P2871 [USACO07DEC]手链Charm Bracelet（01背包模板）

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

输入样例#1： 

4 6
1 4
2 6
3 12
2 7

输出样例#1： 

23

题解： 

　　01背包模板题。

#include<bits/stdc++.h>
using namespace std;
const int N = 3410;
const int M = 13000;
int c[N],w[N],dp[M]={0};
int main()
{
    int n,m;
    scanf("%d%d",&n,&m);
    for (int i=1;i<=n;i++) 
        scanf("%d%d",&c[i],&w[i]);
    for (int i=1;i<=n;i++)
        for (int j=m;j>=c[i];j--)
            dp[j]=max(dp[j],dp[j-c[i]]+w[i]);
    printf("%d
",dp[m]);
    return 0;
}

01背包