# 99 questions/Solutions/19

### From HaskellWiki

(**) Rotate a list N places to the left.

Hint: Use the predefined functions length and (++).

rotate [] _ = [] rotate xs 0 = xs rotate (x:xs) (n+1) = rotate (xs ++ [x]) n rotate xs n = rotate xs (length xs + n)

(Note that this solution uses n+k-patterns which are removed from Haskell 2010.)

There are two separate cases:

- If n > 0, move the first element to the end of the list n times.
- If n < 0, convert the problem to the equivalent problem for n > 0 by adding the list's length to n.

or using cycle:

rotate xs n = take len . drop (n `mod` len) . cycle $ xs where len = length xs

or using list comprehension (only works for sequential increasing elements):

rotate :: (Enum a) => [a] -> Int -> [a] rotate xs n = [(f n) .. last xs] ++ [head xs .. (f (n-1))] where f k = xs !! (k `mod` length xs)

or without mod:

rotate xs n = take (length xs) $ drop (length xs + n) $ cycle xs

or

rotate xs n = if n >= 0 then drop n xs ++ take n xs else let l = ((length xs) + n) in drop l xs ++ take l xs

or

rotate xs n | n >= 0 = drop n xs ++ take n xs | n < 0 = drop len xs ++ take len xs where len = n+length xs

rotate xs n = drop nn xs ++ take nn xs where nn = n `mod` length xs

Using a simple splitAt trick

rotate xs n | n < 0 = rotate xs (n+len) | n > len = rotate xs (n-len) | otherwise = let (f,s) = splitAt n xs in s ++ f where len = length xs

length

rotate xs n | n > 0 = (reverse . take n . reverse $ xs) ++ (reverse . drop n . reverse $ xs) | n <= 0 = (drop (negate n) xs) ++ (take (negate n) xs)

length

rotate :: [a] -> Int -> [a] rotate [] _ = [] rotate x 0 = x rotate x y | y > 0 = rotate (tail x ++ [head x]) (y-1) | otherwise = rotate (last x : init x) (y+1)