Informatics 41 * Fall 2009 * David G. Kay * UC Irvine
ANSWERS TO SAMPLE QUESTIONS
Below are some questions of the sort that could appear on our final exam. This is not a sample exam--it's not the same length, it doesn't have the same mix of questions, it doesn't cover all the topics. But these questions will help you review some important concepts and most of them have appeared on exams in the past. Try to do them by yourself, but then compare your answers with your classmates. Do this long enough in advance that you'll have a chance to ask us if there are issues you can't resolve yourself.
(a.1) Write a definition for the function vector->list. (Hints: Remember that vectors are zero-based. Be careful not to produce a reverse-order list. Use an auxiliary function.)
; vector->list: vector -> list
; Return a list containing the same elements as the vector argument, in the same order.
; (vector->list (vector 1 2 3) returns
(list 1 2 3)
(define (vector->list
V)
(vtl-help V (vector-length V) empty))
(define (vtl-help V i list-so-far)
(cond
((= i 0) list-so-far)
(else (vtl-help V
(sub1 i)
(cons (vector-ref V (sub1 i)) list-so-far)))))
; Scoring: Deduct a point if they don't deal with the vector being zero-based (though they don't have to subtract 1 in the same place the solution above does).
; Deduct a point if they count upwards and thereby produce a reverse-order list.
(a.2) Write a definition for the function list->vector. (Hint: You can do this without an auxiliary function and without vector-set!, but you may use them if you need to.)
; list->vector: list -> vector
; Return a vector containing the same elements as the list argument, in the same order.
; (list->vector (list 1 2 3) returns
(vector 1 2 3)
(define (list->vector
L)
(build-vector (length L) (lambda (n) (list-ref L n))))
; --------------------------------------------------------------- That's
the nice way, but here's the other way:
(define (list-to-vector L)
(ltv-help L (build-vector (length L) (lambda (n) 1)) 0))
(define (ltv-help L V i)
(cond
((empty? L) V)
(else (begin
(vector-set! V i (first L))
(ltv-help (rest L) V (add1 i))))))
(b) Consider the following function:
(define (DoSomething a b) ; assume b >= 0
(cond
((= b 0) a)
(else (DoSomething (sub1 a) (sub1 b)))))
(b.1) What is returned by each of the following statements?
(b.2) In one English word (or in mathematical notation), describe the value this function returns in terms of its arguments.
Subtraction: a - b
(b.3) Now look at this function:
(define (DoSomethingElse a b) ; assume b >= 0
(cond
((= b 0) a)
(else (sub1 (DoSomethingElse a (sub1 b))))))
Does DoSomethingElse produce the same results as DoSomething? If not, explain how the results differ.
Yes, they produce the same results.
(b.4) Which of these routines are tail recursive--DoSomething, DoSomethingElse, neither, or both? For any non-tail-recursive routine, indicate (by circling it) which specific operation in its code makes it non-tail-recursive.
DoSomethingElse is not tail-recursive because of the last subtraction (which is done after returning from the recursive call).
(c) A set is a collection of distinct
objects (i.e., without duplicates). Suppose you have the following operations
defined on sets:
empty-set
is a constant representing the empty set.
(empty? S)
returns true if the set S is empty and false otherwise.
(element? S E)
returns true if E is an element of the set S, and false otherwise.
(insert S E)
returns the set S if E is already in S, or returns S with E added otherwise.
(intersection S1 S2)
returns a set containing only the elements that are in both S1 and S2.
(subtract S1 S2)
returns a set containing the elements of S1 that are not in S2.
(union S1 S2)
returns a set containing every element in either S1 or S2 (without
duplicates, of course).
(c.1) Using any of the above routines where appropriate, but using no list processing functions, define a Scheme function called ski-trip that takes the following four sets as arguments
* friends, the set of all your friends;
* early-risers, the set of people you know (perhaps including people who aren't your friends) who will wake up early enough to get out on the slopes when the lifts open;
* rowdy-people, the set of people who are likely to get too excited and wreck your cabin;
* fun-folks, the set of people who really know how to party
and returns the set of people you'd like to invite on your ski trip over winter break: all your friends who are early risers and fun folks, but not rowdy people.
(define (ski-trip friends early-risers rowdy-people fun-folks)
(subtract (intersection (intersection friends early-risers) fun-folks) rowdy-people))
(c.2) Assuming we implement sets as
normal Scheme lists, write a definition for the function union.
(define union
(lambda (s1 s2)
(cond
((empty? s1) s2)
((element? s2 (first s1)) (union (rest s1) s2))
(else (cons (first s1) (union (rest s1) s2))))))
(c.3) Using the operations map,
filter,
foldr,
and/or for-each,
and without using any explicit recursion, write a definition for the function
intersection.
