Solution: Course Schedule II

Explore how to determine a valid order to complete courses given their prerequisites using topological sort. Understand graph construction, in-degree calculation, and breadth-first search traversal to detect cycles and produce a course sequence in JavaScript. This lesson helps you implement an optimized solution with clear time and space complexity.

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Statement
Solution
- Naive approach
- Optimized approach using topological sort

Statement

You are given n courses, labeled from 0 to n - 1. Some courses have prerequisites, which are provided as a list of pairs: prerequisites[i] $= [a, b]$ . To take course $a$ , you must first complete course $b$ .

Your task is to determine a valid order in which you can complete all the courses and return it as an array of course labels.

If there are multiple valid orderings, you can return any of them.
If it’s impossible to finish all courses (due to a cycle in prerequisites), return an empty array.

Note: There can be a course in the $0$ to $n−1$ range with no prerequisites.