Parallel Courses III

Explore how to use topological sorting to calculate the minimum time needed to complete multiple courses with prerequisite constraints. Understand managing dependencies in directed acyclic graphs and applying this approach to optimize course scheduling problems.

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Statement

You are tasked with determining the minimum time required to complete a set of courses, given their prerequisite relationships and individual durations.

There are n courses labeled from 1 to n. The prerequisite relationships between these courses are provided as a 2D integer array relations, where each entry $\text{relations}[j] = [\text{prevCourse}_j, \text{nextCourse}_j]$ indicates that course $\text{prevCourse}_j$ must be completed before course ${nextCourse}_{j}$ ...