[LeetCode] 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.

解题思路：

这道题可以转换成判断一个有向图是否有环，若有环，则不能完成，否则能完成。现将课程表示成一个有向图，用邻接表来存储。然后通过DSF来遍历图，若存在一个节点被访问了两次，则表明有环。

注意到这个图可能不是全连通图，所以，需要将每个节点作为开始节点来验证。为了减少遍历次数，用数组mark来记录以某个节点起始的节点进行深度遍历是否有环。下面是代码：

class Solution {
public:
    bool canFinish(int numCourses, vector<vector<int>>& prerequisites) {
        int len=prerequisites.size();
        if(len==0){
            return true;
        }
        vector<vector<int>> graph(numCourses, vector<int>());   //邻接表表示的图
        for(int i=0; i<len; i++){
            graph[prerequisites[i][0]].push_back(prerequisites[i][1]);
        }
        bool visit[numCourses];  //是否已经访问过
        memset(visit, 0, numCourses * sizeof(bool));
        bool mark[numCourses];  //是否已经验证过该节点
        memset(mark, 0, numCourses * sizeof(bool));
        
        for(int i=0; i<numCourses; i++){
            if(DFSHasCircle(graph, visit, mark, i)){
                return false;
            }
        }
        return true;
    }
    
    //判断是否有环，思路为若存在一个节点访问了2次，则表明有环
    bool DFSHasCircle(vector<vector<int>>& graph, bool* visit, bool* mark, int current){
        if(visit[current]){
            return true;
        }
        if(mark[current]){
            return false;
        }
        visit[current] = true;      //标记已经访问过
        
        for(int i=0; i<graph[current].size(); i++){
            if(DFSHasCircle(graph, visit, mark, graph[current][i])){
                return true;
            }
        }
        
        mark[current] = true;       //表示以该顶点开始的可达的所有节点构成的子图均没有环
        visit[current] = false;     //去掉已经访问过的标记
        return false;
    }
};

[LeetCode] Course Schedule

原文：http://blog.csdn.net/kangrydotnet/article/details/45560127