/* 

  Coloring countries in Picat.

  Translated from the Prolog code in 
  http://www.inf.ed.ac.uk/teaching/courses/lp/slides/lp5.pdf slide 7ff.

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

*/

main => go.

go ?=>
  colour_countries(Colours),
  println(Colours.sort()),
  nl.

%
% 1) Check that the solution is correct
% 2) Generate all solutions. There are 7776 different solutions.
%
go2 ?=> 
  Map = get_global_map(),
  Map.put(count,0),

  colour_countries(Colours),
  println(Colours.sort()),

  % and then we check that it's correct
  M = new_map([Country=Colour :  $c(Country,Colour) in Colours]),
  foreach(Country in M.keys().sort())
    Colour = M.get(Country),
    println(Country=Colour),
    Neighbours = findall(C, ngb(Country,C)).flatten().sort(),
    println("\tNeighbours:"),
    foreach(N in Neighbours)
      Colour2 = M.get(N),
      printf("\t%w = %w\n",N,Colour2),
      if Colour2 == Colour then
         println("ERROR!")
      end
    end
  end,
  nl,
  Map.put(count,Map.get(count)+1),
  fail,
  nl.

go2 => 
  println(count=get_global_map().get(count)).


neighbour(Country,Country1) =>
  ngb(Country,Neighbours),
  member(Country1,Neighbours).

colour_countries(Colours) =>
  % setof([Country,_], X^ngb(Country,X), Colours), % Picat don't have setof/3 or setof/2.
  findall($c(Country,_), ngb(Country,_)) = Colours,
  colours(Colours).

colours([]) ?=> true.
colours(CRest) =>
   CRest = [$c(Country,Colour)|Rest],
   colours(Rest),
   member(Colour,[yellow,blue,red,green]),
   not (member($c(Country1,Colour),Rest),
        neighbour(Country,Country1)).

index (-,-)
ngb(austria, [germany,switzerland,italy]).
ngb(belgium, [france,germany,netherlands]).
ngb(denmark, [germany]).
ngb(france, [spain,belgium,switzerland,germany,italy]).
ngb(germany, [netherlands,belgium,france,switzerland,austria,denmark]).
ngb(italy, [france,switzerland,austria]).
ngb(netherlands, [belgium,germany]).
ngb(portugal, [spain]).
ngb(spain, [portugal,france]).
ngb(switzerland, [france,germany,austria,italy]).