Fundamentals of Computer Science I (CS151.01 2006F)
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[CSC153 2004S (Rebelsky)]
Distributed: Wednesday, 22 November 2006
Due: 9:00 a.m., Friday, 1 December 2006
No extensions.
This page may be found online at http://www.cs.grinnell.edu/~rebelsky/Courses/CS151/2006F/Exams/exam.03.html
.
This exam is also available in PDF format.
Contents
There are five problems on the exam. Some problems have subproblems. Each problem is worth twenty (20) 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 takehome 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 75 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 (2694410) or at home (2367445).
I will also reserve time at the start of classes next week to discuss any general questions you have on the exam.
Topics: Sorting, Orderings, Higherorder procedures, Objects
As you've probably noticed, there are two key postconditions of a
procedure that sorts lists: The result is a permutation of the original
list and the result is sorted. We're fortunate that the unit
test framework lets us test permutations (with testpermutation!
).
Hence, if we wanted to test merge sort in the unit test framework, we
might write
(define somelist ...) (testpermutation! (mergesort somelist pred?) somelist)
However, we still need a way to make sure that the result is sorted, particularly if the result is very long.
a. [5 points]
Document a procedure, (sorted? lst mayprecede?)
that checks
whether or not lst
is sorted by mayprecede?
.
b. [5 points] Write that procedure.
For example,
> (sorted? (list 1 3 5 7 9) <) #t > (sorted? (list 1 3 5 4 7 9) <) #f > (sorted? (list "alpha" "beta" "gamma") string<?) #t
Note that we can use that procedure in a test suite for any sorting routine with
(test! (sorted? (sort somelist mayprecede?) mayprecede?) #t)
c. [10 points] Suppose that we are representing students in this class
with objects, as in the file
studentobject.scm
.
Suppose also that we have stored all of the student records in a
list, csc151
.
i. Write an expression that checks whether csc151
is sorted by student id (from alphabetically first to alphabetically
last).
ii. Write an expression that checks whether csc151
is
sorted by participation grade, from largest to smallest.
iii. Write an expression that checks whether csc151
is
sorted by name, from alphabetically first to alphabetically last.
(Students may have the same last name; two students with the same last
name should be ordered by first name.)
iv. Write an expression that checks whether csc151
is
sorted by average exam grade, from largest to smallest.
v. Write an expression that checks whether csc151
is
sorted by graduation year (class) and, within graduation year, is sorted by
last name. (You need not worry about first names.)
map!
for Vectors
Topics: Vectors, Higherorder procedures, map
, Objects
As you may recall, the map
procedure typically takes two
parameters, a unary procedure and a list, and then builds a new list by
applying the procedure to each element of the list. One definition of
this simple version follows. (Advanced Schemers know that the
builtin map
can take more than two parameters; but that's irrelevant to this problem.)
(define map (lambda (proc lst) (if (null? lst) null (cons (proc (car lst)) (map proc (cdr lst))))))
As you've seen many times this semester, we often find it useful to
write vector procedures that mimic (or at least are similar to) list
procedures. For the case of map
, we might write a
map!
that applies a procedure to each element of a vector,
modifying the value in place.
For example,
> (define grades (vector 80 70 85 90)) > grades #4(80 70 85 90) > (map! (ls + 5) grades) ; give everyone five points > grades #4(85 75 90 95) > (map! (compose exact>inexact (rs / 25)) grades) ; Divide grades by 25 for 4point scale > grades #4(3.4 3.0 3.6 3.8)
a. [5 points] Document the map!
procedure.
b. [10 points] Implement the map!
procedure.
c. [5 points] In
studentobject.scm
,
you will find an implementation of a simple student object. Build
a vector of five randomlygenerated student objects. Then, use map!
to give each of them one additional homework grade, a plus.
Topics: Higherorder procedures
As you may recall, we began our investigation of recursion by considering how we might step through a list of numbers, adding them (or multiplying them or ...). Here are variants of the two versions we wrote:
One uses simple recursion:
(define sumr (lambda (numbers) (if (null? (cdr numbers)) (car numbers) (+ (car numbers) (sumr (cdr numbers))))))
The other uses a helper that accumulates the results.
(define suml (letrec ((kernel (lambda (remaining sofar) (if (null? remaining) sofar (kernel (cdr remaining) (+ sofar (car remaining))))))) (lambda (numbers) (kernel (cdr numbers) (car numbers)))))
If you think carefully about it, the two processes compute results
slightly differently. Given the list (n0 n1 n2 n3 n4)
,
the first computes
(+ n0 (+ n1 (+ n2 (+ n3 n4))))
while the second computes
(+ (+ (+ (+ n0 n1) n2) n3) n4)
For addition, this doesn't make a difference. If the operation were subtraction, it would certainly make a difference.
