Recognized it as topological sort pretty fast, which was good.
Model the tasks and dependencies as a directed graph, then perform a topological sort using either Kahn's algorithm (BFS with in-degree tracking) or DFS with cycle detection. Clearly explain how you detect cycles and return an empty list if one exists, and analyze the time and space complexity.
Pro tip: At Amazon, emphasize how your solution scales with large graphs and how you would handle real-world constraints like parallel task execution or dynamic dependencies. Mention that you would validate input and consider edge cases like disconnected components or duplicate edges.
Restate the problem to ensure understanding: n tasks, dependency pairs, return any valid topological order or empty list if cycle. Ask about input format, constraints, and whether multiple valid orders are acceptable.
Select either Kahn's algorithm (BFS) or DFS-based topological sort. Explain why it's suitable: Kahn's naturally detects cycles via in-degree counts, while DFS uses recursion stack for cycle detection.
Describe the steps: build adjacency list and in-degree array (for Kahn's), initialize queue with zero in-degree nodes, process nodes while updating in-degrees, and detect cycle if processed count < n.
State that both algorithms run in O(V + E) time and O(V + E) space, where V is number of tasks and E is number of dependencies. Explain why: each node and edge is visited once.
Compare Kahn's vs DFS: Kahn's is iterative and easier to detect cycles, DFS may be simpler for some. Mention potential optimizations like using a priority queue for lexicographical order or parallel processing.
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