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Master theorem: if n

Master theorem: if n

Database System Concepts
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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Master theorem: if n< d T(n)= 4 aT(n/b)+ f (n) if n2d 1. if f(n) is O(nlos, a-e ), then T(n) is O(noE") log, a 2. if f(n) is O(n" plog, “ log* n), then T(n) is O(n8.“ log** n) k+1 3. if f(n) is Q(no, a*€ ), then T(n) is O(f(n)), provided af (n/ b) < (n) for some 8 < 1. Which of the three cases above applies to an algorithm, the running time of which is described using the following recurrence relation: T(n) = 97(n/2) + nº Type 1 for case 1, and so on. For case 2, also specify a k value after a space, e.g., "2 2" Type N/A if the Master theorem is not applicable to the recurrence relation
Transcribed Image Text:Master theorem: if n< d T(n)= 4 aT(n/b)+ f (n) if n2d 1. if f(n) is O(nlos, a-e ), then T(n) is O(noE") log, a 2. if f(n) is O(n" plog, “ log* n), then T(n) is O(n8.“ log** n) k+1 3. if f(n) is Q(no, a*€ ), then T(n) is O(f(n)), provided af (n/ b) < (n) for some 8 < 1. Which of the three cases above applies to an algorithm, the running time of which is described using the following recurrence relation: T(n) = 97(n/2) + nº Type 1 for case 1, and so on. For case 2, also specify a k value after a space, e.g., "2 2" Type N/A if the Master theorem is not applicable to the recurrence relation
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