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

For loop, for (i = 0; i sequence of statements } Here, the loop e...

for (i = 0; i sequence of statements } Here, the loop executes n times. Thus, the sequence of statements also executes n times. Since we suppose the time complexity of th

Explain all-pair shortest-paths problem, Explain All-pair shortest-paths pr...

Explain All-pair shortest-paths problem Given a weighted linked graph (undirected or directed), the all pairs shortest paths problem asks to find the distances (the lengths of

Algorithm to delete the specific node from binary searchtree, Q. Write down...

Q. Write down an algorithm to delete the specific node from binary search tree. Trace the algorithm to delete a node (10) from the following given tree. Ans. Algor

Multiple queue, How to create multiple queue on single array?

How to create multiple queue on single array?

Explain the arrays in ruby, Explain the Arrays in Ruby Ruby arrays are ...

Explain the Arrays in Ruby Ruby arrays are dynamic arrays which expand automatically whenever a value is stored in a location beyond current end of the array. To the programmer

Advanced trees, Linked list representations contain great advantages of fle...

Linked list representations contain great advantages of flexibility on the contiguous representation of data structures. However, they contain few disadvantages also. Data structur

Relative and direct files, Each data record contains a fixed place in a rel...

Each data record contains a fixed place in a relative file. Each record ought to have associated with it in integer key value which will help identify this slot. Therefore, this ke

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

prove that n/100=omega(n)

Objectives of lists, After going through this unit, you will be able to: ...

After going through this unit, you will be able to: • define and declare Lists; • understand the terminology of Singly linked lists; • understand the terminology of Doubly

Aa-trees, Red-Black trees have introduced a new property in the binary sear...

Red-Black trees have introduced a new property in the binary search tree that means an extra property of color (red, black). However, as these trees grow, in their operations such

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