AVL Tree in Data Structure
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This document discusses AVL trees, which are height-balanced binary search trees. It defines AVL trees, explains why they are useful by comparing insertion performance to regular binary search trees, and covers balance factors, rotations, and the insertion algorithm. Key points made include that AVL trees have logarithmic time complexity for operations through self-balancing, and maintain an extra balance factor field for each node. Various example questions related to building AVL trees from data are also provided.
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We've provided you with an implementation of an unbalanced binary search tree. The tree implements an ordered dynamic set over a generic comparable type T. Supported operations include insertion, deletion, min, max, and testing whether a value is in the set (via the exists method). Because it's a set, duplicates are not allowed, and the insert operation will not insert a value if it is already present.
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· augment the tree to maintain the height of each of its subtrees, as discussed in Studio;
· compute the balance at the root of a subtree (which is the height of the root's left subtree minus that of its right subtree);
· implement the AVL rebalancing operation, along with the supporting rotation operations; and
· call the height maintenance and rebalancing operations at the appropriate times during insertion and deletion.
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· TreeNode.java implements a class TreeNode that represents a node of a binary search tree. It holds a value (the key of the node) along with child and parent pointers. It has a height data member that is currently not used for anything. You should not modify this file, but you need to understand its contents.
· AVLTree.java implements an ordered set as a binary search tree made out of TreeNode objects.
The AVLTree class provides an interface that includes element insertion and deletion, as well as an exists() method that tests whether a value is present in the set. It also offers min() and max() methods. These methods all work as given for (unbalanced) BSTs, using the algorithms we discussed in lecture.
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---
Slide 1: Title Slide
Title: Advanced Data Structures in C++
Topic: AVL Trees – Self-Balancing Binary Search Tree
Presented by: [Your Name]
Subject: Advanced Data Structures
Institute: [Your Institute Name]
---
Slide 2: Introduction
AVL Tree is a type of self-balancing Binary Search Tree.
Named after inventors Adelson-Velsky and Landis.
Balancing is done using rotation operations to maintain performance.
---
Slide 3: Why AVL Trees?
Standard BSTs can degrade to linear time in worst cases.
AVL Trees ensure O(log n) time for insertion, deletion, and lookup.
Used in memory management and indexing.
---
Slide 4: Node Structure in C++
struct Node {
int key;
Node *left, *right;
int height;
};
---
Slide 5: Get Height & Rotation
int height(Node* n) {
return n ? n->height : 0;
}
Node* rightRotate(Node* y) {
Node* x = y->left;
Node* T2 = x->right;
x->right = y;
y->left = T2;
y->height = max(height(y->left), height(y->right)) + 1;
x->height = max(height(x->left), height(x->right)) + 1;
return x;
}
---
Slide 6: Insertion in AVL Tree
Node* insert(Node* node, int key) {
// Normal BST insert logic...
// Then update height, get balance factor
// Perform rotations if needed
}
---
Slide 7: Output Screenshot
Insert a screenshot showing balanced AVL Tree output.
---
Slide 8: Conclusion
AVL Trees are efficient for dynamic datasets.
They guarantee faster access than unbalanced trees.
C++ makes implementation modular and efficient.
---
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Assignment Two Objectives • Understand how the.docxlynettearnold46882 Assignment Two
Objectives
• Understand how the AVL tree works
• Give you further practice with C and data structures
Admin
Marks 10 marks, excluding bonus marks. Marking is based on the correctness and
efficiency of your code. Your code must be well commented.
Group? This assignment is completed individually.
Due Time 23:59:59 pm on Sunday 31 March 2019. 23:59:59 pm on Wed 3 April 2019
Late Submissions Late submissions will not be accepted!
In this assignment, you will implement AVL tree and a set of functions associated with AVL
tree. For simplicity, we make the following assumptions:
1. Each item of an AVL tree contains an integer key and an integer value.
2. No AVL tree contains duplicate items. Two items (k1, v1) and (k2, v2) are duplicates
iff k1=k2 and v1=v2 hold.
3. An AVL tree may contains multiple items with the same key and the number of
duplicate keys is a constant.
A template file named MyAVLTree.c is provided. MyAVLTree.c contains the type definitions of
AVL tree and AVL tree node as well as some basic functions. You can add your own helper
functions and auxiliary data structures for better performance in terms of time complexity.
