Distributed: Wednesday, 3 March 2004
Due: 10:00 a.m., Wednesday, 10 March 2004
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There are four problems on the exam. Some problems have subproblems. Each full problem is worth twenty-five 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
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. If you write your name at the top of each sheet of the printed copy, you will earn two points of extra credit.
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.
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 this week and next to discuss any general questions you have on the exam.
Topics: Recursion, Lists, Vectors, Memory
As you may have noted, in a recent class, Saul suddenly suggested that it would be useful to have a way of making copies of vectors and lists. Erik enthusiastically echoed this request.
a. Write a procedure,
(clone-list lst), that creates a copy of
lst that uses different memory cells.
b. Write a procedure,
(clone-vector vec), that creates a copy of
vec that uses different memory cells.
c. Write a predicate,
(clones? left right) that determines whether or not left and right are clones of each other. Two vectors are clones if they have the same length and contain the same values in corresponding locations, but do not share memory locations. Two lists are clones if (1) their cars are equal, (2) their first pairs are in different memory locations, and (3) their cdrs are clones. No two other values are clones.
You need not document any of these procedures.
Topics: Algorithms, Strings, Comparison, Deep Recursion, Vectors
Cole and Coco Coder are concerned that they have
to keep rewriting similar
less-than? predicates for
binary search and for sorting algorithms. For
example, they must remember to use
(lambda (x y) (string-ci<? (car x) (car y)))for lists whose key is a string found in position 0,
They've decided that
someone should write a general
less-than? predicate that can compare any reasonable pairs
of values. Of course, Cole and Coco are much better at deciding what
they'd like to do than at actually doing it. Hence, they've asked you
less-than? for them. Your sentient
and malicious instructor agrees.
Here's what Cole and Coco would like you to do for
string-ci<?to compare the two parameters.
<to compare the two parameters.
smalleror (2) the given element of one vector or list is smaller than the corresponding element of the other vector or list, in which case the vector or list with the smaller element is smaller.
less-than?should report an error with the
a. Implement the
less-than? procedure. You need not write the full six P's for this procedure, but you should summarize what it does.
b. Theodore and Thelma Theoretician take one look at Cole and Coco'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 basic values, a, b, and c, such that
> (less-than? a b) #t > (less-than? b c) #t > (less-than? a c) #f
basic, I mean that a, b, and c should
not be lists or vectors.
Topics: Higher-order procedures, Sectioning, Variable-Arity procedures
Hiram and Olivia Higher-Order love
left-section because these two procedures not only
take procedures as parameters, but also return new procedures as
results. However, they are concerned that these two procedures are
After all, they reason,
these two procedures do almost exactly the same thing (that is, fill
in one parameter of a two-parameter procedure), why do we need separate
They suggest that we instead create a multi-arity procedure,
section, that takes as parameters
(1) an n-ary procedure,
proc and (2) n
each of which may either be set values or the special symbol
'?. Given k of the special
it creates a new k-ary procedure,
sectioned procedure calls
proc with either
parami is not the
special symbol, or the appropriate parameter to
With the new
section procedure, we can write
(section proc '? val)
(right-section proc val)
(section proc val '?)
(left-section proc val).
For example, we can write a procedure that divides its parameter in half with
(define half (section / '? 2))
Similarly, with the new
section, one can simply
valid-grade? (remember that procedure from early
in the semester?) with
(define valid-grade? (section <= 0 '? 100))
Similarly, we can create a procedure that rolls a 0-5 die with
(define die (section random 6))
'? symbol can also appear multiple times. For example,
you might write a procedure that asks whether two numbers have opposite
(define opposite-sign? (section < '? 0 '?))
Yes, I realize that's not a very good example and that the negative number must come first, but hey, it's early in the morning.
section. You need not document it.
b. Show five interesting uses of
section to simplify the definition of other procedures we've written this semester.
Topics: Documentation, Recursive procedures
An and Al Abbrev object to
the overly-long procedure names that
Sam likes to use. Hence, they tend to choose one-character
names. They also avoid the sixP Ps that I like. Here's a procedure
they've recently written.
(define r (lambda (l p?) (letrec ((c (lambda (p v) (let ((x (if (p? v) 1 0))) (cons (+ (car p) x) (+ (cdr p) (- 1 x)))))) (r (lambda (q m) (if (null? m) (/ (car q) (cdr q)) (r (c q (car m)) (cdr m)))))) (r (cons 0 0) l))))
Document the procedure
r. If you'd like,
you can change the names used within
r) to something more readable.
These are some of the questions students have asked about the exam and my answers to those questions.
eq?to compare memory locations?
#t). If the first element of the first pair is larger, return false (
#f). Otherwise, recurse on the second element.
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 limit such extra credit to five points.
clone-vectorprocedure is not a predicate. [JH, 1 point]
That the have toshould be
That they have to. [IM, 1 point]
numbers. [The guy who wears strange hawaiian shirts and pants that look like strange hawaiian shirts, 1 point]
Tuesday, 2 March 2004 [Samuel A. Rebelsky]
less-than?) is modified from a similar problem from the third exam in CSC151 2003S.
Wednesday, 3 March 2004 [Samuel A. Rebelsky]
Thursday, 4 March 2004 [Samuel A. Rebelsky]
Friday, 5 March 2004 [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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