Homework Assignment 1

CS 2360
Winter 1997
Homework Assignment 1
Due no later than 8:00am, Tuesday, January 21, 1997

Welcome all you budding young LISP hackers.  It's time to get your feet
wet, so here's your first programming assignment.  It's worth a total of 
140 points.  Make sure that you adhere to the constraints of the functional
programming paradigm (e.g., access only information passed as 
parameters, return one value, no side effects, etc.).  Furthermore, 
remember that you're programming for people, not for the benefit of the
computer.  Write your code so that other people can understand it easily.
You may use only the following predefined LISP functions in constructing 
your own functions:  DEFUN, FIRST, REST, CONS, LIST, *, +, /, and -.  
And since we briefly mentioned APPEND in class, you can use that one 
too.  In fact, it will be really handy in at least one of the problems
below.  Here are the problems:

1)  In baseball, a batter's slugging percentage is calculated by
    dividing the number of total bases of all safe hits by the total
    times at bat.  The number of total bases is calculated by awarding
    one base for a single, two bases for a double, three bases for a
    triple, and four bases for a home run.

    Construct a function called SLUGGING which takes five arguments as
    input.  The first argument is a number representing the batter's
    times at bat.  The second argument is a number representing the
    total number of hits.  The third argument is a number representing
    the number of doubles hit by the batter.  The fourth argument is a
    number representing the number of triples hit by the batter.  The
    fifth argument is a number representing the number of home runs hit
    by the batter.  This function returns a number which is the
    batter's slugging percentage.

    Example:

    ? (slugging 585 158 15 4 40)
    0.5145299145299145


2)  When converting between temperatures in degrees Fahrenheit and
    degrees Celsius, it is useful to note that -40 degrees Fahrenheit
    equal -40 degrees Celsius.  This observation makes for the following
    symmetric conversion formulas:

      C = (F + 40) * 5/9 - 40

      F = (C + 40) * 9/5 - 40

    Construct conversion functions, F-TO-C and C-TO-F, using these
    formulas.  Each function takes exactly one argument.  The F-TO-C
    function takes a number representing a temperature in Fahrenheit and
    returns a number representing the same temperature in Celsius.  The
    C-TO-F function takes a number representing a temperature in
    Celsius and returns a number representing the same temperature in
    Fahrenheit.

    Examples:

    ? (f-to-c 32)
    0
    ? (f-to-c 98.6)
    37.0
    ? (c-to-f 100)
    212


3)  Construct a function called MY-FOURTH which returns the fourth
    element of a list.

    Examples:

    ? (my-fourth '(a b c d))
    D
    ? (my-fourth '(a b c d e))
    D
    ? (my-fourth '(a b c))
    NIL

    We'll explain the NIL thing on Thursday.


4)  Construct a function called SWAP which exchanges the first
    and fourth elements of any list containing four or more elements.
    Feel free to use the MY-FOURTH function you created above.
    (You can assume the list will have the correct length when
    passed; you don't have to do error checking.)

    Examples:

    ?(swap '(a b c d))
    (D B C A)
    ? (swap '(a b c d e))
    (D B C A E)


5)  Construct a function called ROTATE-LEFT which, when passed
    a list of arbitrary length, returns the original list
    with the first element moved to the end of the list, (thus
    effectively moving all other elements to the left by one position).

    Examples:

    ? (rotate-left '(a b c d))
    (B C D A)
    ? (rotate-left '(a b c d e))
    (B C D E A)
    ? (rotate-left '(a))
    (A)


6)  Construct a function called ADDPAIRS which takes two lists of
    three numbers as its arguments, and returns a single list containing
    the sum of the corresponding numbers from each list.

    Example:

    ? (addpairs '(2 4 6) '(4 5 6))
    (6 9 12)


7)  Finish the QUADRATIC function we started in class.  Add the
    SQRT-OF-DISCRIMINANT function that we didn't construct.  And so as
    not to cause any problems, change the name of DENOMINATOR to
    MY-DENOMINATOR, since the DENOMINATOR function already exists
    in LISP.  Prove to yourself, and to us, that the solution works 
    by getting it to run on some Common LISP system.  Show us the results.

    Examples:

    ? (quadratic 2 0 2)
    (#c(0.0 1.0) #c(0.0 -1.0))

    ? (quadratic 2 2 0)
    (0.0 -1.0)



Copyright 1997 by Kurt Eiselt.  All rights reserved.