/*  $Id$

    Part of SWI-Prolog

    Author:        Jan Wielemaker
    E-mail:        J.Wielemaker@cs.vu.nl
    WWW:           http://www.swi-prolog.org
    Copyright (C): 1985-2011, University of Amsterdam
			      VU University Amsterdam

    This program is free software; you can redistribute it and/or
    modify it under the terms of the GNU General Public License
    as published by the Free Software Foundation; either version 2
    of the License, or (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU Lesser General Public
    License along with this library; if not, write to the Free Software
    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

    As a special exception, if you link this library with other files,
    compiled with a Free Software compiler, to produce an executable, this
    library does not by itself cause the resulting executable to be covered
    by the GNU General Public License. This exception does not however
    invalidate any other reasons why the executable file might be covered by
    the GNU General Public License.
*/

:- module(ordsets,
	  [ is_ordset/1,		% @Term
	    list_to_ord_set/2,		% +List, -OrdSet
	    ord_add_element/3,		% +Set, +Element, -NewSet
	    ord_del_element/3,		% +Set, +Element, -NewSet
	    ord_intersect/2,		% +Set1, +Set2 (test non-empty)
	    ord_intersect/3,		% +Set1, +Set2, -Intersection
	    ord_intersection/3,		% +Set1, +Set2, -Intersection
	    ord_intersection/4,		% +Set1, +Set2, -Intersection, -Diff
	    ord_disjoint/2,		% +Set1, +Set2
	    ord_subtract/3,		% +Set, +Delete, -Remaining
	    ord_union/2,		% +SetOfOrdSets, -Set
	    ord_union/3,		% +Set1, +Set2, -Union
	    ord_union/4,		% +Set1, +Set2, -Union, -New
	    ord_subset/2,		% +Sub, +Super (test Sub is in Super)
					% Non-Quintus extensions
	    ord_empty/1,		% ?Set
	    ord_memberchk/2,		% +Element, +Set,
	    ord_symdiff/3,              % +Set1, +Set2, ?Diff
					% SICSTus extensions
	    ord_member/2,		% ?Element, +Set
	    ord_seteq/2,		% +Set1, +Set2
	    ord_intersection/2		% +PowerSet, -Intersection
	  ]).
:- use_module(library(oset)).
:- set_prolog_flag(generate_debug_info, false).

/** <module> Ordered set manipulation

Ordered sets are lists with unique elements sorted to the standard order
of terms (see sort/2). Exploiting ordering,   many of the set operations
can be expressed in order N rather  than N^2 when dealing with unordered
sets that may contain duplicates. The library(ordsets) is available in a
number of Prolog implementations. Our  predicates   are  designed  to be
compatible  with  common  practice   in    the   Prolog  community.  The
implementation is incomplete and  relies   partly  on  library(oset), an
older ordered set library distributed  with SWI-Prolog. New applications
are advices to use library(ordsets).

Some  of  these  predicates  match    directly   to  corresponding  list
operations. It is adviced to use the  versions from this library to make
clear you are operating on ordered sets.
*/

%%	is_ordset(@Term) is semidet.
%
%	True if Term is an ordered set.   All predicates in this library
%	expect ordered sets as input arguments.  Failing to fullfil this
%	assumption results in undefined   behaviour.  Typically, ordered
%	sets are created by predicates  from   this  library,  sort/2 or
%	setof/3.

is_ordset(Term) :-
	is_list(Term),
	is_ordset2(Term).

is_ordset2([]).
is_ordset2([H|T]) :-
	is_ordset3(T, H).

is_ordset3([], _).
is_ordset3([H2|T], H) :-
	H2 @> H,
	is_ordset3(T, H2).


%%	ord_empty(?List) is semidet.
%
%	True when List is the  empty   ordered  set. Simply unifies list
%	with the empty list. Not part of Quintus.

ord_empty([]).


%%	ord_seteq(+Set1, +Set2) is semidet.
%
%	True if Set1 and Set2  have  the   same  elements.  As  both are
%	canonical sorted lists, this is the same as ==/2.
%
%	@compat sicstus

ord_seteq(Set1, Set2) :-
	Set1 == Set2.


%%	list_to_ord_set(+List, -OrdSet) is det.
%
%	Transform a list into an ordered set.  This is the same as
%	sorting the list.

list_to_ord_set(List, Set) :-
	sort(List, Set).


