P2871 [USACO07DEC] Charm Bracelet S

题目描述

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 from the N (1 ≤ N ≤ 3,402) available charms. Each charm i in the supplied list has a weight Wi (1 ≤ Wi ≤ 400), a ‘desirability’ factor Di (1 ≤ Di ≤ 100), and can be used at most once. Bessie can only support a charm bracelet whose weight is no more than M (1 ≤ M ≤ 12,880).

Given that weight limit as a constraint and a list of the charms with their weights and desirability rating, deduce the maximum possible sum of ratings.

有 $N$ 件物品和一个容量为 $M$ 的背包。第 $i$ 件物品的重量是 $W_i$，价值是 $D_i$。求解将哪些物品装入背包可使这些物品的重量总和不超过背包容量，且价值总和最大。

输入格式

* Line 1: Two space-separated integers: N and M

* Lines 2…N+1: Line i+1 describes charm i with two space-separated integers: Wi and Di

第一行：物品个数 $N$ 和背包大小 $M$。

第二行至第 $N+1$ 行：第 $i$ 个物品的重量 $W_i$ 和价值 $D_i$。

输出格式

* Line 1: A single integer that is the greatest sum of charm desirabilities that can be achieved given the weight constraints

输出一行最大价值。

输入输出样例 #1

输入 #1

4 6
1 4
2 6
3 12
2 7

输出 #1

23

题解

#include<bits/stdc++.h>
using namespace std;
int n, m, f[13000] = {0}, w[3500], d[3500];
int main(){
	cin>>n>>m;
	for(int i=1;i<=n;++i){
		cin>>w[i]>>d[i];
	}
	for(int i=1;i<=n;++i){
		for(int j=m;j>=w[i];j--){
			f[j] = max(f[j], d[i]+f[j-w[i]]); 
		}
	}
	cout<<f[m];
	return 0; 
}