<p>Given <code>n</code> pairs of parentheses, write a function to <em>generate all combinations of well-formed parentheses</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> n = 3
<strong>Output:</strong> ["((()))","(()())","(())()","()(())","()()()"]
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> n = 1
<strong>Output:</strong> ["()"]
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 8</code></li>
</ul>

class Solution {
public:
    vector<string> generateParenthesis(int n) {
        return dfs(n,0,0,"");
    }
    vector<string> dfs(int n, int open, int close, string str)
    {
        if (n == open && n == close)
            return {str};
        
        vector<string> result;
        if (open < n)
        {
            auto temp = dfs(n, open+1, close, str+"(");
            for (auto x : temp)
                result.push_back(x);
        }
        if (close < open)
        {
            auto temp = dfs(n, open, close+1, str+")");
            for (auto x : temp)
                result.push_back(x);
        }
        return result;
    }
};
30018