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Solution: Parallel Courses

Explore how to use topological sorting and depth-first search to determine the minimum number of semesters needed to complete courses considering prerequisite dependencies. Understand cycle detection to identify impossible schedules and use memoization for efficient computations of dependency depths.

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 ...