I knew Kahn's algorithm going in so I wasn't totally lost, but I second-guessed myself on the cycle detection part and spent way too long explaining it before writing any code.
Model the courses and prerequisites as a directed graph and use topological sorting to find a valid order. Detect cycles by checking if the number of processed nodes equals the total number of courses; if not, return an empty array.
Pro tip: At Amazon, emphasize scalability and robustness: mention that your solution handles large inputs efficiently and that you validate the input for edge cases like duplicate prerequisites or self-loops.
Ask clarifying questions about input format, constraints, and expected output. Confirm whether the graph is directed, if there can be multiple valid orders, and how to handle invalid inputs.
Decide between Kahn's algorithm (BFS-based) and DFS-based topological sort. Both are O(V+E) time and space, but Kahn's is often easier to explain and implement iteratively.
Build the graph and compute in-degrees. Use a queue to process nodes with zero in-degree, appending to the result. If the result size is less than the number of courses, a cycle exists.
Walk through simple cases (no prerequisites, linear chain), a cycle case, and a disconnected graph. Verify that the algorithm returns a valid order or an empty array as appropriate.
State that the time and space complexity are O(V+E). Mention that DFS can also detect cycles but may require recursion stack management; Kahn's algorithm is iterative and avoids recursion limits.
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