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:

The input prerequisites is a graph represented by a list of edges, not adjacency matrices. Read more about how
a graph is represented.
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;
}
};