I knew this was topological sort the second I read it, but I fumbled the cycle detection part.
Model the courses and prerequisites as a directed graph and perform a topological sort using Kahn's algorithm (BFS) or DFS. If the sort processes all nodes, return the order; otherwise, a cycle exists, so return an empty array.
Pro tip: Explicitly state that you would clarify input format (e.g., edge list vs. adjacency list) and discuss trade-offs between Kahn's algorithm and DFS, showing you consider real-world engineering constraints.
Confirm the input format (e.g., number of courses and list of prerequisite pairs) and represent the courses as a directed graph where an edge u→v means u must be taken before v.
Select topological sort: either Kahn's algorithm (BFS with in-degree tracking) or DFS with cycle detection. Mention that both have O(V+E) time complexity.
For Kahn's: compute in-degrees, enqueue nodes with in-degree 0, then repeatedly dequeue and reduce in-degrees of neighbors. For DFS: perform depth-first search, tracking visited and recursion stack to detect cycles.
If the topological order contains all courses, return it; otherwise, return an empty array to indicate impossibility due to a cycle.
State time and space complexity (O(V+E) time, O(V+E) space) and discuss edge cases like no prerequisites, disconnected components, or self-loops.
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