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Combination Sum III⚓︎

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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.

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

Solution⚓︎

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class Solution {
private:
    vector<vector<int>> res;
    vector<int> path;
    void backtracking(int k, int n, int sum, int startIndex) {
        if (sum > n) return;
        if (path.size() == k) {
            if (sum == n) res.push_back(path);
            return;
        }
        for (int i = startIndex; i <= 9 - (k - path.size()) + 1; i++) {
            path.push_back(i);
            backtracking(k, n, sum + i, i + 1);
            path.pop_back();
        }
    }
public:
    vector<vector<int>> combinationSum3(int k, int n) {
        backtracking(k, n, 0, 1);
        return res;
    }
};