Functional Problem Solving (CSC 151 2014S) : Assignments
Assigned: Friday, 25 April 2014
A draft version of this examination may be distributed before Friday, 25 April 2014. We will not accept corrections on the exam before class time on Friday.
Due: The due dates for various tasks are as follows.
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 examination has a prologue that must be completed by the Sunday evening before the exam is due. The prologue is intended to help you get started thinking about the examination. The prologue is optional. However, if you intend to invoke the “there's more to life” option (see below), you must turn in the prologue by the specified deadline.
There are 10 problems on this examination. Each problem is worth 10 points, for a total of 100 points. Although each problem is worth the same amount, problems are not necessarily of equal difficulty.
Read the entire exam before you begin.
We 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 hours, depending on how well you've learned the topics and how fast you work. You should not work more than five hours on this exam. Stop at five hours and write “There's more to life than CS” and you will earn at least a 70 on this exam, provided you filled in the prologue by the specified deadline. You may count the time you spend on the prologue toward those five hours. With such evidence of serious intent, your score will be the maximum of (1) your actual score out of 100 or (2) 70. The bonus points for errors are not usually applied in the second situation.
We 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. Because we worry about the amount of time our exams take, we will give two points of extra credit to the first two people who honestly report that they have completed the exam in four hours or less or have spent at least four hours on the exam. In the latter case, they should also report on what work they've completed in the four hours. After receiving such notices, we may change the exam.
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. If you use code that you wrote for a previous lab or homework, cite that lab or homework and any students who worked with you. If you use code that you found on the course Web site, be sure to cite that code. You need not cite the code provided in the body of the examination.
Although you may use the Web for this exam, you may not post your answers to this examination on the Web. And, in case it's not clear, you may not ask others (in person, via email, via IM, via IRC, by posting a please help message, or in any other way) to put answers on the Web.
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.” 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 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.
Exams can be stressful. Don't let the stress of the exam lead you to make decisions that you will later regret.
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 with the subject
CSC 151.02 Exam 3 (Your Name). 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 at least two
points. Failure to turn in both versions may lead to a much worse
While your electronic version is due at 10:30 p.m. Thursday, your physical copy will be submitted in class on Friday. It is presumed the physical copy matches the electronic copy. Any discrepancies (other than formatting) will be considered a misrepresentation of your work and referred to the Committee on Academic Standing.
In many problems, we ask you to write code. Unless we specify otherwise in a problem, you should write working code and include examples that show that you've tested the code. You should use examples other than those that may be provided with the exam. Do not include resulting images; we should be able to regenerate those.
Unless we explicitly tell you not to document your procedures, you must write 6P-style documentation for every globally accessible procedure. (Thus, anonymous and local helper procedures are exempted.)
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. Because we 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. We will limit that form of extra credit to five points.
I will give partial credit for partially correct answers. We are best able to give such partial credit if you include a clear set of work that shows how you derived your answer. You ensure the best possible grade for yourself by clearly indicating what part of your answer is work and what part is your final 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 (8am-10pm), feel free to try to call me (cell phone (text only) - 641-990-2947).
I will also reserve time at the start of each class before the exam is due to discuss any general questions you have on the exam.
Run the following command in a terminal window to tell Racket where
to find a supposedly new-and-improved version of
assoc Professor Weinman wrote while
simultaneously excited and sleep deprived.
/opt/racket/bin/raco link /home/weinman/courses/CSC151
To use that new (and perhaps not-so-improved) version of
assoc, you will need to include the following
line in your definitions.
We have manually tested this procedure using the following input, and it appears to work correctly:
(assoc 3 (list (cons 1 2) (cons 3 4) (cons 5 6)))
'(3 . 4)
(assoc 1 (list 1 2 3))assoc: expected a list of key-value pairs; given (1 2 3)
Unfortunately, one or two experiments are not enough. In fact, the implementation has several bugs.
Using the RackUnit library, write a complete test suite
assoc, as documented in the reading on association
Your test suite should include at least three tests for which the built-in
assoc procedure passes and our buggy procedure fails.
Implement the following procedure.
