39. Combination Sum

1. Description

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.

2. Example

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: []

Example 4:
Input: candidates = [1], target = 1
Output: [[1]]

Example 5:
Input: candidates = [1], target = 2
Output: [[1,1]]

3. Constraints

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

4. Solutions

My Accepted Solution

backtracking
In this problem, it will generate duplicate candidates, if we just generate them and remove them, it will be very slow.
So, we need to find out why there are some duplicate candidates. That’s because the order of candicate numbers is not sorted. So, it will have [2,3] and [3,2], if we sort candidates and iterate them in order, which means move to the end continuelly and never go back, it will not have any duplicates.

class Solution {
public:
    vector<vector<int>> combinationSum(const vector<int> &candidates, const int target) {
        vector<int> sorted_candidates(candidates);
        sort(sorted_candidates.begin(), sorted_candidates.end());

        vector<int> combination;
        _search_combination(sorted_candidates, target, 0, combination);

        return _full_combinaions;
    }

private:
    vector<vector<int>> _full_combinaions;

    void _search_combination(
        const vector<int> &candidates,
        const int target,
        const int index,
        vector<int> &combination) {
        if (target == 0) {
            _full_combinaions.emplace_back(combination);
        } else {
            for (int i = index; i < candidates.size(); ++i) {
                if (candidates[i] <= target) {
                    combination.push_back(candidates[i]);
                    _search_combination(candidates, target - candidates[i], i, combination);
                    combination.pop_back();
                } else {
                    break;
                }
            }
        }
    }
};