39. Combination Sum

Question

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.

Solution 1: Backtrack (Recursive)

class Solution:
    def dfs(self, currentCandidates, sumTarget, currentCombin, ans):
        if sumTarget < 0:
            return
        elif sumTarget == 0:
            ans.append(currentCombin)
            return
        
        for i in range(len(currentCandidates)):
            restCandidates = currentCandidates[i:]
            nextSumTarget = sumTarget - currentCandidates[i]
            newCombin = currentCombin + [currentCandidates[i]]
            self.dfs(restCandidates, nextSumTarget, newCombin, ans)
        
    def combinationSum(self, candidates: List[int], target: int) -> List[List[int]]:
        ans = []
        currentCombin = []
        candidates.sort() # Just to improve the avg case time complexity (Optional)
        self.dfs(candidates, target, currentCombin, ans)
        return ans

Time Complexity: O(2^N)
Space Complexity: O(1)

Solution 2: Backtrack (Iterative)

Time Complexity: O()
Space Complexity: O()

Reference

https://leetcode.com/problems/combination-sum/discuss/1777569/FULL-EXPLANATION-WITH-STATE-SPACE-TREE-oror-Recursion-and-Backtracking-oror-Well-Explained-oror-C%2B%2B
https://leetcode.com/problems/combination-sum/discuss/1777334/C%2B%2BorDetailed-Explanation-w-TREE-DIAGRAMor-RECURSION-%2B-BACKTRACKINGor-EACH-STEP-EXPLAINED
https://www.cnblogs.com/grandyang/p/4419259.html

底下有時間複雜度 & 精進方式的討論
https://leetcode.com/problems/combination-sum/discuss/16510/Python-dfs-solution.