/* 

  Sumbrero grid puzzle in Picat.

  http://www.omegajunior.net/code/sumbrero/
 
  This model was inspired by the discussion in comp.lang.forth:
  https://groups.google.com/forum/#!msg/comp.lang.forth/ZaqK8QgroMI/ZhJyVWCz_XYJ

  Solutions:
    problem = 1
    [1,3,7,2,6,7,9]

    problem = 2
    [3,4,5,1,2,6,7]
 

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

*/

import cp.

main => go.

go =>
  member(P,1..2),
  println(problem=P),
  
  data(P,A,Sums,UseAllDiff),
  
  sumbrero(A,Sums,UseAllDiff, X),
  println(X),
  nl,
  fail,
  nl.


sumbrero(A,Sums,UseAllDiff, X) =>
  Rows = A.len,
  Cols = A[1].len,

  X = new_list(Cols),
  X :: 1..9,

  foreach(I in 1..Rows) 
    sum([X[J]*A[I,J] : J in 1..Cols]) #= Sums[I]
  end,

  if UseAllDiff then
    all_different(X)
  end,

  solve(X).





%
% data
%

%
% Sumbrero 7
% http://www.omegajunior.net/code/sumbrero/
%
% Problem instance from
% https://groups.google.com/forum/#!msg/comp.lang.forth/ZaqK8QgroMI/ZhJyVWCz_XYJ
%
data(1,A,Sums,UseAllDiff) => 
  A = [
  % 1 2 3 4 5 6 7
  % A B C D E F G
   [1,0,0,0,0,1,0], % 1
   [0,1,0,1,0,0,1], % 2
   [0,0,1,0,1,0,0], % 3
   [1,0,0,1,0,0,0], % 4
   [0,1,0,0,1,1,0], % 5
   [0,0,1,0,0,0,1], % 6
   [0,0,0,1,1,0,0], % 7
   [1,1,1,0,0,0,0], % 8
   [0,0,0,0,0,1,1]  % 9
  ],
  Sums = [8,14,13,3,16,16,8,11,16],
  UseAllDiff = false.


%
% Problem instance from
% https://groups.google.com/forum/#!msg/comp.lang.forth/ZaqK8QgroMI/ZhJyVWCz_XYJ
% http://www.omegajunior.net/code/sumbrero/examples.html, Example 1
% "Example 1 'Different numbers from 1 to 7'"
%
data(2,A,Sums,UseAllDiff) => 
  A = [
   % 1 2 3 4 5 6 7
   % A B C D E F G
   [1,0,0,0,0,1,0], % 1
   [0,1,0,1,0,0,1], % 2
   [0,0,1,0,1,0,0], % 3
   [1,0,0,1,0,0,0], % 4
   [0,1,0,0,1,1,0], % 5
   [0,0,1,0,0,0,1], % 6
   [0,0,0,1,1,0,0], % 7
   [1,1,1,0,0,0,0], % 8
   [0,0,0,0,0,1,1]  % 9
  ],
  Sums = [9,12,7,4,12,12,3,12,13],
  UseAllDiff = true.