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

Types of a linked list, A linked list can be of the following types:- ...

A linked list can be of the following types:-  Linear linked list or one way list Doubly linked list or two way list. Circular linked list Header linked list

Steps of pre-order traversal, Pre-order Traversal The method of doing a...

Pre-order Traversal The method of doing a pre-order traversal iteratively then has the several steps(suppose that a stack is available to hold pointers to the appropriate nodes

Array implementation of a multiqueue, Program gives the program segment by ...

Program gives the program segment by using arrays for the insertion of an element to a queue into the multiqueue. Program: Program segment for the insertion of any element to t

Algorithm to merge two sorted arrays with third array, Q. Write down an alg...

Q. Write down an algorithm to merge the two sorted arrays into the third array. Do  not perform the sort function in the third array.                           Ans: void m

Internal sorting, In internal sorting, all of the data to be sorted is obta...

In internal sorting, all of the data to be sorted is obtainable in the high speed main memory of the computer. We will learn the methods of internal sorting which are following:

Adjacency matrix representation of a graph, An adjacency matrix representat...

An adjacency matrix representation of a graph cannot having information of : Parallel edges

Explain memory allocation strategies, Memory Allocation Strategies If i...

Memory Allocation Strategies If it is not desirable to move blocks of due storage from one area of memory to another, it must be possible to relocate memory blocks that have be

Dgsd, Ask question #sdgsdgsdginimum 100 words accepted#

Ask question #sdgsdgsdginimum 100 words accepted#

Encryption the plain-text using the round keys, Encryption the plain-text u...

Encryption the plain-text using the round keys: 1. (Key schedule) Implement an algorithm that will take a 128 bit key and generate the round keys for the AES encryption/decryp

Time required to delete a node x from a doubly linked list, The time needed...

The time needed to delete a node x from a doubly linked list having n nodes is O (1)

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