## Saturday, July 22, 2017

### [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]

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:    }
``````