[LeetCode]207. Course Schedule

• descrption
  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?
  For example:
  2, [[1,0]]
  There are a total of 2 courses to take. To take course 1 you should have finished course 0. So it is possible.
  2, [[1,0],[0,1]]
  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.
  2.You may assume that there are no duplicate edges in the input prerequisites.

• 解题思路
  这道题是很明显的有关拓扑排序的题目，我们把每个课程当作一个node，提前需要学习的课程node用边指向学习它后才能学习这门课的课程node，如果图中有环，那么证明无法学习完所有的课程。这样问题就可以转换为一个图是否是一个有向无环图。首先我们根据给定的课程总数目和课程对（pair）构造图，遍历存储课程对的vector，记录每个节点的入度，记录从每个节点出去的边。之后遍历每个节点，如果该节点入度为0，那么删去这个节点，并且将这个节点指向的节点的入度减一，重复上述操作直至所有节点都被删除或者找不到入度为0的节点停止，如果所有节点都被删除那么这个图就是有向无环图，如果找不到入度为0的节点但还有节点没有被删除，那么这个图中就有环，这样课程就不能学习完。

• 代码如下

class Solution {public:    bool canFinish(int numCourses, vector<pair<int, int>>& prerequisites) {        if(numCourses == 0)            return false;        //记录每个节点的入度和从该节点发出的边        vector<int> indegree(numCourses, 0);        unordered_map<int, multiset<int>> edges;        for(auto node : prerequisites){            indegree[node.second]++;            edges[node.first].insert(node.second);        }    //遍历每个节点，找到入度为0的节点删除，并将指向节点的入度减1        for(int i = 0, j; i < numCourses; i++){            for(j = 0; j < numCourses; j++)                if(indegree[j] == 0)                    break;            if(j == numCourses)                return false;            indegree[j] --;            for(auto edge : edges[j]){                     indegree[edge]--;            }        }        return true;    }};

原题地址
如有错误请指正，谢谢！