Overview

• We look at general quiz issues.
• We do some sample quiz questions.
• We gather additional questions and arrange them.
• I attempt answers.
• More Q&A, as appropriate.

About the Quiz

Topics

• image-compute
• let and let*
• New list operations (cons, car, cdr)
• Conditionals (if, when, cond)
• Anonymous procedures (using lambda, section, o, l-s, r-s)

Some things to know about

• Similarities and differences between let and let*.
• Similarities and differences between lists and list-like things.
• Similarities and differences between the three conditional operations.
• Different ways to make anonymous procedures: section, l-s, r-s, o, lambda.

Types of Questions

• What is the value of this expression?
• Write code to __.
• Document the following procedure.
• Summarize tests for the following procedure. (You will not have to write them as Rackunit tests.)
• Random silly extra credit question

Sample Quiz Questions

There are enough of these that you should check the eboard.

Values of Expressions

What is the value of (reverse (append (iota 5) (iota 5)))?

What is the value of (reverse (append (iota 5) 5))?

What is the value of (cadr (reverse (iota 5)))?

What is the value of (cdar (reverse (iota 5)))?

Sketch the image that results from the following code.

    (let ([red (irgb 255 0 0)]
          [blue (irgb 0 0 255)]
          [white (irgb 255 255 255)])
      (image-show (image-compute
                   (lambda (col row)
                     (cond
                       [(< col 100)
                        red]
                       [(< row 100)
                        blue]
                       [else
                        white]))
                   200 200)))

What is the value of (map (l-s - 2) (iota 5))?

What is the value of (map (r-s - 2) (iota 5))?

What is the value of (map (o (l-s - 2) (r-s * 3)) (cons 4 (iota 5)))?

What is the value of (map (lambda (x) (* 3 (+ 2 x))) (iota 5))?

What is the value of (let ([a 10] [b 5]) (list a b))?

What is the value of (let ([a 10] [b (square a)]) (list a b))?

What is the value of (let* ([a 10] [b (square a)]) (list a b))?

Code to Write

Write a procedure to get the last value in a list.

Without using lambda, write a procedure to remove the last value in a list (or, more precisely, to return a list that contains all but the last value of its parameter list).

    > (remove-last (list 1 2 3))
    '(1 2)
    > (remove-last (reverse (iota 5)))
    '(4 3 2 1)

Using image-compute, write an expression to create a 100x100 image with a red circle of radius 30 centered at (40,50).

The following code makes way too many lists. Rewrite it using a single call to map.

    (map hshift-drawing
         (make-list 20 5)
         (map vshift-drawing
              (map * (make-list 20 10) (iota 20))
              (make-list 20 drawing-unit-circle)))

Documentation

Document the following procedure using the six P's.

    (define rac (o car reverse))

Document the following procedure using the six P's.

    (define something
      (lambda (img x y)
        (when (< x y)
          (image-select-rectangle! img REPLACE 0 0 x y)
          (context-set-fgcolor! (irgb (random 256) (random 256) (random 256)))
          (image-fill! img)
          (image-select-nothing! img))))

Tests

List the tests you would conduct for the following procedure.

    ;;; Procedure:
    ;;;   trim-ends
    ;;; Parameters:
    ;;;   lst, a list
    ;;; Purpose:
    ;;;   Removes the last and first elements, if they exist.
    ;;; Produces:
    ;;;   trimmed, a list
    ;;; Postconditions:
    ;;;   If lst is empty, returns an empty list
    ;;;   If lst has only one element, returns an empty list
    ;;;   Otherwise
    ;;;     We have removed two elements
    ;;;       (length trimmed) = (length lst) - 2
    ;;;     The second to the penultimate are in the same relative position
    ;;;       For all i < (length trimmed)
    ;;;         (list-ref trimmed i) = (list-ref lst (+ i 1))

Questions

Can you briefly go over l-s and r-s?

(l-s fun left) == (section fun left <>) == (lambda (right) (fun left right)) (r-s fun right) == (section fun <> right) == (lambda (left) (fun left right))

When does cdar work?

(cdar val) == (cdr (car val)). So this only works if the first element of val is itself a list.

