CSC151.02 2010S Functional Problem Solving : Labs
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Related Courses: [CSC151.01 2010S (Weinman)] [CSC151 2009F (Rebelsky)]
Misc: [SamR] [MediaScript] [GIMP]
Summary: In this laboratory, you will continue to explore the use of recursion.
a. Make a copy of list-recursion-revisited-lab.scm
, which contains useful definitions
for this lab.
b. Review the file to see what procedures and values are in the list.
In the code for this lab, you will see three lists of grey values with remarkably similar code. Can we generalize that code? We know how to make lists of numbers. And, once we have a list of numbers, we can certainly figure out what scale factor to use to make greys: It's 255 (or 256) divided by the largest value in the list of numbers. Putting it all together, we get
(define greys (lambda (vals) (let ((factor (/ 256 (largest vals)))) (map (lambda (n) (rgb-new (* factor n) (* factor n) (* factor n))) vals))))
But how do we find the largest value in the list of numbers? As you've
observed, (
computes the largest of max
val1
val2
)val1
and
val2
. We want to generalize this procedure to
work with a list of values.
a. Write (
, a procedure that computes the largest value in a list of real numbers.
largest
vals
)
b. What results do you expect for the following expressions?
>
(map rgb->string (greys (list 1 2 3 4)))
>
(map rgb->string (greys (list 1 5 2 3 6 1)))
>
(map rgb->string (greys (list 8 4 2 0)))
c. Check your answers experimentally.
d. Create some lists of shades of grey using iota
rather
than by building the list of numbers by hand.
You may recall that the procedure append
takes as parameters two lists, and joins the two lists together.
Let's generalize that procedure so that it works with more than
two lists.
a. Write a procedure, lists-join
, that,
given a nonempty list of lists as a parameter, joins the member lists together
using append
.
>
(list (list 1 2 3))
((1 2 3))
>
(lists-join (list (list 1 2 3)))
(1 2 3)
>
(list (list 1 2 3) (list 10 11 12))
((1 2 3) (10 11 12))
>
(lists-join (list (list 1 2 3) (list 10 11 12)))
(1 2 3 10 11 12)
>
(list (list 1 2 3) (list 10 11 12) (list 20 21))
((1 2 3) (10 11 12) (20 21))
>
(lists-join (list (list 1 2 3) (list 10 11 12) (list 20 21)))
(1 2 3 10 11 12 20 21)
>
(list null (list 1 2 3))
(() (1 2 3))
>
(lists-join (list null (list 1 2 3)))
(1 2 3)
>
(list (list 1 2 3) null)
((1 2 3) ())
>
(lists-join (list (list 1 2 3) null))
(1 2 3)
>
(lists-join (list null (list 1 2 3) null null null null (list 100 99 98) null))
(1 2 3 100 99 98)
Note: At first glance, it may be puzzling to work with a list of lists. However, you can disassemble that list just as you do any other list: the car of a list-of-lists is a list, the cdr of a list-of-lists is a list-of-lists, but with the first list removed.
Hint: Think about when you have a base case, what
you do in the base case, and what to do with the result of the recursive
case. (Remember, append
is generally used to join
two lists.)
b. Use lists-join
to join some of the color lists
your created in the preliminaries.
Here are possible answers for exercises 1 and 2.
(define largest (lambda (lst) (if (null? (cdr lst)) (car lst) (max (car lst) (largest (cdr lst)))))) (define lists-join (lambda (lst) (if (null? (cdr lst)) (car lst) (append (car lst) (lists-join (cdr lst))))))
You'll notice that both do a similar thing: They take a two-parameter
procedure (max
or append
)
and generalize it to a list of values. The process of repeatedly
applying a two-parameter procedure so as to process a list is
often called folding the procedure.
You'll also notice that they both lists-join
and
largest
use similar code. When we identify a
common structure for similar procedures, it can be helpful to
generalize and then to explore that generalization. You will do
so in this exercise.
a. Sketch a template of the common parts of lists-join
and largest
(with blanks to fill in for the rest).
b. Identify one or two other procedures from the reading that follow the same pattern.
c. Using your template, write a procedure,
(
,
that finds the smallest value in a list.
smallest
lst
)
d. Using your template, write a procedure,
(
,
that finds the darkest color in a list of RGB colors.
rgb-darkest
lst
)
Hint: You may find
it useful to build a utility procedure, (
,
that finds the darker of two colors.
rgb-darker
rgb1
rgb2
)
e. Using your template, write a procedure,
(
, that finds the darkest color in
a list of color names. (You'll need to convert color names to RGB
colors in order to compare them. However, you should return a
color name, not an RGB color.)
color-name-darkest
lst
)
Hint: Again, you'll find it useful to write a utility procedure, such
as color-name-darker
.
f. Using your template, write a procedure,
(
, that, given a list of positive
and negative numbers, finds the number in the list closest to zero.
closest-to-zero
lst
)
You may recall that in the reading we explored ways to build predicates that apply to lists by starting with predicates that apply to individual values. Let's try writing a few such procedures.
a. Write a procedure, (
, that, given a list of RGB colors,
determines if all of the colors are bright.
rgb-all-bright?
colors
)
b. Write a procedure, (
, that, given a list of RGB colors,
determines if any of them are bright.
rgb-any-bright?
colors
)
a. Write a procedure, (
, that, given a list of colors,
determines if all of the colors are primary colors (that is, are
red, blue, or green).
rgb-all-primary?
colors
)
b. Write a procedure, (
, that, given a list of colors,
determines if any of them are primary colors.
rgb-any-primary?
colors
)
One way to start writing the previous procedures is to define a
rgb-primary?
predicate.
(define rgb-primary? (let ((red (rgb-new 255 0 0)) (green (rgb-new 0 255 0)) (blue (rgb-new 0 0 255))) (lambda (color) (or (equal? color red) (equal? color green) (equal? color blue)))))
Can we generalize this technique for determining whether a value is
one of a number of values? Certainly. Let's write a procedure,
(
that holds only if
member?
val
vals
)val
appears in vals
.
We know that
val
does not appear in the empty list.
val
appears in a non-empty
vals
if val
is the
car of vals
or if it appears in the
cdr of vals
.
a. Translate this description into Scheme. That is, write
member?
.
b. Add member?
to your library.
c. We can use member?
to define the following
interesting procedure.
(define greenish? (let ((greens (map color-name->rgb (context-list-colors "green")))) (lambda (color) (member? color greens))))
Explain what this procedure does.
d. What result do you expect from the following expressions?
>
(map greenish? greens)
>
(map greenish? my-colors)
>
(map greenish? (list (rgb-new 0 0 0) (rgb-new 255 0 0) (rgb-new 128 0 0)))
e. Check your answers experimentally.
Primary: [Front Door] [Schedule] - [Academic Honesty] [Instructions]
Current: [Outline] [EBoard] [Reading] [Lab] - [Assignment]
Groupings: [Assignments] [EBoards] [Examples] [Exams] [Handouts] [Labs] [Outlines] [Projects] [Readings]
References: [A-Z] [By Topic] - [Scheme Report (R5RS)] [R6RS] [TSPL4]
Related Courses: [CSC151.01 2010S (Weinman)] [CSC151 2009F (Rebelsky)]
Misc: [SamR] [MediaScript] [GIMP]
Copyright (c) 2007-10 Janet Davis, Matthew Kluber, Samuel A. Rebelsky, and Jerod Weinman. (Selected materials copyright by John David Stone and Henry Walker and used by permission.)
This material is based upon work partially supported by the National Science Foundation under Grant No. CCLI-0633090. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
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