# LeetCode — Combination Sum (Blind Curated 21)

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?

Solution:

Time complexity:** O(N²)**

Space complexity: **O(N)**