CSC151.02 2010S Functional Problem Solving : Labs
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Summary: In this laboratory, you will explore some basic concepts in recursing over lists.
In this laboratory, we will not be working with images (just with colors and with lists), so you need not create an image.
a. Make a copy of recursion-basics-lab.scm
, which contains most of the code from the reading.
b. Review the procedures in the file so that you understand their purpose (if not necessarilly the process by which they acheive their purpose).
c. Create a list of a dozen or so RGB colors (red, black, green,
blue, yellow, orange, magenta, white, black, etc.). Name it
my-colors
. You may find it easiest to create a
list of color names and convert it to RGB colors using
map
.
(define my-colors (map color->rgb (list "red" "orange" "yellow" "green" "blue" "indigo" "violet" "black" "white" "grey" "magenta")))
a. Read through sum
so that you have a sense of its
approach to accomplishing its purpose
b. Verify that sum
produces the same results as in the corresponding reading.
c. What value do you expect sum
to produce for the empty
list?
d. Check your answer experimentally.
e. What value do you expect sum
to produce for
a singleton list? (A “singleton list” is a list with only
one value.)
f. Check your answer experimentally.
g. Try sum
for a few other lists, too.
h. What do you expect the following to compute?
>
(sum 1 2 3)
i. Check your answer experimentally.
a. Read through the definition of rgb-filter-out-dark
to
try to understand what it does.
b. Determine which colors in my-colors
are dark with
(map rgb-dark? my-colors)
.
c. Create a list of non-dark colors with (rgb-filter-out-dark
my-colors)
.
d. Verify that all the resulting colors are not dark, using a technique similar to the one that you used in step b.
e. Find out the names of the non-dark colors with
>
(map rgb->color-name (rgb-filter-out-dark my-colors))
Suppose the length
procedure, which computes the
length of a list, were not defined. We could define it by recursing
through the list, counting 1 for each value in the list. In some sense,
this is much like the definition of sum
, except that we
use the value 1 rather than the value of each element.
a. Using this idea, write a recursive procedure,
(
that finds the length of a list. You may not use
list-length
lst
)length
in defining list-length
.
b. Check your answer on a few examples: the empty list, the list of colors you created, and a few more lists of your choice.
Write a recursive procedure, (
, that computes the product of a
list of numbers. You should feel free to use product
nums
)sum
as a template for product
. However, you should
think carefully about the base case.
The length
procedure counts the number of values
in a list. What if we don't want to count every value in a list?
For example, what if we only want to count the dark values in a list
of colors? In this case, we still recurse through the list, but
we sometimes count 1 (when the color is dark) and sometimes count 0
(when the color is not dark).
a. Using this idea, write a procedure,
(
, that, given a list of colors,
counts how many are dark.
rgb-tally-dark
colors
)
b. Test your procedure.
In the past, we've found it useful to find the average of two colors. Let's
consider how we might find the average of a list of colors. First, we
would need to find the number of colors in the list. That's easy, we just
use the length
procedure. Next, we need to find the sum of
each component. That's a bit harder, but let's suppose we can do it.
We next divide each sum by the length, and get the average of
that component. Finally, we put it all together with rgb-new
.
That is, we might write
(define rgb-list-average (lambda (colors) (let ((count (length colors))) (rgb-new (/ (sum-red colors) count) (/ (sum-green colors) count) (/ (sum-blue colors) count)))))
Of course, for this to work, we need to write sum-red
,
sum-blue
, and sum-green
. For
now, we'll write one of the three. (One we've written that one,
the other two should be obvious.)
a. Write a procedure, (
, that computes the sum of the
red components in a list of colors. You should use direct recursion
in your definition sum-red
colors
)sum-red
. (That is, you
should use recursion, and not take advantage of the already-written
sum
procedure, other than as a template for
your code.) You may want to base your definition on the definition
of sum
.
b. Test your procedure on a list of a single color.
c. Test your procedure on the my-colors
list you wrote earlier.
d. It is possible to write sum-red
without
using direct recursion. How? An appropriate combination of
map
and sum
. Try doing so.
If you can't find a solution, look at the notes on this problem.
Write a procedure, (
, that filters out all elements
of filter-out-reds
colors
)colors
with a red component of at least 128.
Write a procedure,
(
,
that, given a nonempty list of colors, finds the darkest of those
colors.
rgb-darkest
colors
)
Write a procedure, (
, that, given a list of real
numbers (including both positive and negative numbers), returns the
value closest to zero in the list.
closest-to-zero
values
)
Hint: Think about how, given two numbers, you determine which is closer to zero.
Hint: Think about how this problem is similar to a problem or problems we've solved before.
We've seen how to average two colors and a list of colors. But what if we want to do something different: Given a list of colors, we want averages, but only of neighboring elements in the list.
Write a procedure, (
, that, given a list of colors,
computes a new list of colors, by averaging subsequent pairs of
colors. For example, if the input list is the standard seven
rainbow colors (red, orange, yellow, green, blue, indigo, and violet),
the output list will consist of
a red-orange average, an orange-yellow average, a yellow-green
average, a green-blue average, a blue-indigo average, and an
indigo-violet average.
rgb-averages
colors
)
Once again, the length of the result list is one less than the length of the input list.
We can use map
to extract the red component of
each color.
(map rgb-red colors)
That gives us a list of numbers, which we can sum with sum
.
(sum (map rgb-red colors))
Putting it all together in a procedure, we get
(define sum-red (lambda (colors) (sum (map rgb-red colors))))
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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