Python permutations of both sequence and subsequences

Question

Question: How do I implement double_permutations(s) below?

>>> s = [('a', 'b'), ('c', 'd'), ('e', 'f')]
>>> for answer in double_permutation(s):
...     print(answer)   # in some order
[('a', 'b'), ('c', 'd'), ('e', 'f')]
[('a', 'b'), ('d', 'c'), ('e', 'f')]
[('a', 'b'), ('c', 'd'), ('f', 'e')]
[('a', 'b'), ('d', 'c'), ('f', 'e')]
[('a', 'b'), ('e', 'f'), ('c', 'd')]
[('a', 'b'), ('f', 'e'), ('c', 'd')]
[('a', 'b'), ('e', 'f'), ('d', 'c')]
[('a', 'b'), ('f', 'e'), ('d', 'c')]

What I've tried (breaks down once the outer list is longer than 3 elements)

from itertools import permutations

def double_permutation(l):

    def double_permutation_recur(s, r):
        if not r:
            yield s
        else:
            for permutation in permutations(r):
                s1 = s + [permutation[0]]
                s2 = s + [(permutation[0][1], permutation[0][0])]
                for perm1 in double_permutation_recur(s1, permutation[1:]):
                    yield perm1
                for perm2 in double_permutation_recur(s2, permutation[1:]):
                    yield perm2

    return double_permutation_recur([l[0]], l[1:])

This should yield double_factorial(n-1) answers for a list of length n. This works up through n = 3, but breaks down at n = 4 (which yields 96 instead of 48 answers).

Answer 1

You can build this up from the primitives in the itertools module

import itertools
s = [('a', 'b'), ('c', 'd'), ('e', 'f')]

Is this what you're describing?

def permute(it):
    return itertools.product(*(itertools.permutations(i) for i in it))

>>> for i in permute(s):
...     print i
(('a', 'b'), ('c', 'd'), ('e', 'f'))
(('a', 'b'), ('c', 'd'), ('f', 'e'))
(('a', 'b'), ('d', 'c'), ('e', 'f'))
(('a', 'b'), ('d', 'c'), ('f', 'e'))
(('b', 'a'), ('c', 'd'), ('e', 'f'))
(('b', 'a'), ('c', 'd'), ('f', 'e'))
(('b', 'a'), ('d', 'c'), ('e', 'f'))
(('b', 'a'), ('d', 'c'), ('f', 'e'))

---

Or do you want:

def permute2(it):
    return itertools.chain.from_iterable(
        permute(p)
        for p in itertools.permutations(it)
    )

>>> for i in permute2(s):
...      print i    
(('a', 'b'), ('c', 'd'), ('e', 'f'))
(('a', 'b'), ('c', 'd'), ('f', 'e'))
(('a', 'b'), ('d', 'c'), ('e', 'f'))
(('a', 'b'), ('d', 'c'), ('f', 'e'))
(('b', 'a'), ('c', 'd'), ('e', 'f'))
(('b', 'a'), ('c', 'd'), ('f', 'e'))
(('b', 'a'), ('d', 'c'), ('e', 'f'))
(('b', 'a'), ('d', 'c'), ('f', 'e'))
(('a', 'b'), ('e', 'f'), ('c', 'd'))
(('a', 'b'), ('e', 'f'), ('d', 'c'))
(('a', 'b'), ('f', 'e'), ('c', 'd'))
(('a', 'b'), ('f', 'e'), ('d', 'c'))
(('b', 'a'), ('e', 'f'), ('c', 'd'))
(('b', 'a'), ('e', 'f'), ('d', 'c'))
(('b', 'a'), ('f', 'e'), ('c', 'd'))
(('b', 'a'), ('f', 'e'), ('d', 'c'))
(('c', 'd'), ('a', 'b'), ('e', 'f'))
(('c', 'd'), ('a', 'b'), ('f', 'e'))
(('c', 'd'), ('b', 'a'), ('e', 'f'))
(('c', 'd'), ('b', 'a'), ('f', 'e'))
(('d', 'c'), ('a', 'b'), ('e', 'f'))
(('d', 'c'), ('a', 'b'), ('f', 'e'))
(('d', 'c'), ('b', 'a'), ('e', 'f'))
(('d', 'c'), ('b', 'a'), ('f', 'e'))
(('c', 'd'), ('e', 'f'), ('a', 'b'))
(('c', 'd'), ('e', 'f'), ('b', 'a'))
(('c', 'd'), ('f', 'e'), ('a', 'b'))
(('c', 'd'), ('f', 'e'), ('b', 'a'))
(('d', 'c'), ('e', 'f'), ('a', 'b'))
(('d', 'c'), ('e', 'f'), ('b', 'a'))
(('d', 'c'), ('f', 'e'), ('a', 'b'))
(('d', 'c'), ('f', 'e'), ('b', 'a'))
(('e', 'f'), ('a', 'b'), ('c', 'd'))
(('e', 'f'), ('a', 'b'), ('d', 'c'))
(('e', 'f'), ('b', 'a'), ('c', 'd'))
(('e', 'f'), ('b', 'a'), ('d', 'c'))
(('f', 'e'), ('a', 'b'), ('c', 'd'))
(('f', 'e'), ('a', 'b'), ('d', 'c'))
(('f', 'e'), ('b', 'a'), ('c', 'd'))
(('f', 'e'), ('b', 'a'), ('d', 'c'))
(('e', 'f'), ('c', 'd'), ('a', 'b'))
(('e', 'f'), ('c', 'd'), ('b', 'a'))
(('e', 'f'), ('d', 'c'), ('a', 'b'))
(('e', 'f'), ('d', 'c'), ('b', 'a'))
(('f', 'e'), ('c', 'd'), ('a', 'b'))
(('f', 'e'), ('c', 'd'), ('b', 'a'))
(('f', 'e'), ('d', 'c'), ('a', 'b'))
(('f', 'e'), ('d', 'c'), ('b', 'a'))

---

Or to "anchor" the first element:

def permute3(s):
    return s[:1] + list(p) for p in permute2(s[1:])

>>> for i in permute3(s):
...     print i    
[('a', 'b'), ('c', 'd'), ('e', 'f')]
[('a', 'b'), ('c', 'd'), ('f', 'e')]
[('a', 'b'), ('d', 'c'), ('e', 'f')]
[('a', 'b'), ('d', 'c'), ('f', 'e')]
[('a', 'b'), ('e', 'f'), ('c', 'd')]
[('a', 'b'), ('e', 'f'), ('d', 'c')]
[('a', 'b'), ('f', 'e'), ('c', 'd')]
[('a', 'b'), ('f', 'e'), ('d', 'c')]