Please type your answer here! Match the Master Theorem CASE to the T(n) result.T(n) € (nog(base b] (a)*lg(n))T(n) = (f(n))T(n) = (nog (base b) (a))1.2.3.If the CASE test f(n) = O(n¹0g (baseb] (a) - e) | e > 0 are TRUE then T(n)= ???If the CASE test f(n) = (n¹08{base b}(a)) | e > 0 are TRUE then T(n) =???If the CASE test f(n) € (no(baseb] (a) + e) | e > 0 AND a*f(n/b)<c* f(n) | c < 1 are TRUE then T(n) =???

Answered: Match the Master Theorem CASE to the…

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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Match the Master Theorem CASE to the T(n) result.
T(n) € (nog(base b] (a)*lg(n))
T(n) = (f(n))
T(n) = (nog (base b) (a))
1.
2.
3.
If the CASE test f(n) = O(n¹0g (base
b] (a) - e) | e > 0 are TRUE then T(n)
= ???
If the CASE test f(n) = (n¹08{base b}
(a)) | e > 0 are TRUE then T(n) =
???
If the CASE test f(n) € (no(base
b] (a) + e) | e > 0 AND a*f(n/b)<
c* f(n) | c < 1 are TRUE then T(n) =
???

Expert Solution

Step 1

In the Master Theorem, T(n) represents the time complexity of a recursive algorithm, and the function f(n) represents the cost of dividing the problem into subproblems, which is added to the time complexity of merging the subproblems. The Master Theorem provides a way to analyze the time complexity of a recursive algorithm by comparing f(n) with different expressions involving nlog(base b) (a), where a is the number of subproblems, b is the factor by which the input size is reduced, and n is the input size.

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