(Hint: This can be quite short.)
(define intersection
(lambda (s1 s2)
(filter (lambda (E) (element? s1 E)) s2)))
(c.4) Write a definition for subtract
and rewrite a definition for union,
using the operations map,
filter,
foldr,
and/or for-each
and no explicit recursion.
(define subtract
(lambda (s1 s2)
(filter (lambda (E) (not (element? s2 E))) s1)))
(define union
(lambda (s1 s2)
(foldr insert s1 (subtract (s2 s1)))))
(d) In the restaurants program
(a copy of which is provided), define the following function that could
be used at the top level of the program (i.e., without knowing whether the
collection is implemented as a list, a BST, a vector, or whatever; that
means you have to call collection-change).
;; increase-price-for-cuisine: collection
number symbol -> collection
;; The symbol is the name of a cuisine; the number is a number of dollars
;; to add to the price of each restaurant serving that cuisine. Return
the
;; collection with those price changes.
(define increase-price-for-cuisine
(lambda (RC amount c)
(collection-change RC
(lambda (r) (eq? (rrant-cuisine r) c))
(lambda (r) (make-rrant (rrant-name r) (rrant-cuisine
r) (rrant-phone r)
(rrant-dish r) (+ amount (rrant-price
r))))))
(e) [This one is tough towards the
end, probably tougher than would be on the test.]
Anteater Airlines stores each of its scheduled flights in a structure with
five fields:
(e.1) Define the structure flight with the field names given above.
(define-struct flight (origin departure destination arrival passengers))
The parentheses here have to be correct. In general, all the parentheses have to be correct, except for counting the parentheses at the end of a definition.
(e.2) Complete the following definition for the predicate function valid-flight?, which takes an expression and checks whether it appears to be a valid flight.
(define valid-flight?
(lambda (X)
(and ; and, like +, can take more than 2 arguments
(________________ X) ; is it a flight structure at all? flight?
(airport-code-valid? (flight-origin X))
(time-valid? (________________ X)) ; is the departure time valid?flight-departure
(airport-code-valid? (flight-destination X))
(time-valid? (________________ X)) ; is the arrival time valid? flight-arrival
(list-of-strings? (flight-passengers X))))
(e.3) Assume that you have already
defined the variable airport-code-list,
which is a list of all the valid three-letter airport abbreviations (e.g.,
LAX, SFO, SNA). Write a definition for the predicate function airport-code-valid?,
which takes a symbol (an atom) and returns true if the symbol is contained
in airport-code-list.
(Hint: You can do this without recursion if you use a function we defined
in class and in the book.)
(define airport-code-valid?
(lambda (c)
(member? c airport-code-list)))
; Okay if the order of arguments to member? is switched. Don't deduct
but make a note if they use a cond to explicitly return #t or #f. It's
also okay if they write it out recursively and don't use member?
(e.4) The predefined predicate string?
takes a single argument and returns true (#t)
if and only if the argument is a string. Write a definition for the predicate
list-of-strings?,
which takes a list and returns true if and only if every element of the
list is a string (or if the list is empty).
(define list-of-strings?
(lambda (L)
(cond
((null? L) #t)
((string? (first L)) (list-of-strings? (rest L)))
(else #f))))
This can also be done in just two cond clauses, with the second using AND.
(e.5) Define the predicate flight-goes-to?,
which takes two arguments, a flight structure and a symbol (representing
an airport code), and returns true if the flight's destination matches
that symbol.
(define flight-goes-to?
(lambda (F d)
(equal? (flight-destination F) d)))
; Okay to use eq? or symbol=? instead of equal?
(e.6) Anteater Airlines stores all of its scheduled flights in a list of flight structures--the same flight structure you defined in the previous problem.
Write a definition for the function first-flight-to,
which takes a flight list and a symbol (representing an airport code) and
returns the first flight on the list whose destination matches that symbol
(or the null list if there's no match). Use flight-goes-to?
as described above, whether or not your definition was correct.
(define first-flight-to
(lambda (L d)
(cond
((null? L) '())
((flight-goes-to? (first L) d) (first L))
(else (first-flight-to (rest L) d))))
(e.7) Write a definition for the function
keep-flights-to,
which takes a flight list and a symbol (representing an airport code) and
returns a list of flights containing only those flights in the original
list whose destination matches that symbol.
(define keep-flights-to
(lambda (L d)
(cond
((null? L) '())
((flight-goes-to? (first L) d) (cons (first L) (keep-flights-to
(rest L) d)))
(else (keep-flights-to (rest L) d))))
(e.8) To enhance security, an anonymous
air marshal will be assigned to every Anteater Airlines flight. Write a
definition of add-marshals,
which takes a flight list and a code name and adds that code name at the
beginning of the passenger list of each flight. (Hint: First write a function
to take a single flight and add the name; then call that function from your
definition of add-marshals.)
