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

Surrounding of sub division method, Surrounding of sub division method ...

Surrounding of sub division method A polygon surrounds a viewport if it completely encloses or covers the viewport. This happens if none of its sides cuts any edge of the viewp

Illustrate the visual realism applications, Illustrate the Visual realism a...

Illustrate the Visual realism applications a)   Robot Simulations : Visualization of movement of their links and joints  and end effector movement etc. b)  CNC programs ver

Example of telephone directory, A telephone directory having n = 10 records...

A telephone directory having n = 10 records and Name field as key. Let us assume that the names are stored in array 'm' i.e. m(0) to m(9) and the search has to be made for name "X"

State an algorithm which inputs 3 - digit code for 280 items, A small shop ...

A small shop sells 280 different items. Every item is identified by a 3 - digit code. All items which start with a zero (0) are cards, all items which start with a one (1) are swee

Explain the rgb model, RGB Model The RGB model is based on the assumpti...

RGB Model The RGB model is based on the assumption that any desired shade of colour can be obtained by mixing the correct amounts of red, green, and blue light. The exact hues

#title.state charts., explain two strategies to implement state charts with...

explain two strategies to implement state charts with the help of an example of each.

Types of tree ?, Binary: Each node has one, zero, or two children. This ...

Binary: Each node has one, zero, or two children. This assertion creates many tree operations efficient and simple. Binary Search : A binary tree where each and every left

Quick sort method, Q. Explain quick sort? Sort the given array using quick ...

Q. Explain quick sort? Sort the given array using quick sort method. 24 56 47 35 10 90 82 31

What is diffuse illumination, Diffuse Illumination Diffuse illuminatio...

Diffuse Illumination Diffuse illumination means light that comes from all directions not from one particular source. Think about the light of a grey cloudy day as compared to

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