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

Random searching, write a program that find,search&replace a text string

write a program that find,search&replace a text string

Sorting algorithm for singly linked lists, Q. Which sorting algorithm can b...

Q. Which sorting algorithm can be easily adaptable for singly linked lists? Explain your answer as well.        Ans: The simple Insertion sort is sim

Example of single node with multiple elements, The class Element represents...

The class Element represents a single node that can be part of multiple elements on a hotplate and runs in its own thread. The constructor accepts the initial temperature and a hea

Selection sort, how to reduce the number of passes in selection sort

how to reduce the number of passes in selection sort

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

The time and space complexities of an algorihm, Relation between the time a...

Relation between the time and space complexities of an algorithm The examining of algorithm focuses on time complexity and space complexity. As compared to time analysis, the a

Signals, How does cpu''s part tming and controls generate and controls sign...

How does cpu''s part tming and controls generate and controls signls in computer?

Rooted tree, It does not have any cycles (circuits, or closed paths), which...

It does not have any cycles (circuits, or closed paths), which would imply the existence of more than one path among two nodes. It is the most general kind of tree, and might be co

Bubble sort, Q. The reason bubble sort algorithm is inefficient is that it ...

Q. The reason bubble sort algorithm is inefficient is that it continues execution even after an array is sorted by performing unnecessary comparisons. Therefore, the number of comp

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