Solve the following recurrence relations. You do not need to give a () bound for (a), (b), (c); it suffices to give the O() bound that results from applying the Master theorem. You may assume that T(n) = O(1) for n = 0(1). (a) T(n) = 2T(n/3) + 1. (b) T(n) = 7T(n/7) + n. (c) T(n) = 9T(n/3) + n².

Solve the following recurrence relations. You do not need to give a () bound for (a), (b), (c); it suffices to give the O() bound that results from applying the Master theorem. You may assume that T(n) = O(1) for n = 0(1). (a) T(n) = 2T(n/3) + 1. (b) T(n) = 7T(n/7) + n. (c) T(n) = 9T(n/3) + n².

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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Concept explainers

Recurrence relation

A recurrence relation or recursive relation is an equation that represents a function in terms of the values of its smaller inputs. Every recurrence relation T(n) is a recursive function of integer n and consists of a base case and a recursive case.

Question

Solve the following recurrence relations. You do not need
to give a () bound for (a), (b), (c); it suffices to give the O() bound
that results from applying the Master theorem. You may assume that
T(n) = O(1) for n = = 0(1).
(a) T(n) = 2T(n/3) + 1.
(b) T(n) = 7T(n/7) + n.
(c) T(n) = 9T(n/3) + n².
(d) T(n) = T(n-1) +2.

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