Distributed: Friday, 27 October 2006
Due: 9:00 a.m., Friday, 3 November 2006
No extensions.
This page may be found online at http://www.cs.grinnell.edu/~rebelsky/Courses/CS151/2006F/Exams/exam.02.html.
This exam is also available in PDF format.
Contents
There are four problems on the exam. Some problems have subproblems.
Each problem is worth twenty-five (25) 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 as restricted by 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, via IM, by posting a please help
message, or in any
other way) 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.
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. In particular, 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 also appreciate it if you would write down the amount of time
each problem takes. Each person who does so will earn two points of
extra credit. 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 Professor Rebelsky (that's me) or Professor Davis.
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 present your exam to me in two forms: both physically and
electronically. That is, you must write all of your answers using the
computer, print them out, number the pages, put your name on the top
of every page, and hand me the printed copy. You must also email me
a copy of your exam. You should create the emailed version by copying
the various parts of your exam and pasting them into an email message.
In both cases, you should put your answers in the same order as the
problems. Failure to name and number the printed pages will lead to a
penalty of two points. Failure to turn in both versions may lead to
a much worse penalty.
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.
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 will also reserve time at the start of classes next week
to discuss any general questions you have on the exam.
Topics: Vectors, Recursion, Searching, Unit Testing.
As you may recall, we have found it useful to write a member?
procedure for lists. This procedure takes two parameters, a value and
a list, and returns true (#t) if the value appears in the list
and false (#f) otherwise. It is useful to write a similar
procedure for vectors. However, since indices are important for vectors,
the procedure should return the index of the value if it appears, and
#f if the value does not appear. We'll call this procedure
index-of.
For example,
> (index-of "Samuel" (vector "Samuel" "Alexander" "Rebelsky"))
0
> (index-of "Rebelsky" (vector "Samuel" "Alexander" "Rebelsky"))
2
> (index-of "SamR" (vector "Samuel" "Alexander" "Rebelsky"))
#f
> (index-of 13 (vector 2 3 5 7 11 13 17 23))
5
> (index-of 9 (vector 2 3 5 7 11 13 17 23))
#f
a. [5 points] Document index-of.
b. [10 points] Implement index-of. You may not use vector->list in your implementation.
c. [10 points] Write a test suite for index-of, using the Unit Testing
framework we studied.
Topics: Strings, Trees, Deep Recursion
In past semesters, students have asked me how Scheme prints lists.
To explain, I've been known to write a short procedure that converts
lists of symbols to strings (because lists of symbols provide a
sufficiently complex and sufficiently simple example). Here's the
procedure:
;;; Procedure:
;;; symbols->string
;;; Parameters:
;;; symbols, a list of symbols [unverified]
;;; Purpose:
;;; Converts the list to a string similar to one that might be
;;; printed for the list.
;;; Produces:
;;; symstr, a string
;;; Preconditions:
;;; (none)
;;; Postconditions:
;;; symstr is a value such that if you write symstr to a file using
;;; write, then you get the same result as if you'd written symbols
;;; to a file using display.
;;; Process:
;;; We treat the empty string as a special case, and just print
;;; the open and close parens.
;;; For all other cases, we concatenate an open paren, the first
;;; symbol, the remaining symbols, and a close paren.
;;; We use a recursive kernel to process the remaining symbols.
;;; Because we've printed one symbol already, we can precede each
;;; remaining symbol with a space.
(define symbols->string
(letrec ((kernel (lambda (symbols)
(cond
((null? symbols) "")
(else (string-append " "
(symbol->string (car symbols))
(kernel (cdr symbols))))))))
(lambda (symbols)
(cond
((null? symbols) "()")
(else (string-append "("
(symbol->string (car symbols))
(kernel (cdr symbols))
")"))))))
a. [10 points] As you've probably noted, this procedure works only with lists of symbols.
However, it should be possible to make it work with things very much like
lists, except that they end with a symbol, rather than null. Rewrite it
so that it accepts such structures.
> (symbols->string (list 'a 'b 'c))
"(a b c)"
> (symbols->string null)
"()"
> (symbols->string (cons 'a 'b))
"(a . b)"
> (symbols->string (cons 'a (cons 'b 'c)))
"(a b . c)"
Hint: Add another base case in the kernel, one that checks if
symbols is a single symbol.
b. [5 points] Some folks think it's useful to make procedures like
symbols->string work with singleton values in addition
to pair structures. Extend symbols->string so that it
accepts a single symbol as a parameter and returns a string for that
symbol.
