動機

這比上一題(40)簡單

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 = 7Output: [[1,2,4]]Explanation:1 + 2 + 4 = 7There are no other valid combinations.

Example 2:

Input: k = 3, n = 9Output: [[1,2,6],[1,3,5],[2,3,4]]Explanation:1 + 2 + 6 = 91 + 3 + 5 = 92 + 3 + 4 = 9There are no other valid combinations.

Example 3:

Input: k = 4, n = 1Output: []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.

Example 4:

Input: k = 3, n = 2Output: []Explanation: There are no valid combinations.

Example 5:

Input: k = 9, n = 45Output: [[1,2,3,4,5,6,7,8,9]]Explanation:1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45There are no other valid combinations.

 

Constraints:

  • 2 <= k <= 9
  • 1 <= n <= 60

Sol

class Solution:
    def combinationSum3(self, k: int, n: int) -> List[List[int]]:
        def bt(nums, acc, cnt, k):
            if k == 0 and cnt == n:
                return [acc]
            elif cnt > n or not nums or k < 0:
                return []
            else:
                return bt(nums[1:], acc+[nums[0]], cnt+nums[0], k-1) + bt(nums[1:], acc, cnt, k)
        return bt(list(range(1,10)), [], 0, k)