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

Tree, application of threaded binary treee

application of threaded binary treee

Frequency count, what is frequency count with examble

what is frequency count with examble

Enumerate about the concept of container, Enumerate about the concept of co...

Enumerate about the concept of container A Container can have a size() operation. We can also ask (somewhat redundantly) whether a Container is empty. And even though a Contain

Graph, multilist representation of graph

multilist representation of graph

Create a binary tree , Create a class "box" that will contain a random inte...

Create a class "box" that will contain a random integer value v such that O

Question, A binary search tree is used to locate the number 43. Which of th...

A binary search tree is used to locate the number 43. Which of the following probe sequences are possible and which are not? Explain. (a) 61 52 14 17 40 43 (b) 2 3 50 40 60 43 (c)

What are the different ways of representing a graph, What are the different...

What are the different ways of representing a graph? The different ways of representing a graph is: Adjacency list representation: This representation of graph having of an

The space - time trade off, The Space - Time Trade Off The best algorit...

The Space - Time Trade Off The best algorithm to solve a given problem is one that needs less space in memory and takes less time to complete its implementation. But in practic

Implementation of stack using arrays, A Stack has an ordered list of elemen...

A Stack has an ordered list of elements & an array is also utilized to store ordered list of elements. Therefore, it would be very simple to manage a stack by using an array. Thoug

Define the term counting - pseudocode, Define the term counting - Pseudocod...

Define the term counting - Pseudocode Counting in 1s is quite simple; use of statement count = count + 1 would enable counting to be done (for example in controlling a repeat

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