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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 worstcase,
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 topdown
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.
Pixbased operations are more fully described in the section
on Pixes. See section Pseudoindexes
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.
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