
Sorting Algorithm

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

O(n logn) sorts
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.

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.




$ 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;