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 other sorting algorithms, see Category:Sorting Algorithms, or:
O(n logn) Sorts
Heapsort | Mergesort | Quicksort
O(n log2n) Sorts
Shell Sort
O(n2) Sorts
Bubble sort | Cocktail sort | Comb sort | Gnome sort | Insertion sort | Selection sort | Strand sort
Other Sorts
Bead sort | Bogosort | Counting sort | Pancake sort | Permutation sort | Radix sort | Sleep sort | Stooge 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.

## 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                 11/05/2016BEADSORT CSECT         USING  BEADSORT,R13       base registerSAVEAR   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=1LOOPI1   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 iELOOPI1  LA     R9,1               1         SH     R9,LO              -lo+1         LA     R6,1               i=1LOOPI2   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         IC     R2,BEADS-1(R3)       beads(l)         LA     R2,1(R2)             beads(l)+1         STC    R2,BEADS-1(R3)       beads(l)=beads(l)+1         LA     R6,1(R6)           iterate i         B      LOOPI2             next iELOOPI2  SR     R8,R8              k=0         LH     R6,LO              i=loLOOPI3   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         IC     R10,BEADS-1(R1)      beads(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 jELOOPJ3  AH     R6,=H'1'           iterate i         B      LOOPI3             next iELOOPI3  LA     R7,1               j=1LOOPJ4   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:'      zapONE      LA     R10,PG+7             [email protected]+7         LA     R6,1                 i=1LOOPI4   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                  elseTWO      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 iELOOPI4  XPRNT  PG,80                print buffer         LA     R7,1(R7)             iterate j         B      LOOPJ4             next jELOOPJ4  L      R13,4(0,R13)       epilog         LM     R14,R12,12(R13)    "         XR     R15,R15            "         BR     R14                "         LTORG                     literal tableN        EQU    (S-Z)/2            number of itemsZ        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 zLO       DC     H'32767'           2**31-1HI       DC     H'-32768'          -2**31PG       DC     CL80'   raw:'      bufferXDEC     DS     CL12               tempBEADS    DC     4096X'00'          beads         YREGS         END    BEADSORT`
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
```

## 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?",":"") resMsgBox % res`
Output:
`12,36,54,56,87`

## 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> void bead_sort(int *a, int len){	int i, j, max, sum;	unsigned char *beads;#	define BEAD(i, j) beads[i * max + j] 	for (i = 1, max = a[0]; i < len; i++)		if (a[i] > max) max = a[i]; 	beads = calloc(1, max * len); 	/* mark the beads */	for (i = 0; i < len; i++)		for (j = 0; j < a[i]; j++)			BEAD(i, j) = 1; 	for (j = 0; j < max; j++) {		/* count how many beads are on each post */		for (sum = i = 0; i < len; i++) {			sum += BEAD(i, j);			BEAD(i, j) = 0;		}		/* 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;	}	free(beads);} int main(){	int i, x[] = {5, 3, 1, 7, 4, 1, 1, 20};	int len = sizeof(x)/sizeof(x[0]); 	bead_sort(x, len);	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) {	//*beads* go down into different buckets using gravity (addition).    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};	vector<int> sorted = beadSort(myints, sizeof(myints)/sizeof(int));	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)))))) (defn bead-sort [xs]  (->> 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 2.0identification division.program-id. beadsort.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.start-beadsort.     *> 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'     *> distribute the beads    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    display NL 'initial beads'    perform display-beads     *> drop the beads    perform varying pole from 1 by 1 until pole > a-lim        move a-lim to r2        perform find-opening        compute r1 = r2 - 1        perform find-bead        perform until r1 = 0 *> no bead or no opening            *> drop the bead            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            perform find-bead        end-perform    end-perform    display NL 'dropped beads'    perform display-beads     *> 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    .find-bead.    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    .display-beads.    perform varying r from 1 by 1 until r > a-lim        display row(r)    end-perform    .end program beadsort.`
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)))))) (defun bead-sort (xs)  (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)`

## 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);   // mark the beads   for i := Low(a) to High(a) do    for j := 0 to a[i] - 1 do      beads[i, j] := 1;   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];      beads[i, j] := 0;    end;    //mark bottom sum beads    for i := High(a) + 1 - sum to High(a) do      beads[i, j] := 1;  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;   SetLength(beads, 0, 0);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]]));   BeadSort(x);   for i := 1 to N do    writeln(Format('x[%d] = %d', [i, x[i]]));   readln;end.`

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

## 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]`

## Eiffel

` class	BEAD_SORT 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>>			create beadsort			io.put_string ("unsorted:" + "%N")			across				test as ar			loop				io.put_string (ar.item.out + "%T")			end			io.put_string ("%N" + "sorted:" + "%N")			test := beadsort.bead_sort (test)			across				test as ar			loop				io.put_string (ar.item.out + "%T")			end		end 	beadsort: BEAD_SORT 	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 ; : beadsort ( seq -- newseq ) bead bead ;`
