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
through9
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)