4. Consider the following recursive algorithm.ALGORITHM Q(n)//Input: A positive integer nif n = 1 return 1else return Q(n – 1) + 2 * n – 1a. Set up a recurrence relation for this function's values and solve it to deter-mine what this algorithm computes.b. Set up a recurrence relation for the number of multiplications made by thisalgorithm and solve it.c. Set up a recurrence relation for the number of additions/subtractions madeby this algorithm and solve it.

Answered: wing recurs ALGORITHM Q(n) I/Input: A…

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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4. Consider the following recursive algorithm.
ALGORITHM Q(n)
//Input: A positive integer n
if n = 1 return 1
else return Q(n – 1) + 2 * n – 1
a. Set up a recurrence relation for this function's values and solve it to deter-
mine what this algorithm computes.
b. Set up a recurrence relation for the number of multiplications made by this
algorithm and solve it.
c. Set up a recurrence relation for the number of additions/subtractions made
by this algorithm and solve it.

Expert Solution

Step 1

1- Since you have not provided the language to write the code so I am using java language to solve this algorithm.

2- In this assignment, take the positive input from the scanner class.

3- This is a recursive algorithm, the purpose of the recursive method call to itself till the condition is not satisfied.

4- There are if and else condition require because if the user enters the value 1, it will return 1 only. If the user enters more than 1 value it will calculate and return this value (n-1) + 2 * n-1.

5- Call the recursive method from the main class.

6- Please check the following complete example with comments and screenshots.

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