CSCI 201 -- Introduction to Algorithm Design -- handout 7 (p. 1)

	Problem 5
	Due November 12

[35 points]

In order to speed up the processing of mail, the United States Post
Office has requested that we try to use nine digit ZIP codes.  These
nine digit ZIP codes are written as a five digit and a four digit
number separated by a hyphen, as in 28804-3299.  These nine digit
ZIP codes are then transformed into a machine readable optical bar
code.  You may have noticed these bar codes on the lower right
corner of mail you have received.  They consist of a series
of long and short bars.  For example, the optical bar code for
28804-3299 is
	|..|.||..|.|..|.||....|..|..|.|..|.||.|..|.|...|.|.|

Note that there are 52 vertical bars in the above code.
The beginning and ending vertical bars are always long.
The middle 50 bars are used to encode 10 digits.
(I'll explain why 10 rather than 9 in a minute).
Five vertical bars are used for each digit.  The code
used for each digit is given in the following chart:

          1 = ...||          6 = .||..
          2 = ..|.|          7 = |...|
          3 = ..||.          8 = |..|.
          4 = .|..|          9 = |.|..
          5 = .|.|.          0 = ||...

[You might ponder this for a pattern.]  This particular
encoding is called a two-of-five code by computer
scientists because each digit is encoded with five
bars, two of which are long.  Thus the optical bar code
for 28804-3299 can be decrypted as:

| ..|.| |..|. |..|. ||... .|..| ..|.| ..|.| |.|.. |.|.. .|.|. |
    2     8     8     0     4      3    2     9     9     5

Now, we can explain the 10th digit, in this case a 5.  The tenth digit
is a "check digit".  It is chosen so that if you add up all ten
digits, the resulting number is divisible by ten.  For example,
2+8+8+0+4+3+2+9+9+5 equals 50, which is divisible by ten.  The
machines that sort mail always add up the ten digits of the optical
code to make sure the sum is divisible by ten.  If it isn't, the
machines assume that ZIP code was either improperly encoded or
improperly read.

Finally, let's get to your assignment.  You are to write a program
which prompts its users for a nine digit ZIP code and then prints out
the appropriate optical code.  The nine digit ZIP code will be entered
in the USPO-approved notation (i.e., 28804-3299).  You may read these
two ZIP codes as two integers (i.e., 28804 and -3299)

You are expected to use procedures and functions in this
assignment!  You grade will depend not only on its correctness
but on the structure of your solution into useful and
appropriate procedures and functions.


CSCI 201 -- Introduction to Algorithm Design -- handout 7 (p. 2)


You may find the following function useful in writing
your solution.


FUNCTION CheckDigit(I: INTEGER): INTEGER;

  (***********************************************************)
  (  CheckDigit computes the tenth "check" digit in the       )
  (  optical encoding of ZIP codes used by the USPO.          )
  (                                                           )
  (  Input:  A single integer, I, from 0 to 99999999999.      )
  (      I is the nine-digit ZIP code represented as          )
  (      a single integer.  For example, 28804-3299 should    )
  (      be input as the number 288043299.                    )
  (                                                           )
  (  Output:  The check digit, an integer between 0 and 9.    )
  (***********************************************************)

BEGIN
  VAR
    Irem: INTEGER ;
    Isum: INTEGER ;

    Irem := I;
    Isum := 0;

    (* Loop invariant.
     * Isum + sum-of-digits(Irem) = sum-of-digits(I)
     * sum-of-digits(X) is result of adding all the digits of X.
     *)
    WHILE (Irem > 0) DO
      BEGIN
        Isum := Isum + Irem MOD 10 ;
        Irem := Irem DIV 10
      END;

     CheckDigit := 10 - Isum div 10
  END ;



Warning:  I never tested this function.  But it looks OK.