/*

  Seesaw problem in Picat.

  Marriott & Stuckey "Programming with Constraints", page 257.
 
  Balancing on a seesaw.


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

*/

import cp.

main => go.

% direct modeling
go =>

   LS = [Liz,Fi,Sara],
   LS :: -5..5,

   9 * Liz + 8 * Fi + 4 * Sara #= 0,
   apart(Liz, Fi, 3),
   apart(Liz, Sara, 3),
   apart(Sara, Fi, 3),

   % symmetry breaking
   Sara #>= 0,
   solve([], LS),

   writeln([liz=Liz,fi=Fi,sara=Sara]),nl.

%
% Page 258 suggests cumulative instead of apart.
%
go2 =>
   LS = [Liz,Fi,Sara],
   LS  :: -5..5,

   9 * Liz + 8 * Fi + 4 * Sara #= 0,
   % symmetry breaking
   Sara #>= 0,

   LD = [3,3,3],
   LR = [1,1,1],
   Limit = 1,
   cumulative(LS, LD, LR, Limit),

   solve(LS),

   write([liz=Liz,fi=Fi,sara=Sara]),nl,nl.


apart(X, Y, N) =>
   (X #>= Y + N) #\/ (Y #>= X + N).