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# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution(object):
    def generateTrees(self, n):
        """
        :type n: int
        :rtype: List[TreeNode]
        """
        if n == 0:
            return []
        return self.build(1,n)
    
    def build(self, start, end):
        res = []
        if start > end:
            res.append(None)
            return res
        else:
            for rootIndex in range(start,end+1):
                leftList = self.build(start, rootIndex-1)
                rightList = self.build(rootIndex+1, end)
                for eachLeft in leftList:
                    for eachRight in rightList:
                        root = TreeNode(rootIndex)
                        root.left = eachLeft
                        root.right = eachRight
                        res.append(root)
        return res

https://leetcode.com/problems/unique-binary-search-trees-ii/#/description

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

For example,
Given n = 3, your program should return all 5 unique BST's shown below.
```
   1         3     3      2      1
    \       /     /      / \      \
     3     2     1      1   3      2
    /     /       \                 \
   2     1         2                 3
```