:- use_module(library(lists),[member/2]).

path([StartPoint|RestPath]) :-
	StartPoint = (1,1),
	Visited = [StartPoint],
	complete_path(1,1,Visited,RestPath).

complete_path(I,J,_,ResultPath) :-
	goto(I,J,final),
	!,
	ResultPath = [].
complete_path(I,J,Visited,ResultPath) :-
	( goto(I,J,Direction) ->
	    true
	;
	    true
	),
	next_square(Direction,I,J,NewI,NewJ),
	\+ bad_move(NewI,NewJ,Visited),
	ResultPath = [(NewI,NewJ)|TailResultPath],
	complete_path(NewI,NewJ,[(NewI,NewJ)|Visited],TailResultPath).

bad_move(I,J,Visited) :- member((I,J),Visited).
bad_move(I,J,      _) :- (I < 1 ; J < 1).
bad_move(I,J,      _) :- size(N), (I > N ; J > N).

next_square(   up, I,J,    I,NewJ) :- NewJ is J + 1.
next_square( down, I,J,    I,NewJ) :- NewJ is J - 1.
next_square( left, I,J, NewI,   J) :- NewI is I - 1.
next_square(right, I,J, NewI,   J) :- NewI is I + 1.