(define add-marshals
(lambda (L name)
(cond
((null? L) '())
(else (cons (enhance (first L) name) (add-marshals
(rest L) name)))))
(define enhance
(lambda (F codename)
(make-flight (flight-origin F) (flight-departure F) (flight-destination
F) (flight-arrival F)
(cons codename (flight-passengers F)))))
(e.9) Write a definition for complete-passengers-list,
which takes a flight list and returns a list of strings containing all the
passengers from all the flights on the list, with no duplications. (You
may assume that all the passengers on a single flight are unique.)
(define complete-passengers-list
(lambda (L)
(cond
((null? L) '())
(else (add-unique (flight-passengers (first L)) (complete-passengers-list
(rest L))))))
(define add-unique
(lambda (one-flights-list master-passengers-list)
(cond
((null? one-flights-list) master-passengers-list)
((member? (first one-flights-list) master-passengers-list)
(add-unique (rest one-flights-list) master-passengers-list))
(else (cons (first one-flights-list) (add-unique (rest
one-flights-list) master-passengers-list)))))
(e.10) (5 points) Write the function
average-passengers
that takes a flight list and returns the average number of passengers on
the flights on the flight list.
(define average-passengers
(lambda (L)
(/ (total-passengers L) (length L))))
(define total-passengers
(lambda (L)
(cond
((null? L) 0)
(else (+ (length (flight-passengers (first L))) (total-passengers
(rest L)))))))
(e.11) Rewrite average-passengers
to make it tail-recursive. (If your answer for part (a) is already
tail-recursive, just write "I did this already," and if you did
it correctly, you'll get full credit.)
(define average-passengers
(lambda (L)
(/ (total-passengers L 0) (length L))))
(define total-passengers
(lambda (L acc)
(cond
((null? L) acc)
(else (total-passengers
(rest L)
(+ acc (length (flight-passengers (first
L)))))))))
(e.12) Anteater Airlines plans to merge with Aardvark Airlines to form a new airline, AAAir. Luckily (and incredibly), both airlines store their flights in a list of flight structures as described above.
Write the function merge-flight-lists, which takes two flight lists and returns a flight list containing all the flights from both arguments, except that when a flight from the first list matches a flight from the second list (i.e., they have the same origin, departure time, destination, and arrival time), the merged list contains just one flight with the two matching flights' passenger lists combined.
You may assume that you have already defined
flights-match?,
which takes two flight structures and returns true if they match as described
above, and merge-lists,
which takes two lists and returns a list that contains all the elements
of both arguments. You may also assume that the names on any single passenger
list are unique and that within each of the original flight lists, no flights
match. (Hint: Be careful and consistent about what types of data come
into and go out of each function.)
(define merge-flight-lists
(lambda (F G)
(cond
((null? F) G)
(else (merge-flight-lists (rest F) (merge-a-flight
(first F) G))))))
(define merge-a-flight
(lambda (f L)
(cond
((null? L) (list f))
((flights-match? f (first L)) (cons (merge-flights
f (first L)) (rest L))
(else (cons (first L) (merge-a-flight (f (rest L)))))))
(define merge-flights
(lambda (f g)
(make-flight (flight-origin f) (flight-departure f) (flight-destination
f) (flight-arrival f)
(merge-lists (flight-passengers f) (flight-passengers
g)))))
(f) Evaluate each of the following expressions. That is, what does the Scheme interpreter (DrScheme in our case) display when each of these expressions is executed?
110 (1 point)
#f or false (1 point)
(f.3) (+
100
(cond
((>= 5 (/ 10 2)) 37)
(else 6)))
137 (2 points)
(g.1) True or false: The features and capabilities of Scheme make it the best choice for the great majority of programming tasks. False
(g.2) True or false: A programmer with a knowledge of Java can be sure that his or her knowledge will be enough to sustain a productive and innovative 40-year career. False
(h) Students in the course Applied Epistemology 101 are graded on two items, a midterm and a final exam, each of which has 100 points possible. The midterm's weight 40% of the course grade; the final is worth 60%.
Write the function AE101-score
that takes two arguments--a student's midterm score and final exam score--and
returns that student's overall weighted score in the class (in the range
0 to 100). Write two constant definitions for the weights, a contract,
a brief purpose statement, the Scheme function definition, and two tests
in the form of boolean expressions that should return true if the function
works correctly.
