<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 {
    unordered_map<string, vector<TreeNode*>> memo;
    vector<TreeNode*> generatetree(int min,int max){
        if(min>max){
            return {nullptr};
        }   
        vector<TreeNode*> tree;
        string key = to_string(min) + "_" + to_string(max);

        if (memo.find(key) != memo.end()) {
            return memo[key];
        }
     
        for(int k=min;k<=max;k++){
            vector<TreeNode*> leftTrees= generatetree(min,k-1); 
            vector<TreeNode*> rightTrees = generatetree(k+1,max);
            for(TreeNode* left : leftTrees){
                for(TreeNode* right:rightTrees){
                    TreeNode* root=new TreeNode(k);
                    root->left=left;
                    root->right=right;
                    tree.push_back(root);
                }
            } 
        }
        memo[key]=tree;
        return tree;
    } 
public:
    vector<TreeNode*> generateTrees(int n) {
        return generatetree(1,n);
    }
};
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