Old Haskell exams for LPP

-- exam 24/01/2018

ex1 :: [Int] -> Int
ex1 [] = 0
ex1 x = aux x 1
    where
        aux [] _ = 0
        aux (x : xs) n = ((2 ^ (n - 1)) * x) + aux xs n+1

ex2 :: [Int] -> Int
ex2 [] = 0
ex2 x = sum (map (\(x, n) -> 2 ^ (n - 1) * x) (zip x [1..]))

-- exam 24/02/2018

ex3 :: (a -> Bool) -> [a] -> [Int]
ex3 _ [] = []
ex3 p x = aux p x 0
    where
        aux _ [] _ = []
        aux p (x : xs) n | p x = n : aux p xs (n + 1)
                         | otherwise = aux p xs (n + 1)

ex4 :: (a -> Bool) -> [a] -> [Int]
ex4 _ [] = []
ex4 p x = map snd (filter (p.fst) (zip x [0..]))

-- exam 18/06/2018

ex5 :: [Int] -> Int -> Int
ex5 [] _ = 0
ex5 x y = aux x y 0
    where
        aux [] _ _ = 0
        aux (x : xs) y n = (x * (y ^ n)) + aux xs y (n+1)

ex6 :: [Int] -> Int -> Int
ex6 [] _ = 0
ex6 x y = sum (map (\(x, n) -> x * (y ^n)) (zip x [0..]))

-- exam 24/07/2018

ex7 :: [Int] -> Int
ex7 [] = 0
ex7 x = aux x 0
    where
        aux [] _ = 0
        aux (x : xs) n | n `mod` 2 == 0 = x + aux xs (n + 1)
                       | otherwise = (- x) + aux xs (n + 1)

ex8 :: [Int] -> Int
ex8 [] = 0
ex8 x = sum (map (\(x, n) -> if n `mod` 2 == 0 then x else - x) (zip x [0..]))