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…

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…

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…

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…

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 > ) {…

题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=6150 题意:"最小点覆盖集"是个NP完全问题 有一个近似算法是说—每次选取度数最大的点(如果有多个这样的点,则选择最后一个) 让你构造一个图,使得其近似算法求出来点数是你给定的覆盖点数的至少3倍. 解法: 可以把左边的点编号1~n,将左边的点进行n次分块,第i次分块中每块的大小为i,对于每一块的点,都在右边创建一个新节点与这些点相连. ①右边的点的度数为n,n-1,n-2,...,n/2,…

Vertex Cover Problem's Link Mean: 给你一个无向图,让你给图中的结点染色,使得:每条边的两个顶点至少有一个顶点被染色.求最少的染色顶点数. analyse: 裸的最小点覆盖问题,二分图的最大匹配,直接套模版即可. Time complexity: O(N^2) view code…

Vertex Cover frog has a graph with nn vertices v(1),v(2),…,v(n)v(1),v(2),…,v(n) and mm 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 least…

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…

思路来自 ICPCCamp /* HDU 6150 - Vertex Cover [ 构造 ] | 2017 中国大学生程序设计竞赛 - 网络选拔赛 题意: 给了你一个贪心法找最小覆盖的算法,构造一组数据,使得这个程序跑出的答案是正解的三倍以上 分析: 构造一个二分图,左边 n 个节点 将左边的点进行 n 次分块,第 i 次分 n/i 块,每块的大小为 i,对于每一块都在右边建一个新的节点和这一块所有的点相连 则右边有 nlogn个节点,且每次一定优先选右边,最后取 nlogn >= 3n */…

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…

洛谷P2891 Dining P1402 酒店之王[类二分图匹配]题解+代码 酒店之王 题目描述 XX酒店的老板想成为酒店之王,本着这种希望,第一步要将酒店变得人性化.由于很多来住店的旅客有自己喜好的房间色调.阳光等,也有自己所爱的菜,但是该酒店只有p间房间,一天只有固定的q道不同的菜. 有一天来了n个客人,每个客人说出了自己喜欢哪些房间,喜欢哪道菜.但是很不幸,可能做不到让所有顾客满意(满意的条件是住进喜欢的房间,吃到喜欢的菜). 这里要怎么分配,能使最多顾客满意呢? 输入格式: 第一行给出三…

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…

https://pintia.cn/problem-sets/994805342720868352/problems/994805346428633088 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, y…

题意 给出一个R*C大小的网格,网格上面放了一些目标.可以在网格外发射子弹,子弹会沿着垂直或者水平方向飞行,并且打掉飞行路径上的所有目标.你的任务是计算最少需要多少子弹,各从哪些位置发射,才能把所有目标全部打掉. 分析 啊!原来这个模型叫 最小覆盖模型啊!难道不是最小割直接做嘛?? 二分图最小覆盖:既选择尽量少的点,使得每条边至少有一个端点被选中.可以证明,最小覆盖数等于最大匹配数. 本题的建模方法: 将每一行看作一个X结点,每一列看作一个Y结点,每个目标对应一条边.这样,子弹打掉左右的目标意味…

1134 Vertex Cover (考察散列查找,比较水~) 我先在CSDN上发布的该文章,排版稍好https://blog.csdn.net/weixin_44385565/article/details/88897469 Input Specification: Each input file contains one test case. For each case, the first line gives two positive integers N and M (both no…

[转http://www.cppblog.com/abilitytao/archive/2009/09/02/95147.html  ->  http://yejingx.ycool.com/post.2801156.html:http://hi.baidu.com/cjhh314/blog/item/ded8d31f15d7510c304e1591.html] 二分图最小覆盖的Konig定理及其证明 一.定义 二分图: 顶点可以分类两个集合X和Y,所有的边关联在两个顶点中,恰好一个属于集合X,…

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…

Source: PAT A1134 Vertex Cover (25 分) Description: 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…

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…

题目 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 Spe…

题意:给一个01矩阵,每次可以选一行或一列,打掉上面所有的1,求打掉所有的1所需的最小次数. 思路:经典的模型了,二分图最小覆盖=最大匹配.所谓最小覆盖是指选最少的点关联所有的边.容易得到将行和列看成点,1看成边,那么就是选尽量少的行和列来关联所有的1,最小覆盖模型,用最大匹配做.可以选择匈牙利算法,或者直接最大流. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33…

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 Specifi…

原题传送门 求树的最小点覆盖,就是一个树形dp 类似于没有上司的舞会 dp的状态为\(f[i][0/1]\),表示i节点是否选择 边界是\(f[x][0]=0\),\(f[x][1]=1\) 转移方程是 \(f[i][0]=\sum_{j=son[i]} f[j][1]\) \(f[i][1]=\sum_{j=son[i]} Min(f[j][0],f[j][1])\) 最后答案就是\(Min(f[1][0],f[1][1])\) #include <bits/stdc++.h> #defin…

大白书355 // UVa11419 SAM I AM // Rujia Liu #include <cstdio> #include <cstring> #include <vector> #include <algorithm> using namespace std; + ; // 单侧顶点的最大数目 // 二分图最大基数匹配 struct BPM { int n, m; // 左右顶点个数 vector<int> G[maxn]; //…

OwO 良心的FFT练手题,包含了所有的多项式基本运算呢 其中一部分解法参考了myy的uoj的blog 二分图计数 1: 实际是求所有图的二分图染色方案和 我们不妨枚举这个图中有多少个黑点 在n个点中选出k个黑点的方案为C(n,k) 白点和黑点之间任意连边,方案为2^(k*(n-k)) 所以得到f(n)=sigma(C(n,k)*2^(k*(n-k)) 由于本题只需要求解一个f(n),枚举并计算就可以了 更高端一点的做法是这样的: 我们可以利用在<DAG计数问题 题解报告>中提到的技巧将n*k…

虚拟化构建二分图 ------BZOJ2080 题解+浅谈几道双栈排序思想的题 本题的题解在最下面↓↓↓ 不得不说,第一次接触类似于双栈排序的这种题,是在BZOJ的五月月赛上. [BZOJ4881][Lydsy2017年5月月赛]线段游戏 传送门 简洁的题面:给你一个1到n(n<=100000)的排列,问你能否将这个排列分成两个升序的子序列,如果能,求方案数.(本人强行将问题拆成两个子任务,原因你一会就会知道~) P.S.:比赛时除太空猫外唯一想出来的题,其实我已经写过一篇题解了,不过当时比赛还…