Basically course schedule from leetcode 207.
Model the courses and prerequisites as a directed graph and detect cycles using either Kahn's algorithm (BFS-based topological sort) or DFS with recursion stack. Explain the chosen approach, walk through a small example, and analyze time and space complexity.
Pro tip: Mention that this is essentially cycle detection in a directed graph, and that Kahn's algorithm is often preferred in interviews because it's iterative and avoids recursion depth issues. Also, clarify edge cases like duplicate prerequisites or self-loops.
Confirm that the input is a directed graph where an edge from course A to course B means A is a prerequisite for B, and that we need to check if all courses can be completed (i.e., no cycles).
Decide between Kahn's algorithm (BFS-based topological sort) and DFS with cycle detection. Explain why you chose one over the other.
Describe the steps of the chosen algorithm, such as computing in-degrees and using a queue for Kahn's, or using a visited set and recursion stack for DFS.
State the time and space complexity: O(V + E) time and O(V + E) space for both approaches.
Discuss edge cases like empty graph, self-loops, duplicate edges, and disconnected components.
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