Backpack IV

Description

Given an integer array nums[] which contains n unique positive numbers, num[i] indicate the size of ith item. An integer target denotes the size of backpack. Find the number of ways to fill the backpack.

Each item may be chosen unlimited number of times

Example

Example1

Input: nums = [2,3,6,7] and target = 7
Output: 2
Explanation:
Solution sets are: 
[7]
[2, 2, 3]

Example2

Input: nums = [2,3,4,5] and target = 7
Output: 3
Explanation:
Solution sets are: 
[2, 5]
[3, 4]
[2, 2, 3]
思路：f[i][j]表示只考虑前i件物品，取到物品重量和为j的方法数量，这题和完全背包做法类似

public class Solution {
    /**
     * @param nums: an integer array and all positive numbers, no duplicates
     * @param target: An integer
     * @return: An integer
     */
   public int backPackIV(int[] nums, int target) {
        // Write your code here
        int m = target;
        int []A = nums;
        int f[][] = new int[A.length + 1][m + 1];
        
        f[0][0] = 1;
        for (int i = 1; i <= A.length; i++) {
            for (int j = 0; j <= m; j++) {
                int k = 0; 
                while(k * A[i-1] <= j) {
                    f[i][j] += f[i-1][j-A[i-1]*k];
                    k+=1;
                }
            } // for j
        } // for i    
        return f[A.length][target];
    }
}