# Difference between Binary Tree and Binary Search Tree

Binary Tree Data Structure

A tree whose elements have at most 2 children is called a binary tree. Since each element in a binary tree can have only 2 children, we typically name them the left and right children.

Binary Search Tree Data Structure

A binary Search Tree is a node-based binary tree data structure that has the following properties:

• The left subtree of a node contains only nodes with keys lesser than the nodeâ€™s key.
• The right subtree of a node contains only nodes with keys greater than the nodeâ€™s key.
• The left and right subtree each must also be a binary search tree.
• There must be no duplicate nodes.

Difference between Binary Tree and Binary Search Tree:

S. No. Basis of Comparison BINARY TREE BINARY SEARCH TREE
1. Definition BINARY TREE is a nonlinear data structure where each node can have at most two child nodes.  BINARY SEARCH TREE is a node based binary tree that further has right and left subtree that too are binary search tree.
2. Types
• Full binary tree
• Complete binary tree
• Extended Binary tree and more
• AVL tree
• Splay Tree
• T-trees and more
3. Structure In BINARY TREE there is no ordering in terms of how the nodes are arranged In BINARY SEARCH TREE the left subtree has elements less than the nodes element and the right subtree has elements greater than the nodes element.
4. Data Representation Data Representation is carried out in a hierarchical format. Data Representation is carried out in the ordered format.
5. Duplicate Values Binary trees allow duplicate values. Binary Search Tree does not allow duplicate values.
6. Speed The speed of deletion, insertion, and searching operations in Binary Tree is slower as compared to Binary Search Tree because it is unordered.  Because the Binary Search Tree has ordered properties, it conducts element deletion, insertion, and searching faster.
7. Complexity Time complexity is usually O(n). Time complexity is usually O(logn).
8. Application It is used for retrieval of fast and quick information and data lookup. It works well at element deletion, insertion, and searching.
9. Usage It serves as the foundation for implementing Full Binary Tree, BSTs, Perfect Binary Tree, and others.  It is utilized in the implementation of Balanced Binary Search Trees such as AVL Trees, Red Black Trees, and so on.

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