting algorithms are not the kind of thing you need / want to do in OpenEdge. If you want to sort simply define a temp-table with one field, populate it and get sorted results with FOR EACH temp-table DESCENDING.

```FUNCTION beadSort RETURNS CHAR (
i_c AS CHAR
):

DEF VAR cresult   AS CHAR.
DEF VAR ii        AS INT.
DEF VAR inumbers  AS INT.
DEF VAR irod      AS INT.
DEF VAR irods     AS INT.
DEF VAR crod      AS CHAR.
DEF VAR cbeads    AS CHAR EXTENT.

inumbers = NUM-ENTRIES( i_c ).

/* determine number of rods needed */
DO ii = 1 TO inumbers:
irods = MAXIMUM( irods, INTEGER( ENTRY( ii, i_c ) ) ).
END.

/* put beads on rods */
DO ii = 1 TO inumbers:
cbeads[ ii ] = FILL( "X", INTEGER( ENTRY( ii, i_c ) ) ).
END.

/* drop beads on each rod */
DO irod = 1 TO irods:
crod = "".
DO ii = 1 TO inumbers:
crod = crod + SUBSTRING( cbeads[ ii ], irod, 1 ).
END.
crod = REPLACE( crod, " ", "" ).
DO ii = 1 TO inumbers.
SUBSTRING( cbeads[ ii ], irod, 1 ) = STRING( ii <= LENGTH( crod ), "X/ " ).
END.
END.

/* get beads from rods */
DO ii = 1 TO inumbers:
cresult = cresult + "," + STRING( LENGTH( REPLACE( cbeads[ ii ], " ", "" ) ) ).
END.

RETURN SUBSTRING( cresult, 2 ).

MESSAGE
"5,2,4,1,3,3,9  -> " beadSort( "5,2,4,1,3,3,9" ) SKIP
"5,3,1,7,4,1,1  -> " beadSort( "5,3,1,7,4,1,1" ) SKIP(1)
Output:
```---------------------------
Message
---------------------------
5,2,4,1,3,3,9  ->  9,5,4,3,3,2,1
5,3,1,7,4,1,1  ->  7,5,4,3,1,1,1

88,84,82,81,78,76,75,73,70,62,44,33,31,20,18,14,12,8,7,5,4,1,0
---------------------------
OK
---------------------------```

## PARI/GP

This implementation uses the counting sort to order the beads in a given row.

```beadsort(v)={
for(i=1,sz,M[,i]=countingSort(M[,i],0,1)~);   \\ Let them fall
vector(#v,i,value(M[i,]))                     \\ Convert back to numbers
};

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
};

value(v)={
if(#v==0 || !v[1], return(0));
if(v[#v], return(#v));
my(left=1, right=#v, mid);
while (right - left > 1,
mid=(right+left)\2;
if(v[mid], left=mid, right=mid)
);
left
};```

## Pascal

```program BDS;
const MAX = 1000;
type
type_matrix = record
lin,col:integer;
matrix: array [1..MAX,1..MAX] of boolean;
end;

type_vector = record
size:integer;
vector: array[1..MAX] of integer;
end;

var
i,j,k,sum:integer;
m:type_matrix;
begin
m.lin:=v.size;

(* the number of columns is equal to the greatest element *)
m.col:=0;
for i:=1 to v.size do
if v.vector[i] > m.col then
m.col:=v.vector[i];

(* initializing the matrix *)
for j:=1 to m.lin do
begin
k:=1;
for i:=m.col downto 1 do
begin
if v.vector[j] >= k then
m.matrix[i,j]:=TRUE
else
m.matrix[i,j]:=FALSE;
k:=k+1;
end;
end;

(* Sort the matrix *)
for i:=1 to m.col do
begin
(* Count the beads and set the line equal FALSE *)
sum:=0;
for j:=1 to m.lin do
begin
if m.matrix[i,j] then
sum:=sum+1;
m.matrix[i,j]:=FALSE;
end;

for j:=m.lin downto m.lin-sum+1 do
m.matrix[i,j]:=TRUE;
end;

