Bus Routes — Python

# Time:  O(|V| + |E|)
# Space: O(|V| + |E|)

import collections


class Solution(object):
    def numBusesToDestination(self, routes, S, T):
        """
        :type routes: List[List[int]]
        :type S: int
        :type T: int
        :rtype: int
        """
        if S == T:
            return 0

        to_route = collections.defaultdict(set)
        for i, route in enumerate(routes):
            for stop in route:
                to_route[stop].add(i)

        result = 1
        q = [S]
        lookup = set([S])
        while q:
            next_q = []
            for stop in q:
                for i in to_route[stop]:
                    for next_stop in routes[i]:
                        if next_stop in lookup:
                            continue
                        if next_stop == T:
                            return result
                        next_q.append(next_stop)
                        to_route[next_stop].remove(i)
                        lookup.add(next_stop)
            q = next_q
            result += 1

        return -1