11. Please Show Your Work!!! Type your scratch work! Thanks Determine the cost function T(n) of the following code fragment. Hint. Assumeworst case for numeric choices.// bool TEST is defined and set by external process before executing this function.It will either be TRUE or FALSE at the start of this function and may change in themiddle of execution.for(int i = 0; i

Answered: Determine the cost function T(n) of the…

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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11. Please Show Your Work!!! Type your scratch work! Thanks

Determine the cost function T(n) of the following code fragment. Hint. Assume
worst case for numeric choices.
// bool TEST is defined and set by external process before executing this function.
It will either be TRUE or FALSE at the start of this function and may change in the
middle of execution.
for(int i = 0; i<n; ++i) {
if(TEST) {
}
for(int j = 0; j<n; ++i) {
score += i+j;
}
} else {
}
score +=i*j;
Assume operator ^ takes a fixed constant amount of time.
REQUIRED: Show line by line costs of T(n) and final T(n).
What is the final order of growth expression with asymptotic assumptions in terms of
O(...)?

Expert Solution

Step 1

Solution:

The cost function T(n) of the given code fragment can be calculated as follows:

Initialization of variables: The initialization of the variable i takes constant time, so the cost is 1.
For loop: The for loop runs n times. Each iteration performs a constant amount of work,

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