Model the course catalog as a directed graph and detect cycles using either DFS with recursion stack or Kahn's topological sort algorithm. Explain the chosen approach, analyze time and space complexity, and discuss handling edge cases like disconnected graphs and self-loops.
Pro tip: Mention that cycle detection in course prerequisites is equivalent to checking if a valid topological ordering exists, and that Kahn's algorithm naturally provides the ordering if no cycle is found—a useful bonus for scheduling.
Confirm that the adjacency list represents directed edges from a course to its prerequisites (or vice versa) and that a cycle means a course depends on itself transitively. Discuss input constraints and edge cases.
Select either DFS with a recursion stack (colors: white, gray, black) or Kahn's topological sort (BFS with in-degree tracking). Briefly justify your choice based on simplicity or additional benefits.
Explain how the algorithm works: for DFS, mark nodes as visiting and visited, and detect a back edge; for Kahn's, repeatedly remove nodes with in-degree zero and check if all nodes are processed.
State time complexity O(V+E) and space complexity O(V+E) for both approaches. Mention handling of disconnected graphs, self-loops, and empty input.
Mention that Kahn's algorithm can also produce a topological order if no cycle exists, and that DFS can be adapted to find the actual cycle. Compare iterative vs recursive DFS for large graphs.
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