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## Problem

Given an integer n, generate all structurally unique BST’s (binary search trees) that store values 1 … n.

Example:

Input: 3
Output:
[
[1,null,3,2],
[3,2,null,1],
[3,1,null,null,2],
[2,1,3],
[1,null,2,null,3]
]
Explanation:
The above output corresponds to the 5 unique BST's shown below:

1         3     3      2      1
\       /     /      / \      \
3     2     1      1   3      2
/     /       \                 \
2     1         2                 3


## Code

/**
* Definition for a binary tree node.
* public class TreeNode {
*     int val;
*     TreeNode left;
*     TreeNode right;
*     TreeNode(int x) { val = x; }
* }
*/
class Solution {
public List<TreeNode> generateTrees(int n) {
if(n == 0) return new ArrayList<>();
return helper(1, n);
}

private List<TreeNode> helper(int start, int end){
List<TreeNode> list = new ArrayList<>();

if(start > end){
return list;
}

for(int i = start; i <= end; i++){
List<TreeNode> leftNodes = helper(start, i - 1);
List<TreeNode> rightNodes = helper(i + 1, end);

for(TreeNode left : leftNodes){
for(TreeNode right : rightNodes){
TreeNode root = new TreeNode(i);
root.left = left;
root.right = right;