Exercise 3.Given the following recurrence relation:T(1) = 1 T(n) = T(n − 1) + n2 for n ≥ 2Indicate a methodology you can use to evaluate a closed form expressionProvide the closed form expression and show the procedure to obtain itProvide a recursive algorithm in pseudo code to calculate a generic T(n)Provide an analysis of the algorithm above

Answer: We have to find the time complexity for the given recurrence relation.Given T(n)=T(n-1)+n2 for n>=2 T(n)=T(n-1)+n2 T(n-1)=T(n-2)+(n-1)2 So T(n)=T(n-2)+(n-1)2 +n2 at n-1 T(n)=T(n-3)+(n-2)2+(n-1)2 +n2 at n-2 T(n)=T(n-4)+(n-3)3+(n-2)2+(n-1)2 +n2 at n-3 for at any instant k T(n)=T(n-k)+(n-k+1)2+(n-k+2)2+..+(n-1)2+n2 if k=n then close form Y(n)=T(0)+12+ 22 +..+n2 But if take upper bound Then 12+ 22 +..+n2 <=n2+n2+....+n2 (n time) Hence T(n)=O(n3)

Answered: xercise 3. Given the following…

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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Exercise 3.

Given the following recurrence relation:

T(1) = 1

T(n) = T(n − 1) + n² for n ≥ 2

Indicate a methodology you can use to evaluate a closed form expression
Provide the closed form expression and show the procedure to obtain it
Provide a recursive algorithm in pseudo code to calculate a generic T(n)
Provide an analysis of the algorithm above

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