Knew the general idea but fumbled a bit deciding between DFS with a visited set versus union-find.
Clarify whether the graph is directed or undirected, as the cycle detection algorithm differs. For undirected graphs, use Union-Find or DFS with parent tracking; for directed graphs, use DFS with recursion stack or topological sort (Kahn's algorithm). Explain the chosen approach, its time and space complexity, and handle edge cases like disconnected graphs and self-loops.
Pro tip: Always discuss trade-offs between approaches: Union-Find is great for undirected graphs with dynamic edge additions, while DFS is simpler for static graphs. Mention that for directed graphs, topological sort can also detect cycles and is useful if you need a topological order.
Ask if the graph is directed or undirected, and if it's represented as an adjacency list or matrix. This determines the algorithm choice.
For undirected: Union-Find or DFS with parent tracking. For directed: DFS with recursion stack or Kahn's algorithm. Explain why the chosen method fits.
Describe the algorithm concisely: e.g., for DFS, mark nodes as unvisited, visiting, visited; if a visiting node is encountered, a cycle exists.
State time and space complexity: typically O(V+E) time and O(V) space for DFS/Union-Find.
Mention disconnected graphs, self-loops, parallel edges, and empty graphs. Ensure the algorithm covers all components.
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