Palo Alto 面试题：Course Schedule（课程依赖排序 / 拓扑排序）

Problem Description

There are a total of numCourses courses you have to take, labeled from 0 to numCourses - 1.

You are given an array prerequisites where prerequisites[i] = [ai, bi] indicates that you must take course bi first if you want to take course ai.

For example, the pair [0, 1] indicates that to take course 0, you have to first take course 1.

Return the ordering of courses you should take to finish all courses.
If there are many valid answers, return any of them.
If it is impossible to finish all courses, return an empty array.

Example 1

Input: 
numCourses = 2
prerequisites = [[1,0]]

Output: [0,1]

Explanation:
There are a total of 2 courses to take.
To take course 1, you should have finished course 0.
So the correct course order is [0,1].

Example 2

Input:
numCourses = 4
prerequisites = [[1,0],[2,0],[3,1],[3,2]]

Output: [0,2,1,3]

Explanation:
There are a total of 4 courses to take.
To take course 3, you should have finished courses 1 and 2.
Both courses 1 and 2 should be taken after you finished course 0.
So one correct course order is [0,1,2,3].
Another correct ordering is [0,2,1,3].

Example 3

Input:
numCourses = 1
prerequisites = []

Output: [0]

这是一个典型的 课程依赖建模问题 ，本质是对有向图进行 拓扑排序 。
如果图中存在环，则无法完成所有课程，需要返回空数组。
常见解法是 入度 + BFS（Kahn 算法） 或 DFS 检测环，时间复杂度为 O(V + E)。