(* Convert the sorted bead matrix to a sorted vector *)
for j:=1 to m.lin do
begin
v.vector[j]:=0;
i:=m.col;
while (m.matrix[i,j] = TRUE)and(i>=1) do
begin
v.vector[j]+=1;
i:=i-1;
end;
end;
end;

procedure print_vector(var v:type_vector);
var i:integer;
begin
for i:=1 to v.size do
write(v.vector[i],' ');
writeln;
end;

var
i:integer;
v:type_vector;
begin
writeln('How many numbers do you want to sort?');
writeln('Write the numbers:');

for i:=1 to v.size do

writeln('Before sort:');
print_vector(v);

writeln('After sort:');
print_vector(v);
end.
```
Output:
```How many numbers do you want to sort?
10
Write the numbers:
23 13 99 45 26 7 63 214 87 45
Before sort:
23 13 99 45 26 7 63 214 87 45
After sort:
7 13 23 26 45 45 63 87 99 214
```

## Perl

Instead of storing the bead matrix explicitly, I choose to store just the number of beads in each row and column, compacting on the fly. At all times, the sum of the row widths is equal to the sum column heights.

```sub beadsort {
my @data = @_;

my @columns;
my @rows;

for my \$datum (@data) {
for my \$column ( 0 .. \$datum-1 ) {
++ \$rows[ \$columns[\$column]++ ];
}
}

return reverse @rows;
}

beadsort 5, 7, 1, 3, 1, 1, 20;
```

## Phix

```with javascript_semantics

sequence poles = repeat(0,max(a))
for i=1 to length(a) do
end for
a[1..\$] = 0
for i=1 to length(poles) do
end for
return a
end function

?beadsort({5, 3, 1, 7, 4, 1, 1, 20})
```
Output:
```{20,7,5,4,3,1,1,1}
```

## PHP

```<?php
function columns(\$arr) {
if (count(\$arr) == 0)
return array();
else if (count(\$arr) == 1)
return array_chunk(\$arr[0], 1);

array_unshift(\$arr, NULL);
// array_map(NULL, \$arr[0], \$arr[1], ...)
\$transpose = call_user_func_array('array_map', \$arr);
return array_map('array_filter', \$transpose);
}

foreach (\$arr as \$e)
\$poles []= array_fill(0, \$e, 1);
return array_map('count', columns(columns(\$poles)));
}

?>
```
Output:
```Array
(
[0] => 7
[1] => 5
[2] => 4
[3] => 3
[4] => 1
[5] => 1
[6] => 1
)```

## PicoLisp

The following implements a direct model of the bead sort algorithm. Each pole is a list of 'T' symbols for the beads.

```(de beadSort (Lst)
(let Abacus (cons NIL)
(for (L Abacus  (ge0 (dec 'N))  (cdr L))
(or (cdr L) (queue 'L (cons)))
(push (cadr L) T) ) )
(make
(while (gt0 (cnt pop (cdr Abacus)))       # Drop and count beads
(link @) ) ) ) )```
Output:
```: (beadSort (5 3 1 7 4 1 1 20))
-> (20 7 5 4 3 1 1 1)```

