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I jumped straight to BFS with in-degree tracking, which worked, but I fumbled a bit explaining why I return empty when there's a cycle.
Model the courses and prerequisites as a directed graph where edges represent prerequisite relationships. Then perform a topological sort using either Kahn's algorithm (BFS with in-degree tracking) or DFS with cycle detection. If a cycle exists, return an empty array; otherwise, return the topological order.
Pro tip: Clarify edge direction upfront: if course A requires course B, the edge should go from B to A (prerequisite to dependent). Also, mention that you'll handle disconnected graphs and multiple valid orders.
Confirm input format (e.g., number of courses and list of prerequisite pairs) and edge direction. Build an adjacency list and in-degree array for each course.
Decide between Kahn's algorithm (BFS) or DFS-based topological sort. Both are O(V+E) time and space; Kahn's is often easier to explain and naturally detects cycles.
For Kahn's: initialize a queue with courses having in-degree 0, then repeatedly dequeue and reduce in-degrees of neighbors. For DFS: perform post-order traversal and detect back edges.
If the result order does not include all courses, a cycle exists—return an empty array. Otherwise, return the order.
State time and space complexity (O(V+E)). Discuss edge cases: no prerequisites, multiple valid orders, disconnected components, and self-loops.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.