Show by induction that T(n) ≤ 3n for all n ≥ 1 S T(|2n/3|) + n ifn> 3T(m) = {otherwiseShow by induction that T(n) < 3n for all n> 1 Master Theorem: If T(n) = aT()+0(n") for some constant a > 0, b > 1, and d > 0, then:T(n) = 0(n")T(n) = 0(nd log n)if d> log, aif d = log, aT(n) = O(nlo5, a)if d< log, a%3!

Sol: T(n)=T(2n/3)+n => T(2n/3)=T(4n/9)+2n/3 => T(4n/9)=T(8n/27)+4n/9…

Answered: T(n) otherwis T(n) < 3n for all n >1

Engineering

Computer Science

T(n) otherwis T(n) < 3n for all n >1

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

Show by induction that T(n) ≤ 3n for all n ≥ 1

Master Theorem: If T(n) = aT()+0(n") for some constant a > 0, b > 1, and d > 0, then:
T(n) = 0(n")
T(n) = 0(nd log n)
if d> log, a
if d = log, a
T(n) = O(nlo5, a)
if d< log, a
%3!

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