Problem:
0-1 Knapsack Problem

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

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 ≤ vi ≤ 1000

1 ≤ wi ≤ 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

Solution in JAVA (judge verdict: Accepted)

import java.util.*;
import java.awt.*;
import static java.lang.System.*;
import static java.lang.Math.*;
//Loopで使う文字列の長さは固定！
//intで大丈夫？オーバーフローしない？
//Loop回数は本当に10⁹以内になってる？Loopは回る？？
public class Main {
    public static void main(String[] args){
        Scanner sc = new Scanner(in);
        int n=sc.nextInt();
        int W=sc.nextInt();
        long[][] dp=new long[n+1][W+1];
        dp[0][0]=0;
        int[] v=new int[n];
        int[] w=new int[n];
        for (int i = 0; i < n; i++) {
            v[i]=sc.nextInt();
            w[i]=sc.nextInt();
        }
        int weight=0;
        long ans=0;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j <=W ; j++) {
                if(j>=w[i]){
                    dp[i+1][j]=max(dp[i][j-w[i]]+v[i],dp[i][j]);
                }else{
                    dp[i+1][j]=dp[i][j];
                }
            }
        }
        out.println(dp[n][W]);
    }
}