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Toy Splay Tree in Haskell
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| import Data.Maybe (isJust) | |
| data Tree a = Leaf | Node (Tree a) a (Tree a) | |
| replace :: a -> Tree a -> Tree a | |
| replace a Leaf = Node Leaf a Leaf | |
| replace a (Node l _ r) = Node l a r | |
| rotateR :: Tree a -> Tree a | |
| rotateR (Node (Node x a y) b z) = Node x a (Node y b z) | |
| rotateL :: Tree a -> Tree a | |
| rotateL (Node x a (Node y b z)) = Node (Node x a y) b z | |
| data Context a = Root | L a (Tree a) (Context a) | R a (Tree a) (Context a) | |
| data Zipper a = Zipper (Tree a) (Context a) | |
| update :: (Tree a -> Tree a) -> Zipper a -> Zipper a | |
| update f (Zipper t c) = Zipper (f t) c | |
| downto :: Ord a => a -> Zipper a -> Zipper a | |
| downto _ z@(Zipper Leaf _) = z | |
| downto a z@(Zipper (Node l b r) c) = case compare a b of | |
| EQ -> z | |
| LT -> downto a $ Zipper l (L b r c) | |
| GT -> downto a $ Zipper r (R b l c) | |
| up :: Zipper a -> Zipper a | |
| up z@(Zipper _ Root) = z | |
| up (Zipper l (L a r c)) = Zipper (Node l a r) c | |
| up (Zipper r (R a l c)) = Zipper (Node l a r) c | |
| fromZipper :: Zipper a -> Tree a | |
| fromZipper (Zipper t Root) = t | |
| fromZipper z = fromZipper $ up z | |
| toZipper :: Tree a -> Zipper a | |
| toZipper = flip Zipper Root | |
| empty :: Tree a | |
| empty = Leaf | |
| splay :: Zipper a -> Zipper a | |
| splay z@(Zipper _ Root) = z | |
| splay z@(Zipper _ (L _ _ Root)) = update rotateR . up $ z | |
| splay z@(Zipper _ (R _ _ Root)) = update rotateL . up $ z | |
| splay z@(Zipper _ (L _ _ (L _ _ _))) = splay . update rotateR . up . update rotateR . up $ z | |
| splay z@(Zipper _ (L _ _ (R _ _ _))) = splay . update rotateL . up . update rotateR . up $ z | |
| splay z@(Zipper _ (R _ _ (L _ _ _))) = splay . update rotateR . up . update rotateL . up $ z | |
| splay z@(Zipper _ (R _ _ (R _ _ _))) = splay . update rotateL . up . update rotateL . up $ z | |
| locate :: Ord a => a -> Tree a -> Maybe (Tree a) | |
| locate a t = case downto a $ toZipper t of | |
| Zipper Leaf _ -> Nothing | |
| z -> Just . fromZipper . splay . update (replace a) $ z | |
| member :: Ord a => a -> Tree a -> Bool | |
| member a = isJust . locate a | |
| insert :: Ord a => a -> Tree a -> Tree a | |
| insert a = fromZipper . update (replace a) . downto a . toZipper | |
| fromList :: Ord a => [a] -> Tree a | |
| fromList = foldr insert empty | |
| toList :: Tree a -> [a] | |
| toList Leaf = [] | |
| toList (Node l a r) = toList l ++ [a] ++ toList r | |
| edges :: Tree a -> [(a, a)] | |
| edges Leaf = [] | |
| edges (Node Leaf _ Leaf) = [] | |
| edges (Node l@(Node _ b _) a Leaf) = (a, b) : edges l | |
| edges (Node Leaf a r@(Node _ b _)) = (a, b) : edges r | |
| edges (Node l@(Node _ b _) a r@(Node _ c _)) = (a, b) : (a, c) : edges l ++ edges r | |
| dot :: Show a => Tree a -> String | |
| dot t = "digraph tree { " ++ concatMap f (edges t) ++ "}" | |
| where f (a, b) = show a ++ " -> " ++ show b ++ "; " | |
| main :: IO () | |
| main = do | |
| let t = fromList [1, 9, 3, 2, 7, 4, 6, 2, 1, 8, 5] | |
| Just t <- return $ locate 1 t | |
| Just t <- return $ locate 2 t | |
| Just t <- return $ locate 3 t | |
| Just t <- return $ locate 4 t | |
| Just t <- return $ locate 5 t | |
| Just t <- return $ locate 6 t | |
| Just t <- return $ locate 7 t | |
| Just t <- return $ locate 8 t | |
| Just t <- return $ locate 9 t | |
| putStrLn . dot $ t |
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