{- | A simple purely functional circular list, or ring, data type. Lets describe what we mean by 'ring'. A ring is a circular data structure such that if you continue rotating the ring, you'll eventually return to the element you first observed. All of our analogies involve sitting at a table who's top surface rotates about its center axis (think of those convenient rotating platforms one often finds in an (Americanized) Chinese Restaurant). Only the closest item on the table is avialable to us. In order to reach other elements on the table, we need to rotate the table to the left or the right. Our convention for this problem says that rotations to the right are a forward motion while rotations to the left are backward motions. We'll use the following circular list for our examples: > 8 7 6 > 9 5 > A 4 > B 3 > C 2 > D 0 1 > ^ The pointer at the bottom represents our position at the table. The element currently in front of is is referred to as the `focus`. So, in this case, our focus is 0. If we were to rotate the table to the right using the `rotR` operation, we'd have the following table. > 9 8 7 > A 6 > B 5 > C 4 > D 3 > 0 1 2 > ^ This yields 1 as our new focus. Rotating this table left would return 0 to the focus position. -} module Data.CircularList ( -- * Data Types CList, -- * Functions -- ** Creation of CLists empty, fromList, singleton, -- ** Update of CList update, reverseDirection, -- ** Converting CLists to Lists leftElements, rightElements, toList, toInfList, -- ** Extraction and Accumulation focus, insertL, insertR, removeL, removeR, -- ** Manipulation of Focus allRotations, rotR, rotL, rotN, rotNR, rotNL, rotateTo, findRotateTo, -- ** List-like functions filterR, filterL, foldrR, foldrL, foldlR, foldlL, -- ** Manipulation of Packing balance, packL, packR, -- ** Information isEmpty, size, ) where import Data.List(find,unfoldr,foldl') import Control.Monad(join) import Test.QuickCheck.Arbitrary import Test.QuickCheck.Gen -- | A functional ring type. data CList a = Empty | CList [a] a [a] {- Creating CLists -} -- | An empty CList. empty :: CList a empty = Empty -- |Make a (balanced) CList from a list. fromList :: [a] -> CList a fromList [] = Empty fromList a@(i:is) = let len = length a (r,l) = splitAt (len `div` 2) is in CList (reverse l) i r singleton :: a -> CList a singleton a = CList [] a [] {- Updating of CLists -} -- |Replaces the current focus with a new focus. update :: a -> CList a -> CList a update v Empty = CList [] v [] update v (CList l _ r) = CList l v r -- |Reverse the direction of rotation. reverseDirection :: CList a -> CList a reverseDirection Empty = Empty reverseDirection (CList l f r) = CList r f l {- Creating Lists -} -- |Starting with the focus, go left and accumulate all -- elements of the CList in a list. leftElements :: CList a -> [a] leftElements Empty = [] leftElements (CList l f r) = f : (l ++ (reverse r)) -- |Starting with the focus, go right and accumulate all -- elements of the CList in a list. rightElements :: CList a -> [a] rightElements Empty = [] rightElements (CList l f r) = f : (r ++ (reverse l)) -- |Make a list from a CList. toList :: CList a -> [a] toList = rightElements -- |Make a CList into an infinite list. toInfList :: CList a -> [a] toInfList = cycle . toList {- Extraction and Accumulation -} -- |Return the focus of the CList. focus :: CList a -> Maybe a focus Empty = Nothing focus (CList _ f _) = Just f -- |Insert an element into the CList as the new focus. The -- old focus is now the next element to the right. insertR :: a -> CList a -> CList a insertR i Empty = CList [] i [] insertR i (CList l f r) = CList l i (f:r) -- |Insert an element into the CList as the new focus. The -- old focus is now the next element to the left. insertL :: a -> CList a -> CList a insertL i Empty = CList [] i [] insertL i (CList l f r) = CList (f:l) i r -- |Remove the focus from the CList. The new focus is the -- next element to the left. removeL :: CList a -> CList a removeL Empty = Empty removeL (CList [] _ []) = Empty removeL (CList (l:ls) _ rs) = CList ls l rs removeL (CList [] _ rs) = let (f:ls) = reverse rs in CList ls f [] -- |Remove the focus from the CList. removeR :: CList a -> CList a removeR Empty = Empty removeR (CList [] _ []) = Empty removeR (CList l _ (r:rs)) = CList l r rs removeR (CList l _ []) = let (f:rs) = reverse l in CList [] f rs {- Manipulating Rotation -} -- |Return all possible rotations of the provided 'CList', where the -- focus is the provided 'CList'. allRotations :: CList a -> CList (CList a) allRotations Empty = singleton Empty allRotations cl = CList ls cl rs where ls = unfoldr (fmap (join (,)) . mRotL) cl rs = unfoldr (fmap (join (,)) . mRotR) cl -- |Rotate the focus to the previous (left) element. rotL :: CList a -> CList a rotL Empty = Empty rotL r@(CList [] _ []) = r rotL (CList (l:ls) f rs) = CList ls l (f:rs) rotL (CList [] f rs) = let (l:ls) = reverse rs in CList ls l [f] -- |A non-cyclic version of 'rotL'; that is, only rotate