(define MT-WEIGHT
0.40) ; Could also be 40, if the arithmetic later is right
(define FINAL-WEIGHT 0.60) ; Could be 60. [ 1 point for defining both correctly]
;; AE101-score: number number -> number [1 point; part credit if "midterm",
e.g., for "number"]
;; Compute weighted score given midterm and final scores (all 0-100) [-1/2
if missing or blatantly untrue]
(define AE101-score
(lambda (midterm final)
(+ (* midterm MT-WEIGHT) (* final FINAL-WEIGHT))))
;; Tests
(= 0 (AE101-score 0 0))
(= 100 (AE101-score 100 100)) [1 point for both correct tests, returning
a boolean]
SCORING THE CODE:
1 point for correct form of define: (define AE101-score (lambda
(ANYTHING..., or (def (A-s ANYTHING) ...)
1 point for correct parameter list---two names in parentheses (with
AE101-score if using Indiana style)
1 point for any attempt to add something involving both arguments
1 point for completely correct arithmetic
1 point for everything else correct. Parentheses must be right except
for counting all the trailing ones.
(i) Complete the definition of the function between? below.
;; between?: number number number ->
boolean
;; Return true if the first argument's value is between the second and
the third, inclusive
;; Examples: (between? 7 0 10) is true; (between 3 3 4) is true; (between
1 2 3) is false
(define between? ;; 1 point for right form: compare value to low and compare value to high
(lambda (value low high) ;; 1 pt for correctness: going right way on =, not switching low and high
(and (>= value low) (<= value high)))) ;; Parens around comparisons must be right (or -1/2); ;; trailing parens don't matter here.
(j) Complete the definition of item-on-list? below.
;; item-on-list?: expression list ->
boolean
;; Return true if the expression occurs on the list
(define item-on-list?
(lambda (item L)
((empty? L) false)
((equal? item (first L)) true)
(else (item-on-list? item (rest L))))))
Scoring: 2 points
for empty case---1 for test, 1 for returning false
2 points for matching case---1 for test, 1 for returning
true
2 points for recursive case---1 for attempt at recursive
call, 1 for getting it all correct.
It's okay if they use some other comparison besides equal?, but note it. It's okay if they split this into nested conds as they do in the book. Minus 3 if they cross out the cond and just call member? (correctly). [If anybody uses member? without deleting the cond--e.g. (cond (true (member? item L))(else 'whatever))--I want to hear about it. They should get credit.] ** You may deduct points for nontrivial syntax problems, but beware of "double jeopardy." ** Some answers may be right but not follow the pattern of the rubric. Score as appropriate and consult with me as necessary.
(k) A date is a structure (make-date month day year), where month is a symbol ('Jan, 'Feb, and so on), day is a number from 1 to 31, and year is a number from 1000 to 3000.
(k.1) Define the structure date with the field names given above.
(define-struct date (month day year))
The parentheses here have to be correct. In general, all the parentheses have to be correct, except for counting the parentheses at the end of a definition. If they get any field names wrong, deduct 1/2 point.
(k.2) Define a date object called TODAY with the appropriate values.
(define TODAY (make-date 'Oct 19 2004))
If the day is off by 1 or 2, I don't think I care.
(k.3) Complete the following definition for the predicate function valid-date?, which takes an expression and checks whether it appears to be a valid date. Use the functions you defined in the previous problems where necessary.
;; valid-date?: anything -> boolean
(define MONTHLIST (list 'Jan 'Feb 'Mar 'Apr 'May 'Jun 'Jul 'Aug 'Sep 'Oct 'Nov 'Dec))
(lambda (D) (line 1) 1 point for date?; (line 2) 1 point for date-month, 1 point for MONTHLIST;
(and (line 3/4) 1 point for both between?s; (line 4) 1 point for 1000 & 3000
(________________ D) ; is it a date structure at all?
(item-on-list? (________________ D)________________) ; is the month valid?
(________________ (date-day D) 1 31) ; is the day valid?
(________________ (date-year D) ________ ________)))) ; is the year valid?
(k.4) Define the predicate function
all-valid-dates?.
;; all-valid-dates?:
list -> boolean
;; Return true if all the items on the list are valid dates.
If the list is empty, return true.
(define
all-valid-dates?
(lambda (L)
(cond
((empty? L) true)
((valid-date? (first L)) (all-valid-dates? (rest L)))
(else false))))
1 point for correct define/lambda/cond
5 points for the rest. Any logically equivalent version (e.g., one with and) is okay. You might give a point each for the empty and non-matching cases and three points for the recursive case.
(l) Suppose you wish to write a spelling checker that takes a string of text as input and returns a list of the misspelled words in that string. Because the input may contain white space and punctuation, we will need to extract the words from the string, where a word is a string of characters that are separated from the next word by white space or punctuation. (The precise characters that count as white space or punctuation we won't worry about here.)
