How would you define a binary search tree?

A binary search tree (BST) is defined as a binary tree that maintains a specific order among its nodes to facilitate efficient searching, insertion, and deletion operations. In a BST, for any given node, all values in the left subtree are less than the node’s value, and all values in the right subtree are greater than the node’s value. This ordered structure allows for optimal search times, typically O(log n), making it significantly faster for searching through sorted data compared to other data structures where elements may not be organized.

This systematic arrangement is key to the functionality of a binary search tree, enabling it to quickly narrow down the search space and locate values with minimal comparisons. The defined order is fundamental to the operations performed on the tree, such as inserting new nodes or finding the minimum and maximum values within the tree.

While it is true that binary trees can exist without this ordering (which could lead to unbalanced trees), the defining characteristic of a binary search tree is this imposed order on the nodes, which distinctly differentiates it from other tree structures.