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

BST has two children, If a node in a BST has two children, then its inorder...

If a node in a BST has two children, then its inorder predecessor has No right child

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

How can a lock object be called in the transaction, How can a lock object b...

How can a lock object be called in the transaction? By calling Enqueue and Dequeue in the transaction.

Number of operations possible on ordered lists and arrays, Q. Enumerate num...

Q. Enumerate number of operations possible on ordered lists and arrays.  Write procedures to insert and delete an element in to array.

Insertion of a key into a b-tree, Example: Insertion of a key 33 into a B-...

Example: Insertion of a key 33 into a B-Tree (w/split) Step 1: Search first node for key closet to 33. Key 30 was determined. Step 2: Node pointed through key 30, is se

Data mining assignment, The assignment aims at consolidating your knowledge...

The assignment aims at consolidating your knowledge on data mining techniques and developing practical skills through solving a problem of transcription factor binding sites recogn

#titlestrings, given the string "Data Structures & , Algorithms", write a p...

given the string "Data Structures & , Algorithms", write a program that uses sequential search to return index of ''&''

What is gouraud shading, Gouraud Shading The faceted appearance of a La...

Gouraud Shading The faceted appearance of a Lambert shaded model is due to each polygon having only a single colour. To avoid this effect, it is necessary to vary the colour ac

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