## PL/I

### version 1

```/* Handles both negative and positive values. */

maxval: procedure (z) returns (fixed binary);
declare z(*) fixed binary;
declare (maxv initial (0), i) fixed binary;
do i = lbound(z,1) to hbound(z,1);
maxv = max(z(i), maxv);
end;
put skip data (maxv); put skip;
return (maxv);
end maxval;
minval: procedure (z) returns (fixed binary);
declare z(*) fixed binary;
declare (minv initial (0), i) fixed binary;

do i = lbound(z,1) to hbound(z,1);
if z(i) < 0 then minv = min(z(i), minv);
end;
put skip data (minv); put skip;
return (minv);
end minval;

/* To deal with negative values, array elements are incremented */
/* by the greatest (in magnitude) negative value, thus making   */
/* them positive. The resultant values are stored in an         */
/* unsigned array (PL/I provides both signed and unsigned data  */
/* types). At procedure end, the array values are restored to   */
/* original values.                                             */

(subrg, fofl, size, stringrange, stringsize):
beadsort: procedure (z);                        /* 8-1-2010 */
declare (z(*)) fixed binary;
declare b(maxval(z)-minval(z)+1) bit (maxval(z)-minval(z)+1) aligned;
declare (i, j, k, m, n) fixed binary;
declare a(hbound(z,1)) fixed binary unsigned;
declare offset fixed binary initial (minval(z));

PUT SKIP LIST('CHECKPOINT A'); PUT SKIP;
n = hbound(z,1);
m = hbound(b,1);

if offset < 0 then
a = z - offset;
else
a = z;

b = '0'b;

do i = 1 to n;
substr(b(i), 1, a(i)) = copy('1'b, a(i));
end;
do j = 1 to m; put skip list (b(j)); end;

do j = 1 to m;
k = 0;
do i =1 to n;
if substr(b(i), j, 1) then k = k + 1;
end;
do i = 1 to n;
substr(b(i), j, 1) = (i <= k);
end;
end;
put skip;
do j = 1 to m; put skip list (b(j)); end;

do i = 1 to n;
k = 0;
do j = 1 to m; k = k + substr(b(i), j, 1); end;
a(i) = k;
end;
if offset < 0 then z = a + offset; else z = a;

### version 2

Translation of: ooRexx

PL/I supports negative array indices!

```*process source attributes xref;
/* Handles both negative and positive values. */
Dcl sysprint Print;
Dcl (hbound,max,min) Builtin;

Dcl z(10) Bin Fixed(31) Init(10,-12,1,0,999,8,2,2,4,4);
Dcl s(10) Bin Fixed(31);
Dcl (init,lo,hi) Bin Fixed(31) Init(0);
Dcl (i,j) Bin Fixed(31) Init(0);

Call minmax(z,init,lo,hi);

Begin;
Do i=1 To hbound(z);
End;
Do i=lo To hi;
j+=1;
s(j)=i;
End;
End;
Put Edit(' Input:',(z(i) Do i=1 To hbound(z)))(skip,a,99(f(4)));
Put Edit('Sorted:',(s(i) Do i=1 To hbound(s)))(skip,a,99(f(4)));
End;

minmax: Proc(z,init,lo,hi);
Dcl z(*) Bin Fixed(31);
Dcl (init,lo,hi) Bin Fixed(31);
Do i=1 To hbound(z);
If init=0 Then Do;
init=1;
lo,hi=z(i);
End;
Else Do;
lo=min(lo,z(i));
hi=max(hi,z(i));
End;
End;
End;

End;```
Output:
``` Input:  10 -12   1   0 999   8   2   2   4   4
Sorted: -12   0   1   2   2   4   4   8  10 999```

## PowerShell

```Function BeadSort ( [Int64[]] \$indata )
{
if( \$indata.length -gt 1 )
{
\$min = \$indata[ 0 ]
\$max = \$indata[ 0 ]
for( \$i = 1; \$i -lt \$indata.length; \$i++ )
{
if( \$indata[ \$i ] -lt \$min )
{
\$min = \$indata[ \$i ]
}
if( \$indata[ \$i ] -gt \$max ) {
\$max = \$indata[ \$i ]
}
} #Find the min & max
\$poles = New-Object 'UInt64[]' ( \$max - \$min + 1 )
\$indata | ForEach-Object {
\$min..\$_ | ForEach-Object {
\$poles[ \$_ - \$min ] += 1
}
\$min..( \$max - 1 ) | ForEach-Object {
\$i = \$_ - \$min
if( \$poles[ \$i ] -gt \$poles[ \$i + 1 ] )
{ #No special case needed for min, since there will always be at least 1 = min
( \$poles[ \$i ] )..( \$poles[ \$i + 1 ] + 1 ) | ForEach-Object {
Write-Output ( \$i + \$min )
}
}
} #Output the results in pipeline fashion
1..( \$poles[ \$max - \$min ] ) | ForEach-Object {
Write-Output \$max  #No special case needed for max, since there will always be at least 1 = max
}
} else {
Write-Output \$indata
}
}

