Set class prototypes
********************

   Set classes maintain unbounded collections of items containing no
duplicate elements.

   These are currently implemented in several ways, differing in
representation strategy, algorithmic efficiency, and appropriateness for
various tasks. (Listed next to each are average (followed by worst-case,
if different) time complexities for [a] adding, [f] finding (via seek,
contains), [d] deleting, elements, and [c] comparing (via ==, <=) and
[m] merging (via |=, -=, &=) sets).

`XPSets'
     implement unordered sets via XPlexes.  ([a O(n)], [f O(n)], [d
     O(n)], [c O(n^2)] [m O(n^2)]).

`OXPSets'
     implement ordered sets via XPlexes.  ([a O(n)], [f O(log n)], [d
     O(n)], [c O(n)] [m O(n)]).

`SLSets'
     implement unordered sets via linked lists ([a O(n)], [f O(n)], [d
     O(n)], [c O(n^2)] [m O(n^2)]).

`OSLSets'
     implement ordered sets via linked lists ([a O(n)], [f O(n)], [d
     O(n)], [c O(n)] [m O(n)]).

`AVLSets'
     implement ordered sets via threaded AVL trees ([a O(log n)], [f
     O(log n)], [d O(log n)], [c O(n)] [m O(n)]).

`BSTSets'
     implement ordered sets via binary search trees. The trees may be
     manually rebalanced via the O(n) `balance()' member function.  ([a
     O(log n)/O(n)], [f O(log n)/O(n)], [d O(log n)/O(n)], [c O(n)] [m
     O(n)]).

`SplaySets'
     implement ordered sets via Sleator and Tarjan's (JACM 1985) splay
     trees. The algorithms use a version of "simple top-down splaying"
     (described on page 669 of the article).  (Amortized: [a O(log n)],
     [f O(log n)], [d O(log n)], [c O(n)] [m O(n log n)]).

`VHSets'
     implement unordered sets via hash tables.  The tables are
     automatically resized when their capacity is exhausted.  ([a
     O(1)/O(n)], [f O(1)/O(n)], [d O(1)/O(n)], [c O(n)/O(n^2)] [m
     O(n)/O(n^2)]).

`VOHSets'
     implement unordered sets via ordered hash tables The tables are
     automatically resized when their capacity is exhausted.  ([a
     O(1)/O(n)], [f O(1)/O(n)], [d O(1)/O(n)], [c O(n)/O(n^2)] [m
     O(n)/O(n^2)]).

`CHSets'
     implement unordered sets via chained hash tables.  ([a O(1)/O(n)],
     [f O(1)/O(n)], [d O(1)/O(n)], [c O(n)/O(n^2)] [m O(n)/O(n^2)]).

   The different implementations differ in whether their constructors
require an argument specifying their initial capacity. Initial
capacities are required for plex and hash table based Sets.  If none is
given `DEFAULT_INITIAL_CAPACITY' (from `<T>defs.h') is used.

   Sets support the following operations, for some class `Set',
instances `a' and `b', `Pix ind', and base element `x'. Since all
implementations are virtual derived classes of the `<T>Set' class, it
is possible to mix and match operations across different
implementations, although, as usual, operations are generally faster
when the particular classes are specified in functions operating on
Sets.

   Pix-based operations are more fully described in the section on
Pixes. See Pix

`Set a; or Set a(int initial_size);'
     Declares a to be an empty Set. The second version is allowed in
     set classes that require initial capacity or sizing specifications.

`a.empty()'
     returns true if a is empty.

`a.length()'
     returns the number of elements in a.

`Pix ind = a.add(x)'
     inserts x into a, returning its index.

`a.del(x)'
     deletes x from a.

`a.clear()'
     deletes all elements from a;

`a.contains(x)'
     returns true if x is in a.

`a(ind)'
     returns a reference to the item indexed by ind.

`ind = a.first()'
     returns the Pix of first item in the set or 0 if the Set is empty.
     For ordered Sets, this is the Pix of the least element.

`a.next(ind)'
     advances ind to the Pix of next element, or 0 if there are no more.

`ind = a.seek(x)'
     Sets ind to the Pix of x, or 0 if x is not in a.

`a == b'
     returns true if a and b contain all the same elements.

`a != b'
     returns true if a and b do not contain all the same elements.

`a <= b'
     returns true if a is a subset of b.

`a |= b'
     Adds all elements of b to a.

`a -= b'
     Deletes all elements of b from a.

`a &= b'
     Deletes all elements of a not occurring in b.