Answered: ir/Madam, May I get an explanation…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Dear Sir/Madam,

May I get an explanation how the computation was obtained?
I do understand why the input size is squared for O(n²) 3000²/ 1000² I just don't know where the idea to square the denominator comes from?

The same for the n * log(n) solution.

Also what topic of Maths deals with calculations of this kind? I would like to learn more to be able to solve similar problems.

The algorithm is considered as O (n²) algorithm.
3000²
1000²
= 9
= 9x5
= 45
The algorithm is considered as O (n³) algorithm.
3000³
1000³
= 2
= 27 x 5
= 135
The algorithm A is considered as O (n log (n)) algorithm.
3000 log(3000)
1000 log(1000)
=
3x3.47
1x3
= 3.47
= 3.47 x 5
= 17.38

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