\$l = 100; BeadSort ( 1..\$l | ForEach-Object { \$Rand = New-Object Random }{ \$Rand.Next( -( \$l - 1 ), \$l - 1 ) } )
```

## PureBasic

```#MAXNUM=100

Dim MyData(Random(15)+5)
Global Dim Abacus(0,0)

Declare PresentData(Array InData(1))

If OpenConsole()
Define i
;- Generate a random array
For i=0 To ArraySize(MyData())
MyData(i)=Random(#MAXNUM)
Next i
PresentData(MyData())
;
;- Sort the array
PresentData(MyData())
;
Print("Press ENTER to exit"): Input()
EndIf

Procedure LetFallDown(x)
Protected y=ArraySize(Abacus(),2)-1
Protected ylim=y
While y>=0
If Abacus(x,y) And Not Abacus(x,y+1)
Swap Abacus(x,y), Abacus(x,y+1)
If y<ylim: y+1: Continue: EndIf
Else
y-1
EndIf
Wend
EndProcedure

Protected i, j, k
NewList T()
Dim Abacus(#MAXNUM,ArraySize(N()))
;- Set up the abacus
For i=0 To ArraySize(Abacus(),2)
For j=1 To N(i)
Abacus(j,i)=#True
Next
Next
For i=0 To #MAXNUM
Next
ForEach T()
Next
;- send it back to a normal array
For j=0 To ArraySize(Abacus(),2)
k=0
For i=0 To ArraySize(Abacus())
k+Abacus(i,j)
Next
N(j)=k
Next
EndProcedure

Procedure PresentData(Array InData(1))
Protected n, m, sum
PrintN(#CRLF\$+"The array is;")
For n=0 To ArraySize(InData())
m=InData(n): sum+m
Print(Str(m)+" ")
Next
PrintN(#CRLF\$+"And its sum= "+Str(sum))
EndProcedure```
```The array is;
4 38 100 25 69 69 16 8 59 71 53 33
And its sum= 545

The array is;
4 8 16 25 33 38 53 59 69 69 71 100
And its sum= 545```

## Python

```#!/bin/python3
from itertools import zip_longest

# This is wrong, it works only on specific examples
return list(map(sum, zip_longest(*[[1] * e for e in l], fillvalue=0)))

# Demonstration code:
```
Output:
`[7, 5, 4, 3, 1, 1, 1]`

## QB64

```#lang QB64
'***************************************************
'* BeadSort is VERY fast for small CGSortLibArray(max)-CGSortLibArray(min). Typical performance is
'* O(NlogN) or better. However as the key values (array values and ranges) go up, the performance
'* drops steeply excellent for small-ranged arrays. Integer only at this point.  Throughput is
'* roughly 900k/GHzS for double-precision, with binary range (0,1). Related to CountingSort()
'***************************************************
SUB BeadSort (CGSortLibArray() AS DOUBLE, start AS LONG, finish AS LONG, order&)
DIM MAX AS DOUBLE: MAX = CGSortLibArray(start)
FOR BeadSort_I = start + 1 TO (finish - start)
NEXT
FOR BeadSort_I = 0 TO (finish - start) - 1
NEXT
NEXT
IF order& = 1 THEN
FOR BeadSort_J = 0 TO MAX
FOR BeadSort_I = 0 TO (finish - start)
NEXT
FOR BeadSort_I = (finish - start) - BeadSort_Sum TO (finish - start)
NEXT
NEXT
FOR BeadSort_I = 0 TO (finish - start)
WEND
NEXT
ELSE
FOR BeadSort_J = MAX TO 0 STEP -1
FOR I = 0 TO (finish - start)
NEXT
FOR I = (finish - start) TO (finish - start) - BeadSort_Sum STEP -1
NEXT
NEXT
FOR BeadSort_I = 0 TO (finish - start)
WEND
NEXT
END IF
END SUB```

