leetocd---207. Course Schedule

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. Read more about how a graph is represented.
2. You may assume that there are no duplicate edges in the input prerequisites.

click to show more hints.

// 这道题就是检验有向图是不是无环，使用拓扑排序进行检验。class Solution {public:    bool canFinish(int numCourses, vector<pair<int, int>>& prerequisites) {        if(!numCourses || prerequisites.empty()) return true;        //依赖数组，存储了该点所有依赖的点        vector<vector<int>> pre(numCourses);        //统计每个点的被依赖数        vector<int> num(numCourses);        //vector+top 模拟入度为0的点的栈        vector<int> one(numCourses);        int top = 0, t = 0;        for(auto k: prerequisites){            pre[k.first].push_back(k.second);            num[k.second]++;        }           for(int i = 0; i<numCourses; i++)            if(!num[i]) {one[++top] = i; t++;}          while(top){            int k = one[top--];            for(auto j: pre[k])                if(!(--num[j])) {one[++top] = j; t++;}         }        //统计度0的点是不是等于总数，是的话说明无环        return t == numCourses;    }};