Sorting algorithms/Bead sort: Difference between revisions
m (Made it slightly shorter) |
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sequence poles = repeat(0,max(a)) |
sequence poles = repeat(0,max(a)) |
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for i=1 to length(a) do |
for i=1 to length(a) do |
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integer ai = a[i] |
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poles[1..ai] = sq_add(poles[1..ai],1) |
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end for |
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end for |
end for |
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sequence res = repeat(0,length(a)) |
sequence res = repeat(0,length(a)) |
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for i=1 to length(poles) do |
for i=1 to length(poles) do |
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integer pi = poles[i] |
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res[1..pi] = sq_add(res[1..pi],1) |
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end for |
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end for |
end for |
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return res |
return res |
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Revision as of 16:41, 10 July 2016
You are encouraged to solve this task according to the task description, using any language you may know.
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
Heap sort | Merge sort | Patience sort | Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
- Task
Sort an array of positive integers using the Bead Sort Algorithm.
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
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. <lang 360asm>* Bead Sort 11/05/2016 BEADSORT CSECT
USING BEADSORT,R13 base register
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
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 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
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 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 BEADS DC 4096X'00' beads
YREGS
END BEADSORT</lang>
- 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
<lang 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 }</lang> Examples:<lang AutoHotkey>for i, val in BeadSort([54,12,87,56,36]) res := val (res?",":"") res MsgBox % res</lang>
- 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.
<lang c>#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; }</lang>
C++
<lang cpp>//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] << ' '; }</lang>
Clojure
<lang 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 + %))))
(-> [5 2 4 1 3 3 9] bead-sort println) </lang>
- Output:
(9 5 4 3 3 2 1)
COBOL
<lang COBOL> >>SOURCE FORMAT FREE
- > This code is dedicated to the public domain
- > This is GNUCOBOL 2.0
identification 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.</lang>
- Output:
prompt$ cobc -xj beadsort.cob 3 2 1 6 1 6 4 9 7 initial array initial beads ooo...... oo....... o........ oooooo... o........ oooooo... oooo..... ooooooooo ooooooo.. dropped beads o........ o........ oo....... ooo...... oooo..... oooooo... oooooo... ooooooo.. ooooooooo 1 1 2 3 4 6 6 7 9 sorted array
Common Lisp
<lang lisp> (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)) </lang>
- Output:
(9 5 4 3 3 2 1)
Delphi
<lang d>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.</lang> --DavidIzadaR 18:12, 7 August 2011 (UTC)
D
A functional-style solution. <lang d>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;
}</lang>
- Output:
[7, 5, 4, 3, 1, 1, 1]
Eiffel
<lang 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 </lang> Test: <lang Eiffel>
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
</lang>
- Output:
unsorted: 1 5 99 2 95 7 7 sorted: 99 95 7 7 5 2 1
Elixir
<lang elixir>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</lang>
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
<lang 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).</lang> Example; <lang erlang>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]</lang>
F#
<lang fsharp>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</lang> Usage: beadSort [2;4;1;3;3] or beadSort2 [2;4;1;3;3]
- Output:
val it : int list = [4; 3; 3; 2; 1]
Factor
<lang 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 ;</lang>
<lang factor>( scratchpad ) { 5 2 4 1 3 3 9 } beadsort . { 9 5 4 3 3 2 1 }</lang>
Fortran
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.
<lang fortran>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</lang>
Go
Sorts non-negative integers only. The extension to negative values seemed a distraction from this fun task. <lang go>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
}
}</lang>
Groovy
Solution: <lang groovy>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()
}
}</lang>
Annotated Solution (same solution really): <lang groovy>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() }
}</lang>
Test: <lang groovy>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])</lang>
- Output:
........................................................................................................................[4, 12, 14, 23, 24, 24, 31, 35, 38, 46, 51, 57, 57, 58, 76, 78, 89, 92, 95, 97, 99] ...............................................................................................................[0, 1, 4, 5, 7, 8, 12, 14, 18, 20, 31, 33, 44, 62, 70, 73, 75, 76, 78, 81, 82, 84, 88]
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.
