Use Master Therom to determine the complexity of the following: 10. int recursiveFun5(int n){}for (i = 0; i

Answered: 10. int recursiveFun5(int n) { } for (i…

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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Use Master Therom to determine the complexity of the following:

10. int recursiveFun5(int n)
{
}
for (i = 0; i<n; i+= 2) {
// do something
}
if (n <=0)
return 1;
else
return 1 + recursiveFun5(n-5);

Expert Solution

Step 1: identify recursive relation:

To determine the time complexity of the provided code using the Master Theorem, we need to identify the recurrence relation. In this code, we have a loop that runs from 0 to n with a step size of 2, and we also have a recursive function recursiveFun5(n-5).

The recurrence relation can be defined as follows:

T(n) is the time complexity of the algorithm for an input of size n.
In each recursive call, we reduce the problem size by 5 (n → n-5).
The loop runs from 0 to n with a step size of 2, so the number of iterations is n/2.

Therefore, we can express the recurrence relation as:

T(n) = T(n - 5) + n/2

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