<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) {
        // dp[i] will store all valid parentheses combinations of length i
        vector<vector<string>> dp(n + 1); 
        dp[0] = {""}; // Base case: 0 pairs of parentheses

        // Build the result for dp[1] to dp[n]
        for (int i = 1; i <= n; ++i) {
            for (int j = 0; j < i; ++j) {
                for (const string& left : dp[j]) {
                    for (const string& right : dp[i - j - 1]) {
                        dp[i].push_back("(" + left + ")" + right);
                    }
                }
            }
        }

        // Return all combinations for n pairs of parentheses
        return dp[n];
    }
};

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