Aa-trees, Data Structure & Algorithms

Assignment Help:

Red-Black trees have introduced a new property in the binary search tree that means an extra property of color (red, black). However, as these trees grow, in their operations such as insertion, deletion, it becomes complexes to retain all the properties, especially in case of deletion. Therefore, a new type of binary search tree can be defined which has no property of having a color, however has a new property introduced depend on the color that is the information for the new. This information of the level of any node is stored into a small integer (might be 8 bits). Now, AA-trees are described in terms of level of each node rather than storing a color bit with each node. A red-black tree utilized to have several conditions to be satisfied regarding its color and AA-trees have also been designed in such a way that it msut satisfy certain conditions regarding its new property, i.e., level.

The level of a node will be as:

1. Same as its parent, if the node is red.

2. One if the node is a leaf.

3. Level will be one less than the level of its parent, if the color of node is black.

Any red-black tree can be changed into an AA-tree by translating its color structure to levels such that left child is always one level lower than its parent & right child is always similar or at one level lower than its parent. While the right child is at same level to its parent, then a horizontal link is established among them. Thus, we conclude that it is essential that horizontal links are always at the right side and that there might not be two consecutive links. Taking into concern of all the above properties, we illustrates AA-tree as follows

After having a look at the AA-tree above, now we look at different operations which can be performed at such trees.


Related Discussions:- Aa-trees

Sequential search of a list is preferred over binary search, What are the c...

What are the conditions under which sequential search of a list is preferred over binary search? Sequential Search is a preferred over binary search when the list is unordered

Example of back face detection method, Example of Back Face Detection Metho...

Example of Back Face Detection Method To illustrate the method, we shall start with the tetrahedron (pyramid) PQRS of     Figure with vertices P (1, 1, 2), Q (3, 2, 3), R (1,

Omega notation, The ?-Notation (Lower Bound) This notation provides a l...

The ?-Notation (Lower Bound) This notation provides a lower bound for a function to within a constant factor. We write f(n) = ?(g(n)), if there are positive constants n 0 and

Division-remainder hashing, According to this, key value is divided by any ...

According to this, key value is divided by any fitting number, generally a prime number, and the division of remainder is utilized as the address for the record. The choice of s

Internal sorting, In internal sorting, all of the data to be sorted is obta...

In internal sorting, all of the data to be sorted is obtainable in the high speed main memory of the computer. We will learn the methods of internal sorting which are following:

Shortest path dijkstras algorithm, * Initialise d & pi* for each vertex ...

* Initialise d & pi* for each vertex v within V( g ) g.d[v] := infinity  g.pi[v] := nil g.d[s] := 0; * Set S to empty * S := { 0 }  Q := V(g) * While (V-S)

Physical database design and sql queries, In this part, students are allowe...

In this part, students are allowed to implement the following simplifications in their table and data design. o Availability for the beauty therapists don't have to be considere

Complete trees, This is a k-ary position tree wherein all levels are filled...

This is a k-ary position tree wherein all levels are filled from left to right. There are a number of specialized trees. They are binary trees, AVL-trees, binary search trees, 2

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