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

ALGORITHM AND TRACING, WRITE AN ALGORITHM TO CONVERT PARENTHIZED INFIX TO P...

WRITE AN ALGORITHM TO CONVERT PARENTHIZED INFIX TO POSTFIX FORM ALSO TRACE ALG ON ((A+B)*C-(D-E)$F+G)

Flowchart, conversion of centrigral to frahenhit

conversion of centrigral to frahenhit

Determine the precondition of a binary search, Determine the precondition o...

Determine the precondition of a binary search For instance, precondition of a binary search is that array searched is sorted however checking this precondition is so expensive

What is bubble sort, What is bubble sort? Bubble Sort: The basic ide...

What is bubble sort? Bubble Sort: The basic idea in bubble sort is to scan the array to be sorted sequentially various times. Every pass puts the largest element in its corr

Define container in terms of object-oriented terms, Define container in te...

Define container in terms of  object-oriented terms A Container is a broad category whose instances are all more specific things; there is never anything which is just a Contai

Using array to execute the queue structure, Q. Using array to execute the q...

Q. Using array to execute the queue structure, write down an algorithm/program to (i) Insert an element in the queue. (ii) Delete an element from the queue.

Luminous Jewels - The Polishing Game, Byteland county is very famous for lu...

Byteland county is very famous for luminous jewels. Luminous jewels are used in making beautiful necklaces. A necklace consists of various luminous jewels of particular colour. Nec

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

Trees, Have you ever thought about the handling of our files in operating s...

Have you ever thought about the handling of our files in operating system? Why do we contain a hierarchical file system? How do files saved & deleted under hierarchical directories

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