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

Write a procedure that produces independent stack, Write a procedure (make-...

Write a procedure (make-stack) that produces independent stack objects, using a message-passing style, e.g. (define stack1 (make-stack))  (define stack2 (make-stack)) W

Example of telephone directory, A telephone directory having n = 10 records...

A telephone directory having n = 10 records and Name field as key. Let us assume that the names are stored in array 'm' i.e. m(0) to m(9) and the search has to be made for name "X"

Algorithm, implement multiple stack in one dimensional array

implement multiple stack in one dimensional array

Explain the question, Merging 4 sorted files having 50, 10, 25 and 15 recor...

Merging 4 sorted files having 50, 10, 25 and 15 records will take time

Proof, prove that n/100=omega(n)

prove that n/100=omega(n)

Multilist file organisation, what is multilist length file organisation? ex...

what is multilist length file organisation? explain with an example

Breadth-first search , 1. Apply the variant Breadth-First Search algorithm ...

1. Apply the variant Breadth-First Search algorithm as shown in Figure 2 to the attached graph. This variant is used for computing the shortest distance to each vertex from the sta

Advantages of the last in first out method, Materials consumed are priced i...

Materials consumed are priced in a systematic and realistic manner. It is argued that current acquisition costs are incurred for the purpose of meeting current production and sales

Write a function that performs the integer mod function, Write a function t...

Write a function that performs the integer mod function. Given the previous functions you have implemented already, this one should be a piece of cake. This function will find the

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