<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:
    void generateStrings(int pos, string curr, int balance, vector<string>& ret) { 
        if (pos == 0) { 
            if (balance == 0) ret.push_back(curr);
            return;
        }

        generateStrings(pos-1, curr + "(", balance + 1, ret);
        if (balance > 0) generateStrings(pos-1, curr + ")", balance - 1, ret);
    }

    vector<string> generateParenthesis(int n) {
        vector<string> ret;
        generateStrings(2*n, "", 0, ret);
        return ret;
    }
};
20298