Assume f(n) = 34/n) and g(n) = 45" and indicate the relationship between the two.Compare. 1: Select the number corresponding to the relationship:• f(n) E o(g(n))• f(n) E O(g(n))• f(n) E w(g(n))

Answered: Assume f(n) = 31/n) and g(n) = 45" and…

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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Assume f(n) = 34/n) and g(n) = 45" and indicate the relationship between the two.
Compare. 1: Select the number corresponding to the relationship:
• f(n) E o(g(n))
• f(n) E O(g(n))
• f(n) E w(g(n))

Expert Solution

Step 1

Given functions are,

$f (n) = 3^{(1 / n^{3})}$

$g (n) = 4^{\log n}$

Big Oh represents the worst case time complexity which is the tightest upper bound.

Big theta represents the average case time complexity which is the average value.

Big omega represents the best case time complexity which is the tightest lower bound.

If we observe the given functions, f(n)<g(n) because if we take any large value for n as 2⁹ then g(n) becomes 4⁹ and f(n) becomes very less because of its fraction.

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