# 216. Combination Sum III

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

Approach 1: DFS.

# Code (Python)

Approach 1:

# Code (C++)

Approach 1:

class Solution {
private:
    vector<vector<int>> com;
    void tryCombination(vector<int>& buf, int num, int k, int n) {
        if (k == 0 && n == 0)
        {
            com.push_back(buf);
            return;
        }
        if (num <= 9)
        {
            if (k > 0 && n >= num)
            {
                buf.push_back(num);
                tryCombination(buf, num + 1, k - 1, n - num);
                buf.pop_back();
            }
            tryCombination(buf, num + 1, k, n);
        }
    }
public:
    vector<vector<int>> combinationSum3(int k, int n) {
        vector<int> buf;
        tryCombination(buf, 1, k, n);
        return com;
    }
};