I went with the in-degree BFS approach because I'd drilled it recently and felt more confident there.
Start by clarifying the graph representation and whether the graph is guaranteed acyclic. Then implement Kahn's algorithm (BFS with in-degree) or DFS with cycle detection, explaining the trade-offs. Finally, discuss time and space complexity and how to handle cycles by returning an error or empty list.
Pro tip: Mention that Kahn's algorithm can detect cycles by comparing the number of processed nodes to the total; if they differ, a cycle exists. This shows you understand both topological sorting and cycle detection in one pass.
Ask about graph representation (adjacency list/matrix), whether the graph is guaranteed acyclic, and expected output for cycles (e.g., empty list or error).
Select either Kahn's algorithm (BFS with in-degree) or DFS with post-order, and briefly describe how it works, including cycle detection.
Trace the algorithm on a small DAG to demonstrate correctness, and then on a graph with a cycle to show how the cycle is detected.
State time and space complexity (O(V+E) for both approaches) and discuss when one might be preferred over the other.
Explain how your chosen method detects cycles and what you return or throw in that case, ensuring the solution meets the requirement.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.