if n< d T(n)= - laT(n/b)+ f(n) if n2 d 1. if f(n) is O(n" 2. if f(n) is O(n™*“ log* n), then T(n) is O(n*.“ log**" n)| 3. if f(n) is 2(n*. *“), then T(n) is O(f (n)), provided af(n/b) S F (n) for some & <1. log, a-e ), then T(n) is O(no") log, a+e Which of the three cases above applies to an algorithm, the running time of which is described using the following recurrence relation: T(n) = 3 T(n/3) + n^/a 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 Answer:

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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Master theorem:
if n< d
T(n)= -
aT(n/b)+ f (n) if n2 d
1. if f(n) is O(n-€ ), then T(n) is O(n®%«
2. if f(n) is O(no, " log* n), then T(n) is O(n"8, «
a-e
k+l
log
log, a+€ ), then T(n) is ©(f(n)),
provided af (n/b)< (n) for some 8 <1.
n)
Which of the three cases above applies to an algorithm, the running time of which is described using the following recurrence relation:
T(n) = 3 T(n/3) + nº/3
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
Answer:
Transcribed Image Text:Master theorem: if n< d T(n)= - aT(n/b)+ f (n) if n2 d 1. if f(n) is O(n-€ ), then T(n) is O(n®%« 2. if f(n) is O(no, " log* n), then T(n) is O(n"8, « a-e k+l log log, a+€ ), then T(n) is ©(f(n)), provided af (n/b)< (n) for some 8 <1. n) Which of the three cases above applies to an algorithm, the running time of which is described using the following recurrence relation: T(n) = 3 T(n/3) + nº/3 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 Answer:
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