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Solve the following recurrence relation and give the Big O value. T(n) = 2T(n-1)+4 forn>0 T(0) = 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

100%

Solve the following recurrence relation and give the Big O value.
T(n) = 2T(n-1) + 4 forn > 0
T(0) = 1

Expert Solution

Step 1

T(n) = 2(2T(n-2) + 4) + 4
= 2(2(2T(n-3) + 4) + 4) + 4
= 2(2(2(2T(n-4) + 4) + 4) + 4) + 4
= ...
= 2^n T(0) + 4(2^(n-1) + 2^(n-2) + ... + 1)
= 2^n + (2^n - 1)4
= O(2^n)

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