Implement `can_finish(num_courses, prerequisites)`. Courses are numbered from `0` through `num_courses - 1`. Each pair `[course, prerequisite]` means the prerequisite must be completed before the course. Return `true` if all courses can be completed and `false` if the dependency graph contains a directed cycle. Courses with no dependencies may be taken immediately. Duplicate prerequisite pairs must not change the answer. Target `O(num_courses + p)` time and space, where `p` is the number of prerequisite pairs after deduplication. ```hint Remove courses with no remaining prerequisites Build indegrees and repeatedly process zero-indegree courses with a queue. ``` ```hint Count what the process removes If fewer than `num_courses` courses are processed, the unprocessed subgraph contains a cycle. ``` ### Discussion Extensions - How would you return one valid course order when the graph is acyclic? - How would a depth-first search with three colors reconstruct one concrete cycle when the graph is cyclic?