yap-6.3/library/clp/clp_distinct.pl

/*  $Id$

    Part of SWI-Prolog

    Author:        Markus Triska
    E-mail:        triska@gmx.at
    WWW:           http://www.swi-prolog.org
    Copyright (C): 2005, Markus Triska

    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(clp_distinct,
	[
		vars_in/2,
		vars_in/3,
		all_distinct/1
	]).
:- use_module(library(lists)).

/** <module> Weak arc consistent all_distinct/1 constraint

@deprecated	Superseded by library(clpfd)'s all_distinct/1.
@author		Markus Triska
*/

% For details, see Neng-Fa Zhou, 2005:
%      "Programming Finite-Domain Constraint Propagators in Action Rules"

/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
This library uses the following arribute value:

	dom_neq(Domain, Left, Right)

Domain is an unbounded  (GMP)  integer   representing  the  domain  as a
bit-vector, meaning N is in the domain iff 0 =\= Domain /\ (1<<N).

Left and Right are both lists of lists of variables. Each of those lists
corresponds to one all_distinct constraint the  variable is involved in,
and "left" and "right" means literally which  variables are to the left,
and which to the right in the first, second etc. of those constraints.

all_distinct([A,B,C,D]), all_distinct([X,Y,C,F,E]) causes the following
attributes for "C":

	Left:  [[A,B],[X,Y]]
	Right: [[D],[F,E]]
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */


vars_in(Xs, From, To) :-
	Bitvec is (1<<(To+1)) - (1<<From),
	vars_in_(Xs, Bitvec).

vars_in(Xs, Dom) :-
	domain_bitvector(Dom, 0, Bitvec),
	vars_in_(Xs, Bitvec).

vars_in_([], _).
vars_in_([V|Vs], Bitvec) :-
	( var(V) ->
		( get_attr(V, clp_distinct, dom_neq(VBV,VLeft,VRight)) ->
			Bitvec1 is VBV /\ Bitvec,
		  	Bitvec1 =\= 0,
		        ( popcount(Bitvec1) =:= 1 ->
				V is msb(Bitvec1)
			;
				put_attr(V, clp_distinct, dom_neq(Bitvec1,VLeft,VRight))
			)
		;
			( popcount(Bitvec) =:= 1 ->
				V is msb(Bitvec)
			;
				put_attr(V, clp_distinct, dom_neq(Bitvec, [], []))
			)
		)
	;
		0 =\= Bitvec /\ (1<<V)
	),
	vars_in_(Vs, Bitvec).

domain_bitvector([], Bitvec, Bitvec).
domain_bitvector([D|Ds], Bitvec0, Bitvec) :-
	Bitvec1 is Bitvec0 \/ (1 << D),
	domain_bitvector(Ds, Bitvec1, Bitvec).


all_distinct(Ls) :-
	all_distinct(Ls, []),
	outof_reducer(Ls).

outof_reducer([]).
outof_reducer([X|Xs]) :-
	( var(X) ->
		get_attr(X, clp_distinct, dom_neq(Dom,Lefts,Rights)),
		outof_reducer(Lefts, Rights, X, Dom)
	;
		true
	),
	outof_reducer(Xs).

/** @pred all_distinct( _Cs_,  _Vs_)

verifies whether all elements of a list are different. Also tests if
all the sums between a list of constants and a list of variables are
different.

This is a formulation of the queens problem that uses both versions of `all_different`:

~~~~~{.prolog}
queens(N, Queens) :-
    length(Queens, N),
    Queens ins 1..N,
    all_distinct(Queens),
    foldl(inc, Queens, Inc, 0, _), % [0, 1, 2, .... ]
    foldl(dec, Queens, Dec, 0, _), % [0, -1, -2, ... ]
    all_distinct(Inc,Queens),
    all_distinct(Dec,Queens),
    labeling([], Queens).

inc(_, I0, I0, I) :-
    I is I0+1.

dec(_, I0, I0, I) :-
    I is I0-1.
~~~~~

The next example uses `all_different/1` and the functionality of the matrix package to verify that all squares in
sudoku have a different value:

~~~~~{.prolog}
    foreach( [I,J] ins 0..2 ,
           all_different(M[I*3+(0..2),J*3+(0..2)]) ),
~~~~~

 
*/
all_distinct([], _).
all_distinct([X|Right], Left) :-
	\+ list_contains(Right, X),
	outof(X, Left, Right),
	all_distinct(Right, [X|Left]).


