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- import itertools
- import collections
-
-
- def make_graph(text):
- graph = collections.defaultdict(set)
- for aa, *bbs in map(str.split, text.replace(':', '').splitlines()):
- graph[aa] |= set(bbs)
- for bb in bbs:
- graph[bb] |= {aa}
- return graph
-
-
- def rank_wires(graph, n_cycles=100, n_top=20):
- tally = collections.Counter()
- for aa, bb in sorted(itertools.combinations(graph, 2))[:n_cycles]:
- path = shortest_path(graph, aa, bb)
- tally.update(frozenset(pair) for pair in zip(path, path[1:]))
- return [k for k, _ in tally.most_common(n_top)]
-
-
- def shortest_path(graph, aa, bb):
- state = {aa: None}
- seen = {}
- while bb not in state:
- state = {new: old for old in state for new in graph[old] if new not in seen}
- seen |= state
-
- path = [bb]
- while path[-1] != aa:
- path.append(seen[path[-1]])
- return path
-
-
- def cut(graph, wires):
- graph = graph.copy()
- for aa, bb in wires:
- graph[aa] = graph[aa] - {bb}
- graph[bb] = graph[bb] - {aa}
- return graph
-
-
- def subgraphs(graph):
- conns = []
- while graph:
- state = {next(iter(graph))}
- seen = set()
- while state:
- state = {new for old in state for new in graph[old] if new not in seen}
- seen |= state
- conns.append(seen)
- for node in seen:
- graph.pop(node)
- return conns
-
-
- text = open(0).read()
- graph = make_graph(text)
- wires = rank_wires(graph)
- for triplet in itertools.combinations(wires, 3):
- mod_graph = cut(graph, triplet)
- subs = subgraphs(mod_graph)
- if len(subs) == 2:
- print(len(subs[0]) * len(subs[1]))
- break
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