CSC 533: Organization of Programming Languages
HW5: Scheme Programming
For this assignment, you are to define the following Scheme functions. For
simplicity, place all of your function definitions in a single file named
hw5.scm. Be sure to comment each function as to its behavior.
- Define functions for converting temperatures from Fahrenheit to Celsius,
and vice versa. The formula for converting from Fahrenheit to Celsius is:
tempInCelsius = (5/9) * (tempInFahrehneit - 32)
For example, (fahr->celsius 212) should evaluate to
100, while (celsius->fahr 0) should evaluate to 32.
- Define a function named wind-chill that takes two inputs, a
temperature (in degrees Fahrenheit) and a wind-speed (in miles per hour), and
returns the corresponding wind-chill factor. The formula for computing the
wind chill is:
| wind-chill =
|| if windSpeed <= 3
| 35.74 + 0.6215*temperature +
For example, (wind-chill 38 2) should evaluate to 38 since a
wind-speed of only 2 miles per hour has no effect on the temperature of
38 degrees Fahrenheit.
- Define a function named num-occur that takes two inputs, an atom
and a list, and returns a count of the number of times the atom appears in the
list. For example, (num-occur 'x '(z x e x)) should evaluate to 2.
- Define a function named subst that takes three inputs, two atoms
and a list, and returns the list with each occurrence of the second atom
replaced by the first. For example, (subst 'a 'x '(z x e x)) should
evaluate to (z a e a).
- Define a function named num-atoms that takes one input, a list
containing arbitrarily nested lists of atoms, and returns the number of atoms
in the list. For example, (num-atoms '(a b c)) should evaluate to 3, while
(num-atoms '(a (b (d e) c))) should evaluate to 5.
- Define functions for converting roman numerals to numbers and back. One
function, roman->num will have one input, a list of characters
representing a roman numeral. It should return the number value
represented by that roman numeral. For example, (roman->num '(X V I))
should evaluate to 16. Conversely, the function num->roman will have
an integer as input, and should return the list of characters
representing the appropriate roman numeral. The following is a list of
the roman letters and numbers they represent:
M = 1000, D = 500, C = 100, L = 50, X = 10, V = 5, I = 1.
You may assume the old roman style of writing letters, where 4 is
represented IIII and 90 is represented LXXXX. A harder problem, which
you may attempt if you like, is to use the modern roman style where
4 is IV and 90 is XC.
- The following function simulates a random 1-dimensional walk. Initially, the
walker is assumed to be at position 0. Depending on a random value, the walker
either moves to the right (in the positive direction) or to the left (in the
negative direction). The simulation ends when the walker reaches the specified goal
(define (random-walk goal-dist)
(define (random-walk-help position goal)
(display position) (newline)
((= (abs position) goal) #t)
((zero? (random 2)) (random-walk-help (add1 position) goal))
(else (random-walk-help (sub1 position) goal))))
(random-walk-help 0 goal-dist))
As is, this function displays each step in the walk and returns #t when
the walk ends. Modify the function so that it keeps track of the number of steps in the
walk and returns this value instead. Your modification should only utilize tail-recursion.
- An interesting unsolved problem in mathematics concerns what is
called the hailstone sequence of integers. This sequence is
defined as follows: start with any integer. If that number is odd, then
multiply it by 3 and add 1. If it is even, then divide it by 2. Now,
repeat. For example, if we start with the number 5, we get the following
sequence: 5, 16, 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, . . .
Here, the subsequence 4, 2, 1 is reached which produces a loop. It is
conjectured that no matter what number you start with, you will always
end up stuck in the 4, 2, 1 loop. It has, in fact, been shown to hold
for all starting values less than 1,200,000,000,000 . However, it still has not
been proven for all numbers. Define a function named hailstone
which has one input, the starting number, and which displays the hailstone sequence
starting with that number and ending with 1. The function should return the
length of the sequence. For example,
(hailstone 1) should display the lone number 1 and evaluate to 1, while
(hailstone 5) should display 5 16 8 4 2 1 and evaluate to 6.
Your function should only utilize tail-recursion
(perhaps a help function will be required).