> (symbols->string 'a)
"a"
c. [10 points] Now that you've made symbols->string work with one form
of pair structure and with singletons, you should be able to make it work
with more general
pair structures. In particular, it should work with trees of symbols and
with lists of lists of symbols.
Rewrite symbols->string so that it works with such values.
For example,
> (symbols->string (list 'a 'b 'c))
"(a b c)"
> (symbols->string null)
"()"
> (symbols->string (cons 'a 'b))
"(a . b)"
> (symbols->string (cons 'a (cons 'b 'c)))
"(a b . c)"
> (symbols->string (cons (cons 'a 'b) (cons 'c 'd)))
"((a . b) c . d)"
> (symbols->string (list (list 'a 'b) (list 'c 'd) (list 'e 'f)))
"((a b) (c d) (e f))"
> (symbols->string (list null (list null)))
"(() (()))"
> (symbols->string (cons 'a (cons (cons (cons 'b 'c) 'd) 'e)))
"(a ((b . c) . d) . e)"
> (symbols->string 'a)
"a"
Hint: Consider the points in which the procedure calls
symbol->string
on the car of a pair. Since you no longer know that the car is a symbol,
you'll need to do something else, since the car may be a symbol, a null,
or a pair. Your primary task is to figure out what you should do.
(To figure out what you might do, reflect on
the reading on deep recursion.)
Topics: Files, Random Generation, Matching
Egelloc College wants to write a simple roommate matching procedure.
For each student, we have last name, first name, year (1, 2, 3, or 4),
smoker?, bedtime (early/late), political views (liberal/conservative),
and favorite color. They have decided to store the values in a
vector and have created a procedure that constructs such vectors.
(define student-info
(lambda (last-name first-name year smokes? bedtime politics color)
(cond
((not (string? last-name))
(error "student-info: first parameter (last-name) must be a string"))
((not (string? first-name))
(error "student-info: second parameter (first-name) must be a string"))
((or (not (integer? year)) (< year 1) (> year 4))
(error "student-info: third parameter (year) must be an integer between 1 and 4"))
((not (boolean? smokes?))
(error "student-info: fourth parameter (smokes?) must be a boolean"))
((not (member bedtime (list 'early 'late)))
(error "student-info: fifth parameter (bedtime) must be 'early or 'late"))
((not (member politics (list 'liberal 'conservative)))
(error "student-info: sixth parameter (politics) must be 'liberal or 'conservative"))
((not (string? color))
(error "student-info: seventh parameter (color) must be a string"))
(else
(vector last-name first-name year smokes? bedtime politics color)))))
They have also provided accessors for all of the fields.
(define get-last-name
(lambda (student)
(vector-ref student 0)))
(define get-first-name
(lambda (student)
(vector-ref student 1)))
(define get-year
(lambda (student)
(vector-ref student 2)))
(define smokes?
(lambda (student)
(vector-ref student 3)))
(define get-bedtime
(lambda (student)
(vector-ref student 4)))
(define get-politics
(lambda (student)
(vector-ref student 5)))
(define get-favorite-color
(lambda (student)
(vector-ref student 6)))
Here's a very short sample file of students (sample-students.scm):
#7("Smith" "Joe" 1 #f early conservative "blue")
#7("Jones" "Jane" 2 #t late liberal "yellow")
#7("Emilyson" "Jacob" 2 #f late liberal "purple")
#7("Smithson" "Jack" 1 #t late liberal "purple")
#7("Sonsmith" "Jenna" 2 #f early liberal "yellow")
a. [15 points] Write and test a procedure, suggest-roommate, that
takes two parameters -- student, a student vector, and
file-of-students, the name of a file containing a list of students,
and (1) makes a list of all the good
matches for student from the file of students, (2) randomly selects
one of those matches, and (3) reports the name of that student in
the form "Last-name, First-name".
A good match is one in which the years match and at least three out of
the remaining four values match.
If there is no good match, have your procedure return #f.
For example, suggest-roommate, given a 2nd-year, smoking,
early-to-bed, liberal, lover of the color yellow and the list above must
return either "Jones, Jane" or "Sonsmith, Jenna",
since each of those students are second year students, and Jane matches
on smoking, politics, and color while Jenna matches on bedtime, politics,
and color. Jacob Emilyson, the only other second year, matches only on
politics, and so should not be considered.
> (suggest-roommate (student-info "Doe" "Dee" 2 #t 'early 'liberal "yellow") "sample-students.scm")
"Jones, Jane"
b. [10 points] Of course, Egelloc would never release information about
its students to a contract programmer, so you will need to generate
simulated data to test your procedure. (You can use the sample above,
but it's pretty short, so you will still need to solve this part of the
problem eventually.)
