EDUCBA

EDUCBA

MENUMENU
  • Free Tutorials
  • Free Courses
  • Certification Courses
  • 360+ Courses All in One Bundle
  • Login
Home Data Science Data Science Tutorials Data Structures Tutorial AVL Tree Deletion
Secondary Sidebar
Data Structures Tutorial
  • Basics
    • Linked List Advantages
    • What is Data Structure
    • Heap Data Structure
    • Types of Trees in Data Structure
    • AVL Tree in Data Structure
    • B Tree in Data Structure
    • B+ Tree in Data Structure
    • DFS Algorithm
    • BFS Algorithm
    • Arrays in Data Structure
    • Graph in Data Structure
    • Graph Representation
    • Breadth First Search
    • Depth Limited Search
    • Hashing in Data Structure
    • Searching in Data Structure
    • Linear Search in Data Structure
    • Linked List in Data Structure
    • Doubly linked list in Data Structure
    • Circular Linked List in Data Structure
    • Pointers in Data Structure
    • Types of Graph in Data Structure
    • Bubble Sort in Data Structure
    • Quick Sort in Data Structure
    • Bitonic Sort
    • Merge Sort in Data Structure
    • Selection Sort in Data Structure
    • Insertion Sort in Data Structure
    • Radix Sort in Data Structure
    • Stack in Data Structure
    • Queue in Data Structure
    • Priority Queue in Data Structure
    • Asymptotic Analysis
    • Tree Traversal in Data Structure
    • Tree Traversal Techniques
    • Trie Data Structure
    • Splay Tree in Data Structure
    • Spanning Tree Algorithm
    • Sparse Matrix in Data Structure
    • Radix Sort Algorithm
    • Counting Sort Algorithm
    • Skip List Data Structure
    • Linked List Algorithm
    • Linked List Types
    • Inorder Traversal of Binary Tree
    • Kruskals Algorithm
    • Prims Algorithm
    • BFS VS DFS
    • BCNF
    • Skip List
    • Hash Table?in Data Structure
    • Data Structure Interview Questions
    • Data Structures & Algorithms Interview
    • AVL Tree Deletion
    • B+ Tree Deletion
    • Decision Tree Advantages and Disadvantages
    • Data Architect Skills
    • Data Architecture Principles
    • Data Engineer Jobs
    • Data Engineer Roadmap
    • Fundamentals of Data Structure
    • Circular queue in Data Structure
    • Spanning Tree in Data Structure
    • Tree traversal types
    • Deque in Data structure
    • Shell Sort in Data Structure
    • Heap sort in data structure
    • Heap data structure C++
    • Heap data structure in Java
    • Binary Search Tree Types
    • Binary Tree in Data Structure
    • Binary Tree Types
    • Binary search tree in data structure
    • Binary Search Tree Advantages
    • Binary Search Tree Properties
    • Binary Search in Data Structure
    • Binary Tree Deletion
    • Sparse Matrix Multiplication
    • Preorder Traversal of Binary Tree
    • Postorder traversal
    • Decision Tree Hyperparameters
    • PostOrder Traversal without Recursion
    • AVL Tree Rotation
    • Avro File Format
    • Decision Tree Types
    • Binomial heap
    • Confluence Jira Integration
    • Timm Sort
    • Depth First Search

Related Courses

All in One Data Science Course

Oracle DBA Course

SQL Certification Course

AVL Tree Deletion

AVL Tree Deletion

Definition of AVL Tree

AVL tree is also known as self-balancing binary search tree (BST) because each node in this tree has extra information about the node or the position of the node known as the balance factor. The balance factor contains -1, 0 or +1.

AVL Tree

Start Your Free Data Science Course

Hadoop, Data Science, Statistics & others

Deletion Operation in AVL Tree

When we delete an element in the AVL tree, this disturbs the balance factor of the whole tree for which the tree needs to be balanced again. To rebalance it, rotations are performed on it namely Left Rotation and Right rotation.

Left Rotation

1. Let’s assume the below AVL tree for left rotation.

AVL Tree 1

2. If N2 has a left subtree, then assign N1 as the parent of the left subtree of N2.

AVL Tree delection 2

• If N1 doesn’t have a parent, make N2 the parent of N1, which is the root of the tree.
• If N1 is the left child of any parent, then make N2 the left child of that parent.
• If the above two conditions don’t work, then make N2 the right child of the parent.

