Solution: Course Schedule II

Explore how to solve the Course Schedule II problem by applying topological sort. Learn to build a graph of course dependencies, identify sources with zero prerequisites, and use breadth-first search to find a valid linear order. Understand how to detect cycles that prevent completion and analyze time and space complexity for this approach.

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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.