`( 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 /)   call beadsort(a)  print *, a contains   subroutine beadsort(a)    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    forall(i=1:m)             ! let beads "fall"; instead of       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,:))   end subroutine beadsort end program BeadSortTest`

## 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 const bead = 'o' func main() {    fmt.Println("before:", a)    beadSort()    fmt.Println("after: ", a)} func beadSort() {    // 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    // Place beads for each number concurrently. (Presumably beads can be    // "snapped on" to the middle of a pole without disturbing neighboring    // beads.)  Also note 'row' here is a row of the abacus.    wg.Add(len(a))    for row, n := range a {        go func(row, n int) {            for pole := 0; pole < n; pole++ {                abacus[pole][row] = bead            }            wg.Done()        }(row, n)    }    wg.Wait()    // Now tip the abacus, letting beads fall on each pole concurrently.    wg.Add(aMax)    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 {                if space == bead {                    // 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                    pole[top] = bead                    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 }    }.transpose().collect{ beadTally ->        beadTally.findAll{ it }.size()    }}`

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 == bead, false == no bead        ([true] * number) + ([false] * (nPoles - number))    }    // each row is an abacus pole    def abacusPoles = beadTallies.transpose()    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    def beadTalliesDrop = abacusPolesDrop.transpose()    beadTalliesDrop.collect{ beadTally -> beadTally.findAll{ it }.size() }}`

Test:

`println beadSort([23,76,99,58,97,57,35,89,51,38,95,92,24,46,31,24,14,12,57,78,4]) println beadSort([88,18,31,44,4,0,8,81,14,78,20,76,84,33,73,75,82,5,62,70,12,7,1])`
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 :: [Int] -> [Int]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    write("Sorting Demo using ",image(beadsort))      writes("  on list : ")      writex(UL := [3, 14, 1, 5, 9, 2, 6, 3])      displaysort(beadsort,copy(UL))    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 34 3 3 2 1   bead bead 5 3 1 7 4 1 17 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 03 2 1 0 0 _1 _2 _3`

## Java

`  public class BeadSort {	public static void main(String[] args)	{		BeadSort now=new BeadSort();		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); 		int[] sort=now.beadSort(arr);		System.out.print("Sorted: ");		now.display1D(sort);	}	int[] beadSort(int[] arr)	{		int max=0;		for(int i=0;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);		*/ 		//Drop the beads		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);		//Count the beads		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); def readout:  . 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 fun beadSort(a: IntArray) {    val n = a.size    if (n < 2) return    var max = a.max()!!    val beads = ByteArray(max * n)    /* mark the beads */    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()}")    beadSort(a)    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 linefunction show (msg, t)    io.write(msg .. ":\t")    for _, v in pairs(t) do io.write(v .. " ") end    print()end -- Return a table of random numbersfunction randList (length, lo, hi)    local t = {}    for i = 1, length do table.insert(t, math.random(lo, hi)) end    return tend -- Count instances of numbers that appear in counting to each list valuefunction 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 talend -- Sort a table of positive integers into descending orderfunction beadSort (numList)    show("Before sort", numList)    local abacus = tally(numList)    show("Tally list", abacus)    local sorted = tally(abacus)    show("After sort", sorted)end -- Main proceduremath.randomseed(os.time())beadSort(randList(10, 1, 10))`
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

`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];]`
```beadsort[{2,1,5,3,6}]
->{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'  beads = Rexx 0  beads[MIN_] = 0  beads[MAX_] = 0   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    beads[val] = beads[val] + 1    end val   harry_sorted = Rexx[harry.length]  bi = 0  loop xx = beads[MIN_] to beads[MAX_]    -- extract beads in value order and insert in result array    if beads[xx] == 0 then iterate xx    loop for beads[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]  sorted = bead_sort(unsorted)  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]beadSort aecho 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) let bead_sort l =  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, :));  endforendfunction 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  beads.=0; Do i=1 To words(in)   z=z.i   beads.z+=1   End j=0 Do i=lo To hi   Do While beads.i>0     j+=1     s.j=i     beads.i-=1     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. */!=beadSort(list)                       /*invoke the bead sort.     */call showL ' after sort',!             /*show  after array elements*/exit  /*─────────────────────────────────[email protected] subroutine────────────*/beadSort: procedure expose _.  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                                        /*now, collect the beads and*/  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 !  /*─────────────────────────────────────[email protected] 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 */   EXTENT( cbeads ) = inumbers.   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 ). END FUNCTION. /* beadSort */ 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)   beadSort( "88,18,31,44,4,0,8,81,14,78,20,76,84,33,73,75,82,5,62,70,12,7,1" )VIEW-AS ALERT-BOX.`
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)={  my(sz=vecmax(v),M=matrix(#v,sz,i,j,v[i]>=j)); \\ Set up beads  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};`

