I went with BFS topological sort because I always fumble the visited-state tracking in DFS under pressure.
Model the courses and prerequisites as a directed graph, then determine if it contains a cycle. Use either Kahn's algorithm (BFS-based topological sort) or DFS with recursion stack to detect cycles. Explain the chosen method, its time and space complexity, and how it applies to course scheduling.
Pro tip: Mention that this is essentially topological sorting and that both Kahn's algorithm and DFS are acceptable, but Kahn's is often preferred for its iterative nature and easy cycle detection. Also, discuss how to handle large inputs and potential follow-ups like returning a valid order.
Confirm that the input is a list of prerequisite pairs (edges) and that we need to determine if all courses can be completed, i.e., if the graph is a DAG. Ask about constraints like number of courses, edge cases (empty list, self-loops), and expected output format.
Select either Kahn's algorithm (BFS with in-degree tracking) or DFS with cycle detection. Explain the trade-offs: Kahn's is iterative and naturally detects cycles when processed nodes < total nodes; DFS uses recursion stack but may risk stack overflow for large graphs.
For Kahn's: compute in-degrees, enqueue nodes with in-degree 0, process until queue empty, count processed nodes. For DFS: perform DFS, track visited and recursion stack, if a node is revisited in the current stack, a cycle exists.
State that both approaches run in O(V + E) time and O(V + E) space, where V is number of courses and E is number of prerequisites. Mention that this is optimal for graph traversal.
Address edge cases: no prerequisites (return true), self-loop (return false), disconnected graph. Mention extensions: returning a valid course order, handling multiple prerequisites, or parallel courses.
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