Basically Kahn's algorithm with a small twist: you also need to reconstruct the order, not just detect cycles.
Model the courses and prerequisites as a directed graph, then perform a topological sort using Kahn's algorithm (BFS) or DFS. If the topological sort includes all n courses, return the ordering; otherwise, return IMPOSSIBLE.
Pro tip: Always clarify edge cases upfront, such as duplicate prerequisite pairs, self-loops, or disconnected graphs, and mention that you'll handle them gracefully. Also, discuss the trade-offs between Kahn's algorithm and DFS-based topological sort in terms of cycle detection and implementation complexity.
Confirm input format, constraints (e.g., course labels 0 to n-1), and output requirements (any valid order or a specific one). Ask about edge cases like duplicate edges or cycles.
Construct an adjacency list for the directed graph and compute in-degrees for each node. Use a set or boolean matrix to handle duplicate edges if necessary.
Use Kahn's algorithm: enqueue nodes with in-degree 0, then repeatedly dequeue, add to order, and decrement in-degrees of neighbors. Alternatively, use DFS with recursion stack for cycle detection.
After processing, if the order contains fewer than n nodes, a cycle exists, so return IMPOSSIBLE. Otherwise, return the order.
State that time complexity is O(n + m) and space complexity is O(n + m) for the graph and auxiliary data structures.
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