What is a binary search tree in C and how is it implemented?

Table of Contents

• Introduction
• Key Properties of Binary Search Trees
• Implementation of a Binary Search Tree in C
  • Node Structure and Basic Operations
• Practical Examples
  • Example 1: Insertion
  • Example 2: Deletion
  • Example 3: Traversal
• Conclusion

Introduction

A Binary Search Tree (BST) is a type of binary tree used to store data in a sorted manner, allowing efficient operations such as search, insertion, and deletion. Each node in a BST contains a value, and the values in the left subtree are less than the node's value, while the values in the right subtree are greater. This property ensures that BST operations can be performed in O(log n) time on average, assuming the tree is balanced.

Key Properties of Binary Search Trees

1. Node Structure: Each node holds a value, and pointers to left and right children.
2. Ordering: Left child nodes contain values less than their parent node, and right child nodes contain values greater.
3. Efficiency: Operations like search, insertion, and deletion are efficient due to the sorted nature of the tree.

Implementation of a Binary Search Tree in C

Node Structure and Basic Operations

Definition of Node and Tree Operations:

Practical Examples

Example 1: Insertion

Inserting a new value involves recursively navigating the tree to find the correct position while maintaining the BST property. The function insertNode performs this task by comparing the new value with the current node's value and placing it accordingly in the left or right subtree.

Example 2: Deletion

Deleting a node in a BST requires handling three scenarios: deleting a node with no children, one child, or two children. The deleteNode function handles these scenarios by finding the appropriate node to replace the deleted node and adjusting the tree structure.

Example 3: Traversal

In-order traversal prints the values of the BST in sorted order. The inOrderTraversal function recursively visits the left subtree, prints the node's value, and then visits the right subtree.

Conclusion

A Binary Search Tree (BST) in C is an essential data structure that maintains a sorted order of elements, facilitating efficient search, insertion, and deletion operations. Implementing a BST involves defining a node structure and providing functions for essential operations such as insertion, deletion, and traversal. Understanding these operations and their implementation helps manage and manipulate data effectively in C.