/* 

  Lace problem in Picat.

  From 
  http://www.sci.brooklyn.cuny.edu/~zhou/prolog_contest/pc2012.txt
  """
  Solutions in B-Prolog for the 2012 Prolog Programming Contest 
  Team members: Christian Theil Have, Nuno Lopes, and Neng-Fa Zhou 
  """

  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.


%% 1. lace.pl
% Example query ?-lace(5).


go =>
  lace(5).

go2 =>
  foreach(N in 1..11)
    writeln(n=N),
    lace(N),
    nl
  end,
  nl.

lace(N) =>
    grid_size(N,S),
    Grid = new_array(S,S),
    R0 = S//2+1, 
    C0 = R0,
    foreach(I in 1..N) draw(I,Grid,R0,C0) end,
    foreach(R in 1..S)
       foreach(C in 1..S)
	   var(Grid[C,R]) -> printf(" ") ; printf("*")
       end,
       nl
    end.
    
draw(I,Grid,R0,C0), I mod 2 == 0 =>
    grid_size(I,S), 
    foreach(Offset in 0..S//2) (Grid[R0-Offset,C0-S//2+Offset] = '*',
				Grid[R0-Offset,C0+S//2-Offset] = '*',
				Grid[R0+Offset,C0-S//2+Offset] = '*',
				Grid[R0+Offset,C0+S//2-Offset] = '*') end.
draw(I,Grid,R0,C0) =>
    grid_size(I,S), 
    foreach(C in C0-S//2..C0+S//2) (Grid[R0-S//2,C] = '*',
				    Grid[R0+S//2,C] = '*') end,
    foreach(R in R0-S//2..R0+S//2) (Grid[R,C0-S//2] = '*',
				    Grid[R,C0+S//2] = '*') end.
	
table (+,-)
grid_size(1,S) => S = 3.
grid_size(N,S) ?=>
    0 == N mod 2,% !,
    N1 = N-1,
    grid_size(N1,S1),
    S = S1 + S1 // 2 * 2.
grid_size(N,S) ?=>
    N1 = N - 1,
    grid_size(N1,S).