<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 {
    vector<string> ret;
    int max;
public:
    void dfs(const string s,int cnt){
        //cout << s <<endl;
        if(s.size() > max || cnt<0 ||cnt > max/2 ){
            return; //invaild
        }
        if(s.size() == max && cnt == 0){
            ret.push_back(s);        
            return;                   
        }

        dfs(s+"(",cnt+1);
        dfs(s+")",cnt-1);
    
    }

    vector<string> generateParenthesis(int n) {
    max = 2*n;

    string single("(");

    int cnt=1;
    dfs(single,cnt);

    cout << ret.size() <<endl;


    return ret;
    }
};
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