My first instinct was just BFS and I kind of went with it before fully thinking through why.
Model the courses and prerequisites as a directed graph where an edge from course A to course B means A is a prerequisite for B. The problem reduces to detecting whether this graph contains a cycle. Use either Kahn's algorithm (BFS-based topological sort) or DFS with recursion stack to check for cycles; if a cycle exists, return false, otherwise true.
Pro tip: Clarify with the interviewer whether the graph is directed and whether prerequisites can be repeated or self-referential. Mention that you'd handle edge cases like no prerequisites or disconnected components, and discuss time/space complexity upfront to show thoroughness.
Restate the problem: given numCourses and prerequisite pairs, determine if all courses can be completed. Ask about input size, whether prerequisites are directed, and if there can be duplicate edges or self-loops.
Represent courses as nodes (0 to numCourses-1) and each prerequisite pair [a, b] as a directed edge b -> a (b must be taken before a). Build an adjacency list and optionally an in-degree array.
Select either Kahn's algorithm (topological sort via BFS) or DFS with a recursion stack. Explain the trade-offs: Kahn's is iterative and easy to reason about; DFS can be more concise but requires careful state tracking.
Write clean code for the chosen algorithm. Walk through a small example (e.g., numCourses=2, prerequisites=[[1,0]]) to show it returns true, and a cyclic example (e.g., [[1,0],[0,1]]) to show it returns false.
State time complexity O(V+E) and space complexity O(V+E). Mention edge cases: no prerequisites, disconnected graph, self-loop, and large input. Optionally, discuss how to return the actual course order if needed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.