
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

Implement a permutation sort, which proceeds by generating the possible permutations
of the input array/list until discovering the sorted one.

Pseudocode:

while not InOrder(list) do
    nextPermutation(list)
done



-- Return an iterator to produce every permutation of list
function permute (list)
  local function perm (list, n)
    if n == 0 then coroutine.yield(list) end
    for i = 1, n do
      list[i], list[n] = list[n], list[i]
      perm(list, n - 1)
      list[i], list[n] = list[n], list[i]
    end
  end
  return coroutine.wrap(function() perm(list, #list) end)
end
 
-- Return true if table t is in ascending order or false if not
function inOrder (t)
  for pos = 2, #t do
    if t[pos] < t[pos - 1] then
      return false
    end
  end
  return true
end
 
-- Main procedure
local list = {2,3,1}                 --\   Written to match task pseudocode,
local nextPermutation = permute(list) --\  more idiomatic would be:
while not inOrder(list) do             --\ 
  list = nextPermutation()             --/   for p in permute(list) do
end                                   --/       stuffWith(p)
print(unpack(list))                  --/     end