Now, the process of inserting a binary operation into a list of values
is quite common. We've seen it for addition, subtraction, and multiplication.
We might also use it for appending strings and many other operations.
Computer scientists have various names for such a process. We'll call
it fold, but others use insert (as in insert this
procedure
) or reduce.
a. [5 points] Write a procedure, (foldr proc lst)
that mimics
sumr
, but with proc
in place of
+
. That is,
(foldr proc (list v0 v1 v2 ... vn1 vn))
should compute
(proc v0 (proc v1 (proc v3 (... (proc vn1 vn) ... a))))
For example,
> (foldr + (list 1 2 3 4)) 10 > (foldr * (list 1 2 3 4)) 24 > (foldr  (list 1 2 3 4)) 2 > (foldr (lambda (s1 s2) (stringappend s1 ", " s2)) (list "sentient" "malicious" "powerful" "stupid")) "sentient, malicious, powerful, stupid" > (foldr list (list 'a 'b 'c 'd 'e)) (a (b (c (d e))))
b. [5 points] Write a procedure, (foldl proc lst)
that mimics
suml
, but with proc
in place of +
.
That
is,
(foldl proc (list v0 v1 v2 ... vn1 vn))
should compute
(proc ... (proc (proc (proc v0 v1) v2) v3) ... vn)
For example,
> (foldl + (list 1 2 3 4)) 10 > (foldl * (list 1 2 3 4)) 24 > (foldl  (list 1 2 3 4)) 8 > (foldl (lambda (s1 s2) (stringappend s1 ", " s2)) (list "sentient" "malicious" "powerful" "stupid")) "sentient, malicious, powerful, stupid" > (foldl list (list 'a 'b 'c 'd 'e)) ((((a b) c) d) e)
c. [10 points] Some computer scientists prefer an alternate version of
fold
, which we'll call folder
. Rather than taking
two parameters, their folder
takes only one, proc
, a binary procedure. The
folder
procedure then returns a new, variablearity, procedure,
that inserts proc between its arguments. For example,
> (define commasplice (lambda (s1 s2) (stringappend s1 ", " s2))) > (commasplice "Fred" "Barney") "Fred, Barney" > (commasplice "George" "Jane" "Elroy" "Judy") procedure commasplice: expects 2 arguments, given 4: "George" "Jane" "Elroy" "Judy" > (commasplice "ScoobyDoo") procedure commasplice: expects 2 arguments, given 1: "ScoobyDoo" > (define commasplicer (folderr (lambda (s1 s2) (stringappend s1 ", " s2)))) > (commasplicer "Fred" "Barney") "Fred, Barney" > (commasplicer "George" "Jane" "Elroy" "Judy") "George, Jane, Elroy, Judy" > (commasplicer "ScoobyDoo") "ScoobyDoo"
Implement folderr
or folderl
.
Topics: Binary search, Randomness, Counting Steps
As you may recall, the binary search procedure quickly searches through
sorted vectors by keeping track of a region of the vector in which
a value should fall. At each step
, it identifies the midpoint
of the region, grabs the value at that region, compares it to the
desired value, and narrows the region.
Some have criticized this procedure for being too predictable.
Rather than choosing the middle of the region, they think we should choose
a random
dividing point.
Let's see what happens with this technique for vectors of integers
(so that you don't have to worry about what comparison routine to use).
In particular, we'll define a procedure (rbsi val vals)
that
searches for val
in the sorted vector of integers,
vals
, and returns an index of val
if it
appears or #f
if it does not appear. (Note that
rbsi
stands for random binary search for integers
.)
a. [5 points] Document this alternate version of binary search.
b. [5 points] Implement this alternate version of binary search.
c. [10 points] Traditional binary search takes approximately log_{2}n recursive calls for a vector of length n. Experimentally determine whether this version takes approximately the same number of steps.
