Homework 2 Solution

This assignment is worth 15 points and will be due at 11:00pm. All assignment deadlines are firm and the ability to submit your assignment will be disabled after the deadline elapses. No late work will be accepted. You are encouraged to start this assignment as soon as possible so that you have ample time to seek assistance should you experience difficulties completing or submitting this assignment.




This programming assignment does not have a single solution, and the assignment you submit must be your own original work. Collaboration with other students is not permitted on homework assignments. Any submission may be processed with comparison software and the results will be used to detect unacceptable collaboration between individuals. If you need assistance, you should only consult course staff regarding your program.




Your program must adhere to the course programming standards (available in the course packet and in Blackboard). Please review this document before submitting your assignment, because failure to adhere to it will result in a reduction in points. Your program must include the designated program header (~cs15x/student/hdrProg) at the top of the program (which can be inserted in vi using the hp shortcut while in command mode). The header must include an appropriate description of your program and must contain your official Purdue career account e-mail address. Also note that course standards prohibit the use of advanced programming concepts not yet introduced in the course, unless otherwise specified.




Each of the example executions provided below represents a single execution of the program. Your program must accept input and produce output exactly as demonstrated in the example executions. Your program will be tested with the data seen in the examples below and an unknown number of additional tests making use of reasonable data. Do not include any example outputs with your submission.




A single program file (with the .c extension) must be submitted electronically via the guru server. An example submission was conducted during the first week in lab00. Any attempts to submit via another method will be denied consideration. You may make multiple submissions before the deadline, but only the last attempt is retained and graded. All previous submissions will be over-written and cannot be recovered. The submission script will reject the submission of any file that does not compile. A program must compile to be considered for partial credit. You should always check the confirmation e-mail you receive after a submission to verify that you have submitted the correct file, to the correct assignment, and to the correct lab section. If you have a concern regarding how to submit work, please visit course staff prior to the assignment deadline.

Problem: Data sets are often required to be in a sorted state to make certain types of analysis easier and a variety of sorting algorithms exist to assist scientists and engineers to complete this task. Sorting algorithms are primarily categorized by their run time complexity. This is given in the form of a formula based on the size of the data set (a positive integer n). This generates an estimation of how much “work” is necessary to complete the sort. The reason behind the different complexity of sorting algorithms is that some have more (or fewer) instructions (“work”) which means that each attempt to sort takes a longer (or shorter) amount of time.




Even among sorting algorithms of the same run time complexity there is another factor related to the time it takes to execute the types of individual instructions used and will be represented by a coefficient by which the formula is multiplied.




Given the data set size, the complexity category, and coefficient for two algorithms determine; (1) the run time for each algorithm, (2) identify the faster algorithm, and (3) the difference in time between the two selections.







Example Execution #1:


Notes on Example Execution #1:
-=- Algorithm Complexity
Options -=-
● Both algorithms are from the same




1. Linear time [n]


complexity category (1).


● The first algorithm has a smaller coefficient
2. Logarithmic time [nlog(n)]
3. Exponential time [n^2]


than the second.




● The run time is a product of complexity
Enter the size of the data set to sort - 500
formula, the data set size, and the given
Select complexity option
#1-1
coefficient.
Enter the coefficient of
algorithm #1 - 10


Select complexity option
#2-1


Enter the coefficient of
algorithm #2 - 15


Time for algorithm #1 in
seconds: 5000.000


Time for algorithm #2 in
seconds: 7500.000


Faster algorithm #: 1




Time difference (seconds): 2500.000








Example Execution #2:




-=- Algorithm Complexity
Options -=-





Linear time [n]
Logarithmic time [nlog(n)]
Exponential time [n^2]



Enter the size of
the
data set
to
sort - 100
Select complexity
option
#1 -
1


Enter the coefficient
of
algorithm #1 - 125
Select complexity
option
#2 -
3


Enter the coefficient
of
algorithm #2 - 2
Time for algorithm #1
in
seconds:
12500.000
Time for algorithm #2
in
seconds:
20000.000
Faster algorithm #: 1











Time difference (seconds): 7500.000




Example Execution #3:




Notes on Example Execution #3:
-=- Algorithm Complexity
Options -=-
●
Log is base 2.






1. Linear time [n]




● nlog(n) is the product of n and log(n).








2. Logarithmic time [nlog(n)]




3. Exponential time [n^2]






Enter the size of the
data set to sort - 200




Select complexity option
#1-2




Enter the coefficient
of
algorithm #1 - 5




Select complexity option
#2-1




Enter the coefficient
of
algorithm #2 - 38.3




Time for algorithm #1
in
seconds: 7643.856




Time for algorithm #2
in
seconds: 7660.000




Faster algorithm #: 1








Time difference (seconds): 16.144












Example Execution #4:




Notes on Example Execution #4:
-=- Algorithm Complexity
Options -=-
●
When the time for the two selections is






1. Linear time [n]






identical then display the second algorithm






as being faster.
2. Logarithmic time [nlog(n)]


3. Exponential time [n^2]






Enter the size of the
data set to sort - 760




Select complexity option
#1-1




Enter the coefficient
of
algorithm #1 - 760




Select complexity option
#2-3




Enter the coefficient
of
algorithm #2 - 1




Time for algorithm #1
in
seconds: 577600.000




Time for algorithm #2
in
seconds: 577600.000




Faster algorithm #: 2








Time difference (seconds): 0.000







Additional Notes:




All floating-point variables must be declared to be of the double type to best match our expected results.



The data set size will always be a positive integer value.
Complexity options will always be 1, 2, or 3.
Coefficients will be non-negative.



This assignment uses logic similar to the selection by calculation examples shown in lecture (p. 83-84 of the course packet).



Course standards prohibit the use of programming concepts not yet introduced in lecture. For this assignment you can only consider material in the first 3 chapters of the book, notes, and lectures. Use of advanced programming constructs beyond this material would result in a loss of points.