Question 4) | T(n) = 4T(n/2) + n²lgn a) Consider the above recurrence relation, explain why Case 1 and Case 3 of the Master Theorem do not apply to the recurrence. b) Explain why our expanded definition of Case 2¹ of the Master Theorem does apply and use it to determine a tight bounder.

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
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¹ If there exists a constant k ≥ 0 such that f(n)
=
log a
k
loga, k+1.
lg n), then T(n) = O(n lg 'n)
Ⓒ(n
Transcribed Image Text:¹ If there exists a constant k ≥ 0 such that f(n) = log a k loga, k+1. lg n), then T(n) = O(n lg 'n) Ⓒ(n
Question 4) [
T(n) =
4T(n/2) + n²lgn
a) Consider the above recurrence relation, explain why Case 1 and Case 3 of the Master
Theorem do not apply to the recurrence.
b) Explain why our expanded definition of Case 2¹ of the Master Theorem does apply
and use it to determine a tight bounder.
Transcribed Image Text:Question 4) [ T(n) = 4T(n/2) + n²lgn a) Consider the above recurrence relation, explain why Case 1 and Case 3 of the Master Theorem do not apply to the recurrence. b) Explain why our expanded definition of Case 2¹ of the Master Theorem does apply and use it to determine a tight bounder.
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