1. Description

Given n items with size Ai and value Vi, and a backpack with size m. What's the maximum value can you put into the backpack?

Notice

You cannot divide item into small pieces
the total size of items you choose should smaller or equal to m.

2. Example

Given 4 items with size [2, 3, 5, 7] and value [1, 5, 2, 4], and a backpack with size 10.
The maximum value is 9.

3. Code

public class LintCode0125 {
    public int backPackII(int m, int[] A, int[] V) {
        if (m < 0 || A == null || A.length == 0 ||
            V == null || V.length == 0 || A.length != V.length) {
            return 0;
        }

        int[][] dp = new int[A.length + 1][m + 1];

        for (int i = 0; i < A.length; i++) {
            for (int j = 0; j <= m; j++) {
                dp[i + 1][j] = dp[i][j];
                if (j >= A[i]) {
                    dp[i + 1][j] = Math.max(dp[i][j], dp[i][j - A[i]] + V[i]);
                }
            }
        }

        return dp[A.length][m];
    }

    public static void main(String[] args) {
        LintCode0125 lintcode = new LintCode0125();
        int[] A = new int[] { 2, 3, 5, 7 };
        int[] V = new int[] { 1, 5, 2, 4 };
        System.out.println(lintcode.backPackII(10, A, V));
    }
}