Course Ordering Problem

Problem Statement

Suppose you have m courses labeled from 0 to m-1.

Some courses require others to be completed first. For instance, to enroll in course 2 you might need to finish course 1, represented as a pair: [2, 1].

Given the total number of courses and a list of prerequisite pairs, determine an order in which you can take all courses.

If multiple valid sequences are possible, returning any one of them is acceptable. If no valid ordering exists due to cyclic dependencies, return an empty list.

Examples

Example 1:

Input: 3, [[1,0]]
Output: [0,1,2]
Explanation: There are 3 courses. To take course 1, you must first complete course 0. Course 2 has no prerequisites, so one possible order is [0,1,2].
    

Example 2:

Input: 5, [[1,0],[2,0],[3,1],[4,3]]
Output: [0,1,3,4,2] or [0,2,1,3,4]
Explanation: 
Course 1 and 2 depend on course 0.
Course 3 depends on course 1.
Course 4 depends on course 3.
Multiple valid orders exist, such as [0,1,3,4,2] or [0,2,1,3,4].
    

Constraints

• 1 ≤ m ≤ 2000
• 0 ≤ number of prerequisite pairs ≤ 6000
• Prerequisite pairs are given as a list of edges without duplicates