What if the recurrence is T(n) = 2T(n-1) +1 ? Still Use substitution method to find the time complexity 1n=0T(n)=T(n-1) + 1n>0So, the recurrence is T(n)=T(n-1) + 1--[eq.1]We can solve this if we know what is T(n-1)Since, T(n)=T(n-1) +1T(n-1) = T(n-2) +1So, we can substitute T(n-2) +1 in place of T(n-1). So, the next equation isT(n)=T(n-2) + 1 + 1T(n) =T(n-2) + 2F[eq.2]

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What if the recurrence is T(n) = 2T(n-1) +1 ? Still Use substitution method to find the time complexity

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

What if the recurrence is T(n) = 2T(n-1) +1 ? Still Use substitution method to find the time complexity

1
n=0
T(n)=
T(n-1) + 1
n>0
So, the recurrence is T(n)=T(n-1) + 1
--[eq.1]
We can solve this if we know what is T(n-1)
Since, T(n)=T(n-1) +1
T(n-1) = T(n-2) +1
So, we can substitute T(n-2) +1 in place of T(n-1). So, the next equation is
T(n)=T(n-2) + 1 + 1
T(n) =T(n-2) + 2
F[eq.2]

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