# Combination Sum III

## Description

Find all possible combinations of **k** numbers that add up to a number **n**, given that only numbers from 1 to 9 can be used and each combination should be a unique set of numbers.

**Note:**

* All numbers will be positive integers.
* The solution set must not contain duplicate combinations.

**Example 1:**

```
Input: k = 3, n = 7
Output: [[1,2,4]]
```

**Example 2:**

```
Input: k = 3, n = 9
Output: [[1,2,6], [1,3,5], [2,3,4]]
```

## Solution

```cpp
class Solution {
public:
    vector<vector<int>> combinationSum3(int k, int n) {
        vector<vector<int>> ans;
        if(k > 10 || n > 45 || (1 + k) * k / 2 > n) return ans;
        vector<int> nums;
        dfs(1, k, n, nums, ans);
        return ans;
    }
    
    void dfs(int min_num, int k, int n, vector<int> &nums, vector<vector<int>> &ans){
        if(k == 0){
            if(n == 0) ans.push_back(nums);
            return;
        }
        for(int i = min_num; i <= min(9, n); ++i){
            nums.push_back(i);
            dfs(i + 1, k - 1, n - i, nums, ans);
            nums.pop_back();
        }
    }
};
```
