# Leetcode

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.

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.

It is guaranteed 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 = 7Output: [[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 = 8Output: [[2,2,2,2],[2,3,3],[3,5]]`

Example 3:

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

Example 4:

`Input: candidates = [1], target = 1Output: [[1]]`

Example 5:

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

Constraints:

• `1 <= candidates.length <= 30`
• `1 <= candidates[i] <= 200`
• All elements of `candidates` are distinct.
• `1 <= target <= 500`

Solution(Python3):

`class Solution:    def combinationSum(self, candidates, target):        ret = []        self.dfs(candidates, target, [], ret)        return ret    def dfs(self, nums, target, path, ret):        if target < 0:            return        if target == 0:            ret.append(path)            return        for i in range(len(nums)):            self.dfs(nums[i:], target - nums[i], path+[nums[i]], ret)# TC: O(N^(T/M)+1), where N is the number of candidates, T is the target value, and M is the minimum value among the candidates# SC: O(T/M)`