Solution: Course Schedule II

Explore the topological sort pattern to solve the Course Schedule II problem by determining a valid order to complete courses given their prerequisites. Understand graph construction, source identification, and breadth-first traversal to handle dependencies and detect cycles. Gain techniques to implement efficient solutions with O(v+e) time complexity, preparing you for coding interview questions on task scheduling and dependency resolution.

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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.