
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.




-- 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))