Classic topological sort or cycle detection problem.
Model the courses as a directed graph where edges represent prerequisites, then detect cycles using either Kahn's algorithm (BFS topological sort) or DFS with recursion stack. Clearly explain the graph construction, the chosen algorithm, and its time/space complexity.
Pro tip: Mention that this is a classic topological sort problem and that Kahn's algorithm is often preferred in production for its iterative nature and ability to detect cycles early. Also, relate it to real-world dependency resolution in ML pipelines or build systems.
Confirm that courses are nodes and prerequisites are directed edges. Ask about input format (e.g., number of courses, list of prerequisite pairs) and edge cases like duplicate edges or self-loops.
Select either Kahn's algorithm (BFS-based topological sort) or DFS with cycle detection. Briefly justify your choice based on simplicity, iterative nature, or early termination.
Explain step-by-step how the algorithm works: for Kahn's, compute in-degrees, use a queue, and count processed nodes; for DFS, track visited and recursion stack states.
State time and space complexity (O(V+E) for both). Discuss handling of disconnected graphs, empty input, and cycles that don't include all nodes.
Mention how to return the actual course order (topological sort) and relate the problem to dependency resolution in ML pipelines, build systems, or task scheduling.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.