Combination Sum III

Problem Statement

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.

LeetCode link

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

Code

Python Code

class Solution(object):
    def combinationSum3(self, k, n):
        if k<1 or k> 9 or n<1 or n>45:
            return []
        path, res, index = [], [], 1
        self.dfs(k, n, index, path, res)
        return res

    def dfs(self, k, n, index, path, res):
        if n < 0 or len(path)>k:
            return
        if n == 0 and len(path)==k:
            res.append(path)
        for i in range(index, 10):
            self.dfs(k, n-i, i+1, path+[i], res)