%%	ord_intersect(+Set1, +Set2) is semidet.
%
%	True if both ordered sets have a non-empty intersection.

ord_intersect([H1|T1], L2) :-
	ord_intersect_(L2, H1, T1).

ord_intersect_([H2|T2], H1, T1) :-
	compare(Order, H1, H2),
	ord_intersect__(Order, H1, T1, H2, T2).

ord_intersect__(<, _H1, T1,  H2, T2) :-
	ord_intersect_(T1, H2, T2).
ord_intersect__(=, _H1, _T1, _H2, _T2).
ord_intersect__(>, H1, T1,  _H2, T2) :-
	ord_intersect_(T2, H1, T1).


%%	ord_disjoint(+Set1, +Set2) is semidet.
%
%	True if Set1 and Set2  have  no   common  elements.  This is the
%	negation of ord_intersect/2.

ord_disjoint(Set1, Set2) :-
	\+ ord_intersect(Set1, Set2).


%%	ord_intersect(+Set1, +Set2, -Intersection)
%
%	Intersection  holds  the  common  elements  of  Set1  and  Set2.
%
%	@deprecated Use ord_intersection/3

ord_intersect(Set1, Set2, Intersection) :-
	oset_int(Set1, Set2, Intersection).


%%	ord_intersection(+PowerSet, -Intersection)
%
%	True if Intersection is an  ordered   set  holding  all elements
%	common to all sets in PowerSet.
%
%	@compat sicstus

ord_intersection(PowerSet, Intersection) :-
	key_by_length(PowerSet, Pairs),
	keysort(Pairs, [_-S|Sorted]),
	l_int(Sorted, S, Intersection).

key_by_length([], []).
key_by_length([H|T0], [L-H|T]) :-
	length(H, L),
	key_by_length(T0, T).

l_int([], S, S).
l_int([_-H|T], S0, S) :-
	ord_intersection(S0, H, S1),
	l_int(T, S1, S).


%%	ord_intersection(+Set1, +Set2, -Intersection) is det.
%
%	Intersection holds the common elements of Set1 and Set2.

ord_intersection(Set1, Set2, Intersection) :-
	oset_int(Set1, Set2, Intersection).


%%	ord_intersection(+Set1, +Set2, ?Intersection, ?Difference) is det.
%
%	Intersection  and  difference   between    two   ordered   sets.
%	Intersection is the intersection between   Set1  and Set2, while
%	Difference is defined by ord_subtract(Set2, Set1, Difference).
%
%	@see ord_intersection/3 and ord_subtract/3.

ord_intersection([], L, [], L) :- !.
ord_intersection([_|_], [], [], []) :- !.
ord_intersection([H1|T1], [H2|T2], Intersection, Difference) :-
	compare(Diff, H1, H2),
	ord_intersection2(Diff, H1, T1, H2, T2, Intersection, Difference).

ord_intersection2(=, H1, T1, _H2, T2, [H1|T], Difference) :-
	ord_intersection(T1, T2, T, Difference).
ord_intersection2(<, _, T1, H2, T2, Intersection, Difference) :-
	ord_intersection(T1, [H2|T2], Intersection, Difference).
ord_intersection2(>, H1, T1, H2, T2, Intersection, [H2|HDiff]) :-
	ord_intersection([H1|T1], T2, Intersection, HDiff).


%%	ord_add_element(+Set1, +Element, ?Set2) is det.
%
%	Insert  an  element  into  the  set.    This   is  the  same  as
%	ord_union(Set1, [Element], Set2).

ord_add_element(Set1, Element, Set2) :-
	oset_addel(Set1, Element, Set2).


%%	ord_del_element(+Set, +Element, -NewSet) is det.
%
%	Delete an element from an  ordered  set.   This  is  the same as
%	ord_subtract(Set, [Element], NewSet).

ord_del_element(Set, Element, NewSet) :-
	oset_delel(Set, Element, NewSet).


%%	ord_memberchk(+Element, +Set) is semidet.
%
%	Check membership. This could stop comparing   we have passed the
%	right value, saving scanning  (on  average)   half  the  list if
%	Element is not in Set. Probably the built-in memberchk/2 will be
%	faster.
%
%	@compat Not part of original Quintus library

ord_memberchk(Element, Set) :-
	memberchk(Element, Set).

%%	ord_member(?Element, +Set) is nondet.
%
%	True if Element is a member of   Set.  Stops if further elements
%	are behind Element in the standard order of terms.
%
%	@compat sicstus

ord_member(Element, [H|T]) :-
	(   Element = H
	->  true
	;   Element @>= H,
	    ord_member(Element, T)
	).


