/* 

  Omelet 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.

go => 
   omelet(1,1,D11),
   writeln(d11=D11),
   omelet(2,1,D21),
   writeln(d21=D21),
   omelet(2,7,D27),
   writeln(d27=D27),
   omelet(3,7,D37),
   writeln(d37=D37),

   nl.

%% 4. omelet.pl
% Example queries:
% ?- omelet(1,1,D)
%    D = 1
% ?- omelet(2,1,D)
%    D=1
% ?- omelet(2,7,D)
%    D=4
% ?- omelet(3,7,D)
%    D=3

table (+,+,min)
omelet(_,1,X) => X=1.
omelet(1,H,H2) => H2=H.
omelet(N,H,D) =>
    N>1,
    H>1,
    between(1,H,L),
    N1 = N-1,
    L1 = L-1,
    omelet(N1,L1,D1),
    L2 = H-L,
    omelet(N1,L2,D2),
    D = max(D1,D2)+1.