LeetCode 207 Course Schedule

题目

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:
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.

解法

判断有向图是否有环问题，第一个数字是顶点个数，数组表示两个端点的前后关系，后面顶点是前面顶点的前置条件。用拓扑排序解决这道题，如果拓扑排序之后，还剩下点，则表示有环。
拓扑排序过程：用邻接表来表示度，degree表示顶点的度数，找到图中入度为0的点，进行标记，删除以这些点为出度的边，及与这些点相连的顶点度数降低一，再次寻找入度为0的点，进行以上操作，循环n次（n为图中顶点个数）。

class Solution {public:    bool canFinish(int numCourses, vector<pair<int, int>>& prerequisites) {        map<int, vector<int>> graph;        vector<int> degree(numCourses, 0);          for (int i = 0; i < prerequisites.size(); i++) {            graph[prerequisites[i].second].push_back(prerequisites[i].first);            degree[prerequisites[i].first]++;        }        for(int i = 0; i < numCourses; i++)          {              int j = 0;              while(j < numCourses && degree[j] != 0)                j++;            if(j == numCourses)                 return false;              degree[j] = -1;            for(int k = 0; k < graph[j].size(); k++)                  degree[graph[j][k]]--;         }          return true;     }};