It would work with (cdar (list (iota 5) (iota 4)))

(cdar (list (iota 5) (iota 4))) => (cdr (car (list (iota 5) (iota 4)))) => (cdr (iota 5)) => (1 2 3 4)

Welcome to DrRacket, version 6.1 [3m].
Language: racket [custom]; memory limit: 128 MB.
> (list (iota 5) (iota 4))
'((0 1 2 3 4) (0 1 2 3))
> (car (list (iota 5) (iota 4)))
'(0 1 2 3 4)
> (cdr (list (iota 5) (iota 4)))
'((0 1 2 3))
> (iota 4)
'(0 1 2 3)
> (cdr (car (list (iota 5) (iota 4))))
'(1 2 3 4)
> (cadr (iota 5))
1
> (cdar (iota 5))
. . cdar: contract violation
  expected: (cons/c pair? any/c)
  given: '(0 1 2 3 4)
> (cdr (car (iota 5)))
. . cdr: contract violation
  expected: pair?
  given: 0

Why would anyone use cdar?

Example: I might have a list of students, and each student is a list of the form (name class grade-on-exam1 ...). (cdar students) gives me the name of the first student. (cdar (sort-by-grade students)) gives me the name of the top student.

Why is (cdr (list (iota 5) (iota 4))) equal to (list (iota 4)) rather than just (iota 4)?

What is (cdr (list 5 4))? It's (list 4) or '(4). cdr always gives back a list (if given a list); it just removes the first element.

Should we use the single-quotation mark (aka tick) to make lists?

No! It leads to confusion down the line.

Do we use cdr to traverse down lists?

Yes. Great idea.

Do we have to know cadr?

Yes.

What is (cdr (list 1))?

null

Can you do the sketching one?

    (let ([red (irgb 255 0 0)]
          [blue (irgb 0 0 255)]
          [white (irgb 255 255 255)])
      (image-show (image-compute
                   (lambda (col row)
                     (cond
                       [(< col 100)
                        red]
                       [(< row 100)
                        blue]
                       [else
                        white]))
                   200 200)))

It will be a drawing of size 200x200

The left half will be red.

The top right corner will be blue

The bottom right corner will be white

Can you give some phrases never to say to your professor?

"I don't listen in class."

Write a procedure to get the last value in a list.

Tools: reverse, car, (list-ref lst pos) (gives you the value at the given position, counting at 0)

    (define last
      (lambda (lst)
        (car (reverse lst))))

    (define last
      (lambda (lst)
        (list-ref lst (- (length lst) 1))))

> (define letters (list 'a 'b 'c 'd 'e))
> (list-ref letters 3)
'd
> (list-ref letters 4)
'e
> (length letters)
5
> (list-ref letters 5)
. . list-ref: index too large for list
  index: 5
    in: '(a b c d e)

    (define last (o car reverse))

Without using lambda, write a procedure to remove the last value in a list (or, more precisely, to return a list that contains all but the last value of its parameter list).

    (define remove-last (o reverse cdr reverse))

Using image-compute, write an expression to create a 100x100 image with a red circle of radius 30 centered at (40,50) and white everywhere else.

Start with

    (image-compute
     (lambda (col row)
       ???
     100 100))

We can use the distance formula "square root of ((y2-y1)^2 + (x2-x1)^2)" (sqrt (+ (square (- 50 row)) (square (- 40 col))))

    (image-compute
     (lambda (col row)
       (if (< (sqrt (+ (square (- 50 row)) (square (- 40 col))))
              30)
           (irgb 255 0 0)
           (irgb 255 255 255)))
     100 100)

Rewrite the following.

    (map hshift-drawing
         (make-list 20 5)
         (map vshift-drawing
              (map * (make-list 20 10) (iota 20))
              (make-list 20 drawing-unit-circle)))

It appears that the purpose of this is to take twenty copies of the unit circle, vertically shift each by a separate multiples of 10, and horizontally shift it by 5.

    (map (lambda (i)
           (hshift-drawing 5
                           (vshift-drawing (* 10 i) drawing-unit-circle)))
         (iota 20))

Can you make my brain hurt?

    (map (o (section hshift-drawing 5 <>)
            (section vshift-drawing <> drawing-unit-circle)
            (section * 10 <>))
         (iota 20))

Documentation