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

Red black tree, red black tree construction for 4,5,6,7,8,9

red black tree construction for 4,5,6,7,8,9

Illustrate an example of algorithm, Illustrate an example of algorithm ...

Illustrate an example of algorithm Consider that an algorithm is a sequence of steps, not a program. You might use the same algorithm in different programs, or express same alg

Determine about the post conditions assertion, Determine about the Post con...

Determine about the Post conditions assertion A  post condition is an assertion which should be true at completion of an operation. For instance, a post condition of the squ

Algorithms, Write an algorithm to print all even numbers in descending orde...

Write an algorithm to print all even numbers in descending order and draw the flowchart

Explain b- tree, B- Tree  A B-tree of order m is an m-way true in which...

B- Tree  A B-tree of order m is an m-way true in which  1)  All leaves are on the similar level 2)  All internal nodes except the root have at most m-1(non-empty) childre

Define prims algorithm, Define Prim's Algorithm Prim's  algorithm  is  ...

Define Prim's Algorithm Prim's  algorithm  is  a  greedy  algorithm  for  constructing  a  minimum  spanning  tree  of  a  weighted linked graph. It works by attaching to a bef

What is assertions and abstract data types, Assertions and Abstract Data Ty...

Assertions and Abstract Data Types Even though we have defined assertions in terms of programs, notion can be extended to abstract data types (which are mathematical entities).

Preliminaries, Think of a program you have used that is unacceptably slow. ...

Think of a program you have used that is unacceptably slow. Identify the specific operations that make the program slow. Identify other basic operations that the program performs q

State algorithm to insert node p at the end of a linked list, Algo rithm t...

Algo rithm to Insert a Node p at the End of a Linked List is explained below Step1:   [check for space] If new1= NULL output "OVERFLOW" And exit Step2:   [Allocate fr

Pipelining., How branching takes place in Instruction pipeline. Explain wit...

How branching takes place in Instruction pipeline. Explain with suitable examples

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