ch_4.hs

---- Recursivite


-- maximum' :: (Ord a) => [a] -> a
-- maximum' [] = error "maximum of empty list"
-- maximum' [x] = x
-- maximum' (x:xs)
--   | x > maxTail = x
--   | otherwise = maxTail
--   where maxTail = maximum' xs

maximum' :: (Ord a) => [a] -> a
maximum' [] = error "maximum of empty list"
maximum' [x] = x
maximum' (x:xs) = max x (maximum' xs)


replicate' :: (Num i, Ord i) => i -> a -> [a]
replicate' n x
  | n <= 0    = []
  | otherwise = x:replicate' (n-1) x


take' :: (Num i, Ord i) => i -> [a] -> [a]
take' n _
  | n <= 0  = []
take' _ []  = []
take' n (x:xs) = x : take' (n-1) xs


reverse' :: [a] -> [a]
reverse' [] = []
reverse' (x:xs) = reverse' xs ++ [x]


repeat' :: a -> [a]
repeat' x = x:repeat' x


zip' :: [a] -> [b] -> [(a, b)]
zip' [] _ = []
zip' _ [] = []
zip' (x:xs) (y:ys) = (x,y) : zip' xs ys


elem' :: (Eq a) => a -> [a] -> Bool
elem' a [] = False
elem' a (x:xs)
  | a == x    = True
  | otherwise = a `elem` xs


quicksort :: (Ord a) => [a] -> [a]
quicksort [] = []
quicksort (x:xs) =
  let smallerSorted = quicksort [a | a <- xs, a <= x]
      biggerSorted = quicksort [a | a <- xs, a > x]
  in
    smallerSorted ++ [x] ++ biggerSorted