Linked Implementation of Binary Search Tree 68-89

7.1 Introduction

This section introduces the concept of Binary Search Trees (BST) and their linked implementation. BSTs are a fundamental data structure in computer science, used for efficient searching, insertion, and deletion operations. The section explains that a BST is a type of binary tree where each node contains a key, and the keys in the left subtree are less than the node's key, while the keys in the right subtree are greater. The linked implementation refers to representing each node as an object or structure with pointers to its left and right children, rather than using arrays. The section emphasizes the advantages of linked representations, such as dynamic memory allocation and ease of insertion/deletion. It also sets the stage for the subsequent sections, which will detail the structure, operations, and algorithms associated with BSTs.

• Binary Search Tree (BST) is a special type of binary tree.
• Each node in BST has a key, left child, and right child.
• Linked implementation uses pointers for dynamic memory management.
• BST enables efficient searching, insertion, and deletion.
• Keys in left subtree < node's key; keys in right subtree > node's key.
• BST is widely used in applications like databases and file systems.
• 📌 Binary Search Tree: A binary tree with ordered keys.
• 📌 Linked Implementation: Representation using pointers to child nodes.

7.2 Structure of Binary Search Tree

This section details the structure of a Binary Search Tree using linked representation. Each node is defined as a structure (or class) containing three fields: the key (data), a pointer to the left child, and a pointer to the right child. The section explains how nodes are dynamically created and linked together to form the tree. It also describes the hierarchical nature of BSTs, where each node can have at most two children. The section provides the standard structure definition in C/C++ style, and discusses how the root node is the entry point to the tree. The concept of null pointers is introduced, indicating the absence of a child node. The section also emphasizes the recursive nature of BSTs, as each subtree is itself a BST.

• Each BST node has a key, left pointer, and right pointer.
• Nodes are dynamically allocated in memory.
• Root node is the starting point of the BST.
• Null pointers indicate missing children.
• BST structure supports efficient recursive operations.
• Subtrees of a BST are themselves BSTs.
• 📌 Node: Basic unit of BST containing key and pointers.
• 📌 Null Pointer: Indicates absence of child node.