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Solution: Parallel Courses

Understand how to solve the problem of scheduling university courses with prerequisites by modeling dependencies as a directed graph. Explore using depth-first search to detect cycles and compute the longest dependency chain for determining the minimum semesters needed. You'll learn to implement memoization and cycle detection within a topological sorting framework, ensuring efficient evaluation of course scheduling problems.

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 ...