Leetcode•Apr 19, 2026

Combination Sum III

Hazrat Ali

Leetcode

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.

Solution
var combinationSum3 = function(k, n) {
    let result = [];

    function backtrack(start, path, remaining) {
        if (path.length === k && remaining === 0) {
            result.push([...path]);
            return;
        }

        if (path.length > k || remaining < 0) return;

        for (let i = start; i <= 9; i++) {
            path.push(i);
            backtrack(i + 1, path, remaining - i);
            path.pop();
        }
    }

    backtrack(1, [], n);
    return result;
};



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