
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.




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}]