Array-based representation of a binary tree, Data Structure & Algorithms

Assignment Help:

Assume a complete binary tree T with n nodes where each node has an item (value). Label the nodes of the complete binary tree T from top to bottom & from left to right 0, 1, ..., n-1. Relate with T the array A where the ith   entry of A is the item in the node labeled i of T, i = 0, 1, ..., n-1. Table illustrates the array representation of a Binary tree of Figure

1724_Array-based representation of a Binary Tree.png

Given the index i of a node, we can efficiently & easily compute the index of its parent and left & right children:

Index of Parent: (i - 1)/2, Index of Left Child: 2i + 1, Index of Right Child: 2i + 2.

Node #

Item

Left child

Right child

0

A

1

2

1

B

3

4

2

C

-1

-1

3

D

5

6

4

E

7

8

5

G

-1

-1

6

H

-1

-1

7

I

-1

-1

8

J

-1

-1

9

?

?

?

Table: Array Representation of a Binary Tree

First column illustrates index of node, second column contain the item stored into the node & third & fourth columns mention the positions of left & right children

(-1 shows that there is no child to that specific node.)


Related Discussions:- Array-based representation of a binary tree

A full binary tree with n leaves, A full binary tree with n leaves have:- ...

A full binary tree with n leaves have:- 2n -1 nodes.

State z-buffer algorithm, Z-Buffer Algorithm Also known as the Depth-Bu...

Z-Buffer Algorithm Also known as the Depth-Buffer algorithm, this image-space method simply selects for  display the polygon or portion of a polygon that is nearest to the view

Areas of use - sequential files, Sequential files are most frequently utili...

Sequential files are most frequently utilized in commercial batch oriented data processing where there is the concept of a master file on which details are inserted periodically. F

Functions and modelling the data flows, Read the scenario (Pickerings Prope...

Read the scenario (Pickerings Properties). (a) List the functions of the system, as perceived by an external user. (b) List the external entities. Note that because we are mo

Determine the types of java, Determine the types of JAVA Java has two p...

Determine the types of JAVA Java has two parts... 1. Core language -- variables, arrays, objects o Java Virtual Machine (JVM) runs the core language o Core language is

Give example of assertion and abstract data type, Give example of assertion...

Give example of assertion and abstract data type For illustration, consider Natural ADT whose carrier set is the set of non-negative integers and whose operations are the usual

Representation of sets?, A set s is conveniently shown in a computer store ...

A set s is conveniently shown in a computer store by its characteristic function C(s). This is an array of logical numbers whose ith element has the meaning "i is present in s". As

High-level and bubble algorithm , 1. Give both a high-level algorithm and a...

1. Give both a high-level algorithm and an implementation (\bubble diagram") of a Turing machine for the language in Exercise 3.8 (b) on page 160. Use the ' notation to show the co

What is an unreachable code assertion, What is an unreachable code assertio...

What is an unreachable code assertion An unreachable code assertion can be placed at the default case; if it's every executed, then program is in an erroneous state. A loop in

Graphs, In this unit, we will describe a data structure called Graph. Actua...

In this unit, we will describe a data structure called Graph. Actually, graph is a general tree along no parent-child relationship. In computer science, Graphs have several applica

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