leetcode/work/1/Medium/Array/39.combination-sum.py

"""
39. Combination Sum
Difficulty: Medium
https://leetcode.com/problems/combination-sum/

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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.

The same number may be chosen from candidates an unlimited number of
times. Two combinations are unique if the frequency of at least one of
the chosen numbers is different.

The test cases are generated such that the number of unique
combinations that sum up to target is less than 150 combinations for
the given input.



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
"""


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