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Topological sort, which I knew going in, but I fumbled the cycle detection part longer than I should have.
Model the courses and prerequisites as a directed graph, then perform a topological sort using either Kahn's algorithm (BFS with in-degree tracking) or DFS with cycle detection. If the topological sort produces an ordering containing all courses, return it; otherwise, return an empty array to indicate a cycle.
Pro tip: Explicitly discuss trade-offs between Kahn's algorithm and DFS: Kahn's is iterative and naturally detects cycles via leftover nodes, while DFS uses recursion and detects cycles via back edges. Mentioning both shows depth and helps you choose the right tool for the constraints.
Confirm input format (number of courses, prerequisite pairs) and edge cases (empty input, self-prerequisites). Model courses as nodes and prerequisites as directed edges from prerequisite to dependent course.
Select either Kahn's algorithm (BFS with in-degree) or DFS with cycle detection. Explain why one might be preferred based on constraints like recursion depth or need for early cycle detection.
For Kahn's: compute in-degrees, use a queue to process nodes with zero in-degree, and build the order. For DFS: perform depth-first search, track visited and recursion stack, and append nodes in post-order.
After the sort, check if the result contains all courses. If not, a cycle exists, so return an empty array. For DFS, detect cycles via back edges during traversal.
State time and space complexity (O(V+E) for both). Walk through a simple example and a cycle case to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.