/* prolog  tutorial 2.9 Map coloring redux */

adjacent(X,Y,Map) :-  member([X,Y],Map) ; member([Y,X],Map). 


find_regions([],R,R). 
find_regions([[X,Y]|S], R,A) :- 
 (member(X,R) ->  
  (member(Y,R) -> find_regions(S,R,A) ; find_regions(S,[Y|R],A)) ; 
   (member(Y,R) -> find_regions(S,[X|R],A) ; find_regions(S,[X,Y|R],A) ) ). 


color(Map,Colors,Coloring) :-
        find_regions(Map,[],Regions), 
        color_all(Regions,Colors,Coloring), 
        \+ conflict(Map,Coloring). 
color_all([R|Rs],Colors,[[R,C]|A]) :- 
        member(C,Colors), 
        color_all(Rs,Colors,A). 
color_all([],_,[]). 


conflict(Map,Coloring) :- 
        member([R1,C],Coloring), 
        member([R2,C],Coloring), 
        adjacent(R1,R2,Map). 

map1([[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[3,4],[4,5]] ).