Course Schedule问题及解法

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?

示例:

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.

问题分析：

这是一类图内是否存在环的问题，可以采用DFS方法来求解。

过程详见代码：

class Solution {public:    bool DFS(vector<unordered_set<int>> &matrix, unordered_set<int> &visited, int b, vector<bool> &flag){flag[b] = true;visited.insert(b);for (auto it = matrix[b].begin(); it != matrix[b].end(); ++it)if (visited.find(*it) != visited.end() || DFS(matrix, visited, *it, flag))return true;visited.erase(b);return false;}        bool canFinish(int numCourses, vector<pair<int, int>>& prerequisites) {        vector<unordered_set<int>> matrix(numCourses); // save this directed graphfor (int i = 0; i < prerequisites.size(); ++i)matrix[prerequisites[i].second].insert(prerequisites[i].first);unordered_set<int> visited;vector<bool> flag(numCourses, false);for (int i = 0; i < numCourses; ++i)if (!flag[i])if (DFS(matrix, visited, i, flag))return false;return true;    }};