Unbounded Knapsack

1. You are given a number n, representing the count of items.

2. You are given n numbers, representing the values of n items.

3. You are given n numbers, representing the weights of n items.

3. You are given a number "cap", which is the capacity of a bag you've.

4. You are required to calculate and print the maximum value that can be created in the bag without 

    overflowing it's capacity.

Note: Each item can be taken any number of times. You are allowed to put the same item again 

                  and again.

Input Format

A number n

v1 v2 .. n number of elements

w1 w2 .. n number of elements

A number cap

Output Format

A number representing the maximum value that can be created in the bag without overflowing it's capacity

Constraints

1 <= n <= 20

0 <= v1, v2, .. n elements <= 50

0 < w1, w2, .. n elements <= 10

0 < cap <= 10

Sample Input

5

15 14 10 45 30

2 5 1 3 4

7

Sample Output

100

Solution:

import java.io.*;

import java.util.*;

public class Main {

    public static void main(String[] args) throws Exception {

            Scanner sc = new Scanner(System.in);

            int n = sc.nextInt();

            int val[] = new int[n],wt[] = new int[n];

            for(int i=0;i<n;i++)

                val[i] = sc.nextInt();

            for(int i=0;i<n;i++)

                wt[i] = sc.nextInt();

            int cap = sc.nextInt();

            

            int[] dp = new int[cap+1];

            dp[0] = 0;

            

            for(int i=1;i<=cap;i++){

                int cost = 0;

                for(int j=0;j<n;j++){

                    if(wt[j]<=i){

                        cost = Math.max(cost, val[j]+dp[i-wt[j]]);

                    }

                }

                dp[i] = cost;

            }

            

            System.out.println(dp[cap]);

    }

}