## Racket

```#lang racket
(require rackunit)

(define (columns lst)
(match (filter (λ (l) (not (empty? l))) lst)
['() '()]
[l (cons (map car l) (columns (map cdr l)))]))

(map length (columns (columns (map (λ (n) (make-list n 1)) lst)))))

;; unit test
(check-equal?
(bead-sort '(5 3 1 7 4 1 1))
'(7 5 4 3 1 1 1))
```

## Raku

(formerly Perl 6)

Works with: rakudo version 2016-05
```# routine cribbed from List::Utils;
sub transpose(@list is copy) {
gather {
while @list {
if @list[0] !~~ Positional { @heads = @list.shift; }
else { @heads = @list.map({\$_.shift unless \$_ ~~ []}); }
@list = @list.map({\$_ unless \$_ ~~ []});
}
}
}

(transpose(transpose(map {[1 xx \$_]}, @l))).map(*.elems);
}

my @list = 2,1,3,5;
```
Output:
`(5, 3, 2, 1)`

Here we simulate the dropping beads by using the push method.

```sub beadsort(*@list) {
my @rods;
for words ^«@list -> \$x { @rods[\$x].push(1) }
gather for ^@rods[0] -> \$y {
take [+] @rods.map: { .[\$y] // last }
}
}

```

The ^ is the "upto" operator that gives a range of 0 up to (but not including) its endpoint. We use it as a hyperoperator () to generate all the ranges of rod numbers we should drop a bead on, with the result that \$x tells us which rod to drop each bead on. Then we use ^ again on the first rod to see how deep the beads are stacked, since they are guaranteed to be the deepest there. The [+] adds up all the beads that are found at level \$y. The last short circuits the map so we don't have to look for all the missing beads at a given level, since the missing beads are all guaranteed to come after the existing beads at that level (because we always dropped left to right starting at rod 0).

## REXX

The REXX language has the advantage of supporting sparse arrays, so implementing a bead sort is trivial, the
major drawback is   if   the spread   (difference between the lowest and highest values)   is quite large   (if it's
greater than a few million),   it'll slow up the display   (but not the sorting).

Zero, negative, and duplicate integers (values) can be handled.

```/*REXX program sorts a list (4 groups) of integers using the  bead sort algorithm. */
/* original source by Gerard Schildberger                                          */
/* 20230605 Walter Pachl reformatted and refurbished                               */
/* define  two dozen  grasshopper  numbers.       */
/* source ??                                      */
gHopper=1 4 10 12 22 26 30 46 54 62 66 78 94 110 126 134 138 158 162 186 190 222 254,
270
/* these are also called hexagonal pyramidal #s.  */
/* see https://oeis.org/A002412                   */
greenGrocer=0 4 16 40 80 140 224 336 480 660 880 1144 1456 1820 2240 2720 3264 3876,
4560
/* define twenty-three Bernoulli numerator numbers*/
/* source ?? quotes needed because of negative #s.*/
bernN='1 -1 1 0 -1 0 1 0 -1 0 5 0 -691 0 7 0 -3617 0 43867 0 -174611 0'
/* also called the Reduced Totient function,      */
/* and is also called Carmichael lambda,          */
/* or the LAMBDA function                         */
/* see https://en.wikipedia.org/wiki/Carmichael_function */
psi=1 1 2 2 4 2 6 2 6 4 10 2 12 6 4 4 16 6 18 4 6 10 22 2 20 12 18 6 28 4 30 8 10 16
list=gHopper greenGrocer bernN psi           /*combine the four lists into one list.*/
Call show 'before sort',list                 /*display the  list  before sorting.   */
Say copies('¦', 75)                          /*show long separator line before sort.*/
Call show ' after sort',beadSort(list)       /*display the  list  after sorting.    */
Exit                                         /*stick a fork in it, we're all done.  */
/*----------------------------------------------------------------------------------*/
Parse Arg list 1 low . 1 high .            /* List to be sorted and first value   */
occurences.=0                              /* count stem occurences               */
Do Until list==''                          /* loop through the list               */
Parse Var list bead list                 /* take an element                     */
low= min(low, bead)                      /* track lowest                        */
high=max(high,bead)                      /* and highest number                  */
End
sorted=''                                  /* now, collect the beads              */
Do v=low To high
If occurences.v>0 Then
sorted=sorted copies(v' ', occurences.v)
End
Return sorted
/*----------------------------------------------------------------------------------*/
show:
Parse Arg txt,slist
n=words(slist)
w=length(n)
Do k=1 For n
Say right('element',30) right(k,w) txt':' right(word(slist,k),9)
End
Return
```
output   when using the default input:

