I went with Kahn's algorithm, tracking indegrees and peeling off nodes with zero dependencies via BFS.
Model the courses and prerequisites as a directed graph, then detect whether it contains a cycle 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 makes completion impossible.
Pro tip: Mention that Kahn's algorithm is often preferred in production because it naturally handles large graphs and can be implemented iteratively, avoiding recursion depth limits. Also, briefly discuss how this applies to real-world dependency resolution like build systems or course scheduling.
Confirm the input format: number of courses (n) and list of prerequisite pairs [a, b] meaning b must be taken before a. Ask about edge cases like duplicate pairs, self-loops, or disconnected graphs.
Represent courses as nodes and prerequisites as directed edges from prerequisite to dependent course. Build an adjacency list and compute in-degrees for each node.
Select either Kahn's algorithm (BFS topological sort) or DFS with recursion stack. Explain the trade-offs: Kahn's is iterative and easy to reason about; DFS can be simpler to code but risks stack overflow.
For Kahn's: repeatedly remove nodes with in-degree 0 and decrement neighbors' in-degrees. If all nodes are processed, no cycle exists. For DFS: track visited and recursion stack; if a back edge is found, a cycle exists.
State time complexity O(V+E) and space O(V+E). Discuss handling of empty input, single course, and disconnected components. Mention that the same logic applies to detecting deadlocks or circular dependencies in systems.
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