Hi, I checked the Hackage Splay Tree implementation from. http://hackage.haskell.org/packages/archive/TreeStructures/0.0.1/doc/html/sr... Basically it's based on the strategy mentioned in Okasaki's ``Purely Functional Programming'', Chapter 5.4. That in case we traverse twice in left (or right), we rotate the tree, so in long term of view, the tree turns more and more balanced. There are 3 cases for splay: zig-zig case, zig-zag case and zig case according to http://en.wikipedia.org/wiki/Splay_tree So I wonder if Splay tree can also be implemented by using pattern matching in a similar way as red black tree. Here is a draft source code:
data STree a = E -- Empty | Node (STree a) a (STree a) -- left, element, right deriving (Eq, Show)
-- splay by pattern matching splay :: (Eq a) => STree a -> a ->STree a -- zig-zig splay t@(Node (Node (Node a x b) p c) g d) y = if x == y then Node a x (Node b p (Node c g d)) else t splay t@(Node a g (Node b p (Node c x d))) y = if x == y then Node (Node (Node a g b) p c) x d else t -- zig-zag splay t@(Node (Node a p (Node b x c)) g d) y = if x == y then Node (Node a p b) x (Node c g d) else t splay t@(Node a g (Node (Node b x c) p d)) y = if x == y then Node (Node a g b) x (Node c p d) else t -- zig splay t@(Node (Node a x b) p c) y = if x == y then Node a x (Node b p c) else t splay t@(Node a p (Node b x c)) y = if x == y then Node (Node a p b) x c else t -- otherwise splay t _ = t -- insert by using pattern matching insert :: (Ord a) => STree a -> a -> STree a insert E y = Node E y E insert (Node l x r) y | x < y = splay (Node (insert l y) x r) y | otherwise = splay (Node l x (insert r y)) y <<< I am not quite sure if the solution is correct and what about the efficiency of this code. Regards. -- Larry. LIU Xinyu http://sites.google.com/site/algoxyhttp://sites.google.com/site/algoxy/home