This lab is also available in PDF.
Summary: In the laboratory, you will explore the
running time fo a few algorithm variants.
Contents:
a. In DrScheme, create a new file for this lab, called
analysis-examples.scm.
b. Add the comments and code for reverse-1, reverse-2,
and my-append from the
corresponding reading to your file.
a. Add the following line to the beginning of my-append
(again, immediately after the lambda).
(display (list 'my-append front back)) (newline)
b. Determine how many times my-append is called when
reversing a list of length seven using reverse-1.
c. Add the following line to the kernel of reverse-2
(immediately after the lambda).
(display (list 'reverse-2-kernel remaining reversed)) (newline)
d. Determine how many times reverse-2-kernel is called when
reversing a list of length seven using reverse-2.
e. Comment out the lines that you just added by prefixing them with
a semicolon.
a. Replace the define for reverse-1 with
define$, as in the following.
(define$ reverse-1
(lambda (lst)
...))
b. Find out how many times my-append is called in reversing
a list of seven elements by entering the following command in the
interactions pane.
> (analyze (reverse-1 (list 1 2 3 4 5 6 7)) my-append)
c. Did you get the same answer as in the previous exercise? If not,
why do you think you got a different result?
d. One potential issue is that we haven't told the analyst to include
the recursive calls in my-append. We can do so by replacing
define with define$ in the definition of
my-append.
e. Once again, find out how many times my-append is called
in reversing a list of seven elements by entering the following command
in the interactions pane.
> (analyze (reverse-1 (list 1 2 3 4 5 6 7)) my-append)
f. Did you get the same answer as in exercise 1? If not, what
difference do you see?
g. Replace the define in reverse-2 with
define$.
h. Find out how many times reverse-2-kernel is called in reversing
a list of seven elements by entering the following command in the
interactions pane.
> (analyze (reverse-2 (list 1 2 3 4 5 6 7)) reverse-2-kernel)
i. Did you get the same answer as in exercise 1? If not, what difference
do you see?
In the previous exercise, you considered only a single procedure
in each case (my-append for reverse-1,
reverse-2-kernel for reverse-2). Suppose we
incorporate all of the other procedures. What effect does it have?
a. Find out how many total procedure calls are done in reversing a list
of length seven, using reverse-1, with the following.
> (analyze (reverse-1 (list 1 2 3 4 5 6 7)))
b. How does that number of calls seem to relate to the number of
calls to my-append?
c. Are there any procedures you're surprised to see?
d. Find out how many total procedure calls are done in reversing a list
of length seven, using reverse-2, with the following.
> (analyze (reverse-2 (list 1 2 3 4 5 6 7)))
e. How does that number of calls seem to relate to the number of
calls to kernel?
f. Are there any procedures you're surprised to see?
a. Fill in the following chart to the best of your ability.
| List Length |
r1: Calls to
my-append |
r1: Total calls |
r2: Calls to
kernel |
r2: Total calls |
| 2 |
| | | |
| 4 |
| | | |
| 8 |
| | | |
| 16 |
| | | |
b. Predict what the entries will be for a list size of 32.
c. Check your results experimentally.
d. Write a formula for the columns, to the best of your ability.
Here is a third version of rgb.brightest.
(define rgb.brightest
(lambda (colors)
(rgb.brightest-helper (car colors) (cdr colors))))
(define rgb.brightest-helper
(lambda (brightest-so-far remaining-colors)
(if (null? remaining-colors)
brightest-so-far
(rgb.brightest-helper
(rgb.brighter brightest-so-far (car remaining-colors))
(cdr remaining-colors)))))
a. Find out how many steps this procedure takes on lists of length 2,
4, 8, and 16 in which the elements are arranged from lightest to darkest.
b. Find out how many steps this procedure takes on lists of length 2,
4, 8, and 16 in which the elements are arranged from darkest to lightest.
c. Find out how many steps this procedure takes on lists of length 2,
4, 8, and 16 in which the elements are in no particular order.
d. Predict the number of steps this procedure will take on each kind of
list, where the length is 32.
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