/* 

  Panoz problem in Picat.

  From
  "How to Solve it With B-Prolog?"
  http://www.cs.nmsu.edu/ALP/2010/08/how-to-solve-it-with-b-prolog/
  (Prolog Programming Contest 2010)
  """
  Manhattan has several outlets of the famous Belgian bakery Panoz. During an 
  experiment with a new kind of chocolate pastry, the old bakery has exploded. 
  A new bakery will be built, somewhere in Manhattan, and this occasion is used to 
  optimize the distribution of all the goodies. Clearly Panoz wants the location 
  in Manhattan which minimizes the maximal (Manhattan) distance from the bakery to 
  any outlet.

  Write a predicate panoz/2 whose queries look like ?- panoz(Outlets,Sol). where Sol 
  is the location of the new bakery. The outlet coordinates Outlets are given as 
  a list of tuples, e.g. [(0,1),(0,2),(4,0),(4,3)].

  Here is a typical query and its answer:
  ?- panoz([(0,1),(0,2),(4,0),(4,3)],Sol).
  Sol = (2,2)

  Of course, Sol = (2,1) would also have been a good solution.
  """

  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 => 
  panoz([[0,1],[0,2],[4,0],[4,3]],Sol, Ds),
  writeln([sol=Sol,ds=Ds]),

  % find all optimal solutions
  panoz2([[0,1],[0,2],[4,0],[4,3]],Sols2,Ds),
  writeln(all_solutions=Sols2),
  nl.


panoz(Ps, Sol, Ds) =>
   Xs = [X : [X,_] in Ps],
   Ys = [Y : [_,Y] in Ps],
   X :: min(Xs)..max(Xs),
   Y :: min(Ys)..max(Ys),
   Ds #= max([max(X1-X,X-X1)+max(Y1-Y,Y-Y1) : [X1,Y1] in Ps]),
   solve([$min(Ds)],[X,Y]),
   Sol = [X,Y]. 


panoz2(Ps, Sols,Ds) =>
   Xs = [X : [X,_] in Ps],
   Ys = [Y : [_,Y] in Ps],
   X :: min(Xs)..max(Xs),
   Y :: min(Ys)..max(Ys),
   Ds #= max([max(X1-X,X-X1)+max(Y1-Y,Y-Y1) : [X1,Y1] in Ps]),
   Sols = solve_all([X,Y]).