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?
Example 1:
Input: 2, [[1,0]]
Output: true
Explanation: There are a total of 2 courses to take.
To take course 1 you should have finished course 0. So it is possible.
Example 2:
Input: 2, [[1,0],[0,1]]
Output: false
Explanation: 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.
解题思路
题目的本质是判断有向图中是否有环（不是所有点是否可达），如果有环则返回flase，无环返回true。解题时，我选择用拓扑排序来判断是否有环路存在。其基本思想是，选择图中所有入度为0的顶点，从图中删除该顶点和所有以它为起点的有向边（这些有向边的终点的入度-1）。如果最终图为空，则无环，否则有环。
代码如下：
class Solution {
public:
bool canFinish(int numCourses, vector<pair<int, int>>& prerequisites) {
graph.resize(numCourses);
tag.resize(numCourses);
vector<int> in_degree(numCourses, 0);
for(int i = 0; i < prerequisites.size(); i++) {
int first = prerequisites[i].first;
int second = prerequisites[i].second;
graph[second].push_back(first);
in_degree[prerequisites[i].first]++;
}
bool exist = true;
vector<int> zero_degree;
for(int i = 0; i < numCourses; i++) {
if(in_degree[i] == 0) {
zero_degree.push_back(i);
}
}
if(zero_degree.size() == 0) {
exist = false;
return exist;
}
queue<int> q;
for(int i = 0; i < zero_degree.size(); i++) {
q.push(zero_degree[i]);
}
int count = 0;
while(q.size() != 0) {
int v = q.front(); // 从队列中取出一个顶点
q.pop();
++count;
for(int i = 0; i < graph[v].size(); i++) {
in_degree[graph[v][i]] = in_degree[graph[v][i]] - 1;
if(in_degree[graph[v][i]] == 0) {
q.push(graph[v][i]);
}
}
}
if(count != numCourses) {
exist = false;
}
return exist;
}
private:
vector<vector<int>> graph;
vector<int> tag;
};
注：
c++中的二维向量初始化要注意。我是先定义了一个空二维向量，再使用之前用resize（）函数进行了初始化和赋值。