%PL 2. kisHF Max_K_Atfedok
%Keszitette: Gruber Richard (V1WG4B)


:-use_module(library(lists)).

levag(L,0,L).
levag([_|Farok],K,RESL):- Z is K-1, levag(Farok,Z,RESL).

match([],_).
match([A|T1],[B|T2]):- A=B, match(T1,T2).

katfedo([],[],0).
katfedo(K,X,Y):- X=Y -> false ;
                 (length(X,N),
                  length(Y,M),
                  K>0,
	            R is N-K,
                  R2 is M-K, ((R<0 ; R2<0) -> false	;
	                                        levag(X,R,Marad),match(Marad,Y))).

maxhossz([],0).
maxhossz([X|XL],H1) :-  maxhossz(XL,EDDIGI_MAX),
                        atom_codes(X,ExplodeX),
                        length(ExplodeX,X_HOSSZ),
                        (X_HOSSZ>EDDIGI_MAX -> H1=X_HOSSZ; 
                                               H1=EDDIGI_MAX). 

minK(List,K,MinK) :-  maxhossz(List,MaxH),
                     (MaxH<K -> MinK=MaxH;
                                MinK=K). 

%Kivalogatja az egy elemhez tartozo megoldasokat egy K eseten
maxatfedok(_,_,[],[]).
maxatfedok(_,[],_,[]).
maxatfedok(K,X,[Y|YL],RES) :- atom_codes(X,ExplodeX),	
                              atom_codes(Y,ExplodeY), 
                              (katfedo(K,ExplodeX,ExplodeY)-> maxatfedok(K,X,YL,L2), RES=[K-Y|L2];
                                                              maxatfedok(K,X,YL,RES)).
%Egy elemhez tartozo megoldasok minden K eseten 
maxatfedok2(K,_,_,[]) :- K<1, !.
maxatfedok2(K,X,[Y|YL],RES) :- K2 is K-1,
                               maxatfedok2(K2,X,[Y|YL],L2),
                               maxatfedok(K,X,[Y|YL],L1),
                               append(L2,L1,RES).

%Minden elemre lefuttatja a megoldaskeresest
maxatfedok4(_,[],_,[]).
maxatfedok4(K,[X|XL],[Y|YL],RESList) :- maxatfedok2(K,X,[Y|YL],L1),                                        
                                        maxatfedok4(K,XL,[Y|YL],L2),
                                        ((L1=[]) -> RESList=L2;
                                          RESList = [X-L1|L2] ).

max_k_atfedok(_,[],[]).                                        
max_k_atfedok(K,List,RESList) :- K>0,
                                 sort(List,RList), 
                                 minK(List,K,MinK), 
                                 maxatfedok4(MinK,RList,RList,RESList).