Problem 3. Consider the following recurrence. T()={ T(n)= 37(n/2) + n² (a) Solve this recurrence exactly by the method of substitution. You may assume n is a power of 2. (b) Solve it using the recursion tree method. if n=1 otherwise.

Problem 3. Consider the following recurrence. T()={ T(n)= 37(n/2) + n² (a) Solve this recurrence exactly by the method of substitution. You may assume n is a power of 2. (b) Solve it using the recursion tree method. if n=1 otherwise.

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

Problem 3.
Consider the following recurrence.
T(n) = {(n) = 37(n
T(n) = 3T(n/2) + n²
if n=1
otherwise.
(a) Solve this recurrence exactly by the method of substitution. You may assume n is a
power of 2.
(b) Solve it using the recursion tree method.

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