The first part went fine, queue plus visited set, pretty standard.
Start by clarifying the problem constraints (graph size, memory, whether the graph is static) and then outline an iterative BFS using a queue and a visited set to find the shortest distance. For path reconstruction, maintain a parent map during BFS and backtrack from the target to the source. Discuss scalability considerations such as distributed BFS or bidirectional search for millions of nodes.
Pro tip: Mention that for massive graphs, a standard BFS may be infeasible in memory, so you'd consider bidirectional BFS or distributed graph processing (e.g., Pregel) to reduce the search space and memory footprint. Also, note that Amazon values customer obsession, so tie your solution back to improving user experience (e.g., faster friend recommendations).
Ask about graph size, memory limits, whether the graph is static or dynamic, and if multiple queries will be made. Confirm that the graph is unweighted and undirected.
Use a queue to explore level by level, a visited set to avoid cycles, and a distance array/map to track hops from the source. Return the distance when the target is found.
Maintain a parent map during BFS. Once the target is reached, backtrack from target to source using the parent map to build the path.
Discuss time and space complexity (O(V+E) time, O(V) space). For millions of users, propose optimizations like bidirectional BFS, distributed BFS, or using adjacency lists with compression.
Compare BFS with other methods (e.g., Dijkstra for weighted graphs, A* with heuristics). Mention that for very large graphs, approximate or sampling-based methods might be acceptable.
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