the focus if -- there is a previous (left) element to rotate to. mRotL :: CList a -> Maybe (CList a) mRotL (CList (l:ls) f rs) = Just $ CList ls l (f:rs) mRotL _ = Nothing -- |Rotate the focus to the next (right) element. rotR :: CList a -> CList a rotR Empty = Empty rotR r@(CList [] _ []) = r rotR (CList ls f (r:rs)) = CList (f:ls) r rs rotR (CList ls f []) = let (r:rs) = reverse ls in CList [f] r rs -- |A non-cyclic version of 'rotL'; that is, only rotate the focus if -- there is a previous (left) element to rotate to. mRotR :: CList a -> Maybe (CList a) mRotR (CList ls f (r:rs)) = Just $ CList (f:ls) r rs mRotR _ = Nothing -- |Rotate the focus the specified number of times; if the index is -- positive then it is rotated to the right; otherwise it is rotated -- to the left. rotN :: Int -> CList a -> CList a rotN _ Empty = Empty rotN _ cl@(CList [] _ []) = cl rotN n cl = iterate rot cl !! n' where n' = abs n rot | n < 0 = rotL | otherwise = rotR -- |A wrapper around 'rotN' that doesn't rotate the CList if @n <= 0@. rotNR :: Int -> CList a -> CList a rotNR n cl | n <= 0 = cl | otherwise = rotN n cl -- |Rotate the focus the specified number of times to the left (but -- don't rotate if @n <= 0@). rotNL :: Int -> CList a -> CList a rotNL n cl | n <= 0 = cl | otherwise = rotN (negate n) cl -- |Rotate the 'CList' such that the specified element (if it exists) -- is focused. rotateTo :: (Eq a) => a -> CList a -> Maybe (CList a) rotateTo a = findRotateTo (a==) -- |Attempt to rotate the 'CList' such that focused element matches -- the supplied predicate. findRotateTo :: (a -> Bool) -> CList a -> Maybe (CList a) findRotateTo p = find (maybe False p . focus) . toList . allRotations {- List-like functions -} -- |Remove those elements that do not satisfy the supplied predicate, -- rotating to the right if the focus does not satisfy the predicate. filterR :: (a -> Bool) -> CList a -> CList a filterR = filterCL removeR -- |As with 'filterR', but rotates to the /left/ if the focus does not -- satisfy the predicate. filterL :: (a -> Bool) -> CList a -> CList a filterL = filterCL removeL -- |Abstract away what to do with the focused element if it doesn't -- match the predicate when filtering. filterCL :: (CList a -> CList a) -> (a -> Bool) -> CList a -> CList a filterCL _ _ Empty = Empty filterCL rm p (CList l f r) | p f = cl' | otherwise = rm cl' where cl' = CList (filter p l) f (filter p r) -- |A right-fold, rotating to the right through the CList. foldrR :: (a -> b -> b) -> b -> CList a -> b foldrR = foldrCL rightElements -- |A right-fold, rotating to the left through the CList. foldrL :: (a -> b -> b) -> b -> CList a -> b foldrL = foldrCL leftElements -- |Abstract away direction for a foldr. foldrCL :: (CList a -> [a]) -> (a -> b -> b) -> b -> CList a -> b foldrCL toL f a = foldr f a . toL -- |A (strict) left-fold, rotating to the right through the CList. foldlR :: (a -> b -> a) -> a -> CList b -> a foldlR = foldlCL rightElements -- |A (strict) left-fold, rotating to the left through the CList. foldlL :: (a -> b -> a) -> a -> CList b -> a foldlL = foldlCL leftElements -- |Abstract away direction for a foldl'. foldlCL :: (CList b -> [b]) -> (a -> b -> a) -> a -> CList b -> a foldlCL toL f a = foldl' f a . toL {- Manipulating Packing -} -- |Balance the CList. Equivalent to `fromList . toList` balance :: CList a -> CList a balance = fromList . toList -- |Move all elements to the left side of the CList. packL :: CList a -> CList a packL Empty = Empty packL (CList l f r) = CList (l ++ (reverse r)) f [] -- |Move all elements to the right side of the CList. packR :: CList a -> CList a packR Empty = Empty packR (CList l f r) = CList [] f (r ++ (reverse l)) {- Information -} -- |Returns true if the CList is empty. isEmpty :: CList a -> Bool isEmpty Empty = True isEmpty _ = False -- |Return the size of the CList. size :: CList a -> Int size Empty = 0 size (CList l _ r) = 1 + (length l) + (length r) {- Instances -} instance (Show a) => Show (CList a) where showsPrec d cl = showParen (d > 10) $ showString "fromList " . shows (toList cl) instance (Read a) => Read (CList a) where readsPrec p = readParen (p > 10) $ \ r -> do ("fromList",s) <- lex r (xs,t) <- reads s return (fromList xs,t) instance (Eq a) => Eq (CList a) where a == b = any (identical a) . toList $ allRotations b -- |Determine if two 'CList's are structurally identical. identical :: (Eq a) => CList a -> CList a -> Bool identical Empty Empty = True identical (CList ls1 f1 rs1) (CList ls2 f2 rs2) = f1 == f2 && ls1 == ls2 && rs1 == rs2 identical _ _ = False instance Arbitrary a => Arbitrary (CList a) where arbitrary = frequency [(1, return Empty), (10, arbCList)] where arbCList = do l <- arbitrary f <- arbitrary r <- arbitrary return $ CList l f r shrink (CList l f r) = Empty : [ CList l' f' r' | l' <- shrink l, f' <- shrink f, r' <- shrink r] shrink Empty = [] instance Functor CList where fmap _ Empty = Empty fmap fn (CList l f r) = (CList (fmap fn l) (fn f) (fmap fn r))