:- use_module(library(lists)).
:- use_module(library(ordsets)).

:- mode(1, allnum(-numset)).
allnum([1,2,3,4,5,6,7,8,9]).

:- mode(1, allpos(-posset)).
allpos(PS) :-
	allcord(CS), findall((X,Y), (member(X,CS),member(Y,CS)), L),
	list_to_ord_set(L, PS).
allcord([0,1,2,3,4,5,6,7,8]).

:- mode(1, row(+pos, -posset)).
:- mode(1, column(+pos, -posset)).
:- mode(1, block(+pos, -posset)).

row((_,Y), PS)    :- allcord(CS), findall((X,Y), member(X,CS), PS).
column((X,_), PS) :- allcord(CS), findall((X,Y), member(Y,CS), PS).
box((X,Y), PS) :-
	X0 is (X // 3) * 3, X1 is X0 + 1, X2 is X0 + 2,
        Y0 is (Y // 3) * 3, Y1 is Y0 + 1, Y2 is Y0 + 2,
        findall((XX,YY), (member(XX,[X0,X1,X2]), member(YY,[Y0,Y1,Y2])), L),
	list_to_ord_set(L, PS).

:- mode(1, singleton(-num, +numset)).
:- mode(1, singleton(-pos, +posset)).
singleton(X,[X]).

:- mode(1, ord_intersection(+posset,+posset,-posset)).
:- mode(1, ord_subtract(+posset,+posset,-posset)).
:- mode(1, ord_union(+posset,+posset,-posset)).
:- mode(1, ord_intersection(+numset,+numset,-numset)).
:- mode(1, ord_subtract(+numset,+numset,-numset)).
:- mode(1, ord_union(+numset,+numset,-numset)).

:- mode(1, collectnum(+board, +posset, -numset)).
collectnum(BOARD,PS,NS) :-
	findall(N, (member((X,Y,N), BOARD), member((X,Y), PS)), L),
	list_to_ord_set(L,NS).

:- mode(1, collectpos(+board, +numset, -posset)).
collectpos(BOARD,NS,PS) :-
	findall((X,Y), (member((X,Y,N), BOARD), member(N,NS)), L),
	list_to_ord_set(L,PS).

:- mode(1, collectSafePos(+board,+num,-posset)).
collectSafePos(BOARD,N,PS) :-
	allpos(AP), findall(P, (member(P,AP), safe(BOARD,N,P)), PS).

:- mode(1, collectSafeNum(+board,+pos,-numset)).
collectSafeNum(BOARD,P,NS) :-
	allnum(AN), findall(N, (member(N,AN), safe(BOARD,N,P)), NS).

safe(BOARD,N,P) :- \+( unsafe(BOARD,N,P) ).
unsafe(BOARD, _, (X,Y)) :- member((X,Y,_), BOARD).
unsafe(BOARD, N, (X,_)) :- member((X,_,N), BOARD).
unsafe(BOARD, N, (_,Y)) :- member((_,Y,N), BOARD).
unsafe(BOARD, N, (X,Y)) :- box((X,Y),PS), member((X1,Y1),PS), member((X1,Y1,N),BOARD).

:- mode(1, ((+pos) = (+pos))).

:- mode(1, put(+board, +pos, -num)).
:- determination(put/3, row/2).
:- determination(put/3, column/2).
:- determination(put/3, box/2).
:- determination(put/3, singleton/2).
:- determination(put/3, ord_intersection/3).
:- determination(put/3, collectSafePos/3).
:- determination(put/3, collectSafeNum/3).
:- determination(put/3, '='/2).

:- set(i,5).
:- set(clauselength,5).
:- set(noise,8).
:- set(print,1).


% :- mode(1,putA(+board, +pos, +num)).
% putA(BOARD, P, N) :-
% 	collectSafePos(BOARD,N,PS1),
% 	column(P,PS2),
% 	ord_intersection(PS1,PS2,PS),
% 	singleton(P,PS).
% putA(BOARD, P, N) :-
% 	collectSafePos(BOARD,N,PS1),
% 	row(P,PS2),
% 	ord_intersection(PS1,PS2,PS),
% 	singleton(P,PS).
% putA(BOARD, P, N) :-
% 	collectSafePos(BOARD,N,PS1),
% 	block(P,PS2),
% 	ord_intersection(PS1,PS2,PS),
% 	singleton(P,PS).

putA(A,B,C) :-
   collectSafeNum(A,B,D), singleton(C,D).