最小点覆盖概念:选取最小的点数覆盖二分图中的所有边. 最小点覆盖 = 最大匹配数. 证明:首先假设我们求的最大匹配数为m,那么最小点覆盖必然 >= m,因为仅仅是这m条边就至少需要m个点.然后假如我们已经求得最小覆盖点集,那么在点集中每个点必然有着这样的性质,在于它相连的边里面,一定有一条边的端点不在最小点集中,因为如果连一条这样的边都没有,那这个点完全没有在最小点集的必要,我们任意选取这样的一条边,一定可以形成一个匹配,匹配数与最小点集中的点的个数相等,但现在这仅仅是一个匹配,他必然小于最大…

<题目链接> 题目大意:鲍勃喜欢玩电脑游戏,特别是战略游戏,但有时他无法找到解决方案,速度不够快,那么他很伤心.现在,他有以下的问题.他必须捍卫一个中世纪的城市,形成了树的道路.他把战士的最低数量的节点上,使他们可以观察所有的边.你能帮助他吗?士兵,鲍勃把一个给定的树,你的程序应该发现的最小数目. 解题分析: 最小点覆盖模板题,用最少的点来覆盖所有的边.建立无向图,然后求出其最大匹配,最小点覆盖数=最大匹配数.需要注意的是,本题用邻接矩阵存图跑匈牙利会T,所以用链式前向星存图. #includ…

题目链接:http://acm.hust.edu.cn/vjudge/contest/view.action?cid=106048#problem/B 题意:给出一些点相连,找出最小的点数覆盖所有的 用树形dp来解决 dp[i][0]表示i点不选,dp[i][1]表示i点选,dp[i][0] = sum{ dp[ son[i] ][1] }, // i不选,则i的子节点全选, dp[i][1] = sum { min( dp[ son[i] ][0], dp[ son[i] ][1] ) } +…

d.一颗树,选最少的点覆盖所有边 s. 1.可以转成二分图的最小点覆盖来做.不过转换后要把匹配数除以2,这个待细看. 2.也可以用树形dp c.匈牙利算法(邻接表,用vector实现): /* 用STL中的vector建立邻接表实现匈牙利算法 效率比较高 处理点比较多的效率很高.1500的点都没有问题 */ #include<iostream> #include<stdio.h> #include<algorithm> #include<string.h>…

题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=1054 题目大意:给你一棵树,选取树上最少的节点使得可以覆盖整棵树. 解题思路: 首先树肯定是二分图,因为树可以奇偶分层,从而根据二分图染色的原理可以确定树是二分图.我们可以用染色法确定出两个集合求最大匹配,也可以将边补成双向的,然后将最大匹配/2. 代码: #include<iostream> #include<cstdio> #include<cstring> #incl…

Strategic Game Time Limit: 20000/10000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 8504    Accepted Submission(s): 4094 Problem Description Bob enjoys playing computer games, especially strategic games, but some…

题目链接:https://vjudge.net/problem/HDU-1054 Strategic Game Time Limit: 20000/10000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 8673    Accepted Submission(s): 4174 Problem Description Bob enjoys playing computer gam…

题目链接:http://poj.org/problem?id=1463 给你一棵树形图,问最少多少个点覆盖所有的边. 可以用树形dp做,任选一点,自底向上回溯更新. dp[i][0] 表示不选i点 覆盖子树所有边的最少点个数,那选i点的话,那么i的邻接节点都是必选的,所以dp[i][0] += dp[i.son][1] dp[i][1] 表示选i点 覆盖子树所有边的最少点个数,那么i的邻接点可选可不选(而不是一定不选,看注释样例就知道了),所以dp[i][0] += min(dp[i.son][…

题目链接 题意: 给一颗树,用最少的点覆盖整棵树. 每一个结点可以防守相邻的一个边,求最少的点防守所有的边. 分析: 1:以当前节点为根节点,在该节点排士兵守护道路的最小消耗.在这种情况下,他的子节点可以安排士兵,也可以不安排士兵.可以从各个子节点两个不同状态(存在士兵,不存在士兵)的最值中选出最小的消耗,然后相加就求出了当前节点派士兵的最小消耗. 2:以当前节点为根节点,不存在士兵.这种情况十分清楚,因为当前节点没有士兵,那么这个节点到子节点之间的道路没有人守护,那么子节点就必须要安排士兵,因…

Strategic Game Time Limit: 20000/10000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 6586    Accepted Submission(s): 3066 Problem Description Bob enjoys playing computer games, especially strategic games, but some…

Problem Description Bob enjoys playing computer games, especially strategic games, but sometimes he cannot find the solution fast enough and then he is very sad. Now he has the following problem. He must defend a medieval city, the roads of which for…

Strategic Game Time Limit: 20000/10000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 2925    Accepted Submission(s): 1222 Problem Description Bob enjoys playing computer games, especially strategic games, but somet…

Strategic Game Time Limit: 20000/10000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 4061    Accepted Submission(s): 1791 Problem Description Bob enjoys playing computer games, especially strategic games, but some…