You need to implement the following functions:
1. AVLTree *CreateAVLTree(const char *filename). This function creates an AVL tree by
reading all the items from a text file or from the standard input (keyboard)
depending on the argument filename. If filename is “stdin”, this function will read all
the items from the standard input. Otherwise, it will read all the items from a text
file with filename as its full path name. (2 marks)
An input text file contains zero or more items where each item is of the form (key,
value). Any characters such as white space between two adjacent items are ignored.
For example, the following sample file contains 10 items:
(2, 50) (4, 30) (9, 30) (10, 400) (-5, -40)
(7, 20) (19, 200) (20, 50) (-18, -200) (-2, 29)
Similarly, when reading from the standard input, each input line may have zero or
more items, separated by one or more white space characters. An empty line
indicates the end of input.
In case of an error in the input, this function will print the error and your program
terminates.
You may assume that the input does not contain duplicate items and thus this
function does not need to check for duplicate items.
The time complexity of this function cannot be higher than O(n logn), where n is the
size of the resulting AVL tree. If your time complexity is higher, you will get 0 mark
for this function. You may assume that each call to a C built-in function takes O(1)
time.
2. AVLTree *CloneAVLTree(AVLTree *T). This function creates an identical copy (clone)
of the input AVL tree T, and returns a pointer to the clone tree. (1 mark)
The time complexity of this function cannot be higher than O(n), where n is the size
of T. If your time complexity is high.
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AVL Tree in Data Structure
- 1. Data Structure & Files Unit 5: Advance Tree AVL Tree Ms. Vrushali Dhanokar (M.Tech CSE) Assistant Professor IT Department [email protected]
- 2. Why AVL Tree? Example: Keys are: 1, 2, 3, 4, 5, 6, 7. Generate Binary Tree. • Fig 1: AVL Tree • Fig 2. Binary Tree • Insert 8 in BT: 7 comparisons. • Insert 8 in AVL: 3 comparisons. So, AVL Tree: • Height balance trees. • Insertion and deletion have low time complexity.
- 3. What is AVL Tree? • AVL invented by G.M. Adelson-Velsky and E.M. Landis. So, name is AVL. • AVL tree is a height-balanced binary search tree. • AVL tree, balance factor of every node is either -1, 0 or +1. • Every node maintains an extra information known as balance factor. • Balance factor = heightOfLeftSubtree – heightOfRightSubtree. • Every AVL Tree is a binary search tree but every Binary Search Tree need not be AVL tree. • Operation perform Search, Insertion, Deletion with O(log n) time complexity.
- 4. AVL Tree Rotations: Type 1: RR Relationship (Left Rotation): Type 2: LL Relationship (Right Rotation)
- 5. AVL Tree Rotations: Type 3: LR Relationship (First Left Rotation then Right Rotation) Type 4: RL Relationship (First Right Rotation then Left Rotation)
- 6. Insertion Operations In AVL Tree In AVL Tree, a new node is always inserted as a leaf node. Step 1 - Insert the new element into the tree using Binary Search Tree insertion logic. Step 2 - After insertion, check the Balance Factor of every node. Step 3 - If the Balance Factor of every node is 0 or 1 or -1 then go for next operation. Step 4 - If the Balance Factor of any node is other than 0 or 1 or -1 then that tree is said to be imbalanced. In this case, perform suitable Rotation to make it balanced and go for next operation.
- 7. Example of Insertion Operation in AVL Tree Que. Construct AVL Tree by inserting number from 1 to 8.
- 8. Continue..
- 9. Continue..
- 10. Difference Between Red Black Tree & AVL Tree
- 11. Important Questions By SPPU Exam Pattern 1. Define Balance Factor of a node in a Binary Tree. 2M 2. What are the benefits of AVL Tree over BST? 4M 3. Explain Insertion operation in AVL tree with suitable example. 5M 4. Obtain AVL tree of following data element 50,55,60,15,10,40,20,45,30,70,80. 8M 5. Build AVL Tree of Sun, Fri, Mon, Wed, Tue, Thurs, Sat. 8M 6. Build AVL Tree of A,Z,B,Y,C,X,D,U. 8M 7. Build AVL Tree of MAR,MAY,NOV,AUG,APR,JAN,DEC,JUL. 8M (Use lexicographic order i.e April ……. Sept) 8. Difference Between Red Black Tree & AVL Tree. 6M
- 12. Thank You….!