0-1 Knapsack Problem 背包

You have N items that you want to put them into a knapsack. Item i has value v_i and weight w_i.

You want to find a subset of items to put such that:

• The total value of the items is as large as possible.
• The items have combined weight at most W, that is capacity of the knapsack.

Find the maximum total value of items in the knapsack.

Input

N W
v1 w1
v2 w2
:
vN wN

The first line consists of the integers N and W. In the following lines, the value and weight of the i-th item are given.

Output

Print the maximum total values of the items in a line.

Constraints

• 1 ≤ N ≤ 100
• 1 ≤ v_i ≤ 1000
• 1 ≤ w_i ≤ 1000
• 1 ≤ W ≤ 10000

Sample Input 1

4 5
4 2
5 2
2 1
8 3

Sample Output 1

13

Sample Input 2

2 20
5 9
4 10

Sample Output 2

9

#include<bits/stdc++.h>
using namespace std;

int dp[10000+10];
const int N(1000+10);
int v[N],w[N];

int main(){
    //freopen("in.txt","r",stdin);
    int n,W;
    cin>>n>>W;
    for(int i=0;i<n;i++)
    cin>>v[i]>>w[i];
    for(int i=0;i<n;i++)
    for(int j=W;j>=w[i];j--)
    dp[j]=max(dp[j],dp[j-w[i]]+v[i]);
    cout<<dp[W]<<endl;
//    fclose(stdin);

}