What's the difference 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 is a binary tree with ordered, or sorted, elements.

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 the binary tree has a parent node and zero, one, or two children nodes. The nodes with no children are called leaf nodes. The binary tree does not have any specific order to how the elements or nodes are arranged.

On the other hand, a binary search tree (BST) is a more specialised version of a binary tree. It still follows the rule that each parent node can have at most two children. However, it adds an additional rule for the arrangement of nodes. In a binary search tree, for every single node, all the elements in its left subtree are less than the node, and all the elements in its right subtree are greater than the node. This property makes binary search trees an important tool in searching algorithms, as it allows for efficient search, insert and delete operations.

In summary, while both binary trees and binary search trees are tree-based data structures and have a similar hierarchical structure, the key difference lies in the arrangement of nodes. Binary trees do not have any rules regarding the order of nodes, while binary search trees do. This order in binary search trees is what makes them particularly useful in certain algorithms and operations, especially those involving search or sort operations. Understanding these differences is crucial in selecting the appropriate data structure for your specific needs in computer science.