<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) {
        return rec("", n);
    }

    vector<string> rec(string str, int n){
        vector<string> ans;
        vector<string> aux;
        int qtd_opened = qtd(str, '(');
        int qtd_closed = qtd(str, ')');

        if(qtd_opened == n && n == qtd_closed)
            ans.push_back(str);

        if(qtd_opened < n){
            aux = rec(str + "(", n);
            for(int i = 0; i < aux.size(); i++) ans.push_back(aux[i]);
        }

        if(qtd_opened > qtd_closed && qtd_closed < n){
            aux = rec(str + ")", n);
            for(int i = 0; i < aux.size(); i++) ans.push_back(aux[i]);
        }

        return ans;
    }

    int qtd(string str, char carac){
        int total = 0;

        for(int i = 0; i < str.size(); i++)
            if(str[i] == carac) total++;

        return total;
    }
};
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