[LeetCode] 207. Course Schedule

轉自LeetCode

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

Some courses may have prerequisites, for example to take course 0 you have to first take course 1, which is expressed as a pair: [0,1]

Given the total number of courses and a list of prerequisite pairs, is it possible for you to finish all courses?

Example 1:

Input: 2, [[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: 2, [[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.

Note:

1. The input prerequisites is a graph represented by a list of edges, not adjacency matrices. Read more about how a graph is represented.
2. You may assume that there are no duplicate edges in the input prerequisites.

<Solution>
想法如下

• 這題本質上，是一題有向圖(Directed Acyclic Graph) 的問題

• 如果從題目給的條件所建出來的DAG是有 cycle 在裡面的話，那麼就不可能完成所有的課程

• 在 DAG，可以用 topological sorting 的方式，來檢驗 DAG 是不是有 cycle。只要有 cycle，那麼 topological sorting 就不可能會歷遍到所有的節點

code 如下

Java

Kotlin