AVL Tree delection 3

This is the final balanced tree when we perform Left rotation on it. Right rotation is also done similarly to the AVL tree.

output 1
Algorithm to delete an element in AVL tree

A node should always be deleted as a leaf node. When a node is deleted the balance factors of the tree get disturbed and there is a need to rebalance the tree to get the correct balance factors.

1. Find the node to be deleted using a recursion algorithm.
2. There are three conditions to delete a node
• If the node which is to be deleted is a leaf node, then that node is removed directly.
• If the node contains one child then swap them and then delete the leaf node which contains the key element.
• If the node contains two children, then find the inorder successor of that node which is to be deleted, that is, the value which is less than the key will be at the right subtree.
1. Substitute the node which is to be deleted with the before node.
2. Remove the substituted leaf node.
3. Balance the tree using any suitable rotation techniques.

Source Code

# AVL tree implementation in Python
import sys
# Create a tree node
class TreeNode(object):
def __init__(self, key):
self.key = key
self.left = None
self.right = None
self.height = 1
class AVLTree(object):
# Function to insert a node
def insert_node(self, root, key):
# Find the correct location and insert the node
if not root:
return TreeNode(key)
elif key < root.key:
root.left = self.insert_node(root.left, key)
else:
root.right = self.insert_node(root.right, key)
root.height = 1 + max(self.getHeight(root.left),
self.getHeight(root.right))
# Update the balance factor and balance the tree
balanceFactor = self.getBalance(root)
if balanceFactor > 1:
if key < root.left.key:
return self.rightRotate(root)
else:
root.left = self.leftRotate(root.left)
return self.rightRotate(root)
if balanceFactor < -1:
if key > root.right.key:
return self.leftRotate(root)
else:
root.right = self.rightRotate(root.right)
return self.leftRotate(root)
return root
# Function to delete a node
def delete_node(self, root, key):
# Find the node to be deleted and remove it
if not root:
return root
elif key < root.key:
root.left = self.delete_node(root.left, key)
elif key > root.key:
root.right = self.delete_node(root.right, key)
else:
if root.left is None:
temp = root.right
root = None
return temp
elif root.right is None:
temp = root.left
root = None
return temp
temp = self.getMinValueNode(root.right)
root.key = temp.key
root.right = self.delete_node(root.right,
temp.key)
if root is None:
return root
# Update the balance factor of nodes
root.height = 1 + max(self.getHeight(root.left),
self.getHeight(root.right))
balanceFactor = self.getBalance(root)
# Balance the tree
if balanceFactor > 1:
if self.getBalance(root.left) >= 0:
return self.rightRotate(root)
else:
root.left = self.leftRotate(root.left)
return self.rightRotate(root)
if balanceFactor < -1:
if self.getBalance(root.right) <= 0:
return self.leftRotate(root)
else:
root.right = self.rightRotate(root.right)
return self.leftRotate(root)
return root
# Function to perform left rotation
def leftRotate(self, z):
y = z.right
T2 = y.left
y.left = z
z.right = T2
z.height = 1 + max(self.getHeight(z.left),
self.getHeight(z.right))
y.height = 1 + max(self.getHeight(y.left),
self.getHeight(y.right))
return y
# Function to perform right rotation
def rightRotate(self, z):
y = z.left
T3 = y.right
y.right = z
z.left = T3
z.height = 1 + max(self.getHeight(z.left),
self.getHeight(z.right))
y.height = 1 + max(self.getHeight(y.left),
self.getHeight(y.right))
return y
# Get the height of the node
def getHeight(self, root):
if not root:
return 0
return root.height
# Get balance factore of the node
def getBalance(self, root):
if not root:
return 0
return self.getHeight(root.left) - self.getHeight(root.right)
def getMinValueNode(self, root):
if root is None or root.left is None:
return root
return self.getMinValueNode(root.left)
def preOrder(self, root):
if not root:
return
print("{0} ".format(root.key), end="")
self.preOrder(root.left)
self.preOrder(root.right)
# Print the tree
def printHelper(self, currPtr, indent, last):
if currPtr != None:
sys.stdout.write(indent)
if last:
sys.stdout.write("R----")
indent += " "
else:
sys.stdout.write("L----")
indent += "| "
print(currPtr.key)
self.printHelper(currPtr.left, indent, False)
self.printHelper(currPtr.right, indent, True)
myTree = AVLTree()
root = None
nums = [33, 13, 52, 9, 21, 61, 8, 11] for num in nums:
root = myTree.insert_node(root, num)
myTree.printHelper(root, "", True)
key = 13
root = myTree.delete_node(root, key)
print("After Deletion: ")
myTree.printHelper(root, "", True)

Output:

output

Time Complexity of Deletion in AVL tree

The time complexity of the AVL tree will be the same as Binary Search Tree. Getting the balance factor by performing various rotating operations and updating the height of the balance tree takes constant time. So, the time complexity will be similar to the time complexity of the Binary search tree which is O(h), where h is the height of the tree. Since the height of the AVL tree is log, the time complexity of Deleting an element in the AVL tree will be O(logn).

