Summary: This lab provides practice with simple user-defined procedures.
You may want to glance over the corresponding reading before beginning this lab.
Start DrScheme and make sure that you're in full Scheme mode.
frac procedure from
the reading on procedures
and make sure that it works as advertised.
Write a Scheme procedure
(addtwo a) that returns the sum
a. Define a procedure named
feet->meters that takes one
argument, a real number representing a length measured in feet, and
returns the number that represents the same length as measured in
meters. Note that one foot is equal to exactly 761/2500 meters.
b. Use this procedure to determine the number of meters in one mile (5280 feet).
a. Define a procedure,
poly1, that corresponds to the
polynomial 5x2 - 8x + 2.
b. Test your procedure on the values 0, 1, 2, 3, 4.
a. Write a procedure
(quadratic-root a b c) that finds one
root of a quadratic equation
ax2 + bx + c = 0 using the quadratic formula. Use it to find a root of the above equation. (I don't care which root you find.)
b. Test your procedure by computing
(quadratic-root 1 -5 6) (quadratic-root 2 -10 12) (quadratic-root 1 4 4).
c. Use algebra to check these answers.
d. What are
(quadratic-root 1 0 1) and
(quadratic-root 1 0 2)?
Write a procedure,
swap-first-two, that, given a list as an
argument, creates a new list that interchanges the first two elements of
the original list, leaving the rest of the list unchanged. Thus,
> (swap-first-two (list 'a 'b 'c 'd 'e)) (b a c d e)
In this problem, assume that the list given to
swap-first-two has at least two elements; do not worry
about the possibility that
swap-first-two might be applied
to numbers, empty lists, or lists with only one element.
The volume of a sphere of radius r is 4/3 times pi times r3.
a. Write a procedure named
sphere-volume that takes as its
argument the radius of a sphere (in, say, centimeters) and returns its
volume (in, say, cubic centimeters).
b. Use this procedure to compute the volume of a softball (radius: eight centimeters).
Define a procedure
that takes two arguments, of which the second should be a list.
snoc should return a list just like its second argument,
except that the first argument has been added at the right end:
> (snoc 'alpha (list 'beta 'gamma 'delta)) (beta gamma delta alpha) > (snoc 1 (list 2 3 4 5 6)) (2 3 4 5 6 1) > (snoc 'first null) (first)
Hint: There are at least two ways to define this procedure. One uses calls to
cons; the other uses calls to
Given a nonempty list of elements (e.g.,
(a b c)),
write a procedure,
creates a new list with the original first element moved to the end .
> (rotate (list 'a 'b 'c)) (b c a) > (rotate (list 1 2)) (2 1) > (rotate (rotate '(first second third fourth))) (third fourth first second)
In a figure-skating competition, judges have observed the competitors' performances and awarded three separate scores to each competitor: one for accuracy, one for style, and one for the difficulty of the chosen routine. Each score is in the range from 0 to 10. The rules of the competition specify that a competitor's three scores are to be combined into a weighted average, in which accuracy counts three times as much as difficulty and style counts twice as much as difficulty. The overall result should be a single number in the range from 0 to 10.
a. Write a comment in which you describe the nature and purpose of a procedure that takes three arguments -- a competitor's accuracy, style, and difficulty scores -- and returns their weighted average.
b. Define the procedure that you have described.
c. Test your procedure, looking for cases in which the weighted average is computed incorrectly. (If you find any, make corrections in your definition.)
Tuesday, 5 September 2000
http://www.math.grin.edu/~walker/courses/151.fa00/lab-procedures.html(by Henry Walker; dated 1 September 2000)
http://www.math.grin.edu/~stone/courses/scheme/procedure-definitions.xhtml(by John Stone; dated 17 March 2000)
Wednesday, 31 January 2001
fracprocedure from the reading).
Sunday, 4 February 2001
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