Define the function spell-check,
which takes a string and returns a list of the words in the string that
are misspelled (more precisely, words that don't occur in the dictionary
of all correctly spelled words). You should use each of the following in
your definition:
* first-word,
a function that takes a string and returns the first word in that string
* rest-of-words,
a function that takes a string and returns a copy of that string with the
first word removed
* string-empty?,
a function that takes a string and returns true if it's empty or if
it contains only white space and punctuation
* DICTIONARY,
a (long) list of correctly spelled words, where each word is a string.
;; spell-check: string -> list-of-strings
;; Return a list of the words in the input string that aren't in the
dictionary.
(define
spell-check 1 point -- Correct define, lambda, and argument list
(lambda (s) 1 point -- Dividing the problem into 3 cases
that relate somehow to the arg
(cond 1 point -- Correctly identifying the empty/base
case [continued below]
((string-empty? s) empty)
((item-on-list? (first-word s) DICTIONARY) (spell-check
(rest-of-words s)))
(else
(cons (first-word s) (spell-check (rest-of-words s)))))))
1 point -- Correctly returning empty in the empty/base case
1 point -- Attempt to use both first-word and rest-of-words to traverse
list
1 point -- Correct use of first-word and rest-of-words in at least one case
to traverse list
1 point -- Traversal of list using first-word and rest-of-words completely
correct in both cases
1 point -- Attempt to find first-word in DICTIONARY
1 point -- Correct location of first-word in DICTIONARY (item-on-list? or
member?; -1/2 for rewriting it)
1 point -- Correct case where first-word is in the dictionary (no word added
to return list)
1 point -- Correct case where first-word isn't in dictionary (consing
first-word onto return list)
1 point -- Everything else correct
(m) In this problem you may not use the predefined functions member or list-ref. You may use other functions defined earlier in this exam (and you may lose points if you re-implement here something that was already described above).
(m.1) Define the function position-on-list.
;; position-on-list: any list-of-any ->
number
;; Return the place on the list where the first input occurs, or zero if
list is empty
;; Examples: (position-on-list 'a '(a b c)) is 1; (position-on-list
1 empty) is 0;
;; (position-on-list 3 '(2 3 4)) is 2
(define
position-on-list
(lambda (item L)
(cond
((empty? L) 0)
((equal? item (first L)) 1)
(else (+ 1 (position-on-list item (rest L)))))))
SCORING: 1 for empty case, 2 for matching case, 3 for increment/recursive case.
(m.2) Define the function item-at-position.
;; item-at-position: number list-of-any
-> any
;; From the input list, return the item specified by the input number, or
empty if out of range
;; Examples: (item-at-position 3 '(a b c)) is c; (item-at-position
7 '(a b)) is empty;
;; (item-at-position 0 '(3 4)) is empty
(define
item-at-position
(lambda (n L)
(cond
((empty? L) empty)
((<= n 0) empty)
((= n 1) (first L))
(else (item-at-position (- n 1) (rest L))))))
SCORING: 1 for handling empty input list; 1 for handling index <= 0 (not checking negative is okay); 3 for recognizing the item at the right position and returning it; 3 for the correct recursive case. Partial credit as warranted.
(m.3) Define next-on-list. You may wish to use the predefined function length, which returns the number of items on a list. [Hint: Use prior definitions, not recursion.]
;; next-on-list: any list-of-any -> any
;; Return the item on the input list that follows the first input, or empty
if none
;; Examples: (next-on-list 'b '(a b c)) is c; (next-on-list 'c
(a b c)) is empty;
;; (next-on-list 'x '(a b c)) is empty; (next-on-list
'a empty) is empty
(define
next-on-list
(lambda (item L)
(cond
((= 0 (position-on-list item L)) empty)
((= (length L) (position-on-list item L)) empty)
(else (item-at-position (+ 1 (position-on-list item L)) L)))))
SCORING: 2 points for correctly recognizing input not on list and returning empty; 2 points for correctly recognizing last item on list and returning empty; 3 points for returning correct next item otherwise.
(m.4) Define next-on-circular-list.
;; next-on-circular-list: expression list
-> expression
;; Like next-on-list, but the item after the last on the list is the first
item again
;; Example: (next-on-circular-list 'c '(a b c)) is a.
(define
next-on-circular-list
(lambda (item L)
(cond
((= 0 (position-on-list item L)) empty)
((= (length L) (position-on-list item L)) (first L))
(else (item-at-position (+ 1 (position-on-list item L)) L)))))
SCORING: 3 points for correctly handling the circular case; 2 points for everything else right. Don't deduct for the same mistakes as in the previous part, but do deduct if they messed something new up.
(m.5) Define the function next-month that uses the constant MONTHLIST (see Problem (k)) to take in a symbol ('Jan, 'Feb, ...) representing a month and return the symbol for the following month.
