CS U370 Assignment #3.
Assigned: Friday, 8 October 2004    [corrected!]
Due: Friday, 15 October 2004        [corrected a second time!]

You will complete an implementation in Java of the IntSet ADT
that is specified below.

Collaboration between students is forbidden on this assignment.
You are responsible for keeping your code hidden from all other
students.  Part of your grade will be determined by how well
you hide your code, part of your grade will be determined by
how well you follow the instructions for submitting your code,
part of your grade will depend upon the correctness of your
code, and part of your grade will depend upon the readability
of your code (e.g. formatting and comments).

Turn in your work on this assignment before 4 pm on the due
date by sending electronic mail to

    will@ccs.neu.edu

with subject

    CSU370 assignment 3

and a body that consists of nothing but your IntSet.java
file.  That file should begin with a block comment that lists

    1.  Your name, as you want the instructor to write it.
    2.  Your email address.
    3.  Any remarks that you wish to make to the instructor.

Late assignments may be discounted, and very late assignments
may be discarded.

--------------------------------------------------

Your assignment is to write the code for a single file,
IntSet.java, that implements the specification below.  Note
that IntSet.java must be part of the default package.  A small
test program will be made available in

    /course/csu370wc/Assignments/A3

--------------------------------------------------

Specification of the IntSet ADT.

The IntSet ADT is an immutable abstract data type.  It shall
be implemented by a single file named IntSet.java.  This code
shall be in the default package, and shall define a public
class named IntSet that defines the following static methods,
which have no side effects, and are specified by the equations
below.  Note that the add method is private; the other methods
are public.

    public  static IntSet  emptySet ();
    public  static IntSet  singleton (int);
    public  static IntSet  adjoin (int, IntSet);
    public  static boolean isEmpty (IntSet);
    public  static int     least (IntSet);
    public  static IntSet  butLeast (IntSet);
    public  static int     size (IntSet);
    public  static IntSet  union (IntSet, IntSet);

    private static IntSet  add (int, IntSet);

Algebraic specification:

    singleton (m) = adjoin (m, emptySet())

    adjoin (m, emptySet()) = add (m, emptySet())
    adjoin (m, add (n, s)) = add (m, add (n, s))      if m < n
    adjoin (m, add (n, s)) = add (n, s)               if m = n
    adjoin (m, add (n, s)) = add (n, adjoin (m, s))   if m > n

    isEmpty (emptySet()) = true
    isEmpty (add (n, s)) = false

    least (add (n, s)) = n

    butLeast (add (n, s)) = s

    size (emptySet()) = 0
    size (add (n, s)) = 1 + size (s)

    union (emptySet(), s) = s
    union (add (n, s1), s2) = adjoin (n, union (s1, s2))

Note:  This specification does not define least and butLeast
on an empty set.

--------------------------------------------------