<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> ans;
        stack<tuple<string, int, int>> stk;
        stk.push(make_tuple("", 0, 0));
        while (!stk.empty()) {
            tuple<string, int, int> curr = stk.top();
            string s = get<0>(curr);
            int leftCount = get<1>(curr);
            int rightCount = get<2>(curr);
            stk.pop();
            if (rightCount > leftCount || leftCount > n || rightCount > n) {
                continue;
            }
            if (leftCount == n && rightCount == n) {
                ans.emplace_back(s);
            } else {
                stk.push(make_tuple(s+"(", leftCount + 1, rightCount));
                stk.push(make_tuple(s+")", leftCount, rightCount + 1));
            }
        }
        return ans;
    }
};

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