(Shown at three-quarter size.)

```                       element  1 before sort:         1
element  2 before sort:         4
element  3 before sort:        10
element  4 before sort:        12
element  5 before sort:        22
element  6 before sort:        26
element  7 before sort:        30
element  8 before sort:        46
element  9 before sort:        54
element 10 before sort:        62
element 11 before sort:        66
element 12 before sort:        78
element 13 before sort:        94
element 14 before sort:       110
element 15 before sort:       126
element 16 before sort:       134
element 17 before sort:       138
element 18 before sort:       158
element 19 before sort:       162
element 20 before sort:       186
element 21 before sort:       190
element 22 before sort:       222
element 23 before sort:       254
element 24 before sort:       270
element 25 before sort:         0
element 26 before sort:         4
element 27 before sort:        16
element 28 before sort:        40
element 29 before sort:        80
element 30 before sort:       140
element 31 before sort:       224
element 32 before sort:       336
element 33 before sort:       480
element 34 before sort:       660
element 35 before sort:       880
element 36 before sort:      1144
element 37 before sort:      1456
element 38 before sort:      1820
element 39 before sort:      2240
element 40 before sort:      2720
element 41 before sort:      3264
element 42 before sort:      3876
element 43 before sort:      4560
element 44 before sort:         1
element 45 before sort:        -1
element 46 before sort:         1
element 47 before sort:         0
element 48 before sort:        -1
element 49 before sort:         0
element 50 before sort:         1
element 51 before sort:         0
element 52 before sort:        -1
element 53 before sort:         0
element 54 before sort:         5
element 55 before sort:         0
element 56 before sort:      -691
element 57 before sort:         0
element 58 before sort:         7
element 59 before sort:         0
element 60 before sort:     -3617
element 61 before sort:         0
element 62 before sort:     43867
element 63 before sort:         0
element 64 before sort:   -174611
element 65 before sort:         0
element 66 before sort:         1
element 67 before sort:         1
element 68 before sort:         2
element 69 before sort:         2
element 70 before sort:         4
element 71 before sort:         2
element 72 before sort:         6
element 73 before sort:         2
element 74 before sort:         6
element 75 before sort:         4
element 76 before sort:        10
element 77 before sort:         2
element 78 before sort:        12
element 79 before sort:         6
element 80 before sort:         4
element 81 before sort:         4
element 82 before sort:        16
element 83 before sort:         6
element 84 before sort:        18
element 85 before sort:         4
element 86 before sort:         6
element 87 before sort:        10
element 88 before sort:        22
element 89 before sort:         2
element 90 before sort:        20
element 91 before sort:        12
element 92 before sort:        18
element 93 before sort:         6
element 94 before sort:        28
element 95 before sort:         4
element 96 before sort:        30
element 97 before sort:         8
element 98 before sort:        10
element 99 before sort:        16
░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
element  1  after sort:   -174611
element  2  after sort:     -3617
element  3  after sort:      -691
element  4  after sort:        -1
element  5  after sort:        -1
element  6  after sort:        -1
element  7  after sort:         0
element  8  after sort:         0
element  9  after sort:         0
element 10  after sort:         0
element 11  after sort:         0
element 12  after sort:         0
element 13  after sort:         0
element 14  after sort:         0
element 15  after sort:         0
element 16  after sort:         0
element 17  after sort:         0
element 18  after sort:         1
element 19  after sort:         1
element 20  after sort:         1
element 21  after sort:         1
element 22  after sort:         1
element 23  after sort:         1
element 24  after sort:         2
element 25  after sort:         2
element 26  after sort:         2
element 27  after sort:         2
element 28  after sort:         2
element 29  after sort:         2
element 30  after sort:         4
element 31  after sort:         4
element 32  after sort:         4
element 33  after sort:         4
element 34  after sort:         4
element 35  after sort:         4
element 36  after sort:         4
element 37  after sort:         4
element 38  after sort:         5
element 39  after sort:         6
element 40  after sort:         6
element 41  after sort:         6
element 42  after sort:         6
element 43  after sort:         6
element 44  after sort:         6
element 45  after sort:         7
element 46  after sort:         8
element 47  after sort:        10
element 48  after sort:        10
element 49  after sort:        10
element 50  after sort:        10
element 51  after sort:        12
element 52  after sort:        12
element 53  after sort:        12
element 54  after sort:        16
element 55  after sort:        16
element 56  after sort:        16
element 57  after sort:        18
element 58  after sort:        18
element 59  after sort:        20
element 60  after sort:        22
element 61  after sort:        22
element 62  after sort:        26
element 63  after sort:        28
element 64  after sort:        30
element 65  after sort:        30
element 66  after sort:        40
element 67  after sort:        46
element 68  after sort:        54
element 69  after sort:        62
element 70  after sort:        66
element 71  after sort:        78
element 72  after sort:        80
element 73  after sort:        94
element 74  after sort:       110
element 75  after sort:       126
element 76  after sort:       134
element 77  after sort:       138
element 78  after sort:       140
element 79  after sort:       158
element 80  after sort:       162
element 81  after sort:       186
element 82  after sort:       190
element 83  after sort:       222
element 84  after sort:       224
element 85  after sort:       254
element 86  after sort:       270
element 87  after sort:       336
element 88  after sort:       480
element 89  after sort:       660
element 90  after sort:       880
element 91  after sort:      1144
element 92  after sort:      1456
element 93  after sort:      1820
element 94  after sort:      2240
element 95  after sort:      2720
element 96  after sort:      3264
element 97  after sort:      3876
element 98  after sort:      4560
element 99  after sort:     43867
```