;;; Procedure: ;;; vector-swap! ;;; Parameters: ;;; vec, a vector ;;; i, an integer ;;; j, an integer ;;; Purpose: ;;; Swap the elements in positions i and j of vector. ;;; Produces: ;;; [Nothing; called for the side effect] ;;; Preconditions: ;;; 0 <= i < (vector-length vec) ;;; 0 <= j < (vector-length vec) ;;; I is (vector-ref vec i) ;;; J is (vector-ref vec j) ;;; Postconditions: ;;; (vector-ref vec i) is J. ;;; (vector-ref vec j) is I. ;;; No other elements in the vector have changed.
(define vec (list->vector (iota 5)))
'#(0 1 2 3 4)
(vector-swap! vec 0 3)
'#(3 1 2 0 4)
(vector-swap! vec 0 4)
'#(4 1 2 0 3)
(vector-swap! vec 1 3)
'#(4 0 2 1 3)
Topics: Vectors, iteration, randomness, higher-order procedures.
In many situations, it is useful to permute a vector, that is, rearrange the order of elements. For example, permutation is at the root of shuffle-play in many music applications (and is probably subject to way too many patents). For classrooms, many faculty like to permute the list of students in class when making pairs or calling on students in order.
Write, but do not document, a procedure
(, that rearranges the
elements of the vector by repeatedly swapping elements in two random
indices. How many times should you swap? If there are n
elements in the vector, you should swap n times.
You may not implement
Topics: Turtles, characters.
One way to produce images with the appearance of chaotic randomness is by thinking of characters similar to the way biologists might. Rather than thinking of the characters G, C, T, and A as the instructional DNA for organisms, we can think of all characters as instructional commands for turtles.
Write, but do not document, the procedure
( that moves the turtle forward by
the character's collating sequence number if the character is
uppercase, turns the turtle by the character's collating sequence
number if the character is lowercase, and otherwise turns the turtle
by the negative of the character's collating sequence number.
Topics: Turtles, strings, iteration, higher-order procedures.
What happens when we use the
procedure to visualize a string of text? Write, but do not document,
that takes a string and applies
each character in the string (in order).
(define the-sea (image-new 1024 1024)) (define ishmael (turtle-new the-sea)) (turtle-teleport! ishmael 512 512) (turtle-express-text! ishmael "Call me Ishmael. ...")
Topics: Trees, predicates, tree recursion.
A “balanced” tree is one that has no subtrees (i.e., it is simply a leaf) or whose two subtrees have the same depth and are themselves both balanced.
The following version of a predicate
tree-balanced? is correct, but extremely
inefficient because it involves multiple traversals of the tree. At
each pair, one traversal is done with
tree-depth procedure, and this is followed
by a traversal done with recursive calls
(define tree-balanced-v0? (lambda (tree) (if (pair? tree) (let ([left-depth (tree-depth (car tree))] [right-depth (tree-depth (cdr tree))]) (and (= left-depth right-depth) (tree-balanced-v0? (car tree)) (tree-balanced-v0? (cdr tree)))) #t)))
Write a more efficient
procedure that traverses the tree only once by returning the tree's
depth when the tree is balanced and
Hint: You should not call
tree-depth anywhere in your solution. Instead,
note (and use!) the specified value produced by the recursive calls
Note: The procedure
tree-depth appeared in the first reading on trees.
(tree-balanced? (cons 'a 'b))
(tree-balanced? (cons 'a (cons 'b 'c)))
(tree-balanced? (cons (cons 'a 'b) (cons 'c 'd)))
(tree-balanced? (cons (cons 'a 'b) (cons (cons 'c 'd) 'e)))
Topics: Annotating code, analysis.
a. Using the counters from the reading on analyzing
tree-balanced-v0? to count the total number of
calls made to those two procedures for balanced trees of depths 0, 1,
2, 3, and 4.
b. Similarly annotate your own improved version of
tree-balanced? to count the total number of calls
made to that procedure for balanced trees of depths 0, 1, 2, 3, and 4.
c. Using your results from (a) and (b), complete the following table.
|Balanced Depth||Total calls to
||Total calls to
d. Compare the absolute efficiencies of the two approaches. That is, briefly explain how and why they differ in the number of procedure calls each must make as the number of items in the tree (a function of the depth) grows.
Topics: Higher-order programming, documentation, recursion
Document, but do not write, a procedure,
takes two parameters, a unary procedure
and an integer
n. The value produced is a new
procedure that results from composing together
fun. For example,
(nest square 3)
is equivalent to
(lambda (val) (square (square (square val)))).
n must be at least 1 for
nest to make sense.
