<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>

bool check(std::string const & s)
{
    auto count{0};
    for(auto const & c : s)
    {
        if(c == '(')
        {
            ++count;
        }
        else
        {
            --count;
            if(count < 0)
                return false;
        }
    }
    return count == 0;
}

void generate(std::string const & s, int n, std::vector<std::string> & solutions)
{    
    if(s.size() == (n * 2))
    {
        if(check(s))
            solutions.push_back(s);
    }
    else
    {
        generate(s + "(", n, solutions);
        generate(s + ")", n, solutions);
    }
}

class Solution {
public:
    std::vector<std::string> generateParenthesis(int n)
    {
        std::vector<std::string> solutions{};
        generate("(", n, solutions);
        return solutions;
    }
};
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