[LeetCode] Combination Sum

Well, a typical backtracking problem. Make sure you are clear with the following three problems:

1. What is a partial solution and when is it finished? --- In this problem, the partial solution is a combination and it is finished once it sums to target.
2. How to find all the partial solutions? --- In the following code, I use a for-loop to traverse all the possible elements in candidates.
3. When to make recursive calls? --- In the following code, once an element is added to the partial solution, we call the function to generate the remaining elements recursively.

Of course, remember to recover to the previous status once a partial solution is done. In the following code, line 18 (comb.pop_back()) is for this purpose.

The following should be self-explanatory :)

 1 class Solution {
 2 public:
 3     vector<vector<int>> combinationSum(vector<int>& candidates, int target) {
 4         sort(candidates.begin(), candidates.end());
 5         vector<vector<int> > res;
 6         vector<int> comb;
 7         combination(candidates, 0, target, comb, res);
 8         return res;
 9     }
10 private:
11     void combination(vector<int>& candidates, int start, int remain, vector<int>& comb, vector<vector<int> >& res) {
12         if (!remain) {
13             res.push_back(comb);
14             return;
15         }
16         for (int i = start; i < (int)candidates.size(); i++) {
17             if (remain >= candidates[i]) {
18                 comb.push_back(candidates[i]);
19                 combination(candidates, i, remain - candidates[i], comb, res);
20                 comb.pop_back();
21             }
22         }
23     }
24 };