;; next-month: symbol -> symbol
;; Take a month name ('Jan, 'Feb, ...) and return the name of the
following month.
(define next-month
(lambda (this-month)
(next-on-circular-list this-month MONTHLIST)))
(m.6) Define the function advance-a-month that takes a date (see Problem (k)) and returns that date moved one month into the future.
;; advance-a-month: date -> date
;; Advance the input date by one month (on the same day)
(define
advance-one-month
(lambda (d)
(make-date (next-month (date-month d)) (date-day d)
(cond ((eq? (date-month d) 'Dec) (+ 1 (date-year
d)))
(else (date-year d))))))
SCORING: 2 points for returning a date (call to make-date with three arguments); 2 points for correct call to next-month; 3 points for handling December correctly; 1 point for everything else correct.
(m.7) Suppose you have a list of dates representing events on your calendar, but you decide to take a month's skiing vacation in February. You'll need to postpone all the events scheduled in February, perhaps moving them one month later. Generalize this to the function clear-the-month.
;; clear-the-month: symbol list-of-dates
-> list-of-dates
;; Return the input list after advancing by one month
;; every date whose month matches the input symbol.
(define
clear-the-month
(lambda (m L)
(cond
((empty? L) empty)
((eq? (date-month (first L)) m) (cons (advance-one-month (first
L)) (clear-the-month m (rest L))))
(else (cons (first L) (clear-the-month m (rest L)))))))
SCORING: 1 point for empty case; 4 points for matching-month case; 1 point
for non-matching case.
(m.8) Define this function:
;; days-to-start-of-month: symbol
-> number
;; Return the number of days from January 1 to the start of the named month
in non-leap years
;; Examples: (days-to-start-of-month 'Jan) is 0; (days-to-start-of-month
'Feb) is 31
(define DAYSINMONTH '(31 28 31 30 31 30 31 31 30 31 30 31)) ; this
will be useful
No key
currently available.
(m.9)
Define this function:
;; days-from-jan1: date -> number
;; Return number of days from January 1 of the same year to the specified
date, inclusive
;; Examples: (days-from-jan1 (make-date 'Jan 3 2005)) = 3; (days-from-jan1
(make-date 'Feb 1 2005)) = 32
No key currently available.
(n) For each of the two sets of data shown below, draw the binary search tree that results from inserting the items in the order shown. Distinguish left branches clearly from right branches.
(n.1a) (13 19 22 7 17 10 2) (n.1b) (Scheme Python Java Fortran C Basic)
Balanced (2 points) Linear to the left (2 points)
(n.2) For each of the trees above, if you traverse the tree in order, printing each node, what is the result?
(n.2a) [result of (n.1a)] 2 7 10 13 17 19 22 (n.2b) [result of (n.1b)] Basic C Fortran Java Python Scheme
(o) Evaluate each of the following Scheme expressions:
(local ((define make-checker
(lambda (threshold)
(lambda (n) (< n threshold))))
(define a1 (filter (make-checker 6) '(3 1 4 1 5 9 2 6)))
(define a2 (filter (make-checker 4) '(3 1 4 1 5 9 2 6))))
((3 1 4 1 5 2) (3 1 1 2)) -- Correct numbers and order, but list structure wrong: -1.
Branching the wrong way on equality: another -1
(local ((define make-checker
(lambda (comparison-op threshold)
(lambda (n) (comparison-op n threshold))))
(define b1 (filter (make-checker = 1) '(3 1 4 1 5 9 2 6)))
(define b2 (filter (make-checker >= 3) '(3 1 4 1 5 9 2 6))))
((1 1) (3 4 5 9 6)) -- Don't deduct again for problems mentioned above.
(p) This problem involves the restaurant collection program. For each part below, indicate your answer by making any additions, changes, or deletions to the table of data shown in that part.
(p.1) Suppose the collection C contains
the information shown below.
Thai Dishes Thai 434-3434 Mee Krob 10.95<--
remove
Jacopo's Pizzeria Pizza
343-3434 Goat Cheese Pizza 12.00
Mitsuki Japanese 232-5353 Edamame 4.50
Tommy Tang's Thai 454-4545 Paht Woon Sen
8.75<--
remove
Thai Touch Thai 242-2424
Larb Guy 9.95<--
remove
Kitayama Japanese 335-3535
Okonomiyaki 8.50
What is the result returned by the following
code? (Show your results by making changes to the table above--change values,
cross lines out, add new lines, as appropriate.)
(define Thai?
(lambda (R)
(equal? (rrant-cuisine R)
'Thai)))
(collection-remove C Thai?)
(p.2) Suppose the collection C contains
the information shown below.
