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

Four applications or implementation of the stack, Q. Write down any four ap...

Q. Write down any four applications or implementation of the stack.                                     Ans. (i)       The Conversion of infix to postfix form (ii)

Endogenous model, Question a) Describe how the endogenous model is an ...

Question a) Describe how the endogenous model is an improvement to the neo-classical model in explaining the long-run effect of investment on economic growth of a country.

Sorting, explain quick sort algorithm

explain quick sort algorithm

A linear list of elements in which deletion can be done, A linear list of e...

A linear list of elements in which deletion can be done from one end (front) and insertion can take place only at the other end (rear) is called as a   Queue.

Calculation of time complexity, Example: Assume the following of code: ...

Example: Assume the following of code: x = 4y + 3 z = z + 1 p = 1 As we have been seen, x, y, z and p are all scalar variables & the running time is constant irrespective

Abstract Data Types, A useful tool which is used for specifying the logical...

A useful tool which is used for specifying the logical properties of a data type is called the abstract data type or ADT. The term "abstract data type" refers to the fundamental ma

Enumerate about the carrier set members, Enumerate about the carrier set me...

Enumerate about the carrier set members Ruby is written in C, so carrier set members (which is, individual symbols) are implemented as fixed-size arrays of characters (which is

Declaring a two dimensional array, Declaring a two dimensional array   A...

Declaring a two dimensional array   A two dimensional array is declared same to the way we declare a one-dimensional array except that we state the number of elements in both di

Tree traversals, There are three kinds of tree traversals, namely, Postorde...

There are three kinds of tree traversals, namely, Postorder , Preorder and Inorder. Preorder traversal: Each of nodes is visited before its children are visited; first the roo

Perfect matching polytope ppm, Let G=(V,E) be a graph for which all nodes h...

Let G=(V,E) be a graph for which all nodes have degree 5 and where G is 5-edge is connected. a) Show that the vector x which is indexed by the edges E and for which xe = 1/5 for

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