Notebook

108. Convert Sorted Array to Binary Search Tree

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

Source

In [1]:

# Definition for a binary tree node.
class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

Code

In [2]:

def sorted_array_to_BST(nums):
    """recursive approach"""
    if not nums:
        return None
    if len(nums) == 1:
        return TreeNode(nums[0])
    if length == 2:
        return TreeNode(nums[1], TreeNode(nums[0]))
    mid = length // 2
    return TreeNode(nums[mid], sorted_array_to_BST(nums[:mid]), sorted_array_to_BST(nums[mid+1:]))

In [3]:

def sorted_array_to_BST(nums):
    """alternative version of above solution"""
    if not nums:
        return None
    if len(nums) == 1:
        return TreeNode(nums[0])
    mid = len(nums)//2
    root = TreeNode(nums[mid])
    root.left = sorted_array_to_BST(nums[:mid])
    root.right = sorted_array_to_BST(nums[mid+1:])
    return root