<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 {
private:

    vector<string> result;

    bool check(string str){
        int n = str.size();
        stack<char> st;
        for(char it : str){
            if(st.empty()){
                if(it == ')') return false;
                else st.push(it);
            }
            else{
                if(it == ')') st.pop();
                else st.push(it);
            }
        }

        if(st.empty()) return true;

        return false;
    }

    void solve(string& str, int n,int open,int close){
        
        if(str.size() == 2*n){
            if(check(str)) result.push_back(str);
            return;
        }

        if(open<n){
            str.push_back('(');
            solve(str,n,open+1,close);
            str.pop_back();   
        }

        if(close<open){
            str.push_back(')');
            solve(str,n,open,close+1);
            str.pop_back();    
        }


    }
public:
    vector<string> generateParenthesis(int n) {
        string str = "";
        solve(str,n,0,0);


        return result;

    }


};
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