permutation_unordered_non-duplicate.py

permutation.py

def inverse_natural_sum(num, start):
    for i in range(start, 0, -1):
        num = num - i
        if num == 0: return i
        if num < 0: raise ValueError("number is not a natural sum.")
    
def permutations_unordered_no_repeat(collection):
    def reducer(acc, x):
        if acc == collection[0]:
            return [ (acc, y) for y in collection[1:] ] + [ (x, y) for y in collection[2:] ]
        else:
            start_index = len(collection) - 1 - inverse_natural_sum(len(acc), len(collection) - 1) + 2
            return acc + [ (x, y) for y in collection[start_index:] ]
    return reduce(reducer, collection)