% (1)
% Este funciona tambem para numeros inteiros
% negativos, e falha ao ser resatisfeito

quadrado(N,S) :- N >= 0, soma_impares(N,S).
quadrado(N,S) :- N =< 0, M is - N, soma_impares(M,S).

soma_impares(0,0) :- !.
soma_impares(N,S) :-
	N1 is N - 1,
	soma_impares(N1,S1),
	S is S1 + 2*N -1.

% (2)

last_([X],X).
last_([_|T],L) :- last_(T,L).

% (3)

butlast([_],[]).
butlast([H|T],[H|R]) :- butlast(T,R).

% (4)

append_([],L,L).
append_([H|T],L,[H|R]) :- append_(T,L,R).

% (5)

reverse_(L,R) :- revacc_(L,[],R).

revacc_([],L,L).
revacc_([H|T],L,R) :- revacc_(T,[H|L],R).

% (6)

member_(A,[A|_]).
member_(A,[_|T]) :- member_(A,T).

% (7)

acres(A,[],[A]).
acres(A,[A|T],[A|T]) :- !.
acres(A,[H|T],[H|R]) :- acres(A,T,R).

% (8)

uniao([],A,A).
uniao([H|T],A,U) :-
	uniao(T,A,X),
	acres(H,X,U).

% (9)

inter([],_,[]).
inter([H|T],A,[H|I]) :-
	select(H,A,R), !,
	inter(T,R,I).
inter([_|T],A,I) :-
	inter(T,A,I).

% (10)

set_difference([],_,[]).
set_difference([H|T],S,R) :-
	member(H,S), !,
	set_difference(T,S,R).
set_difference([H|T],S,[H|R]) :-
	set_difference(T,S,R).