# 377. Combination Sum IV
## Problem Statement
\
Given an array of **distinct** integers `nums` and a target integer `target`, return *the number of possible combinations that add up to* `target`.
The test cases are generated so that the answer can fit in a **32-bit** integer.
**Example 1:**
Input: nums = [1,2,3], target = 4
Output: 7
Explanation:
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.
**Example 2:**
Input: nums = [9], target = 3
Output: 0
**Constraints:**
* `1 <= nums.length <= 200`
* `1 <= nums[i] <= 1000`
* All the elements of `nums` are **unique**.
* `1 <= target <= 1000`
**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?
## Intuition
```
Approach:
Start a for loop from start and go till the end, picking each element
Hence no need for tracking index
```
### Links
### Video Links
### Approach 1:
```
```
{% code title="C++" lineNumbers="true" %}
```cpp
class Solution {
public:
vector dp; // Use long long instead of int
long long find_comb(vector& nums, int target) {
if (target == 0)
return 1;
if (target < 0)
return 0;
if (dp[target] != -1)
return dp[target];
long long ans = 0; // Use long long
for (int i = 0; i < nums.size(); i++)
ans += find_comb(nums, target - nums[i]);
return dp[target] = ans;
}
int combinationSum4(vector& nums, int target) {
dp = vector(target + 1, -1); // Adjust the size of the dp array
return static_cast(find_comb(nums, target)); // Convert the result to int
}
};
```
{% endcode %}
### Approach 2:
```
```
{% code title="C++" lineNumbers="true" %}
```cpp
```
{% endcode %}
### Approach 3:
```
```
{% code title="C++" lineNumbers="true" %}
```cpp
```
{% endcode %}
### Approach 4:
```
```
{% code title="C++" lineNumbers="true" %}
```cpp
```
{% endcode %}
### Similar Problems
###
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