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Last Updated: Dec 24, 2023

# Difference between Binary Tree and Binary Search Tree

Shreya Deep
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## Introduction

Binary trees and binary search trees are fundamental hierarchical data structures used in computer science. Unlike linear structures, they allow data to be organized hierarchically, making them valuable in scenarios where data relationships exist.

Binary trees can have up to two child nodes per parent, providing flexibility in structuring data. Binary search trees, a specialized form, arrange nodes so that values to the left are smaller and those to the right are larger, facilitating efficient searching and sorting.

Also see, Types of Binary Trees

Let’s understand the differences between them.

## What is a Binary tree?

Binary Tree is a Data Structure having a root node and at most two children nodes. Each of these children forms the left subtree and the right subtree. The end nodes or the leaf nodes have no children and the left and right children of a leaf node are pointed by a NULL pointer.

You can think of using binary trees in a database, like organizing your files into folders. Each folder (node) represents a record, and this setup makes it easy to find specific records quickly, even if you have a lot of data. It's like having a well-organized filing system for your information.

For example,

In the above example, each node has either 0,1 or 2 children. Therefore, this tree is a binary tree.

Also see, Binary Search in Different Languages

### Basic terminologies used in a Binary tree are:

• Node: A fundamental unit of a binary tree containing data and references to its left and right children

• Root: The topmost node, serving as the tree's starting point

• Parent Node: A node that has child nodes connected to it

• Child Node: Nodes linked below a parent node

• Leaf Node: A node with no children

• Depth: The level or distance of a node from the root

• Height: The maximum depth of the tree, i.e., the longest path from root to leaf
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## What is a Binary Search Tree?

binary search tree  is a type of tree data structure where for every node, all the nodes to the left of this node have a value lesser than the current node’s value. All the nodes to the right of this node have a value greater than the current node’s value, along with the fact that both the left subtree and the right subtree are Binary Search Trees. Both the left and the right subtrees are also BSTs.

For example,

Above is an example of the binary search tree. You can observe that each node has less than or equal to two children. And theleft child’s value is always lesser than the node’s value, and the right child’s value is always greater than the node’s value.

### Characteristics of Binary Search Tree

A binary search tree (BST) is a node-based binary tree data structure which has the following properties:

• Each node contains a data element and two pointers, left and right, which point to its left and right child nodes, respectively

• The left subtree of a node contains only nodes with keys lesser than the node's key

• The right subtree of a node contains only nodes with keys greater than the node's key

• The left and right subtree each must also be a binary search tree

## Binary Tree vs Binary Search Tree

The following table highlights Differences between Binary tree and Binary search tree

### What are the advantages of binary search tree over binary tree?

A binary search tree (BST) offers the advantage of efficient searching, insertion, and deletion operations due to its organized structure. It maintains elements in sorted order, enabling faster retrieval and updates compared to a standard binary tree.

### Which searching technique is best?

The best searching technique depends on the specific context and requirements. Binary search is optimal for sorted data, offering O(log n) time complexity. For unsorted data or dynamic datasets, hashing or linear search may be more suitable, depending on the use case.

### Why is binary search faster?

Binary search is faster because it systematically eliminates half of the remaining elements at each step. This logarithmic time complexity (O(log n)) reduces the number of comparisons significantly in large datasets, making it faster than linear search (O(n)) for sorted data.

## Conclusion

In this article, we’ve discussed the differences between binary trees and binary search trees in detail and then we have discussed each of the one in details like Basic terminologies and characteristics. Finally some of the FAQs has been discussed.

Recommended problems of binary tree:

Recommended problems of binary search tree:

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