← Bytedance Interview Insights
I went straight to topological sort via BFS and it worked, but I fumbled on the self-loop case for an embarrassingly long time.
Model the courses and prerequisites as a directed graph, then check for cycles using either Kahn's algorithm (BFS) or DFS with recursion stack. If a topological ordering exists, all courses can be completed; otherwise, a circular dependency prevents completion.
Pro tip: Mention that Kahn's algorithm is often preferred in interviews because it's iterative and avoids recursion depth issues, and you can easily detect cycles by comparing the number of processed nodes to the total. Also, clarify edge cases like duplicate prerequisites or self-loops upfront.
Confirm input format (e.g., number of courses, list of pairs) and edge cases like duplicate pairs or self-dependencies. Model courses as nodes and prerequisites as directed edges.
Decide between Kahn's algorithm (BFS-based topological sort) or DFS with recursion stack. Explain the trade-offs: Kahn's is iterative and easier to reason about; DFS can be more concise but risks stack overflow.
For Kahn's: compute in-degrees, enqueue nodes with in-degree 0, process while decrementing neighbors' in-degrees, and count processed nodes. For DFS: mark nodes as visiting/visited and detect back edges.
State time and space complexity: O(V+E) time and O(V+E) space for both approaches. Discuss handling of disconnected graphs and empty inputs.
If all nodes are processed (Kahn's) or no back edge found (DFS), return true; else false. Walk through a small example to validate the logic.
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