outof(X, Left, Right) :-
	( var(X) ->
		get_attr(X, clp_distinct, dom_neq(Dom, XLefts, XRights)),
		put_attr(X, clp_distinct, dom_neq(Dom, [Left|XLefts], [Right|XRights]))
	;
		exclude_fire([Left], [Right], X)
	).


exclude_fire(Lefts, Rights, E) :-
	Mask is \ ( 1 << E),
	exclude_fire(Lefts, Rights, E, Mask).

exclude_fire([], [], _, _).
exclude_fire([Left|Ls], [Right|Rs], E, Mask) :-
	exclude_list(Left, E, Mask),
	exclude_list(Right, E, Mask),
	exclude_fire(Ls, Rs, E, Mask).


exclude_list([], _, _).
exclude_list([V|Vs], Val, Mask) :-
	( var(V) ->
		get_attr(V, clp_distinct, dom_neq(VDom0,VLefts,VRights)),
		VDom1 is VDom0 /\ Mask,
		VDom1 =\= 0,
		( popcount(VDom1) =:= 1 ->
			V is msb(VDom1)
		;
			put_attr(V, clp_distinct, dom_neq(VDom1,VLefts,VRights))
		)
	;
		V =\= Val
	),
	exclude_list(Vs, Val, Mask).

attr_unify_hook(dom_neq(Dom,Lefts,Rights), Y) :-
	( ground(Y) ->
		Dom /\ (1 << Y) =\= 0,
		exclude_fire(Lefts, Rights, Y)
	;

		\+ lists_contain(Lefts, Y),
		\+ lists_contain(Rights, Y),
		( get_attr(Y, clp_distinct, dom_neq(YDom0,YLefts0,YRights0)) ->
			YDom1 is YDom0 /\ Dom,
			YDom1 =\= 0,
			( popcount(YDom1) =:= 1 ->
				Y is msb(YDom1)
			;
				append(YLefts0, Lefts, YLefts1),
				append(YRights0, Rights, YRights1),
				put_attr(Y, clp_distinct, dom_neq(YDom1,YLefts1,YRights1))
			)
		;
			put_attr(Y, clp_distinct, dom_neq(Dom,Lefts,Rights))
		)
	).

lists_contain([X|Xs], Y) :-
	( list_contains(X, Y) ->
		true
	;
		lists_contain(Xs, Y)
	).

list_contains([X|Xs], Y) :-
	( X == Y ->
		true
	;
		list_contains(Xs, Y)
	).


outof_reducer([], [], _, _).
outof_reducer([L|Ls], [R|Rs], Var, Dom) :-
	append(L, R, Others),
	N is popcount(Dom),
	num_subsets(Others, Dom, 0, Num),
	( Num >= N ->
		fail
	; Num =:= (N - 1) ->
		reduce_from_others(Others, Dom)
	;
		true
	),
	outof_reducer(Ls, Rs, Var, Dom).


reduce_from_others([], _).
reduce_from_others([X|Xs], Dom) :-
	( var(X) ->
		get_attr(X, clp_distinct, dom_neq(XDom,XLeft,XRight)),
		( is_subset(Dom, XDom) ->
			true
		;
			NXDom is XDom /\ \Dom,
			NXDom =\= 0,
			( popcount(NXDom) =:= 1 ->
				X is msb(NXDom)
			;
				put_attr(X, clp_distinct, dom_neq(NXDom,XLeft,XRight))
			)
		)
	;
		true
	),
	reduce_from_others(Xs, Dom).

num_subsets([], _Dom, Num, Num).
num_subsets([S|Ss], Dom, Num0, Num) :-
	( var(S) ->
		get_attr(S, clp_distinct, dom_neq(SDom,_,_)),
		( is_subset(Dom, SDom) ->
			Num1 is Num0 + 1
		;
			Num1 = Num0
		)
	;
		Num1 = Num0
	),
	num_subsets(Ss, Dom, Num1, Num).


   % true iff S is a subset of Dom - should be a GMP binding (subsumption)

is_subset(Dom, S) :-
	S \/ Dom =:= Dom.

/** @pred attr_portray_hook(+ _AttValue_,+ _Var_) 



Called by write_term/2 and friends for each attribute if the option
`attributes(portray)` is in effect.  If the hook succeeds the
attribute is considered printed.  Otherwise  `Module = ...` is
printed to indicate the existence of a variable.

 
*/
attr_portray_hook(dom_neq(Dom,_,_), _) :-
	Max is msb(Dom),
	Min is lsb(Dom),
	write(Min-Max).