Give asymptotic upper and lower bounds for T(n) in each of the following recurrences. Assume that T(n) is constant for n ≤ 2. Make your bounds as tight as possible, and justify your answers. (a) T(n) = 4T(n/4) +5n (b) T(n) = 4T(n/5)+ 5n (c) T(n) = 5T(n/4) + 4n (d) T(n) = 25T(n/5)+ n²

Give asymptotic upper and lower bounds for T(n) in each of the following recurrences. Assume that T(n) is constant for n ≤ 2. Make your bounds as tight as possible, and justify your answers. (a) T(n) = 4T(n/4) +5n (b) T(n) = 4T(n/5)+ 5n (c) T(n) = 5T(n/4) + 4n (d) T(n) = 25T(n/5)+ n²

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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Question

Give asymptotic upper and lower bounds for T(n) in each of the following recurrences.
Assume that T(n) is constant for n ≤ 2. Make your bounds as tight as possible, and
justify your answers.
(a) T(n) = 4T(n/4) +5n
(b) T(n) = 4T(n/5)+ 5n
(c) T(n) = 5T(n/4) + 4n
(d) T(n) = 25T(n/5)+ n²

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