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];
     }
 }