[Leetcode] Combination Sum IV, Solution

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

Example:

nums = [1, 2, 3]
target = 4

The possible combination ways are:
(1, 1, 1, 1)
(1, 1, 2)
(1, 2, 1)
(1, 3)
(2, 1, 1)
(2, 2)
(3, 1)

Note that different sequences are counted as different combinations.

Therefore the output is 7.

Follow up:
What if negative numbers are allowed in the given array?
How does it change the problem?
What limitation we need to add to the question to allow negative numbers?

[Thoughts]
这是一个DP问题。对于任意个一个数值n

DP[n] = ∑ DP[target - nums[i]]       0<= i< n



[Code]

1:    int combinationSum4(vector<int>& nums, int target) {  
2:      vector<int> count(target +1, 0);  
3:        
4:      count[0] =1;  
5:      for(int i =1; i<=target; i++) {  
6:        for(int j =0; j< nums.size(); j++) {  
7:          if(i - nums[j] >=0) {  
8:            count[i] += count[i-nums[j]];  
9:          }  
10:        }  
11:      }  
12:        
13:      return count[target];  
14:    }