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Solution: Parallel Courses

Explore how to model course scheduling with prerequisites as a graph and use topological sort and depth-first search (DFS) to find the minimum number of semesters required. Understand cycle detection to handle impossible schedules and apply memoization for efficient computation.

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 ...