Clarify the specific graph problem (e.g., shortest path, mutual friends, connected components) and its constraints (directed/undirected, weighted/unweighted, scale). Then outline an algorithm (BFS, DFS, Union-Find, etc.) with complexity analysis, and discuss how to handle large-scale graphs in a production system.
Pro tip: Always start by asking clarifying questions about the graph's properties and the expected scale; this shows you think about real-world constraints and avoids solving the wrong problem. Mention trade-offs between algorithms and how you'd optimize for memory and latency in a distributed setting.
Ask questions to pin down the exact computation, graph type (directed/undirected, weighted/unweighted), size (nodes/edges), and performance requirements. Confirm whether the graph is static or dynamic.
Select an algorithm based on the problem: BFS for shortest path in unweighted graphs, Dijkstra for weighted, DFS or Union-Find for connected components, and set intersections for mutual friends. Explain why it fits.
State time and space complexity (e.g., O(V+E) for BFS/DFS). Discuss edge cases: disconnected graphs, cycles, self-loops, large graphs, and memory limits.
If the graph is large, propose distributed approaches (e.g., Pregel, GraphX, or sharding) and caching. Mention trade-offs between precomputation and on-the-fly queries.
Sketch the code structure (e.g., adjacency list representation) and discuss how you'd test correctness and performance with unit tests and benchmarks.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.