Asteroids Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 17237   td>Accepted: 9375 Description Bessie wants to navigate her spaceship through a dangerous asteroid field in the shape of an N x N grid (1 <= N <= 500). The grid contain…

Description Bessie wants to navigate her spaceship through a dangerous asteroid field in the shape of an N x N grid (1 <= N <= 500). The grid contains K asteroids (1 <= K <= 10,000), which are conveniently located at the lattice points of the…

分析:这里使用树形DP做. 1.最小顶点覆盖做法:最小顶点覆盖 == 最大匹配(双向图)/2. 2.树形DP: dp[i][0]表示i为根节点,而且该节点不放,所需的最少的点数. dp[i][1]表示i为根节点,而且该节点放,所须要的最少的点数. dp[i][0]=sum(dp[son[i][j]][1]) 该点不放.则它的儿子节点必须都放,仅仅有这样之间的边才干够被覆盖. dp[i][1]=sum(min(dp[son[i][j]][0],dp[son[i][j]][1])) 该点放的话,则它…

Machine Schedule Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 11958   Accepted: 5094 Description As we all know, machine scheduling is a very classical problem in computer science and has been studied for a very long history. Scheduli…

Asteroids Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 22905   Accepted: 12421 Description Bessie wants to navigate her spaceship through a dangerous asteroid field in the shape of an N x N grid (1 <= N <= 500). The grid contains K a…

Strategic Game Time Limit: 20000/10000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 8503    Accepted Submission(s): 4093 Problem Description Bob enjoys playing computer games, especially strategic games, but somet…

题目大意:$N*N$的网格中有$n$颗行星,若每次可以消去一整行或一整列,求最小的攻击次数使得消去所有行星. 解题关键:将光束当做顶点,行星当做连接光束的边建图,题目转化为求该图的最小顶点覆盖,图的最小顶点覆盖是$NP$问题,又因为该图是二分图(水平方向的点和竖直方向的点),而二分图的最大匹配=最小顶点覆盖,即可求解该问题. #include<cstdio> #include<cstring> #include<algorithm> #include<cstdli…

问题:POJ3041 分析: 构造二分图:令A = B = { 1, 2, ... , n }, 分别代表行号集与列号集.假如第i行第j列有一颗行星,则连接Ai与Bj, 表示必须从Ai(即第i行),Bj(即第j列)中选择一个射击.最小射击数等价于覆盖所有边的最小点集S的大小.问题转化为最小顶点覆盖问题. 因为最小顶点覆盖=最大匹配数,故直接用匈牙利算法求解. AC代码 //Memory: 1260K Time: 47MS #include <iostream> using namespace…

题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=3861 题目大意:一个有向图,让你按规则划分区域,要求划分的区域数最少. 规则如下:1.有边u到v以及有边v到u,则u,v必须划分到同一个区域内.2.一个区域内的两点至少要有一方能到达另一方.3.一个点只能划分到一个区域内. 解题思路:根据规则1可知必然要对强连通分量进行缩点,缩点后变成了一个弱连通图.根据规则2.3可知即是要求图的最小路径覆盖. 定义: 最小路径覆盖:在图中找一些路径(路径数最少),…

在一个n*m的草地上,.代表草地,*代表水,现在要用宽度为1,长度不限的木板盖住水, 木板可以重叠,但是所有的草地都不能被木板覆盖. 问至少需要的木板数. 这类题的建图方法: 把矩阵作为一个二分图,以行列分别作为2个顶点集 首先以每一行来看,把这一行里面连续的*编号,作为一个顶点 再以每一列来看,把这一列里面连续的*编号,作为一个顶点 则每一个*都有2个编号,以行看时有一个,以列看时有一个,则把这2个编号连边,容量为1 再建一个源点,连接所有行的编号,一个汇点,连接所有列的编号 这道题要求的是,…