Master theorem: if n

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(nos")
2. if f(n) is O(n'
3. if f(n) is 2(n®
provided af (n/b)S (n) for some 8 <l.
log,
gl08s" log* n), then T (n) is O(n8." log*' n)
*), then T(n) is O(ƒ (n)),
log, ate
Which of the three cases above applies to an algorithm, the running time of which is described using the following recurrence relation:
T(n) = T (Vm) + n
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(nos") 2. if f(n) is O(n' 3. if f(n) is 2(n® provided af (n/b)S (n) for some 8 <l. log, gl08s" log* n), then T (n) is O(n8." log*' n) *), then T(n) is O(ƒ (n)), log, ate Which of the three cases above applies to an algorithm, the running time of which is described using the following recurrence relation: T(n) = T (Vm) + n 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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