--1

f1 xs ys = head (zipWith (/=) xs ys)
-- f1 :: Eq a => [a] -> [a] -> Bool

f2 g xs = map g (filter (< (head xs)) xs)
-- f2 :: Ord a => (a -> b) -> [a] -> [b] 

--2

xs = 1 : f xs
     where f (z:zs) = z : f (map (+4) zs)  

--3

gray :: Int -> [String]
gray 0 = [""]
gray n = let xs = gray (n-1) in map ('0':) xs ++ map ('1':) (reverse xs)

{- o equivalentemente 
gray :: Int -> [String]
gray 0 = [""]
gray n = [ '0' : x | x <- prev ] ++ [ '1' : x | x <- reverse prev ]
         where prev = gray (n-1)
-}

--4

--a)

quitarArco g x y = [(w,z) | (w,z) <- g, w /=x || z /= y]
-- quitarArco :: (Eq a, Eq b) => [(b,a)] -> b -> a -> [(b,a)] 

-- b)

-- hayCamino :: Eq a => [(a,a)] -> a -> a -> Bool  
hayCamino g x y 
	| x == y = True
        | null unpaso = False
	| otherwise = or [hayCamino (quitarArco g x w) w y | w <- unpaso]
          where unpaso = [ w | (z,w) <- g, z == x ]


g = [(1,2),(2,3),(1,3),(3,4),(4,2),(5,6)]