## Ruby

```class Array
map {|e| [1] * e}.columns.columns.map(&:length)
end

def columns
y = length
x = map(&:length).max
Array.new(x) do |row|
Array.new(y) { |column| self[column][row] }.compact # Remove nils.
end
end
end

# Demonstration code:
```
Output:
`[7, 5, 4, 3, 1, 1, 1]`

## Seed7

```\$ include "seed7_05.s7i";

const proc: beadSort (inout array integer: a) is func
local
var integer: max is 0;
var integer: sum is 0;
var array bitset: beads is 0 times {};
var integer: i is 0;
var integer: j is 0;
begin
for i range 1 to length(a) do
if a[i] > max then
max := a[i];
end if;
end for;
for j range 1 to max do
sum := 0;
for i range 1 to length(a) do
end for;
for i range length(a) downto length(a) - sum + 1 do
a[i] := j;
end for;
end for;
end func;

const proc: main is func
local
var array integer: a is [] (5, 3, 1, 7, 4, 1, 1, 20);
var integer: n is 0;
begin
for n range a do
write(n <& " ");
end for;
writeln;
end func;```
Output:
```1 1 1 3 4 5 7 20
```

## Sidef

Translation of: Perl
```func beadsort(arr) {

var rows = []
var columns = []

for datum in arr {
for column in ^datum {
++(columns[column] := 0)
++(rows[columns[column] - 1] := 0)
}
}

rows.reverse
}

```
Output:
```[1, 1, 1, 3, 4, 5, 7]
```

## Standard ML

```fun columns l =
case List.filter (not o null) l of
[] => []
| l => map hd l :: columns (map tl l)

fun replicate (n, x) = List.tabulate (n, fn _ => x)

map length (columns (columns (map (fn e => replicate (e, 1)) l)))
```

usage

```- bead_sort [5,3,1,7,4,1,1];
val it = [7,5,4,3,1,1,1] : int list
```

## Tcl

```package require Tcl 8.5

# Special case: empty list is empty when sorted.
if {![llength \$numList]} return
# Set up the abacus...
foreach n \$numList {
for {set i 0} {\$i<\$n} {incr i} {
dict incr vals \$i
}
}
foreach n [dict values \$vals] {
for {set i 0} {\$i<\$n} {incr i} {
dict incr result \$i
}
}
# And the result is...
dict values \$result
}

