Vertex Cover frog has a graph with \(n\) vertices \(v(1), v(2), \dots, v(n)\) and \(m\) edges \((v(a_1), v(b_1)), (v(a_2), v(b_2)), \dots, (v(a_m), v(b_m))\). She would like to color some vertices so that each edge has at least one colored vertex. Fi…

传送门 Vertex Cover frog has a graph with n vertices v(1),v(2),…,v(n)v(1),v(2),…,v(n) and m edges (v(a1),v(b1)),(v(a2),v(b2)),…,(v(am),v(bm))(v(a1),v(b1)),(v(a2),v(b2)),…,(v(am),v(bm)). She would like to color some vertices so that each edge has at leas…

题意: 给出n个点,m条边,将若干个点染色,使得每个边至少有一点染色,问至少染多少个点. 思路: 如果是二分图,那就是最小点覆盖,但是这是一般图. 一般图的最小覆盖是npc问题,但是这题有一个条件比较特殊,就是输入的每条边都保证了至少有一个点小于等于30,所以至多覆盖30个点就可以了. 那么就可以用搜索解决,对于一个点,要么覆盖,要么不覆盖. 如果这个点被覆盖了,就直接往下搜: 如果没有被覆盖,那么就要么覆盖这个点,直接往下搜:要么不覆盖这个点,但把这个点相邻的点全部覆盖,再往下搜. 得剪枝,可…

题意:每一条边至少有一个端点要涂颜色,问最少涂几个点 思路:最小顶点覆盖:用最少的点,让每条边都至少和其中一个点关联,显然是道裸最小顶点覆盖题: 参考:二分图 代码: #include<iostream> #include<algorithm> #include<cstdio> #include<stdio.h> #include<string.h> #include<queue> #include<cmath> #inc…

给你一个一般图 保证每条边的一端下标不大于30 问最小覆盖集的大小为多少 爆搜:枚举前30个点是否在覆盖集内 剪枝1:如果不在的话 那么他所连的下标大于30的点都必须选 剪纸2:最优解剪枝 #include<bits/stdc++.h> using namespace std; int n, m; bitset<> G[], em; int cnt, ans; > a) { if (a.count() >= ans) { return; } || o > ) {…

这里将讲解一下npc问题中set cover和vertex cover分别是什么. set cover: 问题定义: 实例:现在有一个集合A,其中包含了m个元素(注意,集合是无序的,并且包含的元素也是不相同的),现在n个集合,分别为B1.B2.....Bn.并且这n个集合的并集恰好等于A集合,即:B1UB2UB3U...UBn=A. 问题:是否存在B集合的最小子集,且他们的并集也等于A集合? 例子:集合A={1,2,3,4,5},集合B={{1,2,3},{2,4},{3,4},{4,5}}.可…

2038. Minimum Vertex Cover Time limit: 1.0 secondMemory limit: 64 MB A vertex cover of a graph is a set of vertices such that each edge of the graph is incident to at least one vertex of the set. A minimum vertex cover is a vertex cover with minimal…

1134. Vertex Cover (25) 时间限制 600 ms 内存限制 65536 kB 代码长度限制 16000 B 判题程序 Standard 作者 CHEN, Yue A vertex cover of a graph is a set of vertices such that each edge of the graph is incident to at least one vertex of the set. Now given a graph with several…

A vertex cover of a graph is a set of vertices such that each edge of the graph is incident to at least one vertex of the set. Now given a graph with several vertex sets, you are supposed to tell if each of them is a vertex cover or not. Input Specif…

A vertex cover of a graph is a set of vertices such that each edge of the graph is incident to at least one vertex of the set. Now given a graph with several vertex sets, you are supposed to tell if each of them is a vertex cover or not. Input Specif…