leetcode- 207. Course Schedule

一、问题描述

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.

二、思路

此问题等价于判断有向图中是否有环。如果存在环路，无法完成拓扑排序。

三、代码

class Solution {public:    bool canFinish(int numCourses, vector<pair<int, int>>& prerequisites) {        vector<vector<int>> matrix(numCourses);        vector<int> in(numCourses, 0);        int n = prerequisites.size();        for (int i=0; i<n; i++)            matrix[prerequisites[i].second].push_back(prerequisites[i].first);        for (int i=0; i<numCourses; i++) {            for (auto it=matrix[i].begin(); it!=matrix[i].end(); it++) {                in[*it]++;            }        }        for (int i=0; i<numCourses; i++) {            int j;            for (j=0; j<numCourses && in[j]!=0; j++);            if (j == numCourses)                return false;            in[j] = -1;            for (auto it=matrix[j].begin(); it!=matrix[j].end(); it++)                in[*it]--;        }        return true;    }};