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Solution: Parallel Courses

Solution: Parallel Courses

Let’s solve the Parallel Courses problem using the Topological Sort pattern.

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Statement

You are designing a course schedule for a university with n courses, labeled from 1 to n. The prerequisite requirements are given in an array, relations, where each relations[i]=[prevCoursei,nextCoursei]\text{relations}[i] = [\text{prevCourse}_i, \text{nextCourse}_i] means that prevCoursei\text{prevCourse}_i must be completed before you can enroll in nextCoursei\text{nextCourse}_i.

You can take any number of courses during a single semester, as long as the prerequisite for each course has been met in a previous semester.

Your task is to determine the minimum number of semesters required to complete all n courses. If the prerequisites contain a circular dependency (e.g., course A requires B, and course B requires A), it’s impossible to complete them all, so you should return -1.

Constraints:

  • 11 \leq n 5×103\leq 5 \times10^3

  • 11 \leq ...