My first instinct was BFS and I went with it, which was right, but I fumbled explaining why the number of BFS levels equals the answer.
Model the courses and prerequisites as a directed graph, then use topological sorting to detect cycles and compute the longest path (critical path) which represents the minimum semesters. If a cycle exists, return -1; otherwise, the length of the longest path gives the answer.
Pro tip: Emphasize that this is a longest path problem in a DAG, not just topological sort; also discuss how to handle large graphs efficiently with Kahn's algorithm or DFS, and mention edge cases like disconnected graphs.
Clarify that courses can be taken in parallel if prerequisites are met, so the minimum semesters equals the maximum number of courses in any prerequisite chain (longest path).
Represent courses as nodes and prerequisites as directed edges from prerequisite to dependent course. This forms a directed graph.
Use topological sorting (Kahn's algorithm or DFS) to check for cycles. If a cycle exists, it's impossible to complete all courses, so return -1.
During topological sort, compute the longest distance (in terms of semesters) from any source node to each node. The maximum distance is the minimum number of semesters.
If no cycle, return the maximum distance; otherwise, return -1. Discuss time and space complexity: O(V+E) time, O(V+E) space.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify the original problem (likely course scheduling with prerequisites) and the new constraint: at most K courses per semester. Then, model it as a graph problem and adapt the algorithm to respect the per-semester limit, discussing trade-offs between greedy and optimal approaches.
Pro tip: Netflix values scalability and real-world constraints, so mention how you'd handle large inputs and edge cases like K=1 or K greater than the number of courses. Also, proactively discuss time/space complexity and potential optimizations.
Restate the original problem (e.g., course scheduling with prerequisites) and confirm the new constraint: at most K courses per semester. Ask about goals: minimize semesters, check feasibility, or maximize courses?
Represent courses as nodes and prerequisites as directed edges. The problem becomes topological sorting with a per-level (semester) capacity constraint.
Use a modified topological sort (e.g., Kahn's algorithm) where each semester you can take up to K available courses. If more than K are available, choose which to take (e.g., prioritize by some heuristic).
Discuss time/space complexity (O(V+E) for graph traversal). Handle edge cases: K=1 (sequential), K >= max available (original problem), cycles (impossible), and disconnected graphs.
If the goal is to minimize semesters, the greedy choice of taking any K available courses may not be optimal; mention that finding the optimal schedule might require more complex approaches (e.g., binary search on semesters with feasibility check).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.