If you run any of the functions (as opposed to just testing them), comment out the code for running the functions before you submit your solution.
N.B.: Tests are not runs. A test is when you evaluate an expression and compare it to some expected result, while a run is when you evaluate an expression without anticipating any particular result for the expression.
Due date: 11/18 @ NOON
The purpose of this problem set is to practice the implementation of
Solve problems 27.1.4 and 27.1.5 using the world.ss teachpack.
27.3.1, 27.3.6, 28.2.1, 28.2.2, 28.2.3, 28.2.4
Image processing is a ubiquitous application of computing in all kinds of
disciplines. One image-processing operation is to mirror a picture along its
diagonal. The operation is also called a tranposition, because a picture is
often represented as a so-called matrix (a mathematical object) and transposing
a matrix is equivalent to mirroring an image. The goal of this exercise is to
develop a transposition program that can be applied to images in DrScheme.
;; Matrix = (cons (Listof X) (Listof (Listof X)))
;; constraint: all lists in the matrix have the same length
;; Matrix -> Number
(define (height m) (length m))
;; Matrix -> Number
(define (width m) (length (first m)))
Design create-matrix. The function consumes a list lox
and a number n such that (= (remainder (length lox) m) 0). It
produces a matrix of width m. (We really do mean design.)
Design transpose, a function that flips a matrix along the diagonal
from the top-left to the bottom right. Example:
'((a b c)
(1 2 3)
(* & ^)) )
'( (a 1 *)
(b 2 &)
(c 3 ^)))
Design the function mirror, which consumes an image and produces a
mirror image of the image. Hint: Look up image->color-list and
color-list->image in HelpDesk and experiment with them on small
images. --- Apply mirror to an image of yourself.
Testing functions in an interactive program is often difficult. To accomplish
some amount of testing and to stress the function, programmers build test
harnesses that apply these functions to random but legitimate inputs just to
see whether they still produce proper outcomes under "harsh" conditions.
In order to expose you to the idea without getting into complicated details,
let's look at a relatively simple example:
Obviously, you can develop examples and tests for click. Do so. A
different way to test the function, however, is to "throw" randomly chosen
characters at it until some condition is satisfied. At that point, you can
check additional conditions to determine whether the function works according
to your expectations.
;; World = String
;; the chars typed in so far,
;; up to the visible width of the world
(define WIDTH 100)
;; Keystroke World -> World
;; gather chars from the keyboard
(define (click key w)
[(char? key) (cond
[(< (image-width (draw w)) WIDTH)
(string-append w (make-string 1 key))]
;; World -> Image
;; create text image from given world
(define (draw w) (text w 22 'red))
;; --- run program run
(big-bang WIDTH 30 .1 "")
(on-tick-event (lambda (w) (update (draw w) produce w)))
Design the function test. It consumes a world and produces a
boolean. Its purpose is to generate randomly chosen Chars and supply
them to click until the string it produces is wider than
WIDTH. What does this validate? Hint: Look up
char->integer and integer->char in HelpDesk. Use these
functions (with random) to randomly choose alphabetical characters.
Modify test so that when it hits the base condition it also checks
that the world minus the last character does fit into the canvas of the given
width. What does this variant of test validate?