Haskell
<lang haskell>import Data.List
beadSort :: [Int] -> [Int] beadSort = map sum. transpose. transpose. map (flip replicate 1)</lang> Example; <lang haskell>*Main> beadSort [2,4,1,3,3] [4,3,3,2,1]</lang>
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.
<lang Icon>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</lang>
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
<lang j>bead=: [: +/ #"0&1</lang>
Example use:
<lang> bead bead 2 4 1 3 3 4 3 3 2 1
bead bead 5 3 1 7 4 1 1
7 5 4 3 1 1 1</lang>
Extending to deal with sequences of arbitrary integers:
<lang j>bball=: ] (] + [: bead^:2 -) <./ - 1:</lang>
Example use:
<lang> bball 2 0 _1 3 1 _2 _3 0 3 2 1 0 0 _1 _2 _3</lang>
Java
<lang 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(); } } </lang>
- 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 <lang jq># 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)]) ;</lang>
Part 3: read the answer in order of largest-to-smallest <lang jq># 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( . > $i) )]);</lang>
"Bead Sort": <lang jq>def bead_sort: column_sums(max) | readout;</lang>
Example: <lang jq>[734,3,1,24,324,324,32,432,42,3,4,1,1] | bead_sort</lang>
- Output:
<lang sh>$ jq -n -c -f bead_sort.jq [734,432,324,324,42,32,24,4,3,3,1,1,1]</lang>
Julia
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.
<lang Julia>
function beadsort{T<:Integer}(a::Array{T,1})
(lo, hi) = extrema(a)
if lo < 1
throw(DomainError())
end
hi = convert(Int, hi)
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 T[sum(abacus[i,:]) for i in 1:len]
end
a = Uint8[rand(1:typemax(Uint8)) for i in 1:20] println("Sort of Unsigned Bytes:") println(" Before Sort:") println(" ", a) a = beadsort(a) println("\n After Sort:") println(" ", a, "\n")
a = [rand(1:2^10) for i in 1:20] println("Sort of Integers:") println(" Before Sort:") println(" ", a) a = beadsort(a) println("\n After Sort:") println(" ", a) </lang>
- Output:
Sort of Unsigned Bytes:
Before Sort:
Uint8[134,68,81,149,71,92,113,179,123,211,214,207,16,218,27,171,25,30,140,236]
After Sort:
Uint8[16,25,27,30,68,71,81,92,113,123,134,140,149,171,179,207,211,214,218,236]
Sort of Integers:
Before Sort:
[619,289,862,711,591,331,682,775,419,58,434,314,558,265,632,834,671,698,117,46]
After Sort:
[46,58,117,265,289,314,331,419,434,558,591,619,632,671,682,698,711,775,834,862]
Lua
<lang 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 function beadSort (numList)
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()) beadSort(randList(10, 1, 10))</lang>
- 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
<lang 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;;ai]]=1 ]
For[ i = 1 ,i <= m, i++, s = Total[t;;,i]; t;; , i = 0; t1 ;; s , i = 1; ]
For[ i=1,i<=Length[a],i++, sortedi = Total[ti,;;]; ] Print[sorted]; ]</lang>
beadsort[{2,1,5,3,6}]
->{6,3,2,1,0}
NetRexx
<lang 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, ',')']'
</lang>
- 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
<lang 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 a echo a</lang>
- Output:
@[1, 1, 1, 3, 4, 5, 7, 20]
OCaml
<lang 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)))</lang>
usage
# bead_sort [5;3;1;7;4;1;1];; - : int list = [7; 5; 4; 3; 1; 1; 1]
Octave
<lang octave>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])</lang>
ooRexx
version 1
<lang oorexx>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 </lang>
- 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
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). <lang ooRexx>/*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
/*─────────────────────────────────beadSort@ 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 !
