Distributed: Monday, 28 April 2003
Due: 2:15, Friday, 9 May 2003
No extensions.
This page may be found online at
http://www.cs.grinnell.edu/~rebelsky/Courses/CS151/2003S/Exams/exam.03.html.
Contents
There are three problems on the exam. Some problems have subproblems.
Each full problem is worth thirty-three points. The point value associated
with a problem does not necessarily correspond to the complexity
of the problem or the time required to solve the problem.
This examination is open book, open notes, open mind, open computer,
open Web. However, it is closed person. That means you should not talk
to other people about the exam. Other than that limitation, you should
feel free to use all reasonable resources available to you. As always,
you are expected to turn in your own work. If you find ideas in a book
or on the Web, be sure to cite them appropriately.
Although you may use the Web for this exam, you may not post your answers
to this examination on the Web (at least not until after I return exams
to you). And, in case it's not clear, you may not ask others (in person,
via email, or by posting a please help
message) to put answers
on the Web.
This is a take-home examination. You may use any time or times you deem
appropriate to complete the exam, provided you return it to me by the
due date.
This exam is likely to take you about four to six hours, depending on
how well you've learned topics and how fast you work. You should not
work more than eight hours on this exam. Stop at eight hours and
write There's more to life than CS
and you will earn at
least 80 points on this exam. I would appreciate it if
you would write down the amount of time each problem takes. I expect that
someone who has mastered the material and works at a moderate rate should
have little trouble completing the exam in a reasonable amount of time.
Since I worry about the amount of time my exams take, I will give two
points of extra credit to the first two people who honestly report that
they've spent at least five hours on the exam or completed the exam.
(At that point, I may then change the exam.)
You must include both of the following statements on the cover sheet of the
examination. Please sign and date each statement. Note that the
statements must be true; if you are unable to sign either statement,
please talk to me at your earliest convenience. You need not reveal
the particulars of the dishonesty, simply that it happened. Note also that
inappropriate assistance
is assistance from (or to) anyone
other than myself or our teaching assistant.
1. I have neither received nor given inappropriate assistance on this
examination.
2. I am not aware of any other students who have given
or received inappropriate assistance on this examination.
Because different students may be taking the exam at different times,
you are not permitted to discuss the exam with anyone until after I
have returned it. If you must say something about the exam, you are
allowed to say This is among the hardest exams I have ever
taken. If you don't start it early, you will have no chance of
finishing the exam.
You may also summarize these policies.
You may not tell other students which problems you've finished.
You may not tell other students how long you've spent on the exam.
You must both answer all of your questions electronically and turn in a
printed version of your exam. That is, you must write all of your answers
on the computer, print them out, number the pages, put your name on
every page, and hand me the printed copy. You must also email me a copy
of your exam by copying your exam and pasting it into an email message.
Put your answers in the same order as the problems. Make sure that your
solution confirms to the format for
laboratory writeups (except that you should not tell me the location
in the MathLAN or on the Web, since your code should not be published).
In many problems, I ask you to write code. Unless I specify otherwise
in a problem, you should write working code and include examples that show
that you've tested the code.
You should document all of your primary procedures. In most cases, a
few sentences will suffice. In a few cases, I'll ask you to provide
the full documentation (including parameters, purpose, value produced,
preconditions, and postconditions). If you write helper procedures
(and you may certainly write helper procedures) you should document
those with a few short notes. When appropriate, you should include
short comments within your code. You should also take care to format
your code carefully.
Just as you should be careful and precise when you write code and
documentation, so should you be careful and precise when you write prose.
Please check your spelling and grammar. Since I should be equally
careful, the whole class will receive one point of extra credit for each
error in spelling or grammar you identify on this exam. I will limit
that form of extra credit to five points.
I will give partial credit for partially correct answers. You ensure
the best possible grade for yourself by emphasizing your answer and
including a clear set of work that you used to derive the
answer.
I may not be available at the time you take the exam. If you feel that
a question is badly worded or impossible to answer, note the problem you
have observed and attempt to reword the question in such a way that it
is answerable. If it's a reasonable hour (before 10 p.m. and after 8
a.m.), feel free to try to call me in the office (269-4410) or at home
(236-7445). [I'll be gone from noon Friday to 5 p.m. Sunday, so don't
call during those times.]
I will also reserve time at the start of classes this week and next
to discuss any general questions you have on the exam.
Topics:
Algorithms, Strings, Comparison, Deep Recursion, Vectors
Your old pals, Sarah and Steven Schemer, are upset that they have
to keep rewriting similar less-than? predicates. For
example, they must remember to use
-
string-ci<? for strings,
-
< for numbers,
-
(lambda (x y) (string-ci<? (car x) (car y))) for lists
whose key is a string found in position 0,
- and so on and so forth.
