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216. Combination Sum III

Difficulty Topics

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

combination-sum-iii.py
class Solution:
    def combinationSum3(self, k: int, n: int) -> List[List[int]]:
        res = []

        def go(x, curr):
            if x == 10 or len(curr) == k:
                if len(curr) == k and sum(curr) == n:
                    res.append(curr)
                return

            go(x + 1, curr)
            go(x + 1, curr + [x])

        go(1, [])

        return res