<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) {
        
        vector<vector<string>>dp(n+1);

        dp[0] = {""};

        for(int i=1; i<=n; i++)
        {
            for(int j=0; j<i; j++)
            {
                vector<string>left = dp[j];
                vector<string>right = dp[i-j-1];

                for(int k=0; k<left.size(); k++)
                {
                    for(int l=0; l<right.size(); l++)
                    {
                        dp[i].push_back( "(" + left[k] + ")" + right[l]);
                    }
                }


            }
        }

        return dp[n];
    }
};
9666