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
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
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

Transcribed Image Text: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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