Strategic Game Time Limit: 20000/10000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 4697    Accepted Submission(s): 2125 Problem Description Bob enjoys playing computer games, especially strategic games, but somet…

Strategic Game Time Limit: 20000/10000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 3806    Accepted Submission(s): 1672 Problem Description Bob enjoys playing computer games, especially strategic games, but some…

Strategic Game Time Limit: 20000/10000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 10035    Accepted Submission(s): 4691 Problem Description Bob enjoys playing computer games, especially strategic games, but some…

(￣▽￣)" //凡无向图,求匹配时都要除以2 #include<iostream> #include<cstdio> #include<algorithm> #include<cstring> #include<vector> using namespace std; ; int uN; vector<int> g[MAXN]; int link[MAXN]; bool vis[MAXN]; bool DFS(int u)…

二分图匹配模板题 #include <bits/stdc++.h> #define FOPI freopen("in.txt", "r", stdin); #define FOPO freopen("out.txt", "w", stdout); using namespace std; typedef long long LL; + ; int n, k, x, y; int link[maxn], vis[ma…

Strategic Game Time Limit: 20000/10000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 7328    Accepted Submission(s): 3481 Problem Description Bob enjoys playing computer games, especially strategic games, but somet…

Sample Input 4 0:(1) 1 1:(2) 2 3 2:(0) 3:(0) 5 3:(3) 1 4 2 1:(1) 0 2:(0) 0:(0) 4:(0)   Sample Output 1 2 最小点覆盖=最大匹配数 水题,懒的拍了 #include<stdio.h> #include<iostream> #include<algorithm> #include<string.h> #include<vector> using n…

Strategic Game Time Limit: 20000/10000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 10153    Accepted Submission(s): 4744 题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=1054 Description: Bob enjoys playing compute…

题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=1150 有两个机器a和b,分别有n个模式和m个模式.下面有k个任务,每个任务需要a的一个模式或者b的一个模式完成. 两个机器初始都是0模式,一个机器转换一个模式需要重启一次.问你最少需要重启几次能完成所有的任务. 不太明显的二分匹配,将每个任务的两个模式连线,大概就能看出来这是个最小点覆盖问题. /* 将下面任务的a状态和b状态连边,线的个数就是任务个数. 要使重启次数最少,那么就要使选择的点最少而且…

50 years, 50 colors Problem Description On Octorber 21st, HDU 50-year-celebration, 50-color balloons floating around the campus, it's so nice, isn't it? To celebrate this meaningful day, the ACM team of HDU hold some fuuny games. Especially, there wi…

50 years, 50 colors Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 2256    Accepted Submission(s): 1266 Problem Description On Octorber 21st, HDU 50-year-celebration, 50-color balloons floating…

Bob enjoys playing computer games, especially strategic games, but sometimes he cannot find the solution fast enough and then he is very sad. Now he has the following problem. He must defend a medieval city, the roads of which form a tree. He has to…

无题II Time Limit: 2000/2000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 1545    Accepted Submission(s): 692 Problem Description 这是一个简单的游戏,在一个n*n的矩阵中,找n个数使得这n个数都在不同的行和列里并且要求这n个数中的最大值和最小值的差值最小.   Input 输入一个整数T表示T组数据…

题意即求一个最小顶点覆盖. 对于没有孤立点的图G=(V,E),最大独立集+最小顶点覆盖= V.(往最大独立集加点) 问题可以变成求树上的最大独立集合. 每个结点的选择和其父节点选不选有关, dp(u,1)表示父节点选,这时u不可选, dp(u,0)表示父节点不选,这时u可选可不选. #include<bits/stdc++.h> using namespace std; ; ]; ], clk; ],to[maxn<<],ec; void add(int u,int v) { to…

原题链接 此题求二分图的最小点覆盖,数值上等于该二分图的最大匹配.得知此结论可以将图染色,建有向图,然后跑匈牙利/网络流,如下.然而... #include<iostream> #include<cstdio> #include<cstring> using namespace std; const int MAXN=2000+5; int q[MAXN],hd1[MAXN],hd2[MAXN]; int lnk[MAXN]; bool vis[MAXN],bw[MAX…

链接:pid=1054">http://acm.hdu.edu.cn/showproblem.php?pid=1054 题意:一个熊孩子玩策略游戏,他须要用最少的士兵守卫最多的道路.假设这个顶点有士兵.则和这个点相连的全部边都会被保护,问保护全部的道路最少须要的士兵数量. 思路:这实际上就是一个最小点覆盖,二分图的最小点覆盖 == 最大匹配,这不是一个二分图,我们把n个点扩成2 * n个.把他转换为二分图,最后最大匹配再除以2就是原图的最大匹配. Hopcroft-Karp增广模板 #in…

Strategic Game Time Limit: 20000/10000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 7651    Accepted Submission(s): 3645 Problem Description Bob enjoys playing computer games, especially strategic games, but somet…