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Grokking the Coding Interview Patterns

Solution: Parallel Courses III

Explore the use of topological sort to manage course dependencies and calculate the minimum completion time. Understand how to build a directed acyclic graph, use in-degree counts, and update course finish times through a queue-based approach to solve dependency scheduling problems 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 relations[j]=[prevCoursej,nextCoursej]\text{relations}[j] = [\text{prevCourse}_j, \text{nextCourse}_j] ...