目录 01背包问题 完全背包问题 多重背包问题 参考: 背包九讲--哔哩哔哩 背包九讲 01背包问题 01背包问题 描述: 有N件物品和一个容量为V的背包. 第i件物品的体积是vi,价值是wi. 求解将哪些物品装入背包,可使这些物品的总体积不超过背包流量,且总价值最大. 二维动态规划 f[i][j] 表示只看前i个物品,总体积是j的情况下,总价值最大是多少. result = max(f[n][0~V]) f[i][j]: 不选第i个物品:f[i][j] = f[i-1][j]; 选第i个物品:

题意:过山车有n个区域,一个人有两个值F,D,在每个区域有两种选择: 1.睁眼: F += f[i], D += d[i] 2.闭眼: F = F ,     D -= K 问在D小于等于一定限度的时候最大的F. 解法: 用DP来做,如果定义dp[i][j]为前 i 个,D值为j的情况下最大的F的话,由于D值可能会增加到很大,所以是存不下的,又因为F每次最多增加20,那么1000次最多增加20000,所以开dp[1000][20000],dp[i][j]表示前 i 个,F值为j的情况下最小的D.

Team Them Up! Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 7608   Accepted: 2041   Special Judge Description Your task is to divide a number of persons into two teams, in such a way, that: everyone belongs to one of the teams; every t

传送门 Description Hasan and Bahosain want to buy a new video game, they want to share the expenses. Hasan has a set of N coins and Bahosain has a set of M coins. The video game costs W JDs. Find the number of ways in which they can pay exactly W JDs su

题目链接: http://www.51nod.com/onlineJudge/questionCode.html#!problemId=1085 题意: 中文题诶~ 思路: 01背包模板题. 用dp[i][j]表示到第i个物品花去j空间能存储的最大价值, 那么很显然有 ; i<=n; i++){ ; j<=m; j++){ //注意这里的j是从0开始而非a[i] if(j>=a[i]){ dp[i][j]=max(dp[i-][j-a[i]]+b[i], dp[i-][j]); }els

In Action Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 5472    Accepted Submission(s): 1843 Problem Description Since 1945, when the first nuclear bomb was exploded by the Manhattan Project t

题意:给你若干个集合,每个集合内的物品要么选任意一个,要么所有都选,求最后在背包能容纳的范围下最大的价值. 分析:对于每个并查集,从上到下滚动维护即可,其实就是一个01背包= =. 代码如下: #include <stdio.h> #include <algorithm> #include <string.h> #include <vector> using namespace std; + ; int w[N],b[N]; int n,m,W; int r

Charm Bracelet Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 34532   Accepted: 15301 Description Bessie has gone to the mall's jewelry store and spies a charm bracelet. Of course, she'd like to fill it with the best charms possible fro

http://poj.org/problem?id=2184   Description "Fat and docile, big and dumb, they look so stupid, they aren't much fun..." - Cows with Guns by Dana Lyons The cows want to prove to the public that they are both smart and fun. In order to do this,

/* 题意:有 n 个站点(编号1...n),每一个站点都有一个能量值,为了不让这些能量值连接起来,要用 坦克占领这个站点!已知站点的 之间的距离,每个坦克从0点出发到某一个站点,1 unit distance costs 1 unit oil! 最后占领的所有的站点的能量值之和为总能量值的一半还要多,问最少耗油多少! */ /* 思路:不同的坦克会占领不同的站点,耗油最少那就是路程最少,所以我们先将从 0点到其他各点的 最短距离求出来!也就是d[i]的值!然后我们又知道每一个站点的所具有的能量

题目链接 http://acm.split.hdu.edu.cn/showproblem.php?pid=5410 Problem Description Today is CRB's birthday. His mom decided to buy many presents for her lovely son.She went to the nearest shop with M Won(currency unit).At the shop, there are N kinds of pr

题目链接 http://acm.hust.edu.cn/vjudge/contest/130883#problem/C Problem Description Zero Escape, is a visual novel adventure video game directed by Kotaro Uchikoshi (you may hear about ever17?) and developed by Chunsoft. Stilwell is enjoying the first ch

Washing Clothes Time Limit: 1000MS   Memory Limit: 131072K Total Submissions: 9707   Accepted: 3114 Description Dearboy was so busy recently that now he has piles of clothes to wash. Luckily, he has a beautiful and hard-working girlfriend to help him

描述 XC的儿子小XC最喜欢玩的游戏用积木垒漂亮的城堡.城堡是用一些立方体的积木垒成的,城堡的每一层是一块积木.小XC是一个比他爸爸XC还聪明的孩子,他发现垒城堡的时候,如果下面的积木比上面的积木大,那么城堡便不容易倒.所以他在垒城堡的时候总是遵循这样的规则. 小XC想把自己垒的城堡送给幼儿园里漂亮的女孩子们,这样可以增加他的好感度.为了公平起见,他决定把送给每个女孩子一样高的城堡,这样可以避免女孩子们为了获得更漂亮的城堡而引起争执.可是他发现自己在垒城堡的时候并没有预先考虑到这一点.所以他现在

2427: [HAOI2010]软件安装 Time Limit: 10 Sec  Memory Limit: 128 MBSubmit: 960  Solved: 380[Submit][Status][Discuss] Description 现在我们的手头有N个软件,对于一个软件i,它要占用Wi的磁盘空间,它的价值为Vi.我们希望从中选择一些软件安装到一台磁盘容量为M计算机上,使得这些软件的价值尽可能大(即Vi的和最大).但是现在有个问题:软件之间存在依赖关系,即软件i只有在安装了软件j(包

题意:求解01背包价值的第K优解. 分析: 基本思想是将每个状态都表示成有序队列,将状态转移方程中的max/min转化成有序队列的合并. 首先看01背包求最优解的状态转移方程:\[dp\left[ j \right] = \max \left\{ {dp\left[ j \right],dp\left[ {j - a\left[ i \right].w} \right] + a\left[ i \right].v} \right\}\] 如果要求第K优解,那么状态 dp[j] 就应该是一个大小为

Many years ago , in Teddy’s hometown there was a man who was called “Bone Collector”. This man like to collect varies of bones , such as dog’s , cow’s , also he went to the grave …The bone collector had a big bag with a volume of V ,and along his tri

    牛的展览会 题目大意:Bessie要选一些牛参加展览,这些牛有两个属性,funness和smartness,现在要你求出怎么选,可以使所有牛的smartness和funness的最大,并且这两个和都不能为负值 这一题很有意思,首先是这个问题是二维的,它包含两个属性,但是他有一个很重要的条件就是牛只能选一次,所以我们一开始就很容易想到用背包貌似可以求解,但是这一题没有办法直接用背包,因为没有直接给出价值和容量(他给了两个价值). 但是,我们稍微变换一下,这一题就可以做了,我们要把一个看成是

题目链接:http://acm.split.hdu.edu.cn/showproblem.php?pid=3448 Description 0/1 bag problem should sound familiar to everybody. Every earth man knows it well. Here is a mutant: given the capacity of a bag, that is to say, the number of goods the bag can ca

题目链接:http://acm.split.hdu.edu.cn/showproblem.php?pid=3496 //刚看题目以为是简单的二维01背包,but,,有WA点.. 思路:题中说,只能买M个光盘,不能多也不能少,所以就要求把背包装满. 恰好把背包装满,那么在初始化时,除了dp[0]=0,剩下的dp[1~M],均为负无穷(其实设置成-1,到时候在判断一下也是一样的,思想相同) 这样才可以保证最终得到的dp[M]是一种恰好装满背包状态的最优解. 代码: #include<iostream