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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
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<H1>gb_sets</H1>
</CENTER>
<H3>MODULE</H3>
<DIV CLASS=REFBODY>
gb_sets
</DIV>
<H3>MODULE SUMMARY</H3>
<DIV CLASS=REFBODY>
General Balanced Trees
</DIV>
<H3>DESCRIPTION</H3>
<DIV CLASS=REFBODY>
<P> An implementation of ordered sets using Prof. Arne Andersson's
General Balanced Trees. This can be much more efficient than
using ordered lists, for larger sets, but depends on the
application. See notes below for details.
</DIV>
<H3>Complexity note</H3>
<DIV CLASS=REFBODY>
<P> The complexity on set operations is bounded by either O(|S|) or
O(|T| * log(|S|)), where S is the largest given set, depending
on which is fastest for any particular function call. For
operating on sets of almost equal size, this implementation is
about 3 times slower than using ordered-list sets directly. For
sets of very different sizes, however, this solution can be
arbitrarily much faster; in practical cases, often between 10
and 100 times. This implementation is particularly suited for
accumulating elements a few at a time, building up a large set
(more than 100-200 elements), and repeatedly testing for
membership in the current set.
<P> As with normal tree structures, lookup (membership testing),
insertion and deletion have logarithmic complexity.
</DIV>
<H3>EXPORTS</H3>
<P><A NAME="empty/0"><STRONG><CODE>empty()</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Returns new, empty set.
<P> Alias: new(), for compatibility with `sets'.
</DIV>
<P><A NAME="is_empty/1"><STRONG><CODE>is_empty(S)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Returns 'true' if S is an empty set, and 'false' otherwise.
</DIV>
<P><A NAME="size/1"><STRONG><CODE>size(S)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Returns the number of nodes in the set as an
integer. Returns 0 (zero) if the set is empty.
</DIV>
<P><A NAME="singleton/1"><STRONG><CODE>singleton(X)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Returns a set containing only the element X.
</DIV>
<P><A NAME="is_member/2"><STRONG><CODE>is_member(X, S)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Returns `true' if element X is a member of set S, and
`false' otherwise.
<P> Alias: is_element(), for compatibility with `sets'.
</DIV>
<P><A NAME="insert/2"><STRONG><CODE>insert(X, S)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Inserts element X into set S, returns the new set. Assumes
that the element is not present in S.
</DIV>
<P><A NAME="add/2"><STRONG><CODE>add(X, S)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Adds element X to set S, returns the new set. If X is
already an element in S, nothing is changed.
<P> Alias: add_element(), for compatibility with `sets'.
</DIV>
<P><A NAME="delete/2"><STRONG><CODE>delete(X, S)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Removes element X from set S, returns new set. Assumes that
the element exists in the set.
<P> Alias: del_element(), for compatibility with `sets'.
</DIV>
<P><A NAME="delete_any/2"><STRONG><CODE>delete_any(X, T)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Removes key X from set S if the key is present in the set,
otherwise does nothing; returns new set.
</DIV>
<P><A NAME="balance/1"><STRONG><CODE>balance(S)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Rebalances the tree representation of S. Note that this is
rarely necessary, but may be motivated when a large number
of elements have been deleted from the tree without further
insertions. Rebalancing could then be forced in order to
minimise lookup times, since deletion only does not
rebalance the tree.
</DIV>
<P><A NAME="union/2"><STRONG><CODE>union(S1, S2)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Returns a new set that contains each element that is in
either S1 or S2 or both, and no other elements.
</DIV>
<P><A NAME="union/1"><STRONG><CODE>union(Ss)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Returns a new set that contains each element that is in at
least one of the sets in the list Ss, and no other elements.
</DIV>
<P><A NAME="intersection/2"><STRONG><CODE>intersection(S1, S2)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Returns a new set that contains each element that is in both
S1 and S2, and no other elements.
</DIV>
<P><A NAME="intersection/1"><STRONG><CODE>intersection(Ss)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Returns a new set that contains each element that is in all
of the sets in the list Ss, and no other elements.
</DIV>
<P><A NAME="difference/2"><STRONG><CODE>difference(S1, S2)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Returns a new set that contains each element in S1 that is
not also in S2, and no other elements.
<P> Alias: subtract(), for compatibility with `sets'.
</DIV>
<P><A NAME="is_subset/2"><STRONG><CODE>is_subset(S1, S2)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Returns `true' if each element in S1 is also a member of S2,
and `false' otherwise.
</DIV>
<P><A NAME="to_list/1"><STRONG><CODE>to_list(S)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Returns an ordered list of all elements in set S. The list
never contains duplicates (of course).
</DIV>
<P><A NAME="from_list/1"><STRONG><CODE>from_list(List)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Creates a set containing all elements in List, where List
may be unordered and contain duplicates.
</DIV>
<P><A NAME="from_ordset/1"><STRONG><CODE>from_ordset(L)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Turns an ordered-set list L into a set. The list must not
contain duplicates.
</DIV>
<P><A NAME="smallest/1"><STRONG><CODE>smallest(S)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Returns the smallest element in set S. Assumes that
the set S is nonempty.
</DIV>
<P><A NAME="largest/1"><STRONG><CODE>largest(S)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Returns the largest element in set S. Assumes that
the set S is nonempty.
</DIV>
<P><A NAME="take_smallest/1"><STRONG><CODE>take_smallest(S)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Returns {X, S1}, where X is the smallest element in set S,
and S1 is the set S with element X deleted. Assumes that the
set S is nonempty.
</DIV>
<P><A NAME="take_largest/1"><STRONG><CODE>take_largest(S)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Returns {X, S1}, where X is the largest element in
set S, and S1 is the set S with element X deleted. Assumes that the
set S is nonempty.
</DIV>
<P><A NAME="iterator/1"><STRONG><CODE>iterator(S)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Returns an iterator that can be used for traversing the
entries of set S; see `next'. The implementation of this is
very efficient; traversing the whole set using `next' is
only slightly slower than getting the list of all elements
using `to_list' and traversing that. The main advantage of
the iterator approach is that it does not require the
complete list of all elements to be built in memory at one
time.
</DIV>
<P><A NAME="next/1"><STRONG><CODE>next(T)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Returns {X, T1} where X is the smallest element referred to
by the iterator T, and T1 is the new iterator to be used for
traversing the remaining elements, or the atom `none' if no
elements remain.
</DIV>
<P><A NAME="filter/2"><STRONG><CODE>filter(P, S)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Filters set S using predicate function P. Included for
compatibility with `sets'.
</DIV>
<P><A NAME="fold/3"><STRONG><CODE>fold(F, A, S)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Folds function F over set S with A as the initial
accumulator. Included for compatibility with `sets'.
</DIV>
<P><A NAME="is_set/1"><STRONG><CODE>is_set(S)</CODE></STRONG></A><BR>
<DIV CLASS=REFBODY>
<P> Returns 'true' if S appears to be a set, and 'false'
otherwise. Not recommended; included for compatibility with
`sets'.
</DIV>
<H3>SEE ALSO</H3>
<DIV CLASS=REFBODY>
<P> <A HREF="gb_trees.html">gb_trees(3)</A>,
<A HREF="ordsets.html">ordsets(3)</A>,
<A HREF="sets.html">sets(3)</A>
</DIV>
<H3>AUTHORS</H3>
<DIV CLASS=REFBODY>
Richard Carlsson - support@erlang.ericsson.se<BR>
</DIV>
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<SMALL>stdlib 1.13.2<BR>
Copyright © 1991-2004
<A HREF="http://www.erlang.se">Ericsson AB</A><BR>
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