Thai Dishes Thai 434-3434 Mee Krob 10.95
Jacopo's Pizzeria Pizza 343-3434 Goat Cheese Pizza
12.00
Mitsuki Japanese 232-5353 Edamame 4.50<--
remove
Tommy Tang's Thai
454-4545 Paht Woon Sen 8.75
Thai Touch Thai 242-2424 Larb Guy 9.95
Kitayama Japanese 335-3535 Okonomiyaki 8.50<--
remove
What is the result of the following expression?
(collection-remove C (lambda (R) (equal? (rrant-cuisine R) 'Japanese)))
(p.3) Suppose the collection C contains
the information shown below.
Thai Dishes Thai 434-3434 Mee Krob 10.95<--
remove
Jacopo's Pizzeria Pizza
343-3434 Goat Cheese Pizza 12.00
Mitsuki Japanese 232-5353 Edamame 4.50<--
remove
Tommy Tang's Thai
454-4545 Paht Woon Sen 8.75<--
remove
Thai Touch Thai 242-2424
Larb Guy 9.95<--
remove
Kitayama Japanese 335-3535
Okonomiyaki 8.50<--
remove
What is the result of the following expression?
(collection-remove C
(lambda (R)
(or (Thai? R) (equal? (rrant-cuisine
R) 'Japanese))))
(p.4) Suppose the collection C contains
the information shown below.
Thai Dishes Thai 434-3434 Mee Krob 10.95-->
11.95
Jacopo's Pizzeria Pizza
343-3434 Goat Cheese Pizza 12.00
Mitsuki Japanese 232-5353 Edamame 4.50
Tommy Tang's Thai 454-4545 Paht Woon Sen
8.75-->
9.75
Thai Touch Thai 242-2424
Larb Guy 9.95-->
10.95
Kitayama Japanese 335-3535
Okonomiyaki 8.50
What is the result of the following expression?
(define raise-price
(lambda (R)
(make-rrant (rrant-name
R) (rrant-cuisine R) (rrant-phone
R) (rrant-dish
R) (+ 1.00 (rrant-price R)))))
(collection-change C Thai? raise-price)
(p.5) Suppose the collection C contains
the information shown below.
Thai Dishes Thai 434-3434 Mee Krob 10.95<--
remove (was 11.95)
Jacopo's Pizzeria Pizza
343-3434 Goat Cheese Pizza 12.00<--
remove
Mitsuki Japanese 232-5353
Edamame 4.50
Tommy Tang's Thai 454-4545 Paht Woon Sen
8.75-->
9.75
Thai Touch Thai 242-2424
Larb Guy 9.95<--remove
(was 10.95)
Kitayama Japanese 335-3535
Okonomiyaki 8.50
What is the result of the following expression?
(collection-remove (collection-change
C Thai? raise-price) ; raise-price is defined above
(lambda (R) (>
(rrant-price R) 10.00)))
(p.6) Suppose the collection C contains
the information shown below.
Thai Dishes Thai 434-3434 Mee Krob 10.95-->
8.95
Jacopo's Pizzeria Pizza
343-3434 Goat Cheese Pizza 12.00-->10.00
Mitsuki Japanese 232-5353
Edamame 4.50<--remove
Tommy Tang's Thai
454-4545 Paht Woon Sen 8.75<--remove
Thai Touch Thai 242-2424
Larb Guy 9.95-->
7.95
Kitayama Japanese 335-3535
Okonomiyaki 9.50
What is the result of the following expression?
(collection-change
(collection-remove C (lambda
(R) (< (rrant-price R) 9.00)))
(lambda (R) (or (equal? (rrant-cuisine
R) 'Pizza) (equal? (rrant-cuisine R) 'Thai))) (lambda
(R) (make-rrant (rrant-name R) (rrant-cuisine R)
(rrant-phone R)
(rrant-dish R) (-
(rrant-price R) 2.00))))
(q) Below are the definitions of five functions.
(q.1) Write "R" next to each of the five routines below that is recursive.
(q.2) Write "T" next to each of the five routines that is tail-recursive.
Some routines may be both "R" and "T"; some may be neither. Consider each function independently of the others (i.e., pay no attention to the other functions a given function calls).
(define print-stars-A R
(lambda (N)
(cond
[(zero? N) (newline)]
[else (begin ; do these two things,
in the order shown:
(print-stars-A (- N 1)) ; print n-1 stars
(display "*"))]))) ; print out a star
(define print-stars-B RT
(lambda (N)
(cond
[(zero? N) (newline)]
[else (begin ; do these two
things, in the order shown:
(display "*")
; print out a star
(print-stars-B (- N 1)))]))) ; print n-1 stars
(define keep-matches-A R
(lambda (L X)
(cond
[(null? L) empty]
[(equal? X (first L)) (cons (first L) (keep-matches-A (rest L)
X))]
[else (keep-matches-A (rest L) X)])))
(define keep-matches-B neither
(lambda (L X)
(keep-matches-help L X '())))
(define keep-matches-B-help RT
(lambda (L X list-so-far)
(cond
[(null? L) list-so-far]
[(equal? X (first L)) (keep-matches-B-help (rest L)
X
(cons (first L) list-so-far))]
[else (keep-matches-B-help (rest L) X list-so-far)])))
(r) Suppose we have a list called RL of restaurants with menus, according to the usual definitions:
(define-struct rrant (name cuisine phone
menu))
where menu is a list of dishes
(define-struct dish (name price)).
