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Solution: Course Schedule II

Explore how to use topological sort and breadth-first search to find a valid order for completing courses with prerequisites. Understand how to build and traverse graphs representing course dependencies, detect cycles, and implement an optimized solution with linear time complexity to solve the Course Schedule II problem.

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]= [a, b]. To take course aa, you must first complete course bb.

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 00 to n1n−1 range with no prerequisites.

Constraints:

Let nn be the number of courses.

  • 1n15001 \leq n \leq 1500
  • 00 \leq
...