Convert Sorted List to Binary Search Tree

This challenge asks you to build a Binary Search Tree (BST) from a sorted list of integers. BSTs are fundamental data structures used in many algorithms and applications, and this problem tests your ability to construct one efficiently from a pre-sorted input. Successfully completing this challenge demonstrates understanding of BST properties and recursive tree construction.

Problem Description

You are given a sorted list of integers. Your task is to convert this sorted list into a balanced Binary Search Tree (BST). A balanced BST is one where the left and right subtrees of every node have approximately the same number of nodes. This helps to ensure efficient search, insertion, and deletion operations.

What needs to be achieved:

• Create a BST where each node's value is an element from the input list.
• Maintain the BST property: For every node, all values in its left subtree are less than the node's value, and all values in its right subtree are greater than the node's value.
• Strive for a balanced tree to optimize performance.

Key Requirements:

• The input list will always be sorted in ascending order.
• The output should be a representation of the constructed BST (the specific representation depends on the language you choose - e.g., a root node of the tree).
• The tree should be balanced as much as possible given the sorted input.

Expected Behavior:

The function should take the sorted list as input and return the root node of the constructed BST. If the input list is empty, the function should return null or an equivalent representation of an empty tree.

Edge Cases to Consider:

• Empty input list.
• Input list with a single element.
• Input list with an even number of elements (balancing becomes more critical).
• Large input lists (performance considerations).

Examples

Example 1:

Input: [-10, -3, 0, 5, 9]
Output:  (A BST with root 0, left child -3, right child 9, and further subtrees as appropriate)
Explanation: The middle element (0) becomes the root. The left half [-10, -3] becomes the left subtree, and the right half [5, 9] becomes the right subtree.  This process is recursively applied to the sublists.

Example 2:

Input: [1, 3]
Output: (A BST with root 3, left child 1)
Explanation: The middle element (3) becomes the root. The left half [1] becomes the left subtree. The right half is empty.

Example 3:

Input: []
Output: null
Explanation: An empty list results in an empty tree.

Constraints

• The input list will contain integers.
• The length of the input list can range from 0 to 10000.
• The integers in the list can be positive, negative, or zero.
• The solution should aim for a time complexity of O(n), where n is the length of the input list. A naive approach could result in O(n^2) complexity.

Notes

A common and efficient approach to this problem is to use a recursive strategy. The middle element of the sorted list is a natural choice for the root of the BST. Then, the left half of the list becomes the left subtree, and the right half becomes the right subtree. This recursive division helps to create a balanced tree. Consider how to handle the case where the list has an odd number of elements. The middle element is the root, and the remaining elements are split evenly between the left and right subtrees.