Assignment 02 questions (PDF) - Student.cs.uwaterloo.ca

CS 116 Winter 2014!
Assignment 02!
Due at 11:00am on Tuesday, January 28!
• This assignment consists mostly of material from Module 02, on functional
abstraction and functions as values.
• You must use abstract list functions (map, filter, foldr, build-list)
where appropriate. You may use the function length.
•
For full marks, each question must use abstract list functions in a nontrivial
way. You may NOT use explicit/structural recursion in any of your
solutions.
• For this assignment, unless otherwise noted, you cannot use named helper
functions. This includes those that are defined outside of a function and those
defined within a local. In essence you should only use local to define
constants and you should use lambda for any functions.
• You are expected to use the design recipe when writing functions from scratch.
For lambda functions embedded in larger functions you do not need comments
(i.e. contracts or purpose).
• Do not copy the purpose directly from the assignment description. The purpose
should be written in your own words and reference the parameter names of
your functions.
• The solutions you submit must be entirely your own work. Do not look up either
full or partial solutions on the Internet or in printed sources.
• Download the interface file from the course Web page.
• Read the course Web page for more information on assignment policies and how
to organize and submit your work. Follow the instructions in the style guide.
Specifically your solutions should be placed in files a02qY.rkt where Y is a value
from 1 to 4.
• Read each questions carefully for restrictions. Test data for all questions will
always meet the stated assumptions for consumed values.
• Assignments will not be accepted through email. Course staff will not debug
code emailed to them.
• Read the assignment carefully before asking any questions on Piazza.
• You may want to review the string and characters resource on the course
website.
!
Coverage: Module 02
Language Level: Intermediate Student Scheme with lambda
!
1. A triangular number is one which represents the number of “balls” required to make an
equilateral triangle. For example the numbers 1, 3 and 6 are the first three triangular
numbers (note how they correspond to the images below).
!
!
!
k = 1; b = 1 k = 2; b = 3 k = 3; b = 6

CS 116 Winter 2014!
Assignment 02!
Due at 11:00am on Tuesday, January 28!
!
!
!
!
In general the number of balls b required to make a triangle with k rows is given by:
(a)
b = 1 + 2 + 3 + 4 + … + k = k(k+1)/2
Use the formula above, k(k+1)/2, to write a Scheme function first-n-triangular
that consumes a positive natural number n and produces a list of the first n triangular
numbers.
For example,
(first-n-triangular 1) => (list 1)
(first-n-triangular 4) => (list 1 3 6 10)
!
(b)
!
Write a Scheme function first-n-triangular—v2 that consumes a positive natural
number n and produces a list of the first n triangular numbers. In this function you
cannot use the formula k(k+1)/2.
!
2. (a) Write a Scheme function all-letters-sorted that consumes a list of lowercase
alphabetic strings los and produces a single string containing all of the letters in los
ordered alphabetically.
!
For example,
(all-letters-sorted (list "bob" "mob" "cob" "dave" "rob")) =>
"abbbbbcdemoooorv"
!
!
!
!
Use the function sort in your solution. From the Racket reference:
(sort lst less-than?)
Returns a list sorted according to the less-than? procedure, which takes two elements of lst and returns a
true value if the first is less (i.e., should be sorted earlier) than the second.
!
Examples:!
> (sort '(1 3 4 2)

CS 116 Winter 2014!
Assignment 02!
Due at 11:00am on Tuesday, January 28!
!
For example,
(unique-letters-sorted
(list "bob" "mob" "cob" "dave" "rob"))
=> "abcdemorv"
!
3. Consider the new structure
(define-struct lottery-ticket (game value))
;; A Lottery-Ticket is a structure (make-lottery-ticket g v), where
;; g is one of the symbols 'Keno, 'Powerball, 'Lottario,
;; v is an integer representing the “earnings” on that ticket
;;(earnings could be negative)
!
Write a Scheme function game-summary that consumes a symbol game and a list of
Lottery-ticket structures, called all-tickets, and produces a function. The
produced function accepts a symbol (either 'won 'lost or 'net) and produces the total
amount won, lost or net (see table below) for that particular game across all tickets.
!
Value
Meaning
won
lost
sum of all positive earnings
absolute value of the sum of all negative earnings
net
won - lost (i.e. total value)
!
For example,
(define powerball-summary
(game-summary 'Powerball
(list (make-lottery-ticket 'Powerball 25)
(make-lottery-ticket 'Keno -9)
(make-lottery-ticket 'Powerball -20)
(make-lottery-ticket 'Lottario 17)
(make-lottery-ticket 'Powerball 10)
(make-lottery-ticket 'Keno 10)
(make-lottery-ticket 'Powerball -30))))
!
(powerball-summary 'won) => 35
(powerball-summary 'net) => -15
(powerball-summary 'lost) => 50
!
4. Write a Scheme function letter-with-position that consumes a list of strings
wordlist and produces a list of lists of strings according to the following:
!
• For each non-empty string w in wordlist the function should produce a list of strings
e a c h w i t h 3 o r m o r e c h a r a c t e r s w h e r e t h e f i r s t c h a r a c t e r i s a l e t t e r f r o m w, the second
character is an underscore _ and third (and possibly 4th and 5th etc.) character(s)
represent the position of that letter in w (indexed by zero).

CS 116 Winter 2014!
Assignment 02!
Due at 11:00am on Tuesday, January 28!
• For each empty string produce empty.
• If wordlist is empty produce empty.
!
!
!
!
!
For example,
(letter-with-position (list "hello" "goodbye")) =>
(list
(list "h_0" "e_1" "l_2" "l_3" "o_4")
(list "g_0" "o_1" "o_2" "d_3" "b_4" "y_5" "e_6"))
(letter-with-position (list "business suits" "" "4 u")) =>
(list
(list "b_0" "u_1" "s_2" "i_3" "n_4" "e_5" "s_6" "s_7" " _8"
"s_9" "u_10" "i_11" "t_12" "s_13")
empty
(list "4_0" " _1" "u_2"))
The order of the letters should correspond to their order in the original word.