<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<string> ans;
    dfs(n, n, "", ans);
    return ans;
  }

 private:
  void dfs(int l, int r, string&& path, vector<string>& ans) {
    if (l == 0 && r == 0) {
      ans.push_back(path);
      return;
    }

    if (l > 0) {
      path.push_back('(');
      dfs(l - 1, r, std::move(path), ans);
      path.pop_back();
    }
    if (l < r) {
      path.push_back(')');
      dfs(l, r - 1, std::move(path), ans);
      path.pop_back();
    }
  }
};
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