Combination Sum -- LeetCode 39

[Question]
Given a set of candidate numbers (C) and a target number (T), find all unique combinations in C where the candidate numbers sums to T.

The same repeated number may be chosen from C unlimited number of times.

Note:

• All numbers (including target) will be positive integers.
• Elements in a combination (a1, a2, … , ak) must be in non-descending order. (ie, a1 ≤ a2 ≤ … ≤ ak).
• The solution set must not contain duplicate combinations.

For example, given candidate set 2,3,6,7 and target 7,
A solution set is:
[7]
[2, 2, 3] 

[Thoughts]
Since the candidate array has no duplicates, a combination can be picked up by a starting position, a reduced target and a current candidate list. Therefore, the kind of combination problems can be solved by a backtracking function, which tracks the reduced target, start position, candidate sub-list, and usually a bag of current results.

[Solution]
class Solution {
    void co_sum (vector<int>& cand, int target, int start, vector<int>& sub_res, vector<vector<int>>& res){
        if (target==0) res.push_back(sub_res);

        for (int i=start; i<cand.size(); i++ ) {
         
            for (int j=1; cand[i]*j<=target; j++) {
                for (int k=0; k<j; k++) sub_res.push_back(cand[i]);
                co_sum(cand, target-cand[i]*j, i+1, sub_res, res);
                for (int k=0; k<j; k++) sub_res.pop_back();
            }

        }
    }
public:
    vector<vector<int>> combinationSum(vector<int>& cand, int target) {
        sort(cand.begin(), cand.end(), greater<int>());
        vector<vector<int>> res;
        vector<int> sub_res;
        co_sum(cand, target, 0, sub_res, res);
        return res;
    }
};