You may find the following procedure useful for building sorted vectors:
(define randomsortedvector (letrec ((kernel (lambda (vec pos len seed) (if (= pos len) vec (begin (vectorset! vec pos seed) (kernel vec (+ pos 1) len (+ seed (random 5)))))))) (lambda (len) (kernel (makevector len 0) 0 len (random 5)))))
For example,
> (randomsortedvector 15) #15(3 3 7 9 10 12 15 17 21 25 27 28 30 34 36) > (randomsortedvector 15) #15(3 6 7 10 11 12 13 17 20 22 24 28 31 31 35) > (randomsortedvector 15) #15(0 3 4 6 7 8 11 14 16 19 23 26 30 33)
You may find the following procedure useful for figuring out the value of log_{2}n
(define log2 (lambda (x) (/ (log x) (log 2))))
For example,
> (log2 16) 4.0 > (log2 1024) 10.0 > (log2 1000) 9.965784284662087 > (log2 (* 1024 1024)) 20.0
Topics: Higherorder procedures, map
Although we've used the map
procedure with two parameters,
a procedure and a list, it can take an arbitrary number of parameters.
For example,
> (map list (list 1 2 3) (list 'a 'b 'c) (list "he" "she" "it")) ((1 a "he") (2 b "she") (3 c "it")) > (map + (list 1 2 3) (list 4 4 4) (list 2 3 5) (list 100 200 300)) (107 209 312)
Scheme also provides an apply
procedure, which acts
similarly to the stremeapply
we've written previously.
> (apply + (list 1 2 3)) 6 > (apply sqrt (list 4)) 2
a. [10 points]: By conducting some experiments (that is, by entering
a variety of expressions and seeing their results) and by reading
documentation, figure out what
map
does when given more than two parameters. Explain
it in your own words. (Make sure to note any restrictions on the parameters.)
Include at least three illustrative examples.
b. [10 points]: By conducting some experiments (that is, by entering
a variety of expressions and seeing their results) and by reading
documentation, figure out what
apply
does. Explain
it in your own words. (Make sure to note any restrictions on the parameters.)
Include at least three illustrative examples.
These are some of the questions students have asked about the exam and my answers to those questions.
csc151
?(define csc151 (list (randomstudent) (randomstudent) (randomstudent)))
mayprecede?
is <
?mayprecede?
should be <=
rather than <
(which is more accurately
precedes?
). However, you can do whatever you see
fit, provided you document what you've done.(sorted? csc151 (lambda (s1 s2) ...))
studentobject.scm
?(load "/home/rebelsky/Web/Courses/CS151/2006F/Examples/studentobject.scm")
map!
procedure support?map!
procedure should accept any vector as its
second argument. The first argument should be a procedure. It
is up to you to document any restrictions on the procedure argument.map!
need to support empty vectors?studentobject.scm
?(student ':addhomework! 'plus)
returns void?map!
to modify the vector?vector>list
?folderr
?(define folderr (lambda (proc) (lambda params ...)))
(define folderr (letrec ((kernel (lambda (proc params) ...))) (lambda (proc) (lambda params ...))))
Whatever floats your boat, as they say.
folderl
and
folderr
?foldr
or foldl
have to handle empty
lists?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.
ain the middle of Scheme code. [SR, 1 point]
list or random studentsinstead of
list of random students. [DB, 1 point]
a region of of the vector. [JP, 1 point]
addgrade!
when he meant to write
addhomework!
. [PR, 1 point]
sorted?
in the wrong order;
(sorted? pred lst)
rather than the correct
(sorted? lst pred)
.
[JB]
Thursday, 16 November 2006 [Samuel A. Rebelsky]
Saturday, 18 November 2006 [Samuel A. Rebelsky]
Tuesday, 21 November 2006 [Samuel A. Rebelsky]
sorted?
problem.
map!
problem.
Wednesday, 22 November 2006 [Samuel A. Rebelsky]
Monday, 27 November 2006 [Samuel A. Rebelsky]
Tuesday, 28 November 2006 [Samuel A. Rebelsky]
[Skip to Body]
Primary:
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[Syllabus]
[Glance]
[Search]

[Academic Honesty]
[Instructions]
Current:
[Outline]
[EBoard]
[Reading]
[Lab]
[Homework]
Groupings:
[EBoards]
[Examples]
[Exams]
[Handouts]
[Homework]
[Labs]
[Outlines]
[Projects]
[Readings]
Reference:
[Scheme Report (R5RS)]
[Scheme Reference]
[DrScheme Manual]
Related Courses:
[CSC151.02 2006F (Davis)]
[CSCS151 2005S (Stone)]
[CSC151 2003F (Rebelsky)]
[CSC153 2004S (Rebelsky)]
Disclaimer:
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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The source to the document was last modified on Thu Nov 30 10:55:13 2006.
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.
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