They've decided that someone
should write a general
less-than? predicate that can compare any reasonable pairs
of values. Of course, Sarah and Steven are much better at deciding what
they'd like to do than at actually doing it. Hence, they've asked you
to implement less-than? for them. Your sentient
and malicious instructor agrees, although he is willing to let you forgo
the careful documentation that he usually requires. He is also willing
to forgo having you implement every possible type.
Here's what he'd like you to do for less-than?.
- If both parameters are strings,
less-than?
should use string-ci<? to compare the two parameters.
- Otherwise, if both parameters are real numbers (including integers
and rational numbers),
it should use
< to compare the two parameters.
- Otherwise, if one parameter is a real number and one is a string,
it should convert the number to a string and compare the two values
using
string-ci<? to compare the two strings.
- Otherwise, if both parameters are vectors, it should compare each
element in turn (i.e., element 0 of each vector, then element 1 of
each vector, then element 2 of each vector, and so on and so forth)
until either (1) one vector runs out of elements, in which case that
vector is
smaller
or (2) the given element of one vector is
smaller than the corresponding element of the other vector, in which
case the vector with the smaller element is smaller.
- Otherwise, if one parameter is a vector and one parameter is not, it
should compare element 0 of the vector to the value using the
technique described above.
- Otherwise,
less-than? should report an error with
the error procedure.
1. Theodore and Thelma Theoretician take one look at Sarah and Steven's
suggestions and start to chuckle. They say
One of the key characteristics of the standard may-precede?
parameter to sorting and searching algorithms is that it is
transitive. That is, if a may precede b
and b may precede c, then a may precede
c. Unfortunately, there are values for which less-than?
is not transitive.
Find three values, a, b, and c, such
that
> (less-than? a b)
#t
> (less-than? b c)
#t
> (less-than? a c)
#f
You should not use vectors in solving this problem.
Hint: Consider cases in which you need to modify one or
both of the parameters.
This problem is worth 2 points of extra credit.
2. Extend less-than? to handle symbols. This problem
is worth 2 points of extra credit.
Topics:
Higher-Order Procedures, Vectors, Files
One of the tasks faculty frequently encounter is the assignment of a
letter grade based on the numeric grades that students have received
over the course of a semester. Grading rubrics differ greatly. Some
faculty simply average grades; others sum grades; others give different
aspects different weights.
Suppose we've decided to store all the grades for a class in a file.
One mechanism would be to have one vector for each student in the class.
The vector will have the form
#(last-name first-name email grade1 grade2 ... graden)
For example, here are the grades for a fictitious class in which
students have received four grades (presumably for three exams and a
final).
#("Aardvark" "Arnie" "aa@grinnell.edu" (100 50 80 90))
#("Beetle" "Betty" "bb@grinnell.edu" (85 85 90 85))
#("Chihuahua" "Chuck" "cc@grinnell.edu" (90 90 90 0))
#("Dingo" "Donna" "dd@grinnell.edu" (95 95 95 80))
#("Elephant" "Ernie" "ee@grinnell.edu" (5 0 0 0))
#("Fox" "Fiona" "ff@grinnell.edu" (80 80 80 100))
#("Giraffe" "Gene" "gg@grinnell.edu" (50 50 50 50))
You can find this example in the file
samplegrades.
How will we process the file of grades? By reading each entry
from the file, calling an appropriate grading procedure, and
doing something with the result. For example, we might write
the results to a file.
If we write the results to a file, the procedure we write for processing
grades needs at least two parameters: the name of the input file and the
name of the output file.
Are there others? To make our procedure as
general as possible, we can also make the grading procedure a parameter.
For example, if a faculty member's rubric is average the grades
,
the procedure can be
(lambda (grades) (divide (sum grades) (length grades)))
Similarly, if a faculty member's rubric is
average the grades after dropping the lowest
, the
procedure can be
(lambda (grades)
(divide (- (sum grades) (min grades))
(- (length grades) 1))
For the more complex best two of three
exams count 50%; final counts 50%
, we might write
(lambda (grades)
(let* ((sedarg (reverse grades))
(final (car sedarg))
(exams (cdr sedarg)))
(+ (divide final 2)
(divide (- (sum exams) (min exams)) 4))))
Note that for computing grades, we don't care about the name or
email; we care only about the numbers.
Problem:
Document, write, and test a procedure,
(process-grades infile outfile gradeproc),
that reads a sequence of grade entries from the file named infile,
processes each entry with gradeproc, creates a new vector that
includes the result (along with the original components), and writes all
the new vectors to outfile.
For example, for the example above with the rubric of
use the best grade
, the output file might contain
#("Aardvark" "Arnie" "aa@grinnell.edu" (list 100 50 80 90) 100)
#("Beetle" "Betty" "bb@grinnell.edu" (list 85 85 90 85) 90)
#("Chihuahua" "Chuck" "cc@grinnell.edu" (list 90 90 90 0) 90)
#("Dingo" "Donna" "dd@grinnell.edu" (list 95 95 95 80) 95)
#("Elephant" "Ernie" "ee@grinnell.edu" (list 5 0 0 0) 5)
#("Fox" "Fiona" "ff@grinnell.edu" (list 80 80 80 100) 100)
#("Giraffe" "Gene" "gg@grinnell.edu" (list 50 50 50 50) 50)
In grading this problem, I will look at how well you process the
input file, how well you generate the output file, and how you deal
with procedures as parameters. If you cannot do everything right, you
should attempt to show your ability to do some aspects by simplifying
some parts of the problem (e.g., by reading grades from a list rather
than a file, by generating a list rather than a file, or by hard-coding
the grading procedure).