Define the following function:
;; name-and-phone-serving-dish: (listof
rrant) string -> (listof name-phone-list)
;; Returns a list of the names and phone numbers of all the restaurants
that
;; serve the dish named in the second input. Each name/phone-number pair
;; should be in its own list; for example
;; (("Cobras and Matadors" "343-3434") ("La Cote
Basque" "344-3334")).
(define name-and-phone-serving-dish
(lambda (RL dishname)
(map make-name-phone
(filter (lambda (R) (rrant-serves-dish? R dishname))
RL))
Probably the best
way to handle this is to define functions like these individually first:
;; menu-includes?: menu string -> boolean [This appears above]
;; Return true if string is the name of a dish on menu
(define (menu-includes? M s)
(> (length (filter (lambda (D) (string=? (dish-name D) s)) M)) 0))
;; rrant-serves-dish?:
rrant string ->boolean
;; Return true if string is the name of any menu item in rrant
(define (rrant-serves-dish? R s)
(menu-includes? (rrant-menu R) s))
;; make-name-phone:
rrant -> list
;; Returns list containing rrant's name and phone
(define (make-name-phone R)
(list (rrant-name R) (rrant-phone R)))
Determining whether a given restaurant serves the specified dish: 3 points (2 points for examining the menu and 1 point for extracting the menu from the restaurant). In my solution, the 2 points are captured by menu-includes?; if they rewrote the same thing they wrote for (b.2), rather than just calling it, they should lose a point; if they did the task some different way, that's okay. The 1 point is captured by rrant-serves-dish?, but again, it's okay if they achieve this some other way.
Selecting restaurants from the list that pass some test [ideally, the test is whether the restaurant serves the dish in question, but for this point, credit if they select some restaurants from the list using any criterion]: 1 point
Specifying the correct restaurant-choice criterion [i.e., correctly applying the equivalent of rrant-serves-dish? to the list]: 1 point
Returning a list of name/phone pairs [two-element lists---not technically pairs]: 2 points. In my solution, this is captured in make-name-phone, but they could get the same result some other way.
Everything else correct (including not using explicit recursion): 2 points [So this says if they coded it right using recursion, they can get 7/9]
(s) Below are definitions of map and filter.
(define (map f L) (define (filter p? L)
(cond (cond
((empty? L) empty) ((empty? L) empty)
(else (cons (f (first L)) ((p? (first L))
(map f (rest L)))))) (cons (first L) (filter p? (rest L))))
(else (filter p? (rest L)))))
(s.1) Write a definition for the function
process
that abstracts both map
and filter.
(Hint: You may find it useful to think about these two functions:
(define (always-true x) true)
and (define (no-change x) x).)
(define (process
f p? L)
(cond
((empty? L) empty)
((p? (first L)) (cons (f (first L)) (process f p? (rest L))))
(else (process f p? (rest L)))))
(s.2) Write new one-line definitions
for map
and filter
that call process.
(define (map2
f L) (process f always-true L))
(define (filter2 p? L) (process no-change p? L))
(t) A nested list of items (NL) is either
1. empty
2. (cons item NL), or
3. (cons NL NL).
Write a definition for the function deep-unique
as described below.
; deep-unique: NL -> list-of-items
; Return a list of all the items that occur in the input, no matter how
deeply nested,
; with no duplications. Order of result doesn't matter.
; Example: (deep-unique '(3 17 (3 Huey) Huey ((17)))) returns (3 17
Huey)
You may assume that the predicate list?
is already defined to return true if its argument is a list and false otherwise.
(define (deep-unique
L) (deep-unique-aux L empty))
(define (deep-unique-aux L unique-list)
(cond ((empty?
L) unique-list)
((list? (first L)) (deep-unique-aux (rest L) (deep-unique-aux
(first L) unique-list)))
((member? (first L) unique-list) (deep-unique-aux (rest
L) unique-list))
(else (deep-unique-aux (rest L) (cons (first L) unique-list)))))
; produces reverse order, fwd or rev OK
Written by David G. Kay, 1995-2004. Corrections
to some solutions by Felix Morariu, Fall 2005.
Wednesday, November 23, 2005 -- 8:40 AM