<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> result;
        stack<tuple<string, int, int>> parenStack;

        parenStack.push(make_tuple("", 0, 0));

        while(!parenStack.empty()){
            auto currTuple = parenStack.top();
            string str = get<0>(currTuple);
            int open = get<1>(currTuple);
            int close = get<2>(currTuple);

            parenStack.pop();
            if(str.length() == 2*n){
                result.push_back(str);
                continue;
            }
            if(open < n){
                parenStack.push(make_tuple(str + "(", open + 1, close));
            }
            if(close < open){
                parenStack.push(make_tuple(str + ")", open, close + 1));
            }
        }
        return result;
    }
};
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