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.

解题思路：拓扑排序模版题。

class Solution {
public:
    bool topologicalSort(int& numCourses,vector<vector<int>>& G,vector<int>& degree){
        int num=0;
        queue<int>q;
        for(int i=0;i<numCourses;i++){
            if(!degree[i])q.push(i);
        }
        while(!q.empty()){
            int u=q.front();
            q.pop();
            for(int i=0;i<G[u].size();i++){
                if(--degree[G[u][i]]==0){
                    q.push(G[u][i]);
                }
            }
            num++;
        }
        return num==numCourses;
        
    }
    bool canFinish(int numCourses, vector<pair<int, int>>& prerequisites) {
        vector<vector<int>>G(numCourses);
        vector<int>degree(numCourses,0);
        for(int i=0;i<prerequisites.size();i++){
            G[prerequisites[i].second].push_back(prerequisites[i].first);
            degree[prerequisites[i].first]++;
        }
        return topologicalSort(numCourses,G,degree);
    }
};