L125 Backpack II

Givenn_items with size Aiand 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 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 size10. The maximum value is9.

Challenge

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

每个只能取一次。所以取上一行dp[i - 1]的

例子：

size	val		0	1	2	3	4	5	6	7	8	9	10
		0	0	0	0	0	0	0	0	0	0	0	0
2	1	1	0	0	1	1	1	1	1	1	1	1	1
3	5	2	0	0	1	5	5	6	6	6	6	6	6
5	2	3	0	0	1	5	5	6	6	6	7	7	8
7	4	4	0	0	1	5	5	6	6	6	7	7	9

public int backPackII(int m, int[] A, int V[]) {
    if (m < 0 || A.length == 0 || V.length == 0) {
        return -1;
    }

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

    for (int i = 1; i <= A.length; i++) {
        for (int j = 1; j <= m; j++) {
            dp[i][j] = dp[i - 1][j];
            if ((j >= A[i - 1])) {
                dp[i][j] = Math.max(dp[i][j], V[i - 1] + dp[i - 1][j - A[i - 1]]);//因为物品有限，从dp[i-1]取
            }
        }
    }

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