## Description

Given an array where elements are sorted in ascending order, convert it to a height balanced BST.

For this problem, a height-balanced binary tree is defined as a binary tree in which the depth of the two subtrees of every node never differ by more than 1.

Example:

Given the sorted array: [-10,-3,0,5,9],

One possible answer is: [0,-3,9,-10,null,5], which represents the following height balanced BST:

0
/ \
-3   9
/   /
-10  5


## Solutions

这题考验理解 BST 的本质，首先大小关系，再者左右子树深度之差不超过 1。如何让树的高度最小呢？左右子树分到的结点个数尽量小即可。

### 1. DFS-递归

注意，解不是唯一的！

# Time: O(nlogn)
# Space: O(n)
# Definition for a binary tree node.
class TreeNode:
def __init__(self, x):
self.val = x
self.left = None
self.right = None

class Solution:
def sortedArrayToBST(self, nums: List[int]) -> TreeNode:
return self.dfs(nums, 0, len(nums) - 1)

def dfs(self, nums, l, r):
if l > r:
return None
mid = l + ((r - l) >> 1)
root = TreeNode(nums[mid])
root.left = self.dfs(nums, l, mid - 1)
root.right = self.dfs(nums, mid + 1, r)
return root

# 32/32 cases passed (64 ms)
# Your runtime beats 97.52 % of python3 submissions
# Your memory usage beats 100 % of python3 submissions (15.1 MB)


### 2. 迭代方法

参考发现，迭代方法太复杂，使用两个栈。