
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.




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