
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



def factorial = { (it > 1) ? (2..it).inject(1) { i, j -> i*j } : 1 }
 
def makePermutation;
makePermutation = { list, i ->
    def n = list.size()
    if (n < 2) return list
    def fact = factorial(n-1)
    assert i < fact*n
 
    def index = i.intdiv(fact)
    [list[index]] + makePermutation(list[0..<index] + list[(index+1)..<n], i % fact)
}
 
def sorted = { a -> (1..<(a.size())).every { a[it-1] <= a[it] } }
 
def permutationSort = { a ->
    def n = a.size()
    def fact = factorial(n)
    def permuteA = makePermutation.curry(a)
    def pIndex = (0..<fact).find { print "."; sorted(permuteA(it)) }
    permuteA(pIndex)
}