Combination Sum III

Problem

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

/**
 * @param {number} k
 * @param {number} n
 * @return {number[][]}
 */
var combinationSum3 = function(k, n) {
    const res = [];
    backtrack(res, [], 1, 9, k, n);
    return res;
};

var backtrack = function(res, path, start, end, size, remain) {
    if (remain < 0) {
        return;
    } else if (size === path.length) {
        if (remain === 0) {
            res.push([...path]);
        }
        return;
    } else {
        for (let i = start; i <= end; i++) {
            path.push(i);
            backtrack(res, path, i + 1, end, size, remain - i);
            path.pop();
        }
    }
};

We will implement a backtracking (DFS) solution. The logic is the same as Combination Sum combined with Combinations, except we must take into consideration that all valid combinations must be size n.

Problem​

Solution​

Problem

Solution