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

Multiplication, Implement multiple stacks in a single dimensional array. Wr...

Implement multiple stacks in a single dimensional array. Write algorithms for various stack operations for them.

Graph, Multilist Representation of graph

Multilist Representation of graph

Convertion, how we can convert a graph into tree

how we can convert a graph into tree

Binary search, An unsorted array is searched through linear search that sca...

An unsorted array is searched through linear search that scans the array elements one by one until the wanted element is found. The cause for sorting an array is that we search

Interest, I=PR/12 numbers of years : Interest Rate up to 1 years : 5...

I=PR/12 numbers of years : Interest Rate up to 1 years : 5.50 Up to 5 years : 6.50 More than 5 year : 6.75 please design an algorithm based on the above information

Convertion, how we can convert a graph into tree

how we can convert a graph into tree

Linear search, Linear search is not the most efficient way to search an ite...

Linear search is not the most efficient way to search an item within a collection of items. Though, it is extremely simple to implement. Furthermore, if the array elements are arra

State hsv colour model, HSV Colour Model Instead of a set of colour pri...

HSV Colour Model Instead of a set of colour primaries, the HSV model uses colour descriptions that have a more intuitive appeal to a user. To give a colour specification, a use

String pattern matching, Document processing is quickly becoming one of the...

Document processing is quickly becoming one of the dominant functions of computers. Computers are utilized to edit, search & transport documents over the Internet, and to display d

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