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

Implementation of stack, In this unit, we have learned how the stacks are i...

In this unit, we have learned how the stacks are implemented using arrays and using liked list. Also, the advantages and disadvantages of using these two schemes were discussed. Fo

Er diagram, Ask queConsider the following functional dependencies: Applican...

Ask queConsider the following functional dependencies: Applicant_ID -> Applicant_Name Applicant_ID -> Applicant_Address Position_ID -> Positoin_Title Position_ID -> Date_Position_O

Dynamic programming., Count Scorecards(30 points) In a tournament, N playe...

Count Scorecards(30 points) In a tournament, N players play against each other exactly once. Each game results in either of the player winning. There are no ties. You have given a

What are the example of area subdivision method, Example of Area Subdivisio...

Example of Area Subdivision Method The procedure will be explained with respect to an illustrative problem, with the image consisting of five objects, namely a triangle (T), qu

What are the properties of colour, Properties of colour Colour descript...

Properties of colour Colour descriptions and specifications generally include three properties: hue; saturation and brightness. Hue associates a colour with some position in th

Define approximating smooth surfaces with polygon nets, Approximating smoot...

Approximating smooth surfaces with Polygon nets Networks of polygons are used to represent smooth surfaces. They are, of course, only an approximation to the true surface, but

Inorder traversal, Inorder traversal: The left sub tree is visited, then t...

Inorder traversal: The left sub tree is visited, then the node and then right sub-tree. Algorithm for inorder traversal is following: traverse left sub-tree visit node

Progrrame, how to write a code for for a company , for calculate the salary...

how to write a code for for a company , for calculate the salary pay

Linked lists, what are grounded header linked lists?

what are grounded header linked lists?

Definitions of graph, A graph G might be defined as a finite set V of verti...

A graph G might be defined as a finite set V of vertices & a set E of edges (pair of connected vertices). The notation utilized is as follows: Graph G = (V, E) Consider the g

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