Write a procedure, (generate-random-students filename
n) that generates n random student entries and
shoves them in the file with the given name.
Topics: Husk/Kernel programming, List recursion, Local bindings
In grading, I often end up with a list of name/grade pairs for the
students in my class. It would be convenient if I could separate that
big list into four lists: students with A's, B's, C's, and D's. Assume
that every pair contains a string as its car and an integer as its cdr.
a. [15 points] Write a procedure, process-grades, that takes a list
of name/grade pairs as parameters and produces a list of four lists,
- The first list contains all students that deserve A's (have a grade of 90 or higher).
- The second list contains all students that deserve B's (have a grade between 80 and 89, inclusive).
- The third lists contains all students that deserve C's (have a grade between 70 and 79, inclusive).
- The final list contains all students that deserve D's (have a grade below 70).
The order of the names within the individual lists does not matter.
Here's an example of process-grades in action:
> (process-grades (list (cons "Sam" 90)
(cons "Eryn" 85)
(cons "Emily" 85)
(cons "Joe" 60)
(cons "Jane" 65)
(cons "Janet" 100)))
(("Sam" "Janet") ("Eryn" "Emily") () ("Joe" "Jane"))
You need not test preconditions for part a of the problem.
b. [10 points] Of course, it is useful to test preconditions. Hence for this part
of the problem, you must wrap your answer from the previous step in a
husk/kernel for precondition testing (in particular, that the list is
of the appropriate form and that all the grades are in the range 0-100).
You must make the kernel local.
You should report errors using the following protocol:
- If the parameter is not a list, report grades: expects a list as a parameter
- If the parameter contains an entry that is not of the form (cons string number), report grades: expects each list element to be a string/number pair.
- If the parameter contains an entry with a grade below 0 or over 100, report grades: all grades must be in the range [0..100]. However, name has a
grade of grade.
These are some of the questions students have asked about the
exam and my answers to those questions.
- My
index-of works fine if the values are all symbols,
but not if they're strings. Why?
- I'd guess that you're using
eq? rather than
equal? to compare values. Recall that identical
strings may occupy different areas of memory, so eq?
does not suffice from comparing strings.
- Should we support both lists and vectors as the second parameter of
index-of?.
- No, you only need to support vectors.
- Can you remind me of the structure of procedures that recurse over
vectors?
- Sure. Here's one that only extracts values from the vector. (You'd
do something different if you were modifying the the vector.)
(define recursive-vector-proc
(letrec ((kernel (lambda (pos vec len)
(if (= pos len)
(BASE-CASE)
(COMBINE (vector-ref vec pos)
(kernel (+ pos 1) vec len))))))
(lambda (vec)
(kernel 0 vec (vector-length vec)))))
- Do we have to document kernel and husk?
- If the kernel is local, you need not document it.
- How many P's?
- The basic six P's.
- Will we get extra credit for using more than six P's?
- It depends on (a) the correctness of the extra documentation and (b) my mood. Note that incorrect extra documentation will incur a penalty.
- Do we have to record all instances the value is in the vector, or just the first time it appears?
- You need only report one of the indices if it appears multiple
times. The first index is fine, but the last is also okay, as is any
other one. Just make sure to document what you've done.
- For part c, should we expect to do a significant rewrite of our answer
for part b, or is it simply a case of making a few key changes?
- You should be able to make only a few changes. As the problem suggests,
you'll need to change each call to
(symbol->string (car symbols)) to something else.
- Was there an error in the sample file, wherein the symbols were quoted?
- Um, yes. It is now fixed.
- Can you remind me of the structure of a procedure that recurses over an
input file, particularly since we learned about local variables and local procedures after we did input and output?
- Sure. Here's the general structure:
(define recursive-read-file-proc
(letrec ((kernel (lambda (input-port)
(let ((val (read input-port)))
(cond
((eof-object? val)
(close-input-port input-port)
(BASE-CASE))
(else
(COMBINE val (kernel input-port))))))))
(lambda (fname)
(kernel (open-input-file fname)))))
- Can you give me some hints as to how to get started?
- You might find it useful to define a separate
(good-match? student1 student2) procedure. You might find it even more useful to make the first version of that procedure return true if the two students are the same year and false otherwise. (That is, to pay attention only to year.) Once you've defined this helper, make suggest-roommate extract just the good matches from the file.
- Okay, I can now select all the
good
matches, randomly select one of them (particularly since you just taught us how), and extract the first and last name. Now I'm back to writing the good-match? helper. I'm trying to figure out how to make sure that at least three attributes match. Any suggestions?