# Demonstration code
puts [beadsort {5 3 1 7 4 1 1}]
```
Output:
`7 5 4 3 1 1 1`

## VBA

Translation of: Phix
```Option Base 1

Private Function sq_add(arr As Variant, x As Double) As Variant
Dim res() As Variant
ReDim res(UBound(arr))
For i = 1 To UBound(arr)
res(i) = arr(i) + x
Next i
End Function

Private Function beadsort(ByVal a As Variant) As Variant
Dim poles() As Variant
ReDim poles(WorksheetFunction.Max(a))
For i = 1 To UBound(a)
For j = 1 To a(i)
poles(j) = poles(j) + 1
Next j
Next i
For j = 1 To UBound(a)
a(j) = 0
Next j
For i = 1 To UBound(poles)
For j = 1 To poles(i)
a(j) = a(j) + 1
Next j
Next i
End Function

Public Sub main()
Debug.Print Join(beadsort([{5, 3, 1, 7, 4, 1, 1, 20}]), ", ")
End Sub```
Output:
`20, 7, 5, 4, 3, 1, 1, 1`

## Wren

A translation of the Python code in the Wikipedia article. Only works properly for lists of non-negative integers.

```var beadSort = Fn.new { |a|
var res = []
var max = a.reduce { |acc, i| (i > acc) ? i : acc }
var trans = [0] * max
for (i in a) {
for (n in 0...i) trans[n] = trans[n] + 1
}
for (i in a) {
res.add(trans.count { |n| n > 0 })
for (n in 0...trans.count) trans[n] = trans[n] - 1
}
return res[-1..0] // return in ascending order
}

var array = [ [4, 65, 2, 31, 0, 99, 2, 83, 782, 1], [7, 5, 2, 6, 1, 4, 2, 6, 3] ]
for (a in array) {
System.print("Before: %(a)")
System.print("After : %(a)")
System.print()
}
```
Output:
```Before: [4, 65, 2, 31, 0, 99, 2, 83, 782, 1]
After : [0, 1, 2, 2, 4, 31, 65, 83, 99, 782]

Before: [7, 5, 2, 6, 1, 4, 2, 6, 3]
After : [1, 2, 2, 3, 4, 5, 6, 6, 7]
```

## XPL0

```include c:\cxpl\codes;

proc BeadSort(Array, Length);   \Sort Array into increasing order
int  Array, Length;             \Array contents range 0..31; number of items
int  Row, I, J, T, C;
[Row:= Reserve(Length*4);       \each Row has room for 32 beads
for I:= 0 to Length-1 do        \each Row gets Array(I) number of beads
Row(I):= ~-1<<Array(I);     \(beware for 80186..Pentium <<32 doesn't shift)
for J:= 1 to Length-1 do
for I:= Length-1 downto J do
[T:= Row(I-1) & ~Row(I); \up to 31 beads fall in a single pass
Row(I-1):= Row(I-1) | T; \(|=xor, !=or)
Row(I):= Row(I) | T;
];
for I:= 0 to Length-1 do        \count beads in each Row
[C:= 0;  T:= Row(I);
while T do
[if T&1 then C:= C+1;  T:= T>>1];
Array(I):= C;               \count provides sorted order
];
];

int A, I;
[A:= [3, 1, 4, 1, 25, 9, 2, 6, 5, 0];
for I:= 0 to 10-1 do [IntOut(0, A(I));  ChOut(0, ^ )];
]```
Output:
```0 1 1 2 3 4 5 6 9 25
```

## zkl

Translation of: D
```fcn columns(m){ // m is list of lists of zeros/beads, # beads is n, eg (0,0,0)==3
m
.apply("len")   // (0,0,0)-->3
```T(5,3,1,7,4,1,1):beadSort(_).println();
```L(7,5,4,3,1,1,1)