The basic BFS part was fine, I coded it up without much trouble.
Start by explaining standard BFS for shortest path in an unweighted graph, then introduce bidirectional BFS as an optimization that expands from both source and target simultaneously. Compare their time and space complexities, and discuss when bidirectional BFS is beneficial and its practical tradeoffs.
Pro tip: Mention that bidirectional BFS can reduce the search space from O(b^d) to O(b^(d/2)), but it requires careful handling of the meeting condition and may not be worth it for small graphs or when the branching factor is low.
Confirm that the graph is unweighted, edges are undirected, and we need the shortest path in terms of number of edges. Ask about constraints like graph size and whether multiple queries are expected.
Describe BFS: use a queue to explore level by level, track visited nodes, and stop when the target is reached. Analyze time and space complexity as O(V+E).
Explain that bidirectional BFS runs two simultaneous BFS searches—one from source and one from target—and stops when they meet. This reduces the explored nodes significantly.
Discuss tradeoffs: bidirectional BFS can be faster (O(b^(d/2)) vs O(b^d)) but has higher constant factors, requires more memory for two frontiers, and is more complex to implement. It's most effective when the branching factor is high and the graph is large.
Summarize when to use each: standard BFS for simplicity and small graphs; bidirectional BFS for large graphs with high branching factor where performance is critical.
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