LN : leetcode 207 Course Schedule

lc 207 Course Schedule

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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.

DFS Accepted##

这是一个非常典型的拓扑排序问题，整个问题可以总结为如何判断有向图是否有环。通过对图上的每一个点做DFS，如果都是无环的，则能证明课程安排是合理的。注意，点的状态有三种，分别是没被访问，第一次访问后以及第二次访问后。

class Solution {
public:
    bool canFinish(int numCourses, vector<pair<int, int>>& prerequisites) {
        vector<set<int>> graph(numCourses);
        bool cycle = false;
        for (auto prev : prerequisites) {
            graph[prev.second].insert(prev.first);
        }
        vector<int> visited(numCourses, 0);
        for (int i = 0; i < numCourses; i++) {
            if (cycle) return false;
            if (visited[i] == 0) dfs(i, graph, visited, cycle);
        }
        return !cycle;
    }
    
    void dfs(int nodei, vector<set<int>> &graph, vector<int> &visited, bool &cycle) {
        if (visited[nodei] == 1) {
            cycle = true;
            return;
        }
        visited[nodei] = true;
        for (auto i : graph[nodei]) {
            dfs(i, graph, visited, cycle);
            if (cycle) return;
        }
        visited[nodei] = 2;
    }
};