How to undo combinations of order 2?

Question

I have a set of pairs:

inputs = {
    ('id1', 'id2'), ('id1', 'id3'), ('id1', 'id4'),
    ('id2', 'id3'), ('id2', 'id4'),
    ('id3', 'id4'), ('id3', 'id5'),
    ('id4', 'id5'),
    ('id5', 'id6'),
}

And I would like to reverse the combinations of order 2, like this:

recombinations = [
    ('id1', 'id2', 'id3', 'id4'),
    ('id3', 'id4', 'id5'),
    ('id5', 'id6'),
]

I managed to do it using brute-force:

ids = list(sorted( {i for i in itertools.chain(*inputs)} ))

excludes = set()
recombinations = {tuple(i) for i in map(sorted, inputs)}

for i in range(3, len(ids)+1):
    for subset in itertools.combinations(ids, i):
        for j in range(i-1, len(subset)):
            combs = set(itertools.combinations(subset, j))
            if all(tup in recombinations for tup in combs):
                recombinations.add(subset)
                excludes = excludes.union(combs)

for tup in excludes:
    recombinations.remove(tup)

print(recombinations)

{('id1', 'id2', 'id3', 'id4'), ('id3', 'id4', 'id5'), ('id5', 'id6')}

My question is: is there a smarter way to do it or some optimizations that I could implement in the code?

Asked By: Fravadona

||

Source

Answer 1

Using the networkx library, this is quite simple, since it has a function that does exactly what you’re asking for: finding all maximal cliques in a graph.

Here:

import networkx as nx

G = nx.Graph()

pairs_of_connected_nodes = [
    ('id1', 'id2'), ('id1', 'id3'), ('id1', 'id4'),
    ('id2', 'id3'), ('id2', 'id4'),
    ('id3', 'id4'), ('id3', 'id5'),
    ('id4', 'id5'),
    ('id5', 'id6')
]

G.add_edges_from(pairs_of_connected_nodes)

maximal_cliques = list(nx.find_cliques(G))

for clique in maximal_cliques:
    print(clique)

Output:

['id3', 'id4', 'id2', 'id1']
['id3', 'id4', 'id5']
['id6', 'id5']

Of course if your assignment is to implement the Bron-Kerbosch algorithm yourself, you’d have to code it up – but then asking on StackOverflow kind of defeats the purpose, unless you have a specific problem with your solution that you need help with?

If you’re just asking for a review of your code, ask on Code Review Stack Exchange, but expect to get told to use networkx as well.

Answered By: Grismar

How to undo combinations of order 2?

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