Conclusion

  • AVL tree is also known as self-balancing binary search tree(BST) because each node in this tree has extra information about the node or the position of the node known as the balance factor.
  • We delete an element only in the leaf node in an AVL tree, if the key is not present in the leaf node we perform in order operations to bring it to the leaf node, then we delete the element.
  • When we delete an element in the AVL tree, this disturbs the balance factor of the whole tree for which the tree needs to be balanced again.
  • The time complexity of the Deletion operation of an AVL tree is O(logn)

Recommended Articles

This is a guide to AVL Tree Deletion. Here we discuss the definition, Deletion Operation in AVL Tree, Algorithm to delete an element in the AVL tree. You may also have a look at the following articles to learn more –

  1. Binary Tree JavaScript
  2. Spanning Tree Algorithm
  3. Tree Traversal Python
  4. Binary Tree in Data Structure
Popular Course in this category
Data Scientist Training (85 Courses, 67+ Projects)
  85 Online Courses |  67 Hands-on Projects |  660+ Hours |  Verifiable Certificate of Completion
4.8
Price

View Course

Related Courses

All in One Data Science Bundle(360+ Courses, 50+ projects)
Python TutorialMachine LearningAWSArtificial Intelligence
TableauR ProgrammingPowerBIDeep Learning
Price
View Courses
360+ Online Courses | 50+ projects | 1500+ Hours | Verifiable Certificates | Lifetime Access
4.7 (86,060 ratings)
All in One Data Science Bundle (360+ Courses, 50+ projects)4.9
Oracle DBA Database Management System Training (2 Courses)4.8
SQL Training Program (7 Courses, 8+ Projects)4.7
0 Shares
Share
Tweet
Share
Primary Sidebar
Footer
About Us
  • Blog
  • Who is EDUCBA?
  • Sign Up
  • Live Classes
  • Corporate Training
  • Certificate from Top Institutions
  • Contact Us
  • Verifiable Certificate
  • Reviews
  • Terms and Conditions
  • Privacy Policy
  •  
Apps
  • iPhone & iPad
  • Android
Resources
  • Free Courses
  • Database Management
  • Machine Learning
  • All Tutorials
Certification Courses
  • All Courses
  • Data Science Course - All in One Bundle
  • Machine Learning Course
  • Hadoop Certification Training
  • Cloud Computing Training Course
  • R Programming Course
  • AWS Training Course
  • SAS Training Course

ISO 10004:2018 & ISO 9001:2015 Certified

© 2022 - EDUCBA. ALL RIGHTS RESERVED. THE CERTIFICATION NAMES ARE THE TRADEMARKS OF THEIR RESPECTIVE OWNERS.

EDUCBA
Free Data Science Course

SPSS, Data visualization with Python, Matplotlib Library, Seaborn Package

*Please provide your correct email id. Login details for this Free course will be emailed to you

By signing up, you agree to our Terms of Use and Privacy Policy.

EDUCBA Login

Forgot Password?

By signing up, you agree to our Terms of Use and Privacy Policy.

EDUCBA
Free Data Science Course

Hadoop, Data Science, Statistics & others

*Please provide your correct email id. Login details for this Free course will be emailed to you

By signing up, you agree to our Terms of Use and Privacy Policy.

EDUCBA

*Please provide your correct email id. Login details for this Free course will be emailed to you

By signing up, you agree to our Terms of Use and Privacy Policy.

Let’s Get Started

By signing up, you agree to our Terms of Use and Privacy Policy.

This website or its third-party tools use cookies, which are necessary to its functioning and required to achieve the purposes illustrated in the cookie policy. By closing this banner, scrolling this page, clicking a link or continuing to browse otherwise, you agree to our Privacy Policy

Loading . . .
Quiz
Question:

Answer:

Quiz Result
Total QuestionsCorrect AnswersWrong AnswersPercentage

Explore 1000+ varieties of Mock tests View more