Cycle detection in a directed graph, basically.
Model the courses and prerequisites as a directed graph where an edge from course A to course B means A is a prerequisite for B. The problem reduces to detecting whether this graph contains a cycle; if it does, completing all courses is impossible. Use either Kahn's algorithm (BFS-based topological sort) or DFS with recursion stack to detect cycles efficiently.
Pro tip: Clarify edge direction upfront: whether the edge goes from prerequisite to course or vice versa, as this affects the algorithm's implementation. Also, mention that Kahn's algorithm naturally provides a topological order if no cycle exists, which can be a bonus for scheduling.
Represent courses as nodes and prerequisites as directed edges. Decide on edge direction (e.g., prerequisite -> course) and build an adjacency list.
Select either Kahn's algorithm (BFS with in-degree tracking) or DFS with a recursion stack. Explain why the chosen method is suitable.
For Kahn's: compute in-degrees, enqueue nodes with in-degree 0, process and decrement neighbors. For DFS: traverse with visited and recursion stack arrays to detect back edges.
If all nodes are processed (Kahn's) or no cycle is found (DFS), return true; otherwise, return false. Optionally, return the topological order if needed.
State that both methods run in O(V + E) time and O(V + E) space, where V is the number of courses and E is the number of prerequisite pairs.
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