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

Explain Hashing, What do you mean by hashing? Hashing gives the direct ...

What do you mean by hashing? Hashing gives the direct access of record from the file no matter where the record is in the file. This is possible with the help of a hashing func

Unification algorithm, i want to write code for unification algorithm with ...

i want to write code for unification algorithm with for pattern matching between two expression with out representing an expression as alist

Explain linked list, Linked List  A linked list is a linear collection...

Linked List  A linked list is a linear collection of data elements called nodes. The linear order is given by pointer. Every node is divided into 2 or more parts.

If else, design algorithm and flow chart that computes the absolute differe...

design algorithm and flow chart that computes the absolute difference of two values x and y

Compute the shortest paths to all network nodes, (i)  Consider a system usi...

(i)  Consider a system using flooding with hop counter. Suppose that the hop counter is originally set to the "diameter" (number of hops in the longest path without traversing any

Calculate the k-th power and recursive algorithem, 1. The following is a r...

1. The following is a recursive algorithm to calculate the k -th power of 2. Input k a natural number Output kth power of 2 Algorithem: If k =0then return 1 Else return 2* po

Size of stack, The size of stack was declared as ten. Thus, stack cannot ho...

The size of stack was declared as ten. Thus, stack cannot hold more than ten elements. The major operations which can be performed onto a stack are push and pop. However, in a prog

Determine about the push operation, Determine about the push operation ...

Determine about the push operation A Container may or may not be accessible by keys, so it can't make assumptions about element retrieval methods (for example, it cannot have a

Algorithm for insertion into the circular queue, Algorithm for insertion of...

Algorithm for insertion of any element into the circular queue: Step-1: If "rear" of the queue is pointing at the last position then go to step-2 or else Step-3 Step-2: make

Java, Ask consider the file name cars.text each line in the file contains i...

Ask consider the file name cars.text each line in the file contains information about a car ( year,company,manufacture,model name,type) 1-read the file 2-add each car which is repr

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