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.

分析

背包DP

    public int backPackII(int m, int[] A, int[] V) {
        // write your code here
        int x = A.length;

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