Here are some examples using
(define plus5 (nest (l-s + 1) 5))
(define list5 (nest list 5))
(define sqqqr (nest square 3))
(nest list 0)nest: parameter n must be a positive integer, given 0
(define duplicate (lambda (val n) ((nest (l-s c ons val) n) null)))
(duplicate "hello" 5)
'("hello" "hello" "hello" "hello" "hello")
Note that in documenting
nest, you may find it
useful to express the postconditions recursively.
Topics: Higher-order programming, documentation, recursion, precondition testing.
nest. In your implementation, make sure
that you verify the preconditions regarding
using a husk-and-kernel style.
Topics: Code reading, procedures as parameters, binary search.
At times, programmers make decisions that lead to programs that are particularly hard to read. For example, many programmers like to use single-character variable names (less typing!) and don't think that indentation makes much difference (“The computer doesn't care, why should I?”).
Consider the following procedure, a form of which often appears in libraries for searching and sorting.
(define f (lambda (l m n) (let ([s (vector-length l)]) (let k ([p 1]) (or (>= p s) (and (n (m (vector-ref l (- p 1))) (m (vector-ref l p))) (k (+ p 1))))))))
a. Figure out what
f does, then rewrite
the code for clarity. That is, fix the indentation and rename the
variables and procedure name.
b. Write 6P documentation for the renamed procedure.
c. Write a seventh P, Process, that explains the details of the underlying algorithm and how the code above manifests an implementation of that algorithm.
Here we will post answers to questions of general interest. Please check here before emailing your questions!
Whatever way seems most sensible/legible. For example, you could use plenty of whitespace (e.g., tabs or spaces) to separate columns. For example, you might make it a comment.
; +----------------+-----------------------------+--------------------+ ; | Balanced depth | Total calls to td? and tbv0 | Total calls to tb? | ; +----------------+-----------------------------+--------------------+ ; | 0 | | | ; +----------------+-----------------------------+--------------------+ ; | 1 | | | ; +----------------+-----------------------------+--------------------+ ; | 2 | | | ; +----------------+-----------------------------+--------------------+ ; | 3 | | | ; +----------------+-----------------------------+--------------------+ ; | 4 | | | ; +----------------+-----------------------------+--------------------+
You might also make it a Scheme structure, which would allow us to process the data computationally.
(define balanced-data (vector (vector "Balanced depth" "Total calls to tree-depth? and tree-balanced-v0?" "Total calls to tree-balanced?") (vector 0 ___ ___) (vector 1 ___ ___) (vector 2 ___ ___) (vector 3 ___ ___) (vector 4 ___ ___)))
(nest fun 1)is and one that defines
(nest fun n)in terms of
(nest fun (smaller n)), for
ngreater than greater than one and some definition of
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. We usually limit such extra credit to five points. However, if we make an astoundingly large number of errors, then we will provide more extra credit. (And no, we don't count errors in the errata section or the question and answer sections.)
tree-balanced-v0?had the wrong base case value. [JW, 1 point]
nestwas inconsistently named. [AC, 1 point]
turtle-dna!shown in the image was different than that given in the description. Lowercase letters should represent turning. Uppercase letters should represent moving forward. [Various, 1 point]
Many of the problems on this exam are based on (and, at times, copied from) problems on previous exams for the course. Those exams were written by Janet Davis, Rhys Price Jones, Samuel A. Rebelsky, John David Stone, Henry Walker, and Jerod Weinman. Many were written collaboratively, or were themselves based upon prior examinations, so precise credit is impossible.
Much of the introductory and concluding text on this examination has a similarly collaborative background. Sections were likely written by different faculty and then updated by others.
Some problems on this exam were inspired by conversations with our students. We thank our students for that inspiration. Usually, a combination of questions or discussions inspired a problem, so it is difficult and inappropriate to credit individual students.
Samuel A. Rebelsky, email@example.com
Copyright (c) 2007-2014 Janet Davis, Samuel A. Rebelsky, and Jerod Weinman. (Selected materials are copyright by John David Stone or Henry Walker and are used with permission.)
This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit
or send a letter to Creative Commons, 543 Howard Street, 5th Floor,
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