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

Design and test a reference array, Instructions Design and test a r...

Instructions Design and test a reference array. Reference array stores the references to user supplied objects of different types. Just think it as a heterogeneous array wh

Minimum cost spanning trees, A spanning tree of any graph is only a subgrap...

A spanning tree of any graph is only a subgraph that keeps all the vertices and is a tree (having no cycle). A graph might have many spanning trees. Figure: A Graph

Algorithm and flow chart, algorithm and flow chart to find weather the give...

algorithm and flow chart to find weather the given numbers are positive or negative or neutral

Train reorganising, A freight train from Melbourne is approaching Sydney, c...

A freight train from Melbourne is approaching Sydney, carrying n cars of cargos. The cargos are to be delivered to n different cities in the metropolitan area of Sydney - one car f

B-TREE and AVL tree diffrance, Explain process of B-TREE and what differen...

Explain process of B-TREE and what difference between AVL Tree Using Algorithms

Functions and modelling the data flows, Read the scenario (Pickerings Prope...

Read the scenario (Pickerings Properties). (a) List the functions of the system, as perceived by an external user. (b) List the external entities. Note that because we are mo

Determine about the logic gates, Determine about the logic gates Many e...

Determine about the logic gates Many electronic circuits operate using binary logic gates. Logic gates essentially process signals that represent true or false or equivalent i.

Dataset for dmi, The following DNA sequences are extracted from promoter re...

The following DNA sequences are extracted from promoter region of genes which are co-regulated by the same transcription factor (TF). The nucleotide segments capitalized in the giv

Draw trace table and determine output of number, Draw trace table and deter...

Draw trace table and determine output from the following flowchart using following data: Number = 45, -2, 20.5

Algorithm for dfs, Step 1: Choose a vertex in the graph and make it the sou...

Step 1: Choose a vertex in the graph and make it the source vertex & mark it visited. Step 2: Determine a vertex which is adjacent to the source vertex and begun a new search if

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