/*─────────────────────────────────────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
</lang>
- 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. <lang progress>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.</lang>
- 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. <lang parigp>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
};</lang>
Pascal
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.
<lang perl>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; </lang>
Perl 6
<lang perl6># 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;</lang>
- Output:
(5, 3, 2, 1)
Here we simulate the dropping beads by using the push method. <lang perl6>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;</lang> 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 $y. The last short circuits the map so we don't have to look for all the missing beads at a given level, since the missing beads are all guaranteed to come after the existing beads at that level (because we always dropped left to right starting at rod 0).
Phix
<lang Phix>function beadsort(sequence a)
sequence poles = repeat(0,max(a))
for i=1 to length(a) do
integer ai = a[i]
poles[1..ai] = sq_add(poles[1..ai],1)
end for
sequence res = repeat(0,length(a))
for i=1 to length(poles) do
integer pi = poles[i]
res[1..pi] = sq_add(res[1..pi],1)
end for
return res
end function
?beadsort({5, 3, 1, 7, 4, 1, 1, 20})</lang>
- Output:
{20,7,5,4,3,1,1,1}
PHP
<lang php><?php function columns($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', $transpose);
}
function beadsort($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))); ?></lang>
- 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. <lang PicoLisp>(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 @) ) ) ) )</lang>
- Output:
: (beadSort (5 3 1 7 4 1 1 20)) -> (20 7 5 4 3 1 1 1)
PL/I
version 1
<lang PL/I> /* 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;</lang>
version 2
PL/I supports negative array indices! <lang pli>*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;</lang>
- Output:
Input: 10 -12 1 0 999 8 2 2 4 4 Sorted: -12 0 1 2 2 4 4 8 10 999
PowerShell
<lang 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 ), $l - 1 ) } )</lang>
PureBasic
<lang PureBasic>#MAXNUM=100
Dim MyData(Random(15)+5) Global Dim Abacus(0,0)
Declare BeadSort(Array InData(1)) Declare PresentData(Array InData(1))
If OpenConsole()
Define i
;- Generate a random array
For i=0 To ArraySize(MyData())
MyData(i)=Random(#MAXNUM)
Next i
PresentData(MyData())
;
;- Sort the array
BeadSort(MyData())
PresentData(MyData())
;
Print("Press ENTER to exit"): Input()
EndIf
Procedure LetFallDown(x)
Protected y=ArraySize(Abacus(),2)-1
Protected ylim=y
While y>=0
If Abacus(x,y) And Not Abacus(x,y+1)
Swap Abacus(x,y), Abacus(x,y+1)
If y<ylim: y+1: Continue: EndIf
Else
y-1
EndIf
Wend
EndProcedure
Procedure BeadSort(Array n(1))
Protected i, j, k
NewList T()
Dim Abacus(#MAXNUM,ArraySize(N()))
;- Set up the abacus
For i=0 To ArraySize(Abacus(),2)
For j=1 To N(i)
Abacus(j,i)=#True
Next
Next
;- sort it in threads to simulate free beads falling down
For i=0 To #MAXNUM
AddElement(T()): T()=CreateThread(@LetFallDown(),i)
Next
ForEach T()
WaitThread(T())
Next
;- send it back to a normal array
For j=0 To ArraySize(Abacus(),2)
k=0
For i=0 To ArraySize(Abacus())
k+Abacus(i,j)
Next
N(j)=k
Next
EndProcedure
Procedure PresentData(Array InData(1))
Protected n, m, sum PrintN(#CRLF$+"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</lang>
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
<lang python>try:
from itertools import zip_longest
except:
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]))</lang>
- Output:
[7, 5, 4, 3, 1, 1, 1]
Racket
<lang 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))
</lang>
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 will slow up the display.
