Backpack II

Given n items with size A[i] and value V[i], 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 and the total size of items you choose should smaller or equal to m.

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.

Challenge

O(n x m) memory is acceptable, can you do it in O(m) memory?

Note

和BackPack I基本一致。依然是以背包空间为限制条件，所不同的是dp[j]取的是价值较大值，而非体积较大值。所以只要把dp[j-A[i]]+A[i]换成dp[j-A[i]]+V[i]就可以了。

Solution

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