See Delphi

## 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; `

## Perl 6

Works with: rakudo version 2016-05
`# routine cribbed from List::Utils;sub transpose(@list is copy) {    gather {        while @list {            my @heads;            if @list[0] !~~ Positional { @heads = @list.shift; }            else { @heads = @list.map({\$_.shift unless \$_ ~~ []}); }            @list = @list.map({\$_ unless \$_ ~~ []});            take [@heads];        }    }} sub beadsort(@l) {    (transpose(transpose(map {[1 xx \$_]}, @l))).map(*.elems);} my @list = 2,1,3,5;say beadsort(@list).perl;`
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 }    }} say beadsort 2,1,3,5;`

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).

## Phix

`function beadsort(sequence a)    sequence poles = repeat(0,max(a))    for i=1 to length(a) do        poles[1..a[i]] = sq_add(poles[1..a[i]],1)    end for    a[1..\$] = 0    for i=1 to length(poles) do        a[1..poles[i]] = sq_add(a[1..poles[i]],1)    end for    return aend function ?beadsort({5, 3, 1, 7, 4, 1, 1, 20})`
Output:
```{20,7,5,4,3,1,1,1}
```

## PHP

`<?phpfunction 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);} function beadsort(\$arr) {    foreach (\$arr as \$e)        \$poles []= array_fill(0, \$e, 1);    return array_map('count', columns(columns(\$poles)));} print_r(beadsort(array(5,3,1,7,4,1,1)));?>`
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 N Lst                                   # Thread beads on poles         (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; end beadsort;`

### version 2

Translation of: ooRexx

PL/I supports negative array indices!

`*process source attributes xref; /* Handles both negative and positive values. */ Beadsort: Proc Options(main); 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; Dcl beads(lo:hi) Bin Fixed(31); beads=0; Do i=1 To hbound(z);   beads(z(i))+=1;   End; Do i=lo To hi;   Do While(beads(i)>0);     j+=1;     s(j)=i;     beads(i)-=1;     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			}		} #Add Beads to the poles, already moved to the bottom		\$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 BeadSort(Array InData(1))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  BeadSort(MyData())  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  WendEndProcedure Procedure BeadSort(Array n(1))  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  ;- sort it in threads to simulate free beads falling down  For i=0 To #MAXNUM    AddElement(T()): T()=CreateThread(@LetFallDown(),i)  Next  ForEach T()    WaitThread(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  NextEndProcedure 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

`try:  from itertools import zip_longestexcept:  try:    from itertools import izip_longest as zip_longest  except:    zip_longest = lambda *args: map(None, *args) def beadsort(l):  return map(len, columns(columns([[1] * e for e in l]))) def columns(l):  return [filter(None, x) for x in zip_longest(*l)] # Demonstration code:print(beadsort([5,3,1,7,4,1,1]))`
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)    DIM BeadSort_Sum AS DOUBLE    DIM BeadSort_I AS LONG    DIM BeadSort_J AS LONG    FOR BeadSort_I = start + 1 TO (finish - start)        IF (CGSortLibArray(BeadSort_I) > MAX) THEN MAX = CGSortLibArray(BeadSort_I)    NEXT    REDIM beads((finish - start), MAX)    FOR BeadSort_I = 0 TO (finish - start) - 1        FOR BeadSort_J = 0 TO CGSortLibArray(BeadSort_I) - 1            beads(BeadSort_I, BeadSort_J) = 1        NEXT    NEXT    IF order& = 1 THEN        FOR BeadSort_J = 0 TO MAX            BeadSort_Sum = 0            FOR BeadSort_I = 0 TO (finish - start)                BeadSort_Sum = BeadSort_Sum + beads(BeadSort_I, BeadSort_J)                beads(BeadSort_I, BeadSort_J) = 0            NEXT            FOR BeadSort_I = (finish - start) - BeadSort_Sum TO (finish - start)                beads(BeadSort_I, BeadSort_J) = 1            NEXT        NEXT        FOR BeadSort_I = 0 TO (finish - start)            BeadSort_J = 0            WHILE BeadSort_J < MAX AND beads(BeadSort_I, BeadSort_J)                BeadSort_J = BeadSort_J + 1            WEND            CGSortLibArray(BeadSort_I) = BeadSort_J        NEXT    ELSE        FOR BeadSort_J = MAX TO 0 STEP -1            BeadSort_Sum = 0            FOR I = 0 TO (finish - start)                BeadSort_Sum = BeadSort_Sum + beads(I, BeadSort_J)                beads(I, BeadSort_J) = 0            NEXT            FOR I = (finish - start) TO (finish - start) - BeadSort_Sum STEP -1                beads(I, BeadSort_J) = 1            NEXT        NEXT        FOR BeadSort_I = 0 TO (finish - start)            BeadSort_J = 0            WHILE BeadSort_J < MAX AND beads(BeadSort_I, BeadSort_J)                BeadSort_J = BeadSort_J + 1            WEND            CGSortLibArray(finish - BeadSort_I) = BeadSort_J        NEXT    END IFEND 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)))])) (define (bead-sort lst)  (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)) `

