课程表

Course Schedule

专题: Algorithmic Programming / 算法编程
难度: L3
来源: Citadel

题目详情

问题：课程表

考察：图

来源：Citadel

链接：https://www.jointaro.com/interviews/questions/course-schedule/

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] = [a_i, b_i] indicates that you must take course b_i first if you want to take course a_i.

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

Return true if you can finish all courses. Otherwise, return false.

Example 1:

Input: numCourses = 2, prerequisites = [[1,0]]
Output: true
Explanation: There are a total of 2 courses to take. 
To take course 1 you should have finished course 0. So it is possible.

Example 2:

Input: numCourses = 2, prerequisites = [[1,0],[0,1]]
Output: false
Explanation: There are a total of 2 courses to take. 
To take course 1 you should have finished course 0, and to take course 0 you should also have finished course 1. So it is impossible.

Constraints:

1 <= numCourses <= 2000
0 <= prerequisites.length <= 5000
prerequisites[i].length == 2
0 <= a_i, b_i < numCourses
All the pairs prerequisites[i] are unique.

解析

思路：把课程依赖建成有向图，若图中存在环就无法完成。可以用入度为 0 的节点做 BFS 拓扑排序，最终能取出的课程数等于总数则可完成。

复杂度：时间 O(V+E)，空间 O(V+E)。