C. Dima and Salad 题意 有n种水果,第i个水果有一个美味度ai和能量值bi,现在要选择部分水果做沙拉,假如此时选择了m个水果,要保证\(\frac{\sum_{i=1}^ma_i}{\sum_{i=1}^mb_i}==k\),问沙拉最大的美味度是多少? 思路 01背包变形. 对于给出的公式,我们化简一下: \(\sum_{i=1}^ma_i-k*\sum_{i=1}^mb_i==0\) 就变成了把a[i]-k*b[i]作为体积,a[i]作为价值,向容量为0的背包里放,可以取得的…

C. Dima and Salad time limit per test 1 second memory limit per test 256 megabytes input standard input output standard output Dima, Inna and Seryozha have gathered in a room. That's right, someone's got to go. To cheer Seryozha up and inspire him to…

C. Dima and Salad time limit per test 1 second memory limit per test 256 megabytes input standard input output standard output Dima, Inna and Seryozha have gathered in a room. That's right, someone's got to go. To cheer Seryozha up and inspire him to…

题意:n件东西,有属性a和属性b.要选取若干件东西,使得\(\frac{\sum a_j}{\sum b_j} = k\).在这个条件下,问\(\sum a_j\)最大是多少. 分析:可以将其转化为0-1背包,令\(c[i] = a[i] - k*b[i]\) 等价于物品的重量,\(a_i\)为物品的价值.因为\(c[i]\)可能小于0,所以用\(dp1[i]\)表示重量为正i时的最大收益,\(dp2[i]\)表示负i时的最大收益.最后求\(dp1[i]+dp2[i]\)的最大值就是答案,注意不…

题目链接:Knapsack problem 大意:给出T组测试数据,每组给出n个物品和最大容量w.然后依次给出n个物品的价值和体积. 问,最多能盛的物品价值和是多少? 思路:01背包变形,因为w太大,转而以v为下标,求出价值对应的最小体积,然后求出能够满足给出体积的最大价值. 经典题目,思路倒是挺简单的,就是初始化总觉得别扭...T_T大概,因为我要找的是最小值,所以初始化为maxn,就结了? 这个问题好像叫01背包的超大背包... 模拟一下样例吧! 1 5 15 // 初始化为dp[0] =…

01背包变形,注意dp过程的时候就需要取膜,否则会出错. 代码如下: #include<iostream> #include<cstdio> #include<cstring> using namespace std; #define MAXW 15005 #define N 155 #define LL long long #define MOD 1000000007 int w1[N],w2[N]; LL dp1[MAXW],dp2[MAXW]; int main(…

Bone Collector II Time Limit: 5000/2000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 4739    Accepted Submission(s): 2470 Problem Description The title of this problem is familiar,isn't it?yeah,if you had took pa…

http://acm.hdu.edu.cn/showproblem.php?pid=2955 [题意] 有一个强盗要去几个银行偷盗,他既想多抢点钱,又想尽量不被抓到.已知各个银行 的金钱数和被抓的概率,以及强盗能容忍的最大被抓概率.求他最多能偷到多少钱? [思路] 01背包:每个物品代价是每个银行钱的数目,物品的价值是在该银行不被抓的概率 (1-被抓概率),背包容量是所有银行钱的总和.01背包求dp[i]表示获得i的钱不被抓的最大概率.最后从大到小枚举出 dp[i]>=(1-P)这个i就是答案了…

Dima and Salad time limit per test 1 second memory limit per test 256 megabytes input standard input output standard output Dima, Inna and Seryozha have gathered in a room. That's right, someone's got to go. To cheer Seryozha up and inspire him to ha…

题目链接:http://codeforces.com/problemset/problem/366/C 题意: 有n个物品,每个物品有两个属性a[i]和b[i]. 给定k,让你选出一些物品,使得 ∑ a[i] / ∑ b[i] = k. 问你选出物品的 ∑ a[i]最大是多少. 题解: 将原式变形: ∑ a[i] - k * ∑ b[i] = 0 可以看做有一个容积为0的箱子,每个物品的价值为a[i],体积为a[i] - k*b[i],问你最大总价值. 这就变成了01背包. 但是体积a[i] -…