I knew this was topological sort the second they said it.
Model the courses and prerequisites as a directed graph where edges point from prerequisite to dependent course. Use topological sorting (Kahn's algorithm or DFS) to find a linear ordering; if a cycle is detected, return an empty array. Clearly explain the algorithm, its time and space complexity, and how you handle edge cases.
Pro tip: At Amazon, emphasize scalability and robustness: mention that your solution handles large inputs efficiently and that you validate the input (e.g., duplicate edges, self-loops) before processing. Also, briefly discuss how you would test the solution with cycles and disconnected components.
Confirm input format and constraints (e.g., number of courses, prerequisite pairs). Model the problem as a directed graph where nodes are courses and edges represent prerequisites.
Decide between Kahn's algorithm (BFS-based) or DFS-based topological sort. Explain why you chose one (e.g., Kahn's is iterative and easy to detect cycles).
For Kahn's: compute in-degrees, use a queue to process nodes with zero in-degree, and build the order. For DFS: perform post-order traversal and detect back edges.
If the topological order doesn't include all courses, a cycle exists—return an empty array. Also handle cases like no prerequisites, disconnected components, and duplicate edges.
State time complexity O(V+E) and space complexity O(V+E). Walk through a small example and a cycle example to verify correctness.
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