%%	ord_subset(+Sub, +Super) is semidet.
%
%	Is true if all element of Sub are in Super

ord_subset([], _).
ord_subset([H1|T1], [H2|T2]) :-
	compare(Order, H1, H2),
	ord_subset_(Order, H1, T1, T2).

ord_subset_(>, H1, T1, [H2|T2]) :-
	compare(Order, H1, H2),
	ord_subset_(Order, H1, T1, T2).
ord_subset_(=, _, T1, T2) :-
	ord_subset(T1, T2).


%%	ord_subtract(+InOSet, +NotInOSet, -Diff) is det.
%
%	Diff is the set holding all elements of InOSet that are not in
%	NotInOSet.

ord_subtract(InOSet, NotInOSet, Diff) :-
	oset_diff(InOSet, NotInOSet, Diff).


%%	ord_union(+SetOfSets, -Union) is det.
%
%	True if Union is the  union  of   all  elements  in the superset
%	SetOfSets. Each member of SetOfSets must  be an ordered set, the
%	sets need not be ordered in any way.
%
%	@author Copied from YAP, probably originally by Richard O'Keefe.

ord_union([], []).
ord_union([Set|Sets], Union) :-
	length([Set|Sets], NumberOfSets),
	ord_union_all(NumberOfSets, [Set|Sets], Union, []).

ord_union_all(N, Sets0, Union, Sets) :-
	(   N =:= 1
	->  Sets0 = [Union|Sets]
	;   N =:= 2
	->  Sets0 = [Set1,Set2|Sets],
	    ord_union(Set1,Set2,Union)
	;   A is N>>1,
	    Z is N-A,
	    ord_union_all(A, Sets0, X, Sets1),
	    ord_union_all(Z, Sets1, Y, Sets),
	    ord_union(X, Y, Union)
	).


%%	ord_union(+Set1, +Set2, ?Union) is det.
%
%	Union is the union of Set1 and Set2

ord_union(Set1, Set2, Union) :-
	oset_union(Set1, Set2, Union).


%%	ord_union(+Set1, +Set2, -Union,	-New) is det.
%
%	True if Union iff ord_union(Set1, Set2, Union) and
%	ord_subtract(Set2, Set1, New).

ord_union([], Set2, Set2, Set2).
ord_union([H|T], Set2, Union, New) :-
	ord_union_1(Set2, H, T, Union, New).

ord_union_1([], H, T, [H|T], []).
ord_union_1([H2|T2], H, T, Union, New) :-
	compare(Order, H, H2),
	ord_union(Order, H, T, H2, T2, Union, New).

ord_union(<, H, T, H2, T2, [H|Union], New) :-
	ord_union_2(T, H2, T2, Union, New).
ord_union(>, H, T, H2, T2, [H2|Union], [H2|New]) :-
	ord_union_1(T2, H, T, Union, New).
ord_union(=, H, T, _, T2, [H|Union], New) :-
	ord_union(T, T2, Union, New).

ord_union_2([], H2, T2, [H2|T2], [H2|T2]).
ord_union_2([H|T], H2, T2, Union, New) :-
	compare(Order, H, H2),
	ord_union(Order, H, T, H2, T2, Union, New).


%%      ord_symdiff(+Set1, +Set2, ?Difference) is det.
%
%	Is true when Difference is the  symmetric difference of Set1 and
%	Set2. I.e., Difference contains all elements that are not in the
%	intersection of Set1 and Set2. The semantics  is the same as the
%	sequence below (but the actual   implementation  requires only a
%	single scan).
%
%	  ==
%		ord_union(Set1, Set2, Union),
%		ord_intersection(Set1, Set2, Intersection),
%		ord_subtract(Union, Intersection, Difference).
%	  ==
%
%	For example:
%
%	  ==
%	  ?- ord_symdiff([1,2], [2,3], X).
%	  X = [1,3].
%	  ==

ord_symdiff([], Set2, Set2).
ord_symdiff([H1|T1], Set2, Difference) :-
	ord_symdiff(Set2, H1, T1, Difference).

ord_symdiff([], H1, T1, [H1|T1]).
ord_symdiff([H2|T2], H1, T1, Difference) :-
	compare(Order, H1, H2),
	ord_symdiff(Order, H1, T1, H2, T2, Difference).

ord_symdiff(<, H1, Set1, H2, T2, [H1|Difference]) :-
	ord_symdiff(Set1, H2, T2, Difference).
ord_symdiff(=, _, T1, _, T2, Difference) :-
	ord_symdiff(T1, T2, Difference).
ord_symdiff(>, H1, T1, H2, Set2, [H2|Difference]) :-
	ord_symdiff(Set2, H1, T1, Difference).

