What is the complexity of T(n)=4T(n/2)+n (choose one from the next 1-4): 1. (n³) 2. (n²) 3. O(nlgn) 4. None of the above Master theorem T(n)=aT(n/b)+f(n) Case 1: O(ng(a)), g(a)=logba, if f(n)= O(ng(n)-e), ε<1 Case 2: (n²(a)Ign), g(a)=logba, if f(n)= O(n²(n) Case 3: (f(n)), if f(n)= (ng(n)+), g(a)=logba, >0 and r.c a*f(n/b)

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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How can I identify which case to use? Such that after knowing which case to use, how to use that case to find the complexity running time?

What is the complexity of T(n)=4T(n/2)+n (choose one from the next 1-4):
1. (n³)
2. O(n²)
3. O(nlgn)
4. None of the above
Master theorem
T(n)=aT(n/b)+f(n)
Case 1: (ng(a)), g(a)=logba, if f(n)= O(ng(n)-e), ε<1
Case 2: (nº(a)Ign), g(a)=logba, if f(n)= O(n²(n))
Case 3: O(f(n)), if f(n)= (n²(n)+), g(a)=logba, >0 and r.c a*f(n/b)<c f(n) where c<1
O 2
O
1
Transcribed Image Text:What is the complexity of T(n)=4T(n/2)+n (choose one from the next 1-4): 1. (n³) 2. O(n²) 3. O(nlgn) 4. None of the above Master theorem T(n)=aT(n/b)+f(n) Case 1: (ng(a)), g(a)=logba, if f(n)= O(ng(n)-e), ε<1 Case 2: (nº(a)Ign), g(a)=logba, if f(n)= O(n²(n)) Case 3: O(f(n)), if f(n)= (n²(n)+), g(a)=logba, >0 and r.c a*f(n/b)<c f(n) where c<1 O 2 O 1
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