Parallel Courses III

Explore how to determine the minimum time to complete a set of courses with prerequisite constraints and varying durations. Learn to apply topological sorting to model dependencies and calculate the shortest completion schedule when multiple courses can run simultaneously. Understand how to handle directed acyclic graphs to ensure all tasks finish efficiently.

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