/*-------------------------------------------------------------------------*/
/* Benchmark (Finite Domain)                                               */
/*                                                                         */
/* Name           : multipl.pl                                             */
/* Title          : unknown multiplication                                 */
/* Original Source: Daniel Diaz - INRIA France                             */
/* Adapted by     : Daniel Diaz for GNU Prolog                             */
/* Date           : June 1995                                              */
/*                                                                         */
/* Find the value of each digit verifying the following multiplication and */
/* such that each digit (0,1,...,9) appears excatly twice:                 */
/*                                                                         */
/*                   X1  X2  X3                                            */
/*                 * X4  X5  X6                                            */
/*                  -----------                                            */
/*                   X7  X8  X9                                            */
/*        +      X10 X11 X12                                               */
/*        + X13 X14 X15                                                    */
/*        = -------------------                                            */
/*          X16 X17 X18 X19 X20                                            */
/*                                                                         */
/* Solution:                                                               */
/* [X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,X17,X18,X19,X20]*/
/* [ 1, 7, 9, 2, 2, 4, 7, 1, 6,  3,  5,  8,  3,  5,  8,  4,  0,  0,  9,  6]*/
/*-------------------------------------------------------------------------*/

go:-     
    statistics(runtime,_),
    mult(Lab,LD), statistics(runtime,[_,Y]), 
    write(LD), nl,
    write('time : '), write(Y), nl.


mult(Lab,LD):-
    LD=[X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,
	X11,X12,X13,X14,X15,X16,X17,X18,X19,X20],

    domain(LD,0,9),
    
    fd_atmost(2,LD,0),
    fd_atmost(2,LD,1),
    fd_atmost(2,LD,2),
    fd_atmost(2,LD,3),
    fd_atmost(2,LD,4),
    fd_atmost(2,LD,5),
    fd_atmost(2,LD,6),
    fd_atmost(2,LD,7),
    fd_atmost(2,LD,8),
    fd_atmost(2,LD,9),

/* This is much slower...

    fd_exactly(2,LD,0),
    fd_exactly(2,LD,1),
    fd_exactly(2,LD,2),
    fd_exactly(2,LD,3),
    fd_exactly(2,LD,4),
    fd_exactly(2,LD,5),
    fd_exactly(2,LD,6),
    fd_exactly(2,LD,7),
    fd_exactly(2,LD,8),
    fd_exactly(2,LD,9),
*/
    Y#=100*X1+10*X2+X3,

    Z1#=100*X7 +10*X8 +X9,
    Z2#=100*X10+10*X11+X12,
    Z3#=100*X13+10*X14+X15,
    
    X6*Y #= Z1,
    X5*Y #= Z2,
    X4*Y #= Z3,

    100*X7 +10*X8 +X9 + 
    1000*X10+100*X11+10*X12    + 
    10000*X13+1000*X14+100*X15          #= 
    10000*X16+1000*X17+100*X18+10*X19+X20,
	
    labeling(LD).