Lecture on AVL Tree Implementation Using C

Introduction

• Topic: AVL Tree implementation in C programming language
• Functions Covered:
  • Inserting a new node
  • Deleting a given node
  • Displaying the AVL tree

Key Operations in AVL Trees

• Insert function involves rotations: left rotate and right rotate
• Delete function may also involve rotations
• Display functions for traversals: pre-order, in-order, post-order

Basic Sub-functions

1. Height Function

   • Calculates the height of a node
   • Returns 0 if the node is null
   • Returns the height of the node otherwise

2. Max Function

   • Returns maximum of two integers

3. New Node Function

   • Creates a new node with a given key
   • Initializes left and right children to null, and height to 1
   • Returns the address of the newly created node

4. Get Balance Function

   • Determines the balance factor of a node
   • Returns height of left subtree minus height of right subtree

5. Minimum Value Node Function

   • Finds the node with the minimum key in a subtree

Rotations in AVL Trees

1. Left Rotation

   • Applied when balance factor becomes -2 followed by -1
   • Steps:
     • Identify critical node
     • Perform rotation
     • Update heights

2. Right Rotation

   • Applied when balance factor becomes 2
   • Steps:
     • Identify critical node
     • Perform rotation
     • Update heights

Main Functions

Insert Function

• Traverses the tree to find the correct position for the new node
• Adds the new node
• Updates heights and balance factors
• Applies necessary rotations based on balance factors

Delete Function

• Traverses the tree to find the node to delete
• Handles deletion based on the number of children (0, 1, or 2)
• Updates heights and balance factors
• Applies necessary rotations based on balance factors

Display Functions

• Pre-order Traversal: Root -> Left -> Right
• In-order Traversal: Left -> Root -> Right
• Post-order Traversal: Left -> Right -> Root

Implementation Details

Structure Definition

• Struct Node
  • Members: key, left, right, height

Main Function

• Initializes the root to null
• Provides a menu for user actions: insert, delete, display, exit
• Calls the appropriate function based on user input

Example Execution

• Inserting nodes and displaying the tree structure
• Deleting nodes and checking tree balance

Conclusion

• Program works correctly with insertion, deletion, and display functions
• Further questions can be asked in the comments
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