Differentiate between a binary tree and a binary search tree.

A binary tree is a tree data structure where each node has at most two children, while a binary search tree (BST) is a binary tree with additional properties.

A binary tree is a type of data structure that has a maximum of two children for each parent node. These two children are typically referred to as the left child and the right child. The topmost node in the tree is known as the root. Each node in a binary tree has a data element, and two pointers to other nodes. The pointers point to the left child and the right child, if they exist. If a child does not exist, the pointer is null. Binary trees are used in many areas of computer science, including parsing expressions in programming languages, network routing algorithms, and in machine learning algorithms.

On the other hand, a binary search tree is a more specialised version of a binary tree. It still has the property that each node can have at most two children. However, it adds an additional constraint: for each node, all elements in the left subtree must be less than the node, and all elements in the right subtree must be greater than the node. This property makes binary search trees an efficient data structure for many search and sorting operations. In a balanced binary search tree, operations such as insertion, deletion, and search can be performed in logarithmic time.

In summary, while both binary trees and binary search trees are tree data structures with nodes that have at most two children, binary search trees have an additional property that dictates a specific order to how the nodes are arranged. This order property of binary search trees allows for efficient searching and sorting of data, making them a useful data structure in many areas of computer science.