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

Program of implementation of stack using arrays, include int choice, st...

include int choice, stack[10], top, element; void menu(); void push(); void pop(); void showelements(); void main() { choice=element=1; top=0; menu()

Row major storage, Q. Take an array A[20, 10] of your own. Suppose 4 words ...

Q. Take an array A[20, 10] of your own. Suppose 4 words per memory cell and the base address of array A is 100. Find the address of A[11, 5] supposed row major storage.

Algorithm, implement multiple stacks in a single dimensional array. write a...

implement multiple stacks in a single dimensional array. write algorithm for various stack operation for them

Computational complexity, Generally, Computational complexity of algorithms...

Generally, Computational complexity of algorithms are referred to through space complexity (space needed for running program) and time complexity (time needed for running the progr

Question, A binary search tree is used to locate the number 43. Which of th...

A binary search tree is used to locate the number 43. Which of the following probe sequences are possible and which are not? Explain. (a) 61 52 14 17 40 43 (b) 2 3 50 40 60 43 (c)

Create algorithm for similarities between documents, Here is a diagram show...

Here is a diagram showing similarities between documents; this is an actual set of physics lab assignments from a large university. Each node (square) in the graph is a doc

Programs, Develop a program that accepts the car registration( hint: LEA 43...

Develop a program that accepts the car registration( hint: LEA 43242010)

Explain how two dimensional arrays are represented in memory, Explain how t...

Explain how two dimensional arrays are represented in memory. Representation of two-dimensional arrays in memory:- Let grades be a 2-D array as grades [3][4]. The array will

Explain the arrays in ruby, Explain the Arrays in Ruby Ruby arrays are ...

Explain the Arrays in Ruby Ruby arrays are dynamic arrays which expand automatically whenever a value is stored in a location beyond current end of the array. To the programmer

Binary search, An unsorted array is searched through linear search that sca...

An unsorted array is searched through linear search that scans the array elements one by one until the wanted element is found. The cause for sorting an array is that we search

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