Given thatT(n) = 2T(n/2) +n for n >= 2,You can assume n= 2k and T(1) = 1Find the kth stepT(n)=2kT(n/2k) +kO T(n) 2kT(n/2k) +nkT(n)=2*T(n/2k) +knT(n) = 2*T(n/2k) +k"T(n) = T(n-1) +n for n >= 2 and T(1) = 1find the 6th stepO(n2)T(n)-T(6-k)+(6+1−k) + (6+ 2−k) +++ (6-1) +6T(n)-T(n-6) + (n+ 1-6) + (n+ 2−6) +---+ (n-1) +nO O(n²)

Dear Student, The answer to your question is given below -

iven that (n) = 2T(n/2) +n for n >= 2, ou can assume n= 2k and T(1) = 1 ind the kth step T(n)-2kT(n/2k) +k OT(n)-2kT(n/2k) +nk OT(n)=2*T(n/2k) +kn T(n)=2*T(n/2k) +k (n) =T(n-1) +n for n >= 2 and T(1) = 1 nd the 6th step O O(n2) © T(n) -T(6-k) + (6+1-k) + (6+2¬k) +++ (6-1) +6

iven that (n) = 2T(n/2) +n for n >= 2, ou can assume n= 2k and T(1) = 1 ind the kth step T(n)-2kT(n/2k) +k OT(n)-2kT(n/2k) +nk OT(n)=2T(n/2k) +kn T(n)=2T(n/2k) +k (n) =T(n-1) +n for n >= 2 and T(1) = 1 nd the 6th step O O(n2) © T(n) -T(6-k) + (6+1-k) + (6+2¬k) +++ (6-1) +6

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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Question

Given that
T(n) = 2T(n/2) +n for n >= 2,
You can assume n= 2k and T(1) = 1
Find the kth step
T(n)=2kT(n/2k) +k
O T(n) 2kT(n/2k) +nk
T(n)=2*T(n/2k) +kn
T(n) = 2*T(n/2k) +k"
T(n) = T(n-1) +n for n >= 2 and T(1) = 1
find the 6th step
O(n2)
T(n)-T(6-k)+(6+1−k) + (6+ 2−k) +++ (6-1) +6
T(n)-T(n-6) + (n+ 1-6) + (n+ 2−6) +---+ (n-1) +n
O O(n²)

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