Combinatorics in Python

Question

I have a sort of a one level tree structure as:

Where p are parent nodes, c are child nodes and b are hypothetical branches.

I want to find all combinations of branches under the constraint that only one parent can branch to only one child node, and two branches can not share parent and/or child.

E.g. if combo is the set of combinations:

combo[0] = [b[0], b[3]]
combo[1] = [b[0], b[4]]
combo[2] = [b[1], b[4]]
combo[3] = [b[2], b[3]]

I think that's all of them. =)

How can this be achived automaticly in Python for arbitrary trees of this structures i.e. the number of p:s, c:s and b:s are arbitrary.

EDIT:

It is not a tree but rather a bipartite directed acyclic graph

Answer 1

Here's one way to do it. There are lot's of micro-optimizations that could be made but their efficacy would depend on the sizes involved.

import collections as co
import itertools as it

def unique(list_):
    return len(set(list_)) == len(list_)

def get_combos(branches):
    by_parent = co.defaultdict(list)

    for branch in branches:
        by_parent[branch.p].append(branch)

    combos = it.product(*by_parent.values())

    return it.ifilter(lambda x: unique([b.c for b in x]), combos)

I'm pretty sure that this is at least hitting optimal complexity as I don't see a way to avoid looking at every combination that is unique by parent.