Model the courses and prerequisites as a directed graph and perform a topological sort using Kahn's algorithm (BFS) or DFS. If the topological sort does not include all courses, a cycle exists, so return an empty array.
Pro tip: Mention that Kahn's algorithm naturally detects cycles by checking if the number of processed nodes equals the total number of courses, and discuss how this approach can be extended to handle real-world scenarios like detecting conflicting prerequisites or parallel course scheduling.
Confirm input format (e.g., number of courses, list of prerequisite pairs) and output expectations (any valid order or specific order). Ask about edge cases like no prerequisites or duplicate edges.
Decide between Kahn's algorithm (BFS-based) and DFS-based topological sort. Explain that Kahn's is often preferred for its intuitive cycle detection and ability to process nodes in parallel.
Create an adjacency list for the graph and an array to track in-degrees of each node. Initialize a queue with all nodes having in-degree zero.
While the queue is not empty, dequeue a node, add it to the result, and for each neighbor, decrement its in-degree; if it becomes zero, enqueue it. After processing, check if the result length equals the number of courses.
If the result length is less than the number of courses, a cycle exists, so return an empty array. Otherwise, return the result as a valid ordering.
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