Binary Search Trees And Its Uses

Binary Search Trees play an essential part in the data structure. It is an efficient structure that performs various operations efficiently. It is essential to computer science and software development due to its efficiency and simplicity. Using binary search trees will help you increase the productivity of the operations you work on, whether you are a developer or a programmer.

Binary search trees are an extension of binary trees. Parent nodes have a maximum of two nodes like binary trees, but they also arrange the smaller element to one side and the larger one to the other, making the structure more effective and precise. In this blog, we will know in detail about binary search trees and their uses.

Table of Contents

What Is A Binary Tree?

Binary Search Trees are a fundamental data structure and a major type of tree used extensively in computer science and programming for various processes like searching, insertion, deletion, etc. It consists of various nodes and edges arranged in a hierarchical structure. It consists of left and right children. They both follow a specific order and are arranged accordingly.

For each node in BST, all elements in the left subtree are less than or equal to its parent or root node. Also, all the elements in the right subtree are greater than their parent nodes. This property ensures that searching can be done easily by binary search, increasing its efficiency and making it an optimal data structure.

For every node in a BST, all elements in its left subtree (if any) are less than or equal to the node’s value, and all elements in its right subtree (if any) are greater than the node’s value. This property ensures that searching for a specific element in the tree can be done efficiently using a binary search algorithm.

However, it’s worth noting that the efficiency of operations in a search tree (BST) relies heavily on how well-balanced the tree is. When a BST is nicely balanced, with each node’s left and right subtrees having heights, we can expect the average case time complexity to hold true. On the other hand, if a BST becomes poorly balanced and resembles more of a linked list structure, the time complexity can deteriorate to O(n), resulting in decreased efficiency.

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Binary Search Tree With Example

All the nodes smaller than the root node are arranged on the left side, and the larger nodes are arranged on the right side of the tree. Let us look at an example and understand the binary search tree with the help of its nodes and edges.

Let us know in detail about the given binary search tree here.

The root node of this binary search tree is 5.
The left node of the root contains node 3, and the right node contains node 8, as it is greater than the root node.
Node 3 has two children, which contains two children.
The left subtree contains 2, which is smaller than the root node 3, and the right subtree contains 4, which is greater than the current root node 3.
Node 8 has one child greater than it; hence, it is arranged at the right-hand side of the root node 8.

Implementation Of Binary Search Trees

Let us check the implementation of binary search trees with the help of a simple example.

Certainly! Let’s create a binary search tree step by step with different values: Let us easily understand this algorithm by taking an example array of 30, 15, 45, 10, 25, and 35.

Step 1: Insert 30

Step 2: Insert 15

Since 15 is smaller than 30, it becomes the left child of 30.

Step 3: Insert 45

Since 45 is greater than 30, it becomes the right child of 30.

Step 4: Insert 10

10 is smaller than 30 and 15, so it becomes the left child of 15.

Step 5: Insert 25

25 is greater than 15 but smaller than 30, so it becomes the right child of 15.

Step 6: Insert 35

Given that 35 is bigger than 30 but smaller than 45, it becomes the left hand of 45.

A recursive or iterative approach can easily implement a binary search tree.

Advantages of Binary Search Tree

Binary search trees offer many advantages, some of which are mentioned here in this article.

1. Efficient Searching: Using the binary search tree, elements can be easily searched in an average time complexity of O(n logn), where n is the number of nodes in the tree. This characteristic makes binary search trees highly efficient for conducting search operations.

2. Efficient Insertion And Deletion: The process of inserting and deleting elements in a search tree while preserving its search properties can also be performed efficiently with an average time complexity of O(log n).

3. Ordered Data Structure: Binary search trees inherently maintain the order of elements, which can benefit applications such as managing sorted lists or implementing algorithms.

Also read: Generative AI vs Machine Learning – Key Differences & Examples

Applications Of Binary Search Tree

Binary search trees are an essential data structure in computer science and have various applications in various domains. Their efficient search, insertion, and deletion operations make them valuable for solving many problems. Here are some common applications of binary search trees:

1. Searching and Retrieval: BST trees are mainly utilized for effective data retrieval and searching operations. The binary search property helps to guarantee that the search operation can be completed in O(log n) time, where n is the number of nodes in the tree.

2. Database Systems: Binary search trees are used in various databases to search and index large, scattered reports. For example, we can store the names using the BST tree structure in the phonebook.

3. Auto-Complete and Spell Check: A binary search tree can implement auto-complete functionality at various places, like search engines. It can quickly suggest completions while typing based on the prefix entered. They are also used in spell-checking algorithms to suggest corrections for incorrectly spelled words.

4. File Systems: Various current version file systems use the binary search algorithm to store files in directories.

5. Priority Queues: They can also be used to implement priority queues. The key of each element represents its priority, and you can efficiently extract the element with the highest (or lowest) priority.

6. Optimization Problems: Binary search trees can be used to solve various optimization problems. For instance, in the field of dynamic programming, BSTs can be used to find the optimal solution for specific problems efficiently.

7. Implement Decision Tree: It can implement decision trees in artificial intelligence and machine learning algorithms. It is used to predict outcomes and decisions of the models. These trees can help in various fields like diagnosis, research, and financial analysis work.

8. Encryption Algorithms: It can help encrypt sensitive information using a key encryption algorithm by generating public and private keys.

9. Compressing Data: It can also help in compressing extensive data and optimizing space. It can help implement various applications like image, file, audio, video, etc.

Major Real-Time Application Of Binary Search Tree

Let us look at some of the real-time applications of binary search trees in data structures.

In searching algorithm.
Huffman coding is implemented with the help of BST.
They are used in implementing dictionaries.
They are used in spelling checking.
BST is used for indexing in DBMS.
They are also used in priority queues.

Also read: Types of Trees in Data Structures

FAQs

Q1. Are the Binary tree and binary search tree the same?

Ans: Binary search trees are extensions of binary trees. It can be called a binary tree with node arrangements. Smaller nodes to the root's left and bigger ones to the right side of the root.

What are the major applications of the binary search tree?

Ans: Some of the major information includes debugging, indexing, databases, searching and retrieval, file systems, encryption, and others. Major applications of binary search trees are given in the article.

Where are the smaller nodes aligned with the root nodes in binary search trees?

Ans: Smaller nodes are aligned to the left of the tree, and bigger elements are arranged to the right. Nodes are compared with the root and then given positions.