216. Combination Sum III

1. Description

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.

2. Example

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. [1,2,1] is not valid because 1 is used twice.

Example 4:
Input: k = 3, n = 2
Output: []
Explanation: There are no valid combinations.

Example 5:
Input: k = 9, n = 45
Output: [[1,2,3,4,5,6,7,8,9]]
Explanation:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
​​​​​​​There are no other valid combinations.

3. Constraints

• 2 <= k <= 9
• 1 <= n <= 60

4. Solutions

My Accepted Solution

Time complexity: I don’t know 🥺
Space complexity:

class Solution {
public:
    // vector<vector<int>> combinationSum3(int k, int n)
    vector<vector<int>> combinationSum3(int count, int sum) {
        vector<int> subSet;
        combine(count, sum, 1, subSet);

        return combinations;
    }

private:
    vector<vector<int>> combinations;

    void combine(int count, int sum, int fitstValidNum, vector<int>& m_subSet) {
        if (sum < 0) {
            return;
        }

        if (count == 0) {
            if (sum == 0) {
                combinations.emplace_back(m_subSet);
            }

            return;
        }

        for (int i = fitstValidNum; i < 10; ++i) {
            m_subSet.push_back(i);
            combine(count - 1, sum - i, i + 1, m_subSet);
            m_subSet.pop_back();
        }
    }
};