/*

  Seseman problem in Picat.

  Description of the problem:
  
  n is the length of a border
  There are (n-2)^2 "holes", i.e.
  there are n^2 - (n-2)^2 variables to find out.
 
  The simplest problem, n = 3 (n x n matrix)
  which is represented by the following matrix:
 
   a b c 
   d   e 
   f g h 
  
  Where the following constraints must hold:
 
    a + b + c = border_sum
    a + d + f = border_sum
    c + e + h = border_sum
    f + g + h = border_sum
    a + b + c + d + e + f = total_sum


  For a (Swedish) discussion of this problem, see
  "Sesemans matematiska klosterproblem samt lite Constraint Logic Programming"
  http://www.hakank.org/webblogg/archives/001084.html
  and
  Seseman's Convent Problem: http://www.hakank.org/seseman/seseman.cgi
  (using ECLiPSe CLP code)

  It was also is commented in the (Swedish) blog post
  "Constraint Programming: Minizinc, Gecode/flatzinc och ECLiPSe/minizinc"
  http://www.hakank.org/webblogg/archives/001209.html
  

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

*/

import cp.

main => go.

go =>
        [Rowsum,Total,FirstNum] = [9,24,1],
        writeln([rowsum=Rowsum,total=total]),
        L = findall(S, seseman(Rowsum, Total, FirstNum, S)),
        foreach(X in L)  write_convent(X) end,
        Len = length(L),
        writeln(solutions=Len).

%
% Using symmetry breaking (seseman2).
%
go2 =>
        Rowsum = 9,
        Total = 24,
        FirstNum = 1,
        writeln([rowsum=Rowsum,total=Total]),
        L = findall(S, seseman2(Rowsum, Total, FirstNum, S)),
        foreach(X in L)  write_convent(X) end,
        Len = length(L),
        writeln(solutions=Len).


write_convent([A,B,C,D,E,F,G,H]) =>
        writef("%d %d %d\n", A,B,C),
        writef("%d _ %d\n", D,E),
        writef("%d %d %d\n", F,G,H),
        writef("\n").


% General constraints
constraints([A,B,C,D,E,F,G,H], Rowsum, Total) =>

        A+B+C #= Rowsum,
        A+D+F #= Rowsum,
        C+E+H #= Rowsum,
        F+G+H #= Rowsum,
        A+B+C+D+E+F+G+H #= Total.


%
% Plain problem (no symmetry breaking)
%
seseman(Rowsum, Total, FirstNum, LD) =>
        % LD = [A,B,C,D,E,F,G,H],
        LD = new_list(8),

        % FirstNum = 0: empty rooms allowed
        % FirstNum = 1: empty rooms not allowed
        LD :: FirstNum..9,

        constraints(LD, Rowsum, Total),

        solve(LD).



%
% With symmetry breaking
%
seseman2(Rowsum, Total, FirstNum, LD) =>

        LD = [A,B,_C,D,E,_F,G,H],

        % FirstNum = 0: empty rooms allowed
        % FirstNum = 1: empty rooms not allowed
        LD :: FirstNum..9,

        % Row sums/Column sums
        constraints(LD, Rowsum, Total),

        % additional constraints for uniqueness (rotation, mirror)
        A #=< H,
        B #=< D,
        D #=< E,
        E #=< G,

        solve(LD).