Classic topological sort / cycle detection problem.
Model the courses and prerequisites as a directed graph and check for cycles using either Kahn's algorithm (BFS topological sort) or DFS with recursion stack. If a topological ordering exists, all courses can be completed; otherwise, a circular dependency prevents completion.
Pro tip: Clarify edge direction early: if course A requires prerequisite B, the edge should go from B to A (prerequisite → dependent) for topological sorting. Also mention that this is essentially cycle detection in a directed graph, which shows you recognize the underlying pattern.
Confirm input format (e.g., numCourses and prerequisite pairs) and edge direction. Build an adjacency list and indegree array to represent the directed graph.
Select either Kahn's algorithm (BFS topological sort) or DFS with a recursion stack. Explain why the chosen method fits the problem and its trade-offs.
For Kahn's: repeatedly remove nodes with indegree 0 and decrement neighbors' indegrees. For DFS: mark nodes as visiting/visited and detect back edges. Track the number of processed nodes.
If all nodes are processed, return true; otherwise, a cycle exists. Discuss edge cases like no prerequisites, disconnected components, and self-loops.
State time and space complexity (O(V+E) for both algorithms). Suggest testing with small examples, including a cycle and a valid DAG.
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