题目传送门：P2871 [USACO07DEC]手链Charm Bracelet

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V的背包。第i件物品的重量是c[i]，价值是w[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。

输入输出格式

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C[i]和价值W[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

4 6

1 4

2 6

3 12

2 7

23

#include<bits/stdc++.h>

using namespace std;

const int N = ;

const int M = ;

int c[N],w[N],dp[M]={};

int main()

{

    int n,m;

    scanf("%d%d",&n,&m);

    for (int i=;i<=n;i++)

        scanf("%d%d",&c[i],&w[i]);

    for (int i=;i<=n;i++)

        for (int j=m;j>=c[i];j--)

            dp[j]=max(dp[j],dp[j-c[i]]+w[i]);

    printf("%d\n",dp[m]);

    return ;

}

01背包