# Combination Sum IV

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?

```
public class Solution {
public int combinationSum4(int[] nums, int target) {
if (nums == null || nums.length == 0) {
return 0;
}
int[] result = new int[target + 1];
result[0] = 1;
for (int i = 1; i <= target; i++) {
for (int num : nums) {
if (i >= num) {
result[i] += result[i - num];
}
}
}
return result[target];
}
}
```

Hope this helps,

Michael