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Went with BFS treating each route as a node rather than each stop.
Model the problem as a graph where each bus route is a node, and edges connect routes that share at least one stop. Then perform BFS from all routes containing the source stop to find the minimum number of routes to reach any route containing the target stop. If the source and target are the same stop, return 0; if no path exists, return -1.
Pro tip: Clarify edge cases upfront: if source equals target, answer is 0; if either stop is not in any route, answer is -1. Also, mention that BFS on routes (not stops) is more efficient because it reduces the graph size and naturally counts the number of buses.
Confirm with the interviewer that source and target are stops, and that a bus route is a loop. Handle trivial cases: if source == target, return 0; if either stop is not in any route, return -1.
Create a mapping from each stop to the list of routes that contain it. This allows quick lookup of which routes serve a given stop.
For each stop, connect all routes that share that stop by adding edges between them. This forms a graph where nodes are routes and edges represent a transfer between routes at a common stop.
Initialize a queue with all routes containing the source stop, marking them as visited with distance 1. Perform BFS: for each route, explore its neighbors (connected routes), incrementing distance. If a route containing the target stop is reached, return the distance.
If BFS completes without reaching any route that contains the target stop, return -1. Otherwise, the first time we reach such a route, return the current distance.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Recognize that this is a shortest path problem on a graph where stops are nodes and bus routes form edges (or hyperedges). Precompute all-pairs shortest paths using BFS from each stop or Floyd-Warshall if the graph is small, then answer each query in O(1) time. Discuss trade-offs between preprocessing time, memory, and query latency.
Pro tip: Mention that if the number of stops is large, you can use a meet-in-the-middle BFS or bidirectional BFS for each query, but for repeated queries, precomputation is key. Also, consider that bus routes may have multiple stops, so model each route as a clique or use a bipartite graph with route nodes to avoid O(k^2) edges per route.
Represent stops as nodes and bus routes as connections. Decide whether to use a simple graph (each route connects all its stops pairwise) or a bipartite graph with route nodes to reduce edge count.
For repeated queries, precompute shortest paths between all pairs of stops. Use BFS from each stop if the graph is unweighted (each bus ride counts as 1), or Floyd-Warshall if the number of stops is small (e.g., <= 500).
If the number of stops is large, consider storing distances in a 2D array if memory allows, or use a more compact representation. Discuss trade-offs: O(V*(V+E)) time for BFS from each node vs O(V^3) for Floyd-Warshall.
After precomputation, each query is simply a lookup in the precomputed distance matrix. If no path exists, return -1 or infinity.
If the graph is too large for all-pairs precomputation, consider using landmarks, contraction hierarchies, or caching frequent queries. Also, mention that if queries are not known in advance, online algorithms like bidirectional BFS may be better.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.