## 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 (four groups)  of integers  using the  bead sort  algorithm.*/                                 /* [↓]  define  two dozen  grasshopper  numbers.       */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.  */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*/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*/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 16y= gHopper greenGrocer bernN psi                 /*combine the four lists into one list.*/call show  'before sort',  y                     /*display the  list  before sorting.   */say copies('░', 75)                              /*show long separator line before sort.*/call show  ' after sort',  beadSort(y)           /*display the  list   after sorting.   */exit                                             /*stick a fork in it,  we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/beadSort: procedure; parse arg low . 1 high . 1 z,\$;  @.=0 /*\$:  the list to be sorted. */             do j=1  until z=='';   parse var  z   x  z    /*pick the meat off the bone.*/             x= x / 1;              @.x= @.x + 1           /*normalize X;  bump counter.*/             low=min(low, x);       high=max(high, x)      /*track lowest and highest #.*/             end   /*j*/                                                           /* [↓] now, collect beads and*/             do m=low  to high;     do @.m;  \$=\$ m;  end   /*let them fall (to zero).   */             end   /*m*/          return \$/*──────────────────────────────────────────────────────────────────────────────────────*/show: parse arg txt,y;            z=words(y);           w=length(z)                      do k=1  for z                      say right('element',30)   right(k,w)   txt":"   right( word(y,k), 9)                      end   /*k*/;              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  def beadsort    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  endend # Demonstration code:p [5,3,1,7,4,1,1].beadsort`
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    beads := length(a) times {};    for i range 1 to length(a) do      if a[i] > max then        max := a[i];      end if;      beads[i] := {1 .. a[i]};    end for;    for j range 1 to max do      sum := 0;      for i range 1 to length(a) do        sum +:= ord(j in beads[i]);        excl(beads[i], j);      end for;      for i range length(a) - sum + 1 to length(a) do        incl(beads[i], j);      end for;    end for;    for i range 1 to length(a) do      for j range 1 to max until j not in beads[i] do        noop;      end for;      a[i] := pred(j);    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: num is 0;  begin    beadSort(a);    for num range a do      write(num <& " ");    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} say beadsort([5,3,1,7,4,1,1])`
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) fun bead_sort l =  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 proc beadsort numList {    # 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	}    }    # Make the beads fall...    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 codeputs [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    sq_add = resEnd 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    beadsort = aEnd 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`

## XPL0

`include c:\cxpl\codes; proc BeadSort(Array, Length);   \Sort Array into increasing orderint  Array, Length;             \Array contents range 0..31; number of itemsint  Row, I, J, T, C;[Row:= Reserve(Length*4);       \each Row has room for 32 beadsfor 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];BeadSort(A, 10);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   .reduce("max")  // largest bead stack   .walker()       // [0..max]   .apply('wrap(i){ m.filter('wrap(s){ s.len() > i }).len().pump(List,0) });} fcn beadSort(data){   data.apply("pump",List,0):columns(_):columns(_).apply("len");}`
`T(5,3,1,7,4,1,1):beadSort(_).println();T(4,3,3,2,1):beadSort(_).println();`
Output:
```L(7,5,4,3,1,1,1)
L(4,3,3,2,1)
```