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: Wrong Answer)


import java.util.*;
import java.io.*;

public class Main{
    static final Reader sc = new Reader();
    static final PrintWriter out = new PrintWriter(System.out,false);

    public static void main(String[] args) throws Exception {
    	int n = sc.nextInt();
    	int w = sc.nextInt();
    	int[] value = new int[n];
    	int[] weight = new int[n];
    	for(int i=0;i<n;i++){
    		value[i] = sc.nextInt();
    		weight[i] = sc.nextInt();
    	}
    	int[][] sum = new int[n][w+1];
    	for(int i=weight[0];i<w+1;i++){
    		sum[0][i] = value[0];
    	}
    	for(int i=1;i<n;i++){
    		for(int j=0;j<=w;j++){
    			if(weight[i]+j>w){
    				continue;
    			}
    			sum[i][weight[i]+j] = Math.max(sum[i-1][weight[i]+j],sum[i-1][j]+value[i]);
    		}
    	}

    	out.println(sum[n-1][w]);
    	out.flush();
        sc.close();
        out.close();
    }

    static void trace(Object... o) { System.out.println(Arrays.deepToString(o));}
}

class Reader {

    private final InputStream in;
    private final byte[] buf = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    public Reader() { this(System.in);}
    public Reader(InputStream source) { this.in = source;}

    private boolean hasNextByte() {
        if (ptr < buflen) return true;
        ptr = 0;
        try{
            buflen = in.read(buf);
        }catch (IOException e) {e.printStackTrace();}
        if (buflen <= 0) return false;
        return true;
    }

    private int readByte() { if (hasNextByte()) return buf[ptr++]; else return -1;}

    private boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}

    private void skip() { while(hasNextByte() && !isPrintableChar(buf[ptr])) ptr++;}

    public boolean hasNext() {skip(); return hasNextByte();}

    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        boolean minus = false;
        long num = readByte();

        if(num == '-'){
            num = 0;
            minus = true;
        }else if (num < '0' || '9' < num){
            throw new NumberFormatException();
        }else{
            num -= '0';
        }

        while(true){
            int b = readByte();
            if('0' <= b && b <= '9')
                num = num * 10 + (b - '0');
            else if(b == -1 || !isPrintableChar(b))
                return minus ? -num : num;
            else
                throw new NoSuchElementException();
        }
    }

    public int nextInt() {
        long num = nextLong();
        if (num < Integer.MIN_VALUE || Integer.MAX_VALUE < num)
            throw new NumberFormatException();
        return (int)num;
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }

    public char nextChar() {
        if (!hasNext()) throw new NoSuchElementException();
        return (char)readByte();
    }

    public String nextLine() {
        while (hasNextByte() && (buf[ptr] == '\n' || buf[ptr] == '\r')) ptr++;
        if (!hasNextByte()) throw new NoSuchElementException();

        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (b != '\n' && b != '\r') {
            sb.appendCodePoint(b);
            b = readByte();
        }

        return sb.toString();
    }

    public int[] nextIntArray(int n) {
        int[] res = new int[n];
        for (int i=0; i<n; i++) res[i] = nextInt();
        return res;
    }

    public char[] nextCharArray(int n) {
        char[] res = new char[n];
        for (int i=0; i<n; i++) res[i] = nextChar();
        return res;
    }

    public void close() {try{ in.close();}catch(IOException e){ e.printStackTrace();}};
}