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

Construction of a binary tree , Q. Construct a binary tree whose nodes in i...

Q. Construct a binary tree whose nodes in inorder and preorder are written as follows: Inorder : 10, 15, 17, 18, 20, 25, 30, 35, 38, 40, 50 Preorder: 20, 15, 10

Implementation of dequeue, Dequeue (a double ended queue) is an abstract da...

Dequeue (a double ended queue) is an abstract data type alike to queue, where insertion and deletion of elements are allowed at both of the ends. Like a linear queue & a circular q

Trees, What is AVL Tree? Describe the method of Deletion of a node from and...

What is AVL Tree? Describe the method of Deletion of a node from and AVL Tree ?

Technique for direct search, Technique for direct search is    Hashing ...

Technique for direct search is    Hashing is the used for direct search.

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

Merging, Merging two sequence using CREW merge

Merging two sequence using CREW merge

Insertion sort, Data array A has data series from 1,000,000 to 1 with step ...

Data array A has data series from 1,000,000 to 1 with step size 1, which is in perfect decreasing order. Data array B has data series from 1 to 1,000,000, which is in random order.

Insertion of a node into an avl tree, Initially Nodes are inserted in an AV...

Initially Nodes are inserted in an AVL tree in the same manner as an ordinary binary search tree. Though, the insertion algorithm for any AVL tree travels back along with the pa

Importance of game theory to decisions, Question: (a) Discuss the impor...

Question: (a) Discuss the importance of game theory to decisions. (b) Explain the following: (i) saddle point, (ii) two-person zero-sum game. (c) Two leading ?rms, ABC Ltd a

Graph search using iterative deepening, Prove that uniform cost search and ...

Prove that uniform cost search and breadth- first search with constant steps are optimal when used with the Graph-Search algorithm (see Figure). Show a state space with varying ste

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