I knew this was topological sort pretty much immediately, but I fumbled the cycle detection explanation for a bit.
Model the tasks and dependencies as a directed graph and use topological sorting to detect cycles and produce a valid order. Explain both Kahn's algorithm (BFS) and DFS-based approaches, then implement one with clear time and space complexity analysis.
Pro tip: Mention that you would clarify edge cases upfront, such as duplicate dependencies, self-loops, or disconnected components, and discuss how to handle them. This shows attention to detail and production readiness.
Ask about input constraints (e.g., n size, duplicate edges, self-dependencies) and confirm that a valid order must include all tasks. Discuss what to return if no valid order exists.
Represent tasks as nodes and dependencies as directed edges from b to a (since a depends on b). Explain that a cycle indicates impossibility.
Describe Kahn's algorithm using in-degree counts and a queue, or DFS with cycle detection. Compare trade-offs: Kahn's is iterative and easy to reason about; DFS can be more concise but recursion depth may be a concern.
Write clean code for the chosen algorithm, ensuring O(n + e) time and O(n + e) space. Walk through a small example to verify correctness.
Mention how to handle large graphs (e.g., iterative DFS to avoid stack overflow), parallel execution possibilities, or detecting all cycles if needed.
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