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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% ECLiPSe library for solving "crossfigures" puzzles.
%
% "Crossfigures" puzzles correspond to problem 21 in the CSPLib.
% See www.csplib.org for more details.
%
% Particular instances can be found at thinks.com/crosswords/xfig.htm.
%
% This module written by Warwick Harvey, IC-Parc, wh@icparc.ic.ac.uk.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
:- module(crossfig).
 
:- export across/6, down/6, init_matrix/3, print_matrix/1.
:- export square/1, prime/1.
 
:- lib(fd).
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% The problem is modelled using an array `Matrix' to represent the puzzle
% "board".  A second array `Template' is used to indicate whether each
% element of `Matrix' should contain a digit or should be blank.  This
% information can also be used to perform some integrity checks, to help
% catch errors in the expression of a problem.
%
% The multidigit numbers used in the "clues" (1 across, 7 down, etc.) are
% set up using the predicates `across/6' and `down/6', which relate these
% numbers to the digits in `Matrix'.  Once these are all set up,
% `init_matrix/3' should be called to complete the initialisation of
% `Matrix', before the clue constraints are added.
%
% Also provided are a number of predicates which are useful for
% expressing clue constraints such as "A square number" and "A prime
% number".
%
% See one of the accompanying problem modules (cf*.pl) for an example of
% how it all works.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
%
% across(Matrix, Template, Across, Len, Row, Col):
%   Constrains `Across' to be equal to the number represented by the
%   `Len' digits starting at position (Row, Col) of the array `Matrix'
%   and proceeding across.
%   `Template' is used for integrity checking, as well as for collecting
%   information about which elements of `Matrix' should contain digits,
%   and which should be empty.
%
 
across(Matrix, Template, Across, Len, Row, Col) :-
    % Constrain `Across' to be equal to the corresponding digits.
    (
        for(I, Len-1, 0, -1),
        fromto(1, Mult, NewMult, _),
        fromto(0, SumIn, SumOut, Across),
        param(Matrix, Row, Col)
    do
        Elem is Matrix[Row, Col + I],
        Elem :: [0..9],
        SumOut #= SumIn + Mult * Elem,
        NewMult is Mult * 10
    ),
 
    % Integrity checks.
    dim(Template, [_Height, Width]),
    (
        Template[Row, Col .. Col + Len - 1] :: 1,
        ( Col > 1            -> Template[Row, Col - 1] :: 0   ; true ),
        ( Col + Len =< Width -> Template[Row, Col + Len] :: 0 ; true )
    ->
        true
    ;
        printf(error, "Crossfigure integrity violation adding "
            "an across figure of length %d,%n"
            "starting at (%d, %d)%n",
            [Len, Row, Col]),
        abort
    ).
 
 
%
% down(Matrix, Template, Down, Len, Row, Col):
%   Constrains `Down' to be equal to the number represented by the
%   `Len' digits starting at position (Row, Col) of the array `Matrix'
%   and proceeding down.
%   `Template' is used for integrity checking, as well as for collecting
%   information about which elements of `Matrix' should contain digits,
%   and which should be empty.
%
 
down(Matrix, Template, Down, Len, Row, Col) :-
    % Constrain `Down' to be equal to the corresponding digits.
    (
        for(I, Len-1, 0, -1),
        fromto(1, Mult, NewMult, _),
        fromto(0, SumIn, SumOut, Down),
        param(Matrix, Row, Col)
    do
        Elem is Matrix[Row + I, Col],
        Elem :: [0..9],
        SumOut #= SumIn + Mult * Elem,
        NewMult is Mult * 10
    ),
 
    % Integrity checks.
    dim(Template, [Height, _Width]),
    (
        Template[Row .. Row + Len - 1, Col] :: 1,
        ( Row > 1             -> Template[Row - 1, Col] :: 0   ; true ),
        ( Row + Len =< Height -> Template[Row + Len, Col] :: 0 ; true )
    ->
        true
    ;
        printf(error, "Crossfigure integrity violation adding "
            "a down figure of length %d,%n"
            "starting at (%d, %d)%n",
            [Len, Row, Col]),
        abort
    ).
 
 
%
% init_matrix(Matrix, Template, Vars):
%   Finishes the initialisation of `Matrix', returning a list of all
%   the variables in it in `Vars'.
%   `Template' is used to determine which elements of `Matrix' should be
%   variables, and which ones should be blank.  Blank elements are
%   filled with a ` '.
%
 
init_matrix(Matrix, Template, Vars) :-
    dim(Matrix, [Row, Col]),
    (
        for(I, 1, Row),
        fromto([], Vars1, Vars4, Vars),
        param(Matrix, Template, Col)
    do
        (
            for(J, 1, Col),
            fromto(Vars1, Vars2, Vars3, Vars4),
            param(Matrix, Template, I)
        do
            T is Template[I, J],
            Elem is Matrix[I, J],
            ( var(T) ->
                T = 0
            ;
                true
            ),
            ( T = 0 ->
                Elem = ' ',
                Vars3 = Vars2
            ;
                Vars3 = [Elem | Vars2]
            )
        )
    ).
 
 
%
% print_matrix(Matrix):
%   Prints `Matrix' in a readable format.
%
 
print_matrix(Matrix) :-
    nl,
    (
        foreacharg(Row, Matrix)
    do
        write(' '),
        (
            foreacharg(Elem, Row)
        do
            write(Elem)
        ),
        nl
    ).
 
 
%-------- Useful constraints for crossfigure puzzles --------%
 
%
% square(N):
%   Constrains N to be a square number.
%
 
square(N) :-
    N #= T * T.
 
 
%
% prime(N):
%   Delays until N is ground, and then succeeds if and only if it is
%   prime.
%
 
prime(N) :-
    ( nonvar(N) ->
        is_prime_2(2, N)
    ;
        suspend(prime(N), 2, N->inst)
    ).
 
is_prime_2(Q, N) :-
    N mod Q =\= 0,
    ( Q * Q < N ->
        Q1 is Q + 1,
        is_prime_2(Q1, N)
    ;
        true
    ).