Topics: Sorting, Higher-Order Procedures, Vectors
Vern and Violet Vector love Amanda-sort (which most computer scientists
typically call Insertion Sort). They are, however, somewhat
frustrated that the standard insertion-sort procedure we've written
only works on lists. They realize that they can sort a vector by
converting it to a list, sorting the list, and converting it back to
a vector. However, they'd rather sort the vector directly.
They happily notice that I've written and documented such a procedure,
insertion-sort!, in the
first reading on sorting. Here's what it looks like:
(define insertion-sort!
(lambda (may-precede? vec)
(let ((len (vector-length vec)))
(let kernel ((boundary 1)) ; The index of the first unsorted value
(if (< boundary len) ; If we have elements left to sort
(begin
(insert! (vector-ref vec boundary)
vec
boundary
may-precede?)
(kernel (+ boundary 1))))))))
To their dismay, they quickly discover that I've failed to implement the
needed insert! procedure. As you may guess, they've turned
to you for help.
a. Document that procedure.
b. Write that procedure.
Hint: Work backward from boundary.
c. Show how to use insertion-sort! to sort the following
vector of faculty by last name. When two or more last names are the
same, order within those last names by first name. You may not use your
less-than? procedure from problem 1.
(define some-faculty
#(("Ferguson" "Pam" "Mathematics")
("Moore" "Tom" "Statistics")
("Ferguson" "Bill" "Economics")
("Montgomery" "Mark" "Economics")
("Moore" "Emily" "Mathematics")
("Strauber" "Ira" "Political Science")
("Ferguson" "Susan" "Sociology")
("Strauber" "Susan" "Art")
))
For those of you who really like sorting and who have some spare time,
here's a question that can earn you five points of extra credit on the
exam. You may not count this problem toward your eight-hour limit.
Assume that we've decided that all list-sorting procedures should
take two parameters, a list to sort and a may-precede?
predicate. These sorting procedures return a new sorted list.
Write a procedure,
(verify-sort sorting-proc may-precede?
unsorted-list unsorted-list), that verifies
that sorting-proc correctly sorts unsorted-list
using may-precede? to order elements.
These are some of the questions students have asked about the
exam and my answers to those questions.
- Which vector is smaller,
#(1 4 1) or #(1 2 3 4)?
#(1 2 3 4), even though it is longer. Why? Because the
2 in position 1 is smaller than the 4 in position
1 in the other vector.- It's really a pain that I sometimes need strict inequality and
sometimes nonstrict inequalty for
less-than?.
- Agreed. Use only strict inequalty (variants of
<
rather than <=).
- When one paramter is a vector and the other is not, what can
the other
be?
- A number or string.
- Will you add some more examples to the exam?
- My DSL is down and I'm spending much of the day at home, waiting
for the repairman to come. So ... some day, but perhaps not today.
- Why doesn't
insertion-sort! have the else-part of
the if expression?
- Remember,
! procedures need not return anything. For example,
vector-set! doesn't return anything. Hence,
insertion-sort! does not need to return anything,
since its purpose is to change the vector in place
.
It certainly doesn't not need the second part of the if
expression, because once it's done sorting
the vector, it has nothing to return.
Here you will find the errors of spelling, grammar, and
external design. Remember, each error found gets the whole class
a point of extra credit on the exam (with a maximum of five such
points).
- Link to
samplegrades broken. [PD, 1 point]
-
Create a new vector that include
should be
includes. [PD, 1 point]
-
strong
instead for string
in the Q&A section.
[PD, 1 point]
- Sam appears unable to spell his last name. [MC, 1 point]
- Random errors in answer to questions on problem 3. [BW, 1 point]
Sunday, 27 April 2003 [Samuel A. Rebelsky]
- Created first version. (Selected problems, etc.)
Monday, 28 April 2003 [Samuel A. Rebelsky]
Tuesday, 29 April 2003 [Samuel A. Rebelsky]
- Updated
less-than? for strict inequality.
- Added extra credit.
Wednesday, 30 April 2003 [Samuel A. Rebelsky]
Thursday, 1 May 2003 [Samuel A. Rebelsky]
- Added more questions and answers.
Friday, 2 May 2003 [Samuel A. Rebelsky]
- Added the first question and answer on problem 3.
Monday, 5 May 2003 [Samuel A. Rebelsky]
- Corrected the spelling of my name in the history.
Tuesday, 6 May 2003 [Samuel A. Rebelsky]
;
;
Check with Bobby