<p>Given an integer <code>n</code>, return <em>all the structurally unique <strong>BST&#39;</strong>s (binary search trees), which has exactly </em><code>n</code><em> nodes of unique values from</em> <code>1</code> <em>to</em> <code>n</code>. Return the answer in <strong>any order</strong>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/18/uniquebstn3.jpg" style="width: 600px; height: 148px;" />
<pre>
<strong>Input:</strong> n = 3
<strong>Output:</strong> [[1,null,2,null,3],[1,null,3,2],[2,1,3],[3,1,null,null,2],[3,2,null,1]]
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> [[1]]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 8</code></li>
</ul>

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    vector<TreeNode*> allPossibleBST(int start, int end, map<pair<int, int>, vector<TreeNode*>>& memo) 
    {
        vector<TreeNode*> res;
        if (start > end) {
            res.push_back(nullptr);
            return res;
        }
        if (memo.find(make_pair(start, end)) != memo.end()) {
            return memo[make_pair(start, end)];
        }
        // Iterate through all values from start to end to construct left and
        // right subtrees recursively.
        for (int i = start; i <= end; ++i) {
            vector<TreeNode*> leftSubTrees = allPossibleBST(start, i - 1, memo);
            vector<TreeNode*> rightSubTrees = allPossibleBST(i + 1, end, memo);

            // Loop through all left and right subtrees and connect them to the
            // ith root.
            for (auto left : leftSubTrees) {
                for (auto right : rightSubTrees) {
                    TreeNode* root = new TreeNode(i, left, right);
                    res.push_back(root);
                }
            }
        }
        return memo[make_pair(start, end)] = res;
    }

    vector<TreeNode*> generateTrees(int n) {
        map<pair<int, int>, vector<TreeNode*>> memo;
        return allPossibleBST(1, n, memo);
    }
};
17500