Cas 05.11.24 : Sudoku

%sep_first_col(X,Ost,R) X | Ost (vizuelno) poveke nameneto za R da e vlez a X i Ost izlez
sep_first_col([X],[Ost],[[X|Ost]]):-!.
sep_first_col([X|OstX],[Ost|OstRest],[[X|Ost]|OstR]):-sep_first_col(OstX,OstRest,OstR).

%Za da moze transponirano da se koristi za naoganje na transponiranata matrica
empty([[]]):-!.
empty([[]|Ost]):-empty(Ost).
e_list([]).
e_list([_|_]).

transponirano([X],R):-sep_first_col(X,Ost,R),empty(Ost),!. %Ova so empty e za da moze da se napise ?- so nepoznato R
transponirano([X|Ost],R):-sep_first_col(X,OstT,R),transponirano(Ost,OstT).

count(_,[],0):-!.
count(X,[X|Ost],R):-!,count(X,Ost,R1),R is R1+1.
count(X,[_|Ost],R):-count(X,Ost,R).

len([],0):-!.
len([_|Ost],R) :-len(Ost,R1), R is R1+1.

red_ok(L):-len(L,R),red_ok(L,R).
red_ok(L,1):-!,count(1,L,1).
red_ok(L,N):-count(N,L,1),N1 is N-1, red_ok(L,N1).

redovi_ok([]):-!.
redovi_ok([X|Ost]):-red_ok(X),redovi_ok(Ost).

col_ok(L):-transponirano(L,R),redovi_ok(R).

seci_red([],[[]],0.0,_):-!.
seci_red(L,[[]|Ost],0.0,Len):-seci_red(L,Ost,Len,Len),!.
seci_red([X|Ost],[[X|Ost1]|Ost2],N,Len):- N1 is N-1,seci_red(Ost,[Ost1|Ost2],N1,Len).
seci_red(L,R):-len(L,N1),N is sqrt(N1),seci_red(L,R,N,N).

seci_redovi([],[]):-!.
seci_redovi([L|OstL],[R|OstR]):-seci_red(L,R),seci_redovi(OstL,OstR).

trgni_nivo([],[]):-!.
trgni_nivo([[X|Ost1]|Ost],[X|OstR]):-trgni_nivo([Ost1|Ost],OstR),!.
trgni_nivo([[]|Ost],R):-trgni_nivo(Ost,R),!.
trgni_nivo([X|Ost],R):-not(e_list(X)),trgni_nivo(Ost,R).

spoi_nadnivo([[]],[]):-!.
spoi_nadnivo([[]|Ost],R):-spoi_nadnivo(Ost,R),!.
spoi_nadnivo([[X|Ost]|Ost2],[X|Ost1]):-spoi_nadnivo([Ost|Ost2],Ost1).

spoi_nadnivoa([],[]):-!.
spoi_nadnivoa([X|Ost],[R|OstR]):-spoi_nadnivo(X,R),spoi_nadnivoa(Ost,OstR).

kvadratiziraj(L,R):- seci_redovi(L,L1),transponirano(L1,L2),seci_redovi(L2,R1),trgni_nivo(R1,R2 ),spoi_nadnivoa(R2,R).
kvad_ok(L):-kvadratiziraj(L,R),redovi_ok(R).

sudoku_ok(R):-redovi_ok(R),col_ok(R),kvad_ok(R).


sudoku(L,R):- len(L,Len),LenP is Len+1, gen_sudoku(L,R,LenP),sudoku_ok(R),!.

gen_sudoku([],[],_).
gen_sudoku([[a|Ost]|Ost1], [[X|OstR]|OstR1], LenP) :-between(1,LenP,X), gen_sudoku([Ost|Ost1], [OstR|OstR1], LenP).
gen_sudoku([[]|Ost],[[]|OstR],LenP):- gen_sudoku(Ost,OstR,LenP).
gen_sudoku( [[X|Ost]|Ost1], [[X|OstR]|OstR1], LenP):-  not(X = a),        gen_sudoku([Ost|Ost1], [OstR|OstR1], LenP).