Backpack VI

Given an integer array nums with all positive numbers and no duplicates, find the number of possible combinations that add up to a positive integer target

Example

Given nums = [1, 2, 4], target = 4

The possible combination ways are:
[1, 1, 1, 1]
[1, 1, 2]
[1, 2, 1]
[2, 1, 1]
[2, 2]
[4]

return 6

一开始用backtracking 发现总是超时，后来网上找到的DP解法 简单有效。。类似于找钱（coin change）的问题

public class Solution {
    /**
     * @param nums an integer array and all positive numbers, no duplicates
     * @param target an integer
     * @return an integer
     */
    public int backPackVI(int[] nums, int target) {
        // Write your code here
        int[] count = new int[target+1];
        count[0] = 1;
        
        for(int i=1;i<=target;i++){
            for(int j=0;j<nums.length;j++){
                if(i-nums[j]>=0){
                    count[i]+=count[i-nums[j]];
                }
            }
        }
        return count[target];
    }
}