Negative and duplicate integers (values) can be handled. <lang rexx>/*REXX program sorts a list of integers using the bead sort algorithm. */ grasshopper=, /*define two dozen grasshopper numbers.*/
1 4 10 12 22 26 30 46 54 62 66 78 94 110 126 134 138 158 162 186 190 222 254 270
/*Green Grocer 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
/*define 23 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*/
psi=, /*also called Carmichael lambda, or the LAMBDA function.*/
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
- = grasshopper greenGrocer bernN psi /*combine the four lists into one list.*/
call show 'before sort', # /*display the list before sorting. */ call show ' after sort', beadSort(#) /* " " " after " */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ beadSort: procedure; parse arg low . 1 high . 1 z,$ /*$: the list to be sorted. */
@.=0 /*set all beads (@.) to zero.*/
do j=1 until z==; parse var z x z /*pick the meat off the bone.*/
if \datatype(x, 'W') then do; say '***error***'
say 'element' j "in list isn't numeric:" x
say; exit 13
end /* [↑] exit pgm with RC=13. */
x=x/1 /*normalize: 4. 004 +4 .4e0 */
@.x=@.x+1 /*indicate this bead has a #.*/
low=min(low,x); high=max(high,x) /*track lowest and highest #.*/
end /*j*/
/* [↓] now, collect beads and*/
do m=low to high /*let them fall (to zero). */
if @.m\==0 then do n=1 for @.m; $=$ m /*have we found a bead here? */
end /*n*/ /* [↑] add it to sorted list*/
end /*m*/
return $
/*──────────────────────────────────────────────────────────────────────────────────────*/ show: parse arg txt,y; _=left(, 20)
w=length(words(y)); do k=1 for words(y) /* [↑] twenty pad blanks. */
say _ 'element' right(k, w) txt":" right(word(y, k), 9)
end /*k*/
say copies('─', 70) /*show a long separator line.*/
return</lang>
output when using the default (internal) numbers:
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
──────────────────────────────────────────────────────────────────────
Ruby
<lang 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
end
end
- Demonstration code:
p [5,3,1,7,4,1,1].beadsort</lang>
- Output:
[7, 5, 4, 3, 1, 1, 1]
Seed7
<lang 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;</lang>
- Output:
1 1 1 3 4 5 7 20
Sidef
<lang ruby>func beadsort(arr) {
var rows = []; var columns = [];
arr.each { |datum|
range(0, datum-1).each { |column|
++(columns[column] := 0);
++(rows[columns[column] - 1] := 0);
}
}
rows.reverse;
}
say beadsort([5,3,1,7,4,1,1]);</lang>
- Output:
[1, 1, 1, 3, 4, 5, 7]
Standard ML
<lang sml>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)))</lang>
usage
- bead_sort [5,3,1,7,4,1,1]; val it = [7,5,4,3,1,1,1] : int list
Tcl
<lang 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 code
puts [beadsort {5 3 1 7 4 1 1}]</lang>
- Output:
7 5 4 3 1 1 1
XPL0
<lang 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]; BeadSort(A, 10); for I:= 0 to 10-1 do [IntOut(0, A(I)); ChOut(0, ^ )]; ]</lang>
- Output:
0 1 1 2 3 4 5 6 9 25
zkl
<lang zkl>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");
}</lang> <lang zkl>T(5,3,1,7,4,1,1):beadSort(_).println(); T(4,3,3,2,1):beadSort(_).println();</lang>
- Output:
L(7,5,4,3,1,1,1) L(4,3,3,2,1)
- Programming Tasks
- Sorting Algorithms
- 360 Assembly
- AutoHotkey
- C
- C++
- Clojure
- COBOL
- Common Lisp
- Delphi
- D
- Eiffel
- Elixir
- Erlang
- F Sharp
- Factor
- Fortran
- Go
- Groovy
- Haskell
- Icon
- Unicon
- J
- Java
- Jq
- Julia
- Lua
- Mathematica
- NetRexx
- Nim
- OCaml
- Octave
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