Distributed: Friday, February 16, 2007
Due: 10:00 a.m., Friday, February 23, 2007
This page may be found online at
This exam is also available in PDF format.
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.
Unless I explicitly ask you to document your procedures, you need not write introductory comments.
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: Types, Predicates, Strings
We've now encountered a wide variety of basic types in our exploration
of Scheme, including integers (exact and inexact), real numbers,
lists, strings, and even procedures. We've used predicates such as
list? that let us ask whether a value is of a particular
type. However, Scheme provides no obvious mechanism for reporting the
type of an arbitrary value.
Write a procedure,
(describe val), that returns a string
describing the type of val. If val is not of a type we've learned about,
report that val is
"a value of unknown type". For example,
> (describe 1) "an exact integer" > (describe 3.4) "an inexact real number" > (describe (list 1 2 3)) "a list" > (describe null) "an empty list" > (describe null?) "a procedure" > (describe (cons 1 2)) "a value of unknown type"
As you might expect, one of the goals of this question is for you to figure out what types you know about.
Note that our version of Scheme does not distinguish real numbers from rational numbers, so you need not do so either. I generally make it a practice to refer to exact non-integral real/rational numbers as rational and to inexact non-integral real/rational numbers as real.
Topics: Conditionals, Booleans, Recursion, Style, Predicates
You may recall that I've written that I don't like to see if statements that explicitly return #t or #f since you can easily rewrite them using some combination of and, or, and not. For example,
(if test1 #t #f)=>
(if test1 #f #t)=>
(if test1 #t test2)=>
(or test1 test2)
(if test1 test2 #f)=>
(and test1 test2)
(if test1 test2 test3)=>
(or (and test1 test2) (and (not test1) test3))
For each of the following predicate procedures:
(a) (5 points)
(define mystery? (lambda (val) (if (symbol? val) #t (if (string? val) #t #f))))
(b) (5 points)
(define puzzle? (lambda (a b c) (if (< a b) (if (< b c) #t #f) (if (< b c) #f #t))))
(c) (5 points)
(define conundrum? (lambda (lst) (if (list? lst) (if (null? lst) #f (null? (cdr lst))) #f)))
(d) (10 points) Note that this procedure is recursive.
(define enigma? (lambda (lst) (if (null? lst) #t (if (symbol? (car lst)) (enigma? (cdr lst)) #f))))
Topics: Lists, List construction procedures, List recursion
Many of you have been a bit frustrated by the problem of choosing whether
creating lists. Rather than having to remember the details each time,
we might instead write a procedure that combines the capabilities of
the three procedures, and perhaps even adds other capabilities.
Define a procedure,
(join val1 val2), that
follows the following four guidelines (labeled a-d)
join is presented with two lists, it appends them
append. For example,
> (join (list 1 2 3) (list 'a 'b)) (1 2 3 a b) > (join null (list "left" "right")) ("left" "right") > (join (list #\a #\b #\c) null) (#\a #\b #\c)
join is presented with a simple value and a list as
parameters (in that order), it prepends the value to the list.
> (join #t (list #f #f #f)) (#t #f #f #f) > (join "silly" null) ("silly")
join is presented with a list and a simple value as
parameters (in that order), it puts the value at the end of the list.
> (join (list "Grinnell" "has" "no") "limits") ("Grinnell" "has" "no" "limits") > (join (list 1 2 3 4) 5) (1 2 3 4 5) > (join null 'llun) (llun)
join is presented with two simple values as
parameters, it puts them into a list.
> (join 'a 'b) (a b) > (join #t #f) (#t #f)
Note that you should define a single
join that has all
four behaviors. If you find it helpful to write helper procedures
(such as a procedure that puts a value at the end of a list), you may
certainly do so.
The preceding refers to
simple values. For the purposes of this
problem, we'll define a value as
simple if it is not a list.
(define simple? (lambda (val) (not (list? val))))
Topics: Recursion, Symbols, Membership
One reason we write programs is to help us manipulate and analyze large (or even medium-sized) collections of information. Suppose we want to create a system that students can use to help select courses. For such a system, we'll need a way to represent information about courses and we need to design useful procedures to manipulate that information.
A complete course system is clearly beyond the scope of an exam, so let's try a simple version of the problem.
We will represent each course at Grinnell as a list whose first element is a string that names the course and whose remaining elements are symbols that represent terms students have used to describe the class. For example, we might represent this course as
("CSC151" geeky challenging morning creative)
We can then represent a collection of courses as a list of these lists. (Note that failure to associate a term with a class does not suggest that the class does not have that characteristic; simply that it was not a term that first came to mind when our subject was asked to describe the class.)
(define some-courses (list (list "CSC151" 'geeky 'challenging 'morning 'creative 'numeric 'technology) (list "HUM101" 'challenging 'classic 'writing) (list "BIO150" 'workshop 'cool 'science) (list "MAT133" 'morning 'afternoon 'numeric 'large) (list "TUT100" 'required 'awesome 'morning 'challenging 'writing) (list "PHY131" 'workshop 'science) (list "MUS219" 'creative 'technology) (list "PHI111" 'morning 'challenging 'essential 'humanistic) (list "PHY457" 'quantum 'easy 'science) (list "ART136" 'creative)))
Write a procedure,
(find-courses category list-of-courses),
that finds the names of all courses that meet a particular characteristic.
> (find-courses 'challenging some-courses) ("CSC151" "HUM101" "TUT100" "PHI111") > (find-courses 'easy some-courses) ("PHY457") > (find-courses 'limitless some-courses) () > (find-courses 'workshop some-courses) ("BIO150" "PHY131")
You may find it helpful to use the
member? procedure you might
have written for a recent lab. That procedure can be defined as
(define member? (lambda (sym lst) (and (not (null? lst)) (or (eq? sym (car lst)) (member? sym (cdr lst))))))
You may also find it helpful to break this problem into parts. First,
write a procedure that, given a characteristic and list of courses, returns
a list of all courses (as lists) that contain the characteristic.
Next, write a procedure that, given a list of courses, returns
a list of the names of those courses. Finally, write
by combining the two.
These are some of the questions students have asked about the exam and my answers to those questions.
"a character"suffices for all characters.
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.
PHI457when he meant
PHY457. [KI, 1 point]
find-courses. [AM, 1 point]
the a listshould be
a list. [JS, 1 point]
(if test1 test2 test3) => (or (and test1 test2) test3)
(if test1 test2 test3) => (or (and test1 test2) (and (not test1) test3))[SR, 1 point]
Thursday, 18 January 2007 [Samuel A. Rebelsky]
Wednesday, 14 February 2007 [Samuel A. Rebelsky and Janet Davis]
Thursday, 15 February 2007 [Samuel A. Rebelsky and Janet Davis]
Friday, 16 February 2007 [Samuel A. Rebelsky]
Sunday, 18 February 2007 [Samuel A. Rebelsky]
Monday, 19 February 2007 [Samuel A. Rebelsky]
Tuesday, 20 February 2007 [Samuel A. Rebelsky]
Wednesday, 21 February 2007 [Samuel A. Rebelsky]
Sunday, 25 February 2007 [Samuel A. Rebelsky]
I usually create these pages
on the fly, which means that I rarely
proofread them and they may contain bad grammar and incorrect details.
It also means that I tend to update them regularly (see the history for
more details). Feel free to contact me with any suggestions for changes.
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