Avl trees, Data Structure & Algorithms

Assignment Help:

An AVL tree is a binary search tree that has the given properties:

  • The sub-tree of each of the node differs in height through at most one.
  • Each sub tree will be an AVL tree.

Figure illustrated an AVL tree.

2083_AVL TREES.jpg

Figure: Balance requirement for AVL tree: the left & right sub tree differ by at most one in height

AVL stands for the names of G.M. Adelson - Velskii & E.M. Landis, two Russian mathematicians, who came up along with this method of keeping the tree balanced.

An AVL tree is a binary search tree that has the balance property and additionally to its key, each of the node stores an additional piece of information: the current balance of its subtree. The three possibilities are following:

  • Left - HIGH (balance factor -1)

The left child contain a height which is greater than the right child by 1.

  • BALANCED (balance factor 0)

 Both of children have the same height

  • RIGHT - HIGH (balance factor +1)

The right child contains a height that is greater by 1.

An AVL tree that remains balanced guarantees O(log n) search time, even into the worst case. Here, n refer to the number of nodes. The AVL data structure gain this property by placing limitation on the difference in heights among the sub- trees of given node and rebalancing the tree even if it violates these limitation.


Related Discussions:- Avl trees

Queue, 1. Show the effect of each of the following operations on queue q. A...

1. Show the effect of each of the following operations on queue q. Assume that y (type Character) contains the character ‘&’. What are the final values of x and success (type boole

Explain the linked list implementation of stack, Question 1 Explain the fo...

Question 1 Explain the following? Arrays Stack Trees Question 2 Explain the Linked list implementation of stack Question 3 What is a binary tree? Expla

Delete a given specific node from a doubly linked list. , D elete a specif...

D elete a specific Node from Double Linked List as follows DELETEDBL(INFO, FORW, BACK, START, AVAIL,LOC) 1. [Delete Node] Set FORW [ BACK [LOC]]:= FORW[LOC]& BACK [FORW[

Define rule-based expert system, 1. Define the following terms in a rule-ba...

1. Define the following terms in a rule-based expert system? a) Knowledge base b) Inference engine 2. What is a fuzzy rule? Explain the difference between classical and fuzzy

Interest rate, explain the determination of interest rate in the classical ...

explain the determination of interest rate in the classical system.

What is a linear array, What is a linear array? An array is a way to re...

What is a linear array? An array is a way to reference a series of memory locations using the similar name. Every memory location is shown by an array element. An  array elemen

Define ordinary variable, Ordinary variable An ordinary variable of a e...

Ordinary variable An ordinary variable of a easy data type can store a one element only

Complexity of an algorithm, Q. Explain the complexity of an algorithm?  Wha...

Q. Explain the complexity of an algorithm?  What are the worst case analysis and best case analysis explain with an example.

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd