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

Flowcharts, draw a flowchart which prints all the even numbers between 1-50...

draw a flowchart which prints all the even numbers between 1-50

Determine the stereo vision, Determine the stereo vision There is still...

Determine the stereo vision There is still one more major item missing, before we can look at a computer display or plot and perceive it just as we see a real object, namely th

C++, #What is the pointer

#What is the pointer

Inorder and preorder traversal to reconstruct a binary tree, Q. Using the f...

Q. Using the following given inorder and preorder traversal reconstruct a binary tree Inorder sequence is D, G, B, H, E, A, F, I, C

Binary search tree, write an algorithm to delete an element x from binary...

write an algorithm to delete an element x from binary search with time complex

Advantages of first in first out method, Advantages of First in First out (...

Advantages of First in First out (FIFO) Costing Advantages claimed for first in first  out (FIFO)  costing method are: 1. Materials used are drawn from the cost record in

Explain the term group support system, (a) Explain the term Group Support S...

(a) Explain the term Group Support System and elaborate on how it can improve groupwork. (b) Briefly explain three advantages of simulation. (c) Explain with the help of a

How do you rotate a binary tree, How do you rotate a Binary Tree?  Rot...

How do you rotate a Binary Tree?  Rotations in the tree: If after inserting a node in a Binary search tree, the balancing factor (height of left subtree - height of right

Algorithm, Ask question #MWhich of the following is not a characteristic of...

Ask question #MWhich of the following is not a characteristic of good algorithm? inimum 100 words accepted#

Frequency count, what is frequency count with examble? examble?

what is frequency count with examble? examble?

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