<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;
        search(n, 0, 0, "", ans);
        return ans;
    }
private:
    void search(int n, int open, int close, string s, vector<string>& ans) {
        if (open == close && close == n) {
            ans.push_back(s);
        }
        if (open <= n) {
            search(n, open + 1, close, s + "(", ans);
        }
        if (open > close) {
            search(n, open, close + 1, s + ")", ans);
        }
    }
};
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