Combination Sum III — LeetCode 216 Python Solution

The 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.

Example

Input

k = 3, n = 7

Output

[[1,2,4]]

Explanation

1 + 2 + 4 = 7

Python solution

class Solution:
    def combinationSum3(self, k: int, n: int) -> List[List[int]]:
        def dfs(i: int, s: int):
            if s == 0:
                if len(t) == k:
                    ans.append(t[:])
                return
            if i > 9 or i > s or len(t) >= k:
                return
            t.append(i)
            dfs(i + 1, s - i)
            t.pop()
            dfs(i + 1, s)

        ans = []
        t = []
        dfs(1, n)
        return ans

Complexity

Pattern: Backtracking

Build candidates one choice at a time and abandon a branch the moment it cannot work. LeetCode 216. Combination Sum III is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Backtracking.

The backtracking guide has the Python template for the pattern and the 105 LeetCode problems that use it.

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