39. Combination Sum

Given an array of distinct integers candidates and a target integer target, return a list of all unique combinations of candidates where the chosen numbers sum to target. You may return the combinations in any order

Example 1:

• Input: candidates = [2,3,6,7], target = 7
• Output: [[2,2,3],[7]]
• Explanation: 2 and 3 are candidates, and 2 + 2 + 3 = 7. Note that 2 can be used multiple times. 7 is a candidate, and 7 = 7. These are the only two combinations.

Example 2:

• Input: candidates = [2,3,5], target = 8
• Output: [[2,2,2,2],[2,3,3],[3,5]]

Example 3:

• Input: candidates = [2], target = 1
• Output: []

Constraints:

• 1 <= candidates.length <= 30
• 2 <= candidates[i] <= 40
• All elements of candidates are distinct.
• 1 <= target <= 40

Solution

class Solution:
    def combinationSum(self, candidates: list[int], target: int) -> list[list[int]]:
        candidates.sort()
        result, path = [], []

        def backtrack(start, remaining):
            if remaining == 0:
                result.append(path[:])
                return
            for i in range(start, len(candidates)):
                if candidates[i] > remaining:
                    break

                path.append(candidates[i])
                backtrack(i, remaining - candidates[i])
                path.pop()

        backtrack(0, target)
        return result