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My first instinct was just BFS with level-by-level traversal, which is the right skeleton.
Model the courses as a directed graph and use topological sorting with level-by-level processing (Kahn's algorithm) to group courses into batches. For each batch, compute the maximum completion time among its courses and accumulate these maxima to get the total time. If not all courses are processed, a cycle exists, so return -1.
Pro tip: Clarify that the batch time is determined by the slowest course, so you must take the max per batch, not sum individual times. Also, mention that this approach naturally detects cycles and runs in O(V+E) time, which is optimal.
Represent courses as nodes and prerequisites as directed edges. Compute the in-degree (number of prerequisites) for each course.
Use a queue to process courses with in-degree 0. For each batch, collect all such courses, compute the maximum completion time among them, and add it to the total time.
For each course in the current batch, decrement the in-degree of its dependent courses. If any dependent's in-degree becomes 0, add it to the next batch.
After processing, if the number of processed courses is less than the total, a cycle exists; return -1. Otherwise, return the accumulated total time.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.