<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) {
        int len = n * 2;
        vector<string> res;
        string path;
        function<void(int, int)> dfs = [&] (int left_c, int right_c) {
            if (left_c + right_c == len) {
                res.push_back(path);
                return ;
            }

            if (left_c < n) {
                path += '(';
                dfs(left_c + 1, right_c);
                path.pop_back();
            }
            if (right_c < left_c) {
                path += ')';
                dfs(left_c, right_c + 1);
                path.pop_back();
            }

            return ;
        };

        dfs(0, 0);
        return res;
    }
};
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