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

Data Mining and Neural Networks, I am looking for some help with a data min...

I am looking for some help with a data mining class with questions that are about neural networks and decision trees. Can you help? I can send document with questions.

State an algorithm which inputs 3 - digit code for 280 items, A small shop ...

A small shop sells 280 different items. Every item is identified by a 3 - digit code. All items which start with a zero (0) are cards, all items which start with a one (1) are swee

Ruby implements range of t abstract data type, Ruby implements Range of T A...

Ruby implements Range of T Abstract data type Ruby implements Range of T ADT in its Range class. Elements of carrier set are represented in Range instances by recording interna

Procedure to delete all terminal nodes of the tree, Q. Let a binary tree 'T...

Q. Let a binary tree 'T' be in memory. Write a procedure to delete all terminal nodes of the tree.       A n s . fun ction to Delete Terminal Nodes from Binary Tree

Representation of arrays, REPRESENTATION OF ARRAYS This is not uncommon...

REPRESENTATION OF ARRAYS This is not uncommon to determine a large number of programs which procedure the elements of an array in sequence. However, does it mean that the eleme

Determine the components of illumination, Determine the Components of Illum...

Determine the Components of Illumination The light reaching the eye when looking at a surface has clearly come from a source (or sources) of illumination and bounced off the su

What is a container taxonomy, What is A Container Taxonomy It's useful ...

What is A Container Taxonomy It's useful to place containers in a taxonomy to help understand their relationships to one another and as a basis for implementation using a class

Types of a linked list, A linked list can be of the following types:- ...

A linked list can be of the following types:-  Linear linked list or one way list Doubly linked list or two way list. Circular linked list Header linked list

Determine about the post conditions assertion, Determine about the Post con...

Determine about the Post conditions assertion A  post condition is an assertion which should be true at completion of an operation. For instance, a post condition of the squ

Depth first search, DEPTH FIRST SEARCH (DFS) The approach adopted into ...

DEPTH FIRST SEARCH (DFS) The approach adopted into depth first search is to search deeper whenever possible. This algorithm frequently searches deeper through visiting unvisite

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