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216. Combination Sum III

Array Backtracking

Problem - Combination Sum III

Medium

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

Solutions

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class Solution:
    def combinationSum3(self, k: int, n: int) -> List[List[int]]:
        result, temp = [], []

        def dfs(i: int, j: int):
            if j == 0:
                if len(temp) == k:
                    result.append(temp[:])
                return

            if i > 9 or i > j or len(temp) > k:
                return

            temp.append(i)
            dfs(i + 1, j - i)
            temp.pop()
            dfs(i + 1, j)

        dfs(1, n)
        return result

Submission Stats:

  • Runtime: 0 ms (100.00%)
  • Memory: 17.9 MB (16.23%)