/*

  Pandigital numbers in Picat.

  From
  Albert H. Beiler "Recreations in the Theory of Numbers", quoted from
  http://www.worldofnumbers.com/ninedig1.htm
  """
  [ Chapter VIII : Digits - and the magic of 9 ]
  [ I found the same exposé in Shakuntala Devi's book
    "Figuring : The Joy of Numbers" ]

  The following curious table shows how to arrange the 9 digits so that
  the product of 2 groups is equal to a number represented by the
  remaining digits."

    12 x 483 = 5796
    42 x 138 = 5796
    18 x 297 = 5346
    27 x 198 = 5346
    39 x 186 = 7254
    48 x 159 = 7632
    28 x 157 = 4396
    4 x 1738 = 6952
    4 x 1963 = 7852
  """

  See also

  * MathWorld http://mathworld.wolfram.com/PandigitalNumber.html
  """
  A number is said to be pandigital if it contains each of the digits
  from 0 to 9 (and whose leading digit must be nonzero). However,
  "zeroless" pandigital quantities contain the digits 1 through 9.
  Sometimes exclusivity is also required so that each digit is
  restricted to appear exactly once.
  """

  * Wikipedia http://en.wikipedia.org/wiki/Pandigital_number


  Model created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import cp.

main => go.

go =>
        L = findall([X1,X2,X3], pandigital([X1,X2,X3])),
        Len = length(L),
        writeln(len=Len).

scalar_product(A, X, Product) => 
   Product #= sum([A[I]*X[I] : I in 1..A.length]).


%
% converts a number Num to/from a list of integer List given a base Base
%
to_num(List, Base, Num) =>
        Len = length(List),
        Num #= sum([List[I]*Base**(Len-I) : I in 1..Len]).


pandigital([X1,X2,X3]) =>
        
        %
        % length of numbers
        %
        % Len1 #>= 1,
        % Len1 #=< 4,
        % Len2 #>= 1,
        % Len2 #=< 4,
        % Len3 #= 4,
        Len1 :: 1..2,
        Len2 :: 3..4,
        Len3 #= 4,

        % Len1 #=< Len2, % symmetry breaking
        Len1 + Len2 + Len3 #= 9,
        
        indomain(Len1),

        % set length of lists
        X1 = new_list(Len1),
        X1 :: 1..9,

        X2 = new_list(Len2),
        X2 :: 1..9,

        X3 = new_list(Len3), % the result
        X3 :: 1..9,

        % convert to number
        Base = 10,
        to_num(X1, Base, Num1),
        to_num(X2, Base, Num2),
        to_num(X3, Base, Res),

        % calculate result
        Num1 * Num2 #= Res,

        Vars = X1 ++ X2 ++ X3,
        all_different(Vars),

        % search
        solve(Vars),

        writef("%2d * %4d = %4d\n",Num1,Num2,Res).
        % writeln([X1,X2,X3]).