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

State about the bit string, State about the Bit String Carrier set of...

State about the Bit String Carrier set of the Bit String ADT is the set of all finite sequences of bits, including empty strings of bits, which we denote λ. This set is {λ, 0

Binary tree and binarytree parts, Q. What do you understand by the term Bin...

Q. What do you understand by the term Binary Tree? What is the maximum number of nodes which are possible in a Binary Tree of depth d. Explain the terms given below with respect to

Define minimum spanning tree, Define Minimum Spanning Tree A minimum sp...

Define Minimum Spanning Tree A minimum spanning tree of a weighted linked graph is its spanning tree of the smallest weight, where the weight of a tree is explained as the sum

Array and two-dimensional array, Q. Describe the term array.  How do we rep...

Q. Describe the term array.  How do we represent two-dimensional arrays in memory?  Explain how we calculate the address of an element in a two dimensional array.

First class Abstract data type , 3. A function to convert a complex number ...

3. A function to convert a complex number in algebraic form to a complex number in phasor form

Direct file organisation, It offers an effective way to organize data while...

It offers an effective way to organize data while there is a requirement to access individual records directly. To access a record directly (or random access) a relationship is

What is binary search, What is binary search?   Binary search is most ...

What is binary search?   Binary search is most useful when list is sorted. In binary search, element present in middle of the list is determined. If key (the number to search)

Develop a material requirements plan, The below figure illustrates the BOM ...

The below figure illustrates the BOM (Bill of Materials) for product A. The MPS (Material requirements Planning) start row in the master production schedule for product A calls for

Explain memory allocation strategies, Memory Allocation Strategies If i...

Memory Allocation Strategies If it is not desirable to move blocks of due storage from one area of memory to another, it must be possible to relocate memory blocks that have be

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