216-combination-sum-iii

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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(Python)

class Solution:
    def combinationSum3(self, k: int, n: int) -> List[List[int]]:
        return self.backtrack(k, n)

    def backtrack(self, k: int, n: int) -> List[List[int]]:
        res = []

        def recur(candidate, i, sum_so_far):
            if sum_so_far == n and len(candidate) == k:
                res.append(candidate[:])

            for j in range(i, 10):
                if len(candidate) > k:
                    continue

                if sum_so_far + j > n:
                    continue

                candidate.append(j)
                sum_so_far += j
                recur(candidate, j + 1, sum_so_far)
                sum_so_far -= j
                candidate.pop()

        recur([], 1, 0)
        return res