Parallel Courses III

Explore how to calculate the minimum time to finish all courses given prerequisites and durations. Understand topological sorting in directed acyclic graphs to solve course scheduling problems efficiently by analyzing dependencies and concurrency.

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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 ${nextCourse}_{j}$ ...