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There are two algorithms A and B for solving the same problem. Algorithm A has a worst-case time complexity T (n) that satisfies the recurrence relation T₁(n) = 7 × TÂ(n/2) + 100 × n², where n is the input size. Algorithm B has a worst-case time complexity TÂ(n) that satisfies the recurrence relation TB (n) = = a × TÂ(n/3) + 200 × n², where n is the input size and a is a positive integer. Assume that a = 9. What is the asymptotic notation of TB (n)? (n¹og₂ a log n) (n¹os3 a log n) ○(n¹og₂ a) (n¹og: a) log3

There are two algorithms A and B for solving the same problem. Algorithm A has a worst-case time complexity T (n) that satisfies the recurrence relation T₁(n) = 7 × TÂ(n/2) + 100 × n², where n is the input size. Algorithm B has a worst-case time complexity TÂ(n) that satisfies the recurrence relation TB (n) = = a × TÂ(n/3) + 200 × n², where n is the input size and a is a positive integer. Assume that a = 9. What is the asymptotic notation of TB (n)? (n¹og₂ a log n) (n¹os3 a log n) ○(n¹og₂ a) (n¹og: a) log3

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
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Question 10 There are two algorithms A and B for solving the same problem. Algorithm A has a worst-case time complexity T (n) that satisfies the recurrence relation TA(n) 7× TA (n/2) + 100 × n², where n is the input size. Algorithm B has a worst-case time complexity TÂ(n) that satisfies the recurrence relation TÂ(n) = a × TÂ(n/3) + 200 × n², where n is the input size and a is a positive integer. = Assume that a = 9. What is the asymptotic notation of TB (n)? O(nloga log n) (n¹0g3 a log n) O(nlog, a) ○(nlog, a)
Transcribed Image Text:Question 10 There are two algorithms A and B for solving the same problem. Algorithm A has a worst-case time complexity T (n) that satisfies the recurrence relation TA(n) 7× TA (n/2) + 100 × n², where n is the input size. Algorithm B has a worst-case time complexity TÂ(n) that satisfies the recurrence relation TÂ(n) = a × TÂ(n/3) + 200 × n², where n is the input size and a is a positive integer. = Assume that a = 9. What is the asymptotic notation of TB (n)? O(nloga log n) (n¹0g3 a log n) O(nlog, a) ○(nlog, a)
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