leetcode 207 Course Schedule
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题目描述
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.
click to show more hints.
Hints:
This problem is equivalent to finding if a cycle exists in a directed graph. If a cycle exists, no topological ordering exists and therefore it will be impossible to take all courses.Topological Sort via DFS - A great video tutorial (21 minutes) on Coursera explaining the basic concepts of Topological Sort.Topological sort could also be done via BFS
题意就是看看这些课程是否能找到一个顺序可以上完全部课程。其实就是一个有向图的是否存在环路的问题。可以用拓扑排序的方法,如果能找到一个完成一个拓扑排序,则有解。另外可以用一个改进的dfs算法,每个节点有三个状态,未访问,正在访问,已经访问过。对每个节点进行dfs。以下是代码:
class Solution {public: bool canFinish(int numCourses, vector<pair<int, int>>& prerequisites) { if (numCourses == 0 || prerequisites.empty()) return true; graph = vector<vector<int> >(numCourses); vis = vector<int>(numCourses, 0); // not visit for (auto i : prerequisites) { graph[i.second].push_back(i.first); } for (int u = 0; u < numCourses; ++u) { if (0 == vis[u] && !dfs(u)) return false; } return true; }private: vector<vector<int> > graph; vector<int> vis; bool dfs(int u) { vis[u] = 1; // visiting for (auto v : graph[u]) { if (vis[v] == 1) return false; if (dfs(v) == false) return false; } vis[u] = 2; // visited return true; };};
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