- One strategy is to write four additional helpers (or simply local variables), each of which evaluates one of the four attributes and returns (takes the value) 0 if the attributes don't match and 1 if the attributes do match. I'll leave it to your imagination how to use those helpers.
- Can we select the first name randomly from a list, or do we need to do something more sophisticated?
- Selecting randomly from a list is fine.
- If we do something more sophisticated, will we receive extra credit?
- If you do something more sophisticated and it's wrong, you will receive negative extra credit. If you do something more sophisticated and it's right, you may or may not receive extra credit, depending on what you've done and the mood I'm in.
- I've written a
random-student helper, and I want to test it. Can you show me a series of commands I'd use to write, say, 3 random students to a file?
- Here goes ...
(define rs (open-output-file "random-students"))
(write (random-student) rs)
(newline rs)
(write (random-student) rs)
(newline rs)
(write (random-student) rs)
(newline rs)
(close-output-port rs)
- Would it help to have some named students?
- Yes. Here are some.
(define joe-smith #7("Smith" "Joe" 1 #f early conservative "blue"))
(define jane-jones #7("Jones" "Jane" 2 #t late liberal "yellow"))
(define dee-doe (student-info "Doe" "Dee" 2 #t 'early 'liberal "yellow"))
- For this problem, I wrote four separate helpers. One extracts the
A names, one extracts the B names, one extracts the C names, and one
extracts the D names. What do you think of this strategy?
- Not much. You traverse the list four times. I'd really prefer that
you traverse the list only once.
- Given that you don't like this nice, clean, straightforward strategy,
how much are you going to take of if I use it anyway?
- Not much. Let's see ... the problem is worth 15 points. That's a
B-level solution. Hence, I'll take off 3 points.
- Do you have a recommendation for how I should check whether grade is in the range 80..89, inclusive?
(<= 80 grade 89)
- Why do you penalize us for doing incorrect extra work? It seems that such penalties will discourage us for trying extra things?
- First, I want you to focus on doing the problems correctly, not on
what else can I do?
Second, I have encountered students in the past who simply throw in anything they can think of with the hope that doing so will earn them a bit of credit. I certainly want to discourage such activities.
- How about if I add something Trogdor-related to the exam?
- If it's pertinent, that may give you some points.
- If someone in the other class catches an error in their version of the exam, and the same error appears in our version, do we get credit for it?
- Not if I fix it before someone in this class tells me.
- Are you concerned about the number of questions and answers that appear here?
- No. A few questions are
resolve ambiguities
and, while a lot of
those would concern me, a few aren't bad. From my perspective, most of the
questions are a variant of Assess what I've done
or Can you
give me a hint?
I've chosen how much help to give in those cases
and, intead of limiting the hint to one student, I've shared it with the
class.
Here you will find errors of spelling, grammar, and design that
students have noted. Remember, each error found corresponds to a
point of extra credit for everyone. I usually limit such extra credit to
five points. However, if I make an astoundingly large number of errors,
then I will provide more extra credit.
- Sam forgot to remove
This exam is currently in draft format!
from the released version. [SR, 1 point]
- Sam doesn't know the difference between lists and vectors. [MP and TP, 2 points]
- purplese is not a color. [MP, 1 point]
- The symbols in the sample file should not be quoted [TP, 2 points].
Additional errors.
- Sam wrote
dr instead of cdr in Problem 4. [SB]
- Sam wrote
Jenna matches on bedtime politics
rather than
Jenna matches on bedtime, politics
, giving a whole different
meaning to the attribute. [TM]
Thursday, 26 October 2006 [Samuel A. Rebelsky]
Friday, 27 October 2006 [Samuel A. Rebelsky]
- Minor updates to clarify problem 2.
- Added point values for subproblems.
- Released.
Saturday, 28 October 2006 [Samuel A. Rebelsky]
- Added questions and answers for problem 1.
Sunday, 29 October 2006 [Samuel A. Rebelsky]
- Added a
recurse over file
template for problem 3.
Monday, 30 October 2006 [Samuel A. Rebelsky]
Tuesday, 31 October 2006 [Samuel A. Rebelsky]
- Lots of questions and answers. Yay!
Wednesday, 1 November 2006 [Samuel A. Rebelsky]
- Reformatted the question and answer section.
- Added a few more questions and answers (mostly from class). The
question on what
index-of should do when a value
appears multiple times is one taken from Dr. Davis's version of the exam,
but the answer is mine Dr. Davis's version of the exam can be found
at http://www.cs.grinnell.edu/~davisjan/csc/151/2006F/exams/exam2.html.
;
