<p>Find all valid combinations of <code>k</code> numbers that sum up to <code>n</code> such that the following conditions are true:</p>

<ul>
	<li>Only numbers <code>1</code> through <code>9</code> are used.</li>
	<li>Each number is used <strong>at most once</strong>.</li>
</ul>

<p>Return <em>a list of all possible valid combinations</em>. The list must not contain the same combination twice, and the combinations may be returned in any order.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> k = 3, n = 7
<strong>Output:</strong> [[1,2,4]]
<strong>Explanation:</strong>
1 + 2 + 4 = 7
There are no other valid combinations.</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> k = 3, n = 9
<strong>Output:</strong> [[1,2,6],[1,3,5],[2,3,4]]
<strong>Explanation:</strong>
1 + 2 + 6 = 9
1 + 3 + 5 = 9
2 + 3 + 4 = 9
There are no other valid combinations.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> k = 4, n = 1
<strong>Output:</strong> []
<strong>Explanation:</strong> There are no valid combinations.
Using 4 different numbers in the range [1,9], the smallest sum we can get is 1+2+3+4 = 10 and since 10 &gt; 1, there are no valid combination.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= k &lt;= 9</code></li>
	<li><code>1 &lt;= n &lt;= 60</code></li>
</ul>

class Solution {
private:
    void combination_helper(vector<vector<int>> &res, vector<int> &cur_combination, int k, int target, vector<bool> used_num, int cur_index){
        if(k == 0) {
            //cout << "k == 0" << endl;
            return;
        }

        //vector<int> tmp_combination = cur_combination;
       //vector<bool> tmp_used = used_num;
        for(int i = cur_index; i < 9; i++){
            // un-used
            if(used_num[i] == false){
                if(target == i + 1 && k == 1){
                    vector<int> tmp_combination = cur_combination;
                    tmp_combination.emplace_back(i + 1);
                    res.emplace_back(tmp_combination);
                    return;
                }
                else if(target >= i + 1){
                    vector<int> tmp_combination = cur_combination;
                    vector<bool> tmp_used = used_num;

                    tmp_combination.emplace_back(i + 1);
                    tmp_used[i] = true;

                    combination_helper(res, tmp_combination, k - 1, target - i - 1, tmp_used, i + 1);
                }
                else{
                    return;
                }
            }
            else{
                continue;
            }
        }
    }
public:
    vector<vector<int>> combinationSum3(int k, int target) {
        vector<vector<int>> res;

        vector<bool> used_num(9, false);
        vector<int> cur_combination;
        combination_helper(res, cur_combination, k, target, used_num, 0);

        return res;
    }
};
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