This lab is also available in PDF.
Summary:
In this laboratory, you will explore some basic concepts in recursing
over lists.
Contents:
Reference:
Here are the definitions from the reading.
;;; Procedure:
;;; sum
;;; Parameters:
;;; numbers, a list of numbers.
;;; Purpose:
;;; Find the sum of the elements of a given list of numbers
;;; Produces:
;;; total, a number.
;;; Preconditions:
;;; All the elements of numbers must be numbers.
;;; Postcondition:
;;; total is the result of adding together all of the elements of numbers.
;;; If all the values in numbers are exact, total is exact.
;;; If any values in numbers are inexact, total is inexact.
(define sum
(lambda (numbers)
(if (null? numbers)
0
(+ (car numbers) (sum (cdr numbers))))))
(define rgb.filter-out-dark
(lambda (colors)
(cond
((null? colors) null)
((rgb.dark? (car colors)) (rgb.filter-out-dark (cdr colors)))
(else (cons (car colors) (rgb.filter-out-dark (cdr colors)))))))
The latter procedure requires rgb.dark?, which follows.
;;; Procedure:
;;; rgb.dark?
;;; Parameters:
;;; color, an RGB color
;;; Purpose:
;;; Determine if the color appears dark.
;;; Produces:
;;; dark?, a Boolean
(define rgb.dark?
(lambda (color)
(> 33 (rgb.brightness color))))
;;; Procedure:
;;; rgb.brightness
;;; Parameters:
;;; color, an RGB color
;;; Purpose:
;;; Computes the brightness of color on a 0 (dark) to 100 (light) scale.
;;; Produces:
;;; b, an integer
;;; Preconditions:
;;; color is a valid RGB color. That is, each component is between
;;; 0 and 255, inclusive.
;;; Postconditions:
;;; If color1 is likely to be perceived as lighter than color2,
;;; then (brightness color1) > (brightness color2).
(define rgb.brightness
(lambda (color)
(round (* 100 (/ (+ (* .30 (rgb.red color))
(* .59 (rgb.green color))
(* .11 (rgb.blue color)))
255)))))
In this laboratory, we will not be working with images (just with colors
and with lists), so you need not create an image.
a. Copy the sum and rgb.filter-out-dark procedures
to your definitions pane.
b. Copy the rgb.dark? and rgb.brightness procedures
to your definitions pane.
c. Create a list of a dozen or so colors (red, black, green, blue, yellow,
orange, magenta, white, black, etc.). Name it my-colors.
a. Read through sum so that you have a sense of its
purpose.
b. Verify that sum produces the same result as in the
corresponding reading.
c. What value do you expect sum to produce for the empty
list? Check your answer experimentally.
d. What value do you expect sum to produce for a singleton
list? Check your answer experimentally.
e. Try sum for a few other lists, too.
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.
Suppose the length procedure 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 at each spot.
a. Using this idea, write a procedure, (my-length lst)
that finds the length of a list (without using length).
b. Check your answer.
Write a procedure, (product nums), that, given a list
of numbers, computes the product of those numbers. You should feel free to use
sum as a template. However, you should think carefully about
the base case.
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 1 (when the color is not dark).
a. Using this idea, write a procedure, (rgb.tally-dark colors), that, given a list of colors, counts how many are dark.
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 average-color
(lambda (colors)
(rgb.new (/ (rgb-list.sum-red colors) (length colors))
(/ (rgb-list.sum-green colors) (length colors))
(/ (rgb-list.sum-blue colors) (length colors)))))
Of course, for this to work, we need to write rgb-list.sum-red,
rgb-list.sum-blue, and rgb-list.sum-green. For
now, we'll write one of the three. (The other two should be obvious.)
a. Write a procedure, (rgb-list.sum-red colors), that computes
the sum of the red components in a color.
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 rgb-list.sum-red without using
direct recursion. How? By an appropriate combination of map
and sum. Try doing so. (If you can't find a solution,
look at the notes on the problem.)
Write a procedure, (rgb-list.filter-reds colors), that
filters out all elements of colors with a red component of at
least 128.
Write a procedure, (spots.bound spots left top right bottom), that filters out all elements of spots
which do not appear in the rectangle bounded at the left by left, at the top by top, at the right by right, and at the bottom by
bottom.
For example, if left is 5, top is 10, right is 8,
and bottom is 20, the procedure should remove any spots whose
column is less than 5 or more than 8 or whose row is less than 10 or
more than 20.
We can use map to extract the red component of each color.
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
(define rgb-list.sum-red
(lambda (colors)
(sum (map rgb.red colors))))
;
