What is the Difference Between Binary Tree and Binary Search Tree?

The main difference between a binary tree and a binary search tree lies in the organization and properties of their nodes. Here are the key differences between the two:

1. Definition: A binary tree is a non-linear data structure in which each node can have at most two children, usually referred to as the left and right child. A binary search tree, on the other hand, is a binary tree that follows a specific order, where the value of the left node must be smaller than the parent node, and the value of the right node must be greater than the parent node.
2. Structure: Binary trees do not have a specific order in terms of how the nodes are arranged. In contrast, binary search trees have a structured organization of nodes, where the left subtree of a node contains only nodes with keys lesser than the node's key, and the right subtree of a node contains only nodes with keys greater than the node's key.
3. Data Representation: Data representation in binary trees is carried out in a hierarchical format. In binary search trees, data representation is carried out in an ordered format.
4. Duplicate Values: Binary trees allow duplicate values. However, binary search trees do not allow duplicate values.
5. Speed: The speed of deletion, insertion, and searching operations in binary trees is generally slower compared to binary search trees because they are unordered.

In summary, a binary tree is a general data structure with no specific ordering of nodes, while a binary search tree is a specialized version of a binary tree that follows an ordered structure based on the values of the nodes. This ordered structure in binary search trees allows for faster search, insertion, and deletion operations compared to binary trees.

Comparative Table: Binary Tree vs Binary Search Tree

Here is a table comparing the differences between a Binary Tree and a Binary Search Tree:

In summary, Binary Trees are non-linear data structures with nodes having at most two children, while Binary Search Trees are a specific type of Binary Tree with a structured organization of nodes based on their keys. Binary Search Trees are used for fast and efficient binary search, insertion, and deletion operations due to their ordered layout.