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

Define min-heap, Define min-heap A min-heap is a complete binary tree i...

Define min-heap A min-heap is a complete binary tree in which each element is less than or equal to its children. All the principal properties of heaps remain valid for min-hea

Draw a flowchart to input start time and end time of vehicle, Speed cameras...

Speed cameras read the time a vehicle passes a point (A) on road and then reads time it passes a second point (B) on the same road (points A and B are 100 metres apart). Speed of t

Algorithm for similar binary tree, Q. The two Binary Trees are said to be s...

Q. The two Binary Trees are said to be similar if they are both empty or if they are both non- empty and left and right sub trees are similar. Write down an algorithm to determine

Recursive implementation of binary tree traversals, There are three typical...

There are three typical ways of recursively traversing a binary tree. In each of these, the left sub-trees & right sub-trees are visited recursively and the distinguishing feature

Hashing, what is hashing? what are diffrent method of hashing?

what is hashing? what are diffrent method of hashing?

Programs, Develop a program that accepts the car registration( hint: LEA 43...

Develop a program that accepts the car registration( hint: LEA 43242010)

Define about the structure - container, Define about the Structure - Contai...

Define about the Structure - Container - Some containers hold elements in some sort of structure, and some don't. Containers with no structure include bags and sets. Containe

Pseudocodes, how to write a pseudo code using Kramer''s rule

how to write a pseudo code using Kramer''s rule

Write stream analogues of list processing functions, (a) Write (delay ) as...

(a) Write (delay ) as a special form for (lambda () ) and (force ), as discussed in class. (b) Write (stream-cons x y) as a special form, as discussed in class. (c) Write

#title.structured programming, what do you understand by structured program...

what do you understand by structured programming?explain with eg. top down and bottem up programming technique

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