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

Construct a minimum spanning tree, Construct G for α, n, and W given as com...

Construct G for α, n, and W given as command line parameters. Throw away edges that have an asymmetric relation between nodes. That is, if A is connected to B, but B is not connect

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

Sorted list using binary search technique, Write an algorithm for searching...

Write an algorithm for searching a key from a sorted list using binary search technique 1.   if (low > high) 2.     return (-1) 3.    mid = (low +high)/2; 4    .if ( X

Advantage of list over arrays, The advantage of list over Arrays is flexibi...

The advantage of list over Arrays is flexibility. Over flood is not a problem until the computer memory is bushed. When the individual record are quite large, it may be difficult t

Circular linked list, In a circular linked list There is no beginning a...

In a circular linked list There is no beginning and no end.

Properties of red- black tree, Any Binary search tree has to contain follow...

Any Binary search tree has to contain following properties to be called as a red- black tree. 1. Each node of a tree must be either red or black. 2. The root node is always b

Binary search trees, In this unit, we discussed Binary Search Trees, AVL tr...

In this unit, we discussed Binary Search Trees, AVL trees and B-trees. The outstanding feature of Binary Search Trees is that all of the elements of the left subtree of the root

Conversion of forest into tree, Conversion of Forest into Tree A binary...

Conversion of Forest into Tree A binary tree may be used to show an entire forest, since the next pointer in the root of a tree can be used to point to the next tree of the for

Graph, Multilist Representation of graph

Multilist Representation of graph

What are the different ways of representing a graph, What are the different...

What are the different ways of representing a graph? The different ways of representing a graph is: Adjacency list representation: This representation of graph having of an

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