----------------------------------------- Zadanie 1 ---------------------------------------------
powerlist [] = [[]]
powerlist (x:xs) = [x:sublist | sublist <- powerlist xs] ++ powerlist xs
----------------------------------------- Zadanie 2 ---------------------------------------------
product xs ys = [x | x <- xs, elem x ys]
----------------------------------------- Zadanie 3 ---------------------------------------------
sum xs ys = xs ++ [y | y <- ys, not (elem y xs)]
----------------------------------------- Zadanie 4 ---------------------------------------------
{-
a) 6 / (12 / (24 / (8 / 2))) = 3.0
  6 / (foldr (/) 2 [12,24,8])
  6 / ( 12 / (foldr (/) 2 [24,8]))
  6 / ( 12 / (24 / (foldr (/) 2 [8])))
  6 / ( 12 / (24 / ( 8 / (foldr (/) 2 []))))
  6 / ( 12 / (24 / ( 8 / 2)))
  6 / ( 12 / (24 /  4 ))
  6 / ( 12 / 6 )
  6 / 2
  3

b) (1 > 2 && (3 > 2 && (5 == 5 && True))) = False
c) (max 3 (max 6 (max 12 (max 4 (max 55 (max 11 18)))))) = 55
d) (max 3 (max 6 (max 12 (max 4 (max 55 (max 11 81)))))) = 81
e) ((((((10 + ((54 + 6) / 2)) / 2) + 4) / 2) + 24) / 2) = 18
f) ((((((((54 + 2) / 2) + 4) / 2) + 10) / 2) + 6) / 2) = 9.5
g) (((64 / 4) / 2) / 4) = 2
  foldl (/) ( 64 / 4) [2, 4]
  foldl (/) ( (64 / 4) / 2 ) [4]
  foldl (/) ( ((64 / 4) / 2) / 4 ) []
  ((16 / 2) / 4)
  (8 / 4)
  2

h) (2*(2*(2*8 + 1) + 2) + 3) = 75
-}
----------------------------------------- Zadanie 5 ---------------------------------------------
check x xs = (==0) $ foldl (\x y -> if x == y then 0 else x) x xs
----------------------------------------- Zadanie 6 ---------------------------------------------
foldlmap f []       = []
foldlmap f (x:xs)   = foldl (\x xs -> (f x):xs) [] (x:xs) --- !!!!!

foldrmap f []       = []
foldrmap f (x:xs)   = foldr (\x xs -> (f x):xs) [] (x:xs)
----------------------------------------- Zadanie 7 ---------------------------------------------
-- a)
foldllast (x:xs) = foldl1 (\x y -> y) (x:xs)
foldrlast (x:xs) = foldr1 (\x y -> y) (x:xs)

-- b)
foldlhead (x:xs) = foldl1 (\x y -> x) (x:xs)
foldrhead (x:xs) = foldr1 (\x y -> x) (x:xs)

-- c)
foldlmax (x:xs) = foldl1 (\x y -> max x y) (x:xs)
foldrmax (x:xs) = foldr1 (\x y -> max x y) (x:xs)
----------------------------------------- Zadanie 8 ---------------------------------------------
tupleunzip [] = ([], [])
tupleunzip xs = (map fst xs, map snd xs)
----------------------------------------- Zadanie 9 ---------------------------------------------
f1 xs = map(\x -> x + 1) xs
f2 xs = foldl1(\x y -> x - y) xs
f3 xs = foldl1(\x y -> x + y) xs
f4 a xs = map(\x -> if x == a then True else False) xs
f5 a xs = map(\x -> if x /= a then True else False) xs
f6 xs = map (\x -> x:xs++[x]) xs