I knew the base version cold, cycle detection in a directed graph, topological sort, done it a hundred times.
Model the courses and prerequisites as a directed graph and check for cycles using topological sorting (Kahn's algorithm) or DFS. For the additional variant, clarify the condition, then adapt the algorithm accordingly, explaining your reasoning and trade-offs.
Pro tip: After solving the standard problem, proactively discuss how you would handle the variant by identifying what changes in the graph model or algorithm, showing adaptability and deep understanding.
Ask questions to understand the exact requirements, especially the additional variant condition, and confirm input/output formats and edge cases.
Represent courses as nodes and prerequisites as directed edges. Explain that a cycle indicates impossibility.
Select topological sort (Kahn's or DFS) to detect cycles. Discuss time and space complexity.
Modify the approach based on the variant condition, such as adding constraints or changing the graph structure, and explain the adjustments.
Walk through examples, including edge cases like no prerequisites or disconnected components, to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.