Fundamentals of Computer Science I: Media Computing (CS151.01 2008S)
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Related Courses: [CSC151.02 2008S (Davis)] [CSC151 2007F (Rebelsky)] [CSC151 2007S (Rebelsky)] [CSCS151 2005S (Stone)]
Summary: In this laboratory, you will explore the running time for a few algorithm variants.
a. In DrScheme, create a new file for this lab, called
analysis-examples.scm
.
b. Add the documentation and code for list-reverse-1
,
list-reverse-2
, and list-append
from the corresponding
reading to your file.
a. Add the following line to the beginning of list-append
(again, immediately after the lambda
).
(display (list 'list-append front back)) (newline)
b. Determine how many times list-append
is called when
reversing a list of length seven using list-reverse-1
.
c. Add the following line to the kernel of list-reverse-2
(immediately after the lambda
).
(display (list 'kernel remaining reversed)) (newline)
d. Determine how many times the kernel
is called when reversing a list of length seven using
list-reverse-2
.
e. Comment out the lines that you just added by prefixing them with a semicolon.
a. Replace the define
for
list-reverse-1
with define$
,
as in the following.
(define$ list-reverse-1 (lambda (lst) ...))
b. Find out how many times list-append
is called
in reversing a list of seven elements by entering the following command
in the interactions pane.
>
(analyze (list-reverse-1 (list 1 2 3 4 5 6 7)) list-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 list-append
.
We can do so by replacing define
with define$
in the definition of
list-append
.
e. Once again, find out how many times list-append
is called in reversing a list of seven elements by entering the
following command in the interactions pane.
>
(analyze (list-reverse-1 (list 1 2 3 4 5 6 7)) list-append)
f. Did you get the same answer as in exercise 1? If not, what difference do you see?
g. Replace the define
in
list-reverse-2
with define$
.
h. Find out how many times kernel
is called in reversing
a list of seven elements by entering the following command in the
interactions pane.
>
(analyze (list-reverse-2 (list 1 2 3 4 5 6 7)) 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 (list-append
for
list-reverse-1
, list-reverse-2-kernel
for list-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 list-reverse-1
, with the following.
>
(analyze (list-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 list-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 list-reverse-2
, by entering the
following command.
>
(analyze (list-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 | rev1: Calls to list-append |
rev1: Total calls | rev2: Calls to kernel |
rev2: 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
.
;;; Procedure: ;;; rgb-brightest ;;; Parameters: ;;; colors, a list of RGB colors ;;; Purpose: ;;; Find the brightest color in the list. ;;; Produces: ;;; brightest, an RGB color. ;;; Preconditions: ;;; rgb-brightness is defined. ;;; colors contains at least one element. ;;; Postconditions: ;;; For any color in colors, ;;; (rgb-brightness color) <= (rgb-brightness brightest) ;;; brightest is an element of colors. (define rgb-brightest-3 (lambda (colors) (let kernel ((brightest-so-far (car colors)) (remaining-colors (cdr colors)))) (if (null? remaining-colors) brightest-so-far (kernel (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.
Consider rgb-brightest-4
, a variant of an efficient
version of rgb-brightest
that has additional error
checking added.
(define rgb-brightest-4 (lambda (colors) (if (not (all-rgb? colors)) (throw "rgb-brightest: expects a list of colors; received" colors)) (if (null? (cdr colors)) (car colors) (rgb-brighter (car colors) (rgb-brightest-2 (cdr colors))))))
a. Predict the number of calls to rgb-brightest-4
in finding the brightest in a list of eight colors.
b. Check your hypothesis.
c. Predict the number of calls to all-rgb?
in
finding the brightest in a list of eight colors.
d. Check your hypothesis.
Rewrite rgb-brightest-4
so that it continues to
check preconditions, but precondition checking does not exact such a
heavy penalty.
Primary: [Front Door] [Syllabus] - [Academic Honesty] [Instructions]
Current: [Outline] [EBoard] [Reading] [Lab] [Assignment]
Groupings: [Assignments] [EBoards] [Examples] [Exams] [Handouts] [Labs] [Outlines] [Projects] [Readings]
References: [A-Z] [Primary] [Scheme Report (R5RS)] [Scheme Reference] [DrScheme Manual]
Related Courses: [CSC151.02 2008S (Davis)] [CSC151 2007F (Rebelsky)] [CSC151 2007S (Rebelsky)] [CSCS151 2005S (Stone)]
Copyright (c) 2007-8 Janet Davis, Matthew Kluber, and Samuel A. Rebelsky. (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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