/* 

  Wijuko grid puzzle in Picat.

  Place 1-9 in the grid, obeying the sums between pairs of squares.

  Here's the template, where X is a square and n is a number between 1 and 9.

    X n X n X
    n   n   n
    X n X n X
    n   n   n
    X n X n X 


  See Martin J. Chlond: "Puzzle - IP in the I"
  http://pubsonline.informs.org/doi/pdf/10.1287/ited.2015.0142


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

*/

% import util.
import cp.

main => go.

go =>
  problem(1,D),
  wujiko(D, X),
  foreach(Row in X)
    println(Row.to_list())
  end,

  nl.

go2 =>
  foreach(P in 1..2) 
    println(problem=P),
    problem(P,D),
    wujiko(D, X),
    foreach(Row in X)
      println(Row.to_list())
    end,
    nl
  end,

  nl.

wujiko(D, X) =>
  N = D[1].length,

  % decision variables
  X = new_array(N,N),
  X :: 1..N*N,

  all_different(X.vars()),
  
  % row constraints
  foreach(I in 1..N, J in 1..2) 
     X[I,J] + X[I,J+1] #= D[(I-1)*2+1,J] 
  end,

  % column constraints
  foreach(I in 1..2,J in 1..N)
     X[I,J] + X[I+1,J] #= D[(I-1)*2+2,J]
  end,

  solve(X.vars()).


%
% Problem instance from Chlond's article:
%
%    X  _  X  7  X
%
%   12     8    13
%
%    X  _  X 14  X
%
%    7     _    15
%
%    X  _  X  _  X 

%
%
problem(1,D) =>
D = 
[[  _,  7, 0],  % row
 [ 12,  8,13],  % column
 [  _, 14, 0],  % row
 [  7, _, 15],  % column
 [  _, _,  0]]. % row



% another example:
% http://www.pressreader.com/search?query=wijuko
% Solution:
%
%  4 9 1
%  8 2 3
%  5 7 6
% 
problem(2,D) =>
D =
[[ 13, _,  0],  %  row
 [  12,11, _],  %  column
 [   _, _, 0],  %  row
 [   _, _, 9],  %  column
 [  12,13, 0]]. %  row