### LeetCode Challenge #216. Combination Sum III

Find all valid combinations of `k` numbers that sum up to `n` such that the following conditions are true:

• Only numbers `1` through `9` are used.
• Each number is used at most once.

Return a list of all possible valid combinations. The list must not contain the same combination twice, and the combinations may be returned in any order.

Example 1:

```Input: k = 3, n = 7
Output: [[1,2,4]]
Explanation:
1 + 2 + 4 = 7
There are no other valid combinations.```

Example 2:

```Input: k = 3, n = 9
Output: [[1,2,6],[1,3,5],[2,3,4]]
Explanation:
1 + 2 + 6 = 9
1 + 3 + 5 = 9
2 + 3 + 4 = 9
There are no other valid combinations.
```

Example 3:

```Input: k = 4, n = 1
Output: []
Explanation: There are no valid combinations.
Using 4 different numbers in the range [1,9], the smallest sum we can get is 1+2+3+4 = 10 and since 10 > 1, there are no valid combination.
```

Constraints:

• `2 <= k <= 9`
• `1 <= n <= 60`
##### Video Solution
###### C++ Solution
```				```
class Solution {
public:
vector<vector<int>> ans;
void solve(int k, int target, vector<int> &x, int start)
{
if(k==0 and target==0)
{
ans.push_back(x);
return;
}
if(k==0 || target==0) return;

for(int i=start; i<=9; i++)
{
if(i<=target)
{
x.push_back(i);
solve(k-1,target-i,x,i+1);
x.pop_back();
}
}
}
vector<vector<int>> combinationSum3(int k, int n) {
vector<int> x;
solve(k,n,x,1);
return ans;
}
};
```
```