
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.




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;
}