Backpack II

题目

125. Backpack II
     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?

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?

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

答案

import java.util.*;
  public class Solution {
    /**
     * @param m: An integer m denotes the size of a backpack
     * @param A: Given n items with size A[i]
     * @param V: Given n items with value V[i]
     * @return: The maximum value
     */
    public int backPackII(int m, int[] A, int[] V) {
        int n = A.length;
        int[][] f = new int[n + 1][m + 1];
        f[0][0] = 1;
        for(int i = 0; i <= m; i++) f[0][i] = 0;
        for(int i = 1; i <= n; i++) Arrays.fill(f[i], -1);
        
        for(int i = 1; i <= n; i++) {
            for(int j = 0; j <= m; j++) {
                int t = -1;
                if(j >= A[i - 1])
                    t = f[i - 1][j - A[i - 1]] + V[i - 1];
                f[i][j] = Math.max(f[i - 1][j], t);        
            }
        }
        return f[n][m];
    }
}