<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 {
public:
    void findAllCombinations(vector<vector<int>> &ans, vector<int> &currCombo, vector<int> nums, vector<bool> &visited, int n, int k, int sum){
        //base case
        if(currCombo.size() == k){
            if(sum == n){
                ans.push_back(currCombo);
            }
            return;
        }
        for(auto &num : nums){
            //skip conditions
            if(!currCombo.empty() && num < currCombo.back()){
                continue;
            }
            if(visited[num]){
                continue;
            }
            visited[num] = true; currCombo.push_back(num); sum += num;
            findAllCombinations(ans, currCombo, nums, visited, n, k, sum);
            //backtracking
            visited[currCombo.back()] = false; sum -= currCombo.back(); currCombo.pop_back();
        }
    }
    vector<vector<int>> combinationSum3(int k, int n) {
        vector<vector<int>> ans;
        vector<int> currCombo;
        vector<int> nums = {1, 2, 3, 4, 5, 6, 7, 8, 9};
        vector<bool> visited(10, false);
        findAllCombinations(ans, currCombo, nums, visited, n, k, 0);
        return ans;
    }
};
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