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

Convertion, how we can convert a graph into tree

how we can convert a graph into tree

Traversing a graph, two standards ways of traversing a graph in data struc...

two standards ways of traversing a graph in data structure

Algorithmic implementation of multiple stacks, So far, we now have been con...

So far, we now have been concerned only with the representation of single stack. What happens while a data representation is required for several stacks? Let us consider an array X

What is quick sort, What is quick sort?   Answer Quick sort is on...

What is quick sort?   Answer Quick sort is one of the fastest sorting algorithm used for sorting a list. A pivot point is chosen. Remaining elements are divided or portio

Multiple stacks, how multiple stacks can be implemented using one dimension...

how multiple stacks can be implemented using one dimensional array

Which sorting algorithms not have running time of o (n2), Which sorting al...

Which sorting algorithms does not have a worst case running time of  O (n 2 ) ? Merge 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

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

Splay trees, Addition of new records in a Binary tree structure always occu...

Addition of new records in a Binary tree structure always occurs as leaf nodes, which are further away from the root node making their access slower. If this new record is to be 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