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

解題思路：

首先明白平衡二叉樹的定義，注意要是每個結(jié)點必須滿足。因為是將一個有序數(shù)組轉(zhuǎn)化為一個平衡二叉樹，因此，答案可能不唯一。

遞歸，將中間元素作為根節(jié)點，然后將數(shù)組分為左右兩部分。左邊數(shù)組用于遞歸創(chuàng)建左子樹，右邊數(shù)組用于遞歸創(chuàng)建右子樹，直到數(shù)組為空。

Python實現(xiàn)：

# 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, num):
        if not num:   # 如果數(shù)組為空
            return None
        mid = len(num) // 2
        root = TreeNode(num[mid])
        root.left = self.sortedArrayToBST(num[:mid])     # 遞歸構(gòu)建左子樹
        root.right = self.sortedArrayToBST(num[mid+1:])  # 遞歸構(gòu)建右子樹
        return root