108. Convert Sorted Array to Binary Search Tree

Easy

Problem:

Given an integer array nums where the elements are sorted in ascending order, convert it to a height-balanced binary search tree.

Input: nums = [-10,-3,0,5,9]
Output: [0,-3,9,-10,null,5]
Explanation: [0,-10,5,null,-3,null,9] is also accepted:

https://leetcode.com/problems/convert-sorted-array-to-binary-search-tree/

Solution:

To create a BST, you just need to keep breaking down a sorted array using binary search. Obviously, it won't work if the array isn't sorted. This is because binary search is an algorithm that can find any value in $Olog(n)$ time when used on a sorted array.

# 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
class Solution:
    def sortedArrayToBST(self, nums: List[int]) -> Optional[TreeNode]:
        if not nums:
            return None
        
        mid = len(nums) // 2

        # Divide-and-Conquer
        node = TreeNode(nums[mid])
        node.left = self.sortedArrayToBST(nums[:mid])
        node.right = self.sortedArrayToBST(nums[mid + 1:])

        return node