99 questions/Solutions/10

(*) Run-length encoding of a list.

Use the result of problem P09 to implement the so-called run-length encoding data compression method. Consecutive duplicates of elements are encoded as lists (N E) where N is the number of duplicates of the element E.

encode xs = map (\x -> (length x,head x)) (group xs)

which can also be expressed as a list comprehension:

[(length x, head x) | x <- group xs]

or

[(length (x:xs), x) | (x:xs) <- group xs]

Or writing it Pointfree (Note that the type signature is essential here to avoid hitting the Monomorphism Restriction):

encode :: Eq a => [a] -> [(Int, a)]
encode = map (\x -> (length x, head x)) . group

Or (ab)using the "&&&" arrow operator for tuples:

encode :: Eq a => [a] -> [(Int, a)]
encode xs = map (length &&& head) $ group xs

Or using the slightly more verbose (w.r.t. (&&&)) Applicative combinators:

encode :: Eq a => [a] -> [(Int, a)]
encode = map ((,) <$> length <*> head) . pack

Or with the help of foldr (pack is the resulting function from P09):

encode xs = (enc . pack) xs
	where enc = foldr (\x acc -> (length x, head x) : acc) []

Or using takeWhile and dropWhile:

encode [] = []
encode (x:xs) = (length $ x : takeWhile (==x) xs, x)
                 : encode (dropWhile (==x) xs)

Or without higher order functions:

encode []     = []
encode (x:xs) = encode' 1 x xs where
    encode' n x [] = [(n, x)]
    encode' n x (y:ys)
        | x == y    = encode' (n + 1) x ys
        | otherwise = (n, x) : encode' 1 y ys

Or we can make use of zip and group:

 
import List
encode :: Eq a => [a] -> [(Int, a)]
encode xs=zip (map length l) h where 
    l = (group xs)
    h = map head l

Or if we ignore the rule that we should use the result of P09,

encode :: Eq a => [a] -> [(Int,a)]
encode xs = foldr f final xs Nothing
  where
    f x r (Just a@(i,q)) | x == q = r (Just (i+1,q))
                         | otherwise = a : r (Just (1, x))
    f x r Nothing = r (Just (1, x))

    final (Just a@(i,q)) = [a]
    final Nothing = []

which can become a good transformer for list fusion like so:

{-# INLINE encode #-}
encode :: Eq a => [a] -> [(Int,a)]
encode xs = build (\c n ->
  let
    f x r (Just a@(i,q)) | x == q = r (Just (i+1,q))
                         | otherwise = a `c` r (Just (1, x))
    f x r Nothing = r (Just (1, x))

    final (Just a@(i,q)) = a `c` n
    final Nothing = n

  in
    foldr f final xs Nothing)

Just one more way with recursion:

encode :: [[t]] -> [(Int, t)]
encode =  let f acc [] = acc
              f acc (x:xs) = f ((length x, head x): acc) xs
          in  reverse . f []