-- Monads https://medium.com/@julianoalves/functors-applicatives-e-monads-explicados-com-desenhos-2c45d5db7d25
data Arv a = Vazia | Node a (Arv a) (Arv a) deriving (Eq, Show, Read)

instance Functor Arv where
    fmap f Vazia = Vazia
    fmap f (Node a l r) = Node (f a) (fmap f l) (fmap f r)

singleton :: a -> Arv a
singleton a = Node a Vazia Vazia

insere :: (Ord a) => a -> Arv a -> Arv a
insere x Vazia = singleton x
insere x (Node a l r)
    | x == a = Node x l r
    | x < a = Node a (insere x l) r
    | x > a = Node a l (insere x r)

criar :: (Ord a) => [a] -> Arv a
criar xs = foldr insere Vazia xs

buscar :: (Ord a) => a -> Arv a -> Bool
buscar _ Vazia = False
buscar x (Node a l r)
    | x == a = True
    | x < a = buscar x l
    | x > a = buscar x r

data Fila a = Empty | Fila a (Fila a) deriving (Show)

vazia :: Fila a
vazia = Empty


-- inserir :: (Maybe a) => a -> Fila a -> Fila a
insereInicio a Empty = Fila (a) (Empty)
insereInicio a (Fila x y) = Fila (a) (Fila x y)

insereFinal a Empty = Fila (Empty) (a)
insereFinal a (Fila x y) = Fila (Fila x y) a