Question

I have found some algorithms online to generate derangements in Python but they’re all exponential in complexity and as a result I can’t get them to converge with a set of 26 elements (the alphabet)!

So I’m trying to find a way to improve the following code (source here):

def derangement(vs):
    l = [None for x in vs]
    sol = set()
    sol.add(tuple(l))
    for v in vs:
        sol1 = set()
        for s in sol:
            for (i, v1) in enumerate(s):
                if not v1 and v != vs[i]:
                    s1 = list(s)
                    s1[i] = v
                    sol1.add(tuple(s1))
        sol = sol1
    return list(sol)

If anyone is curious this is for a bruteforce substitution cipher solver. I’m trying to see how long it takes to bruteforce a cipher!

Answer 1

As permutation algorithms are Ω(n!) nothing will make your code converge. This may be faster, but that means nothing for things of that complexity:

import itertools
def derangement(x):
    p = itertools.permutations(x)
    return (i for i in p if not any(i[k] == x[k] for k in range(len(x))))

It’s a lazy iterator. If you need all values (I doubt you need) just list() it