-- -- Copyright (c) 2009 - 2010 Brendan Hickey - http://bhickey.net -- New BSD License (see http://www.opensource.org/licenses/bsd-license.php) -- module Data.Tree.Splay (SplayTree, head, tail, singleton, empty, null, fromList, fromAscList, toList, toAscList, insert, lookup, (!!), splay, size, delete) where import Prelude hiding (head, tail, lookup, null, (!!)) data (Ord k) => SplayTree k v = Leaf | SplayTree k v Int (SplayTree k v) (SplayTree k v) deriving (Ord, Eq) -- | /O(1)/. 'singleton' constructs a splay tree containing one element. singleton :: (Ord k) => (k,v) -> SplayTree k v singleton (k,v) = SplayTree k v 0 Leaf Leaf -- | /O(1)/. 'empty' constructs an empty splay tree. empty :: (Ord k) => SplayTree k v empty = Leaf -- | /O(1)/. 'null' returns true if a splay tree is empty. null :: (Ord k) => SplayTree k v -> Bool null Leaf = True null _ = False size :: (Ord k) => SplayTree k v -> Int size Leaf = 0 size (SplayTree _ _ d _ _) = d -- | /Amortized O(lg n)/. Given a splay tree and a key, 'lookup' attempts to find a node with the specified key and splays this node to the root. If the key is not found, the nearest node is brought to the root of the tree. lookup :: (Ord k) => k -> SplayTree k v -> SplayTree k v lookup _ Leaf = Leaf lookup k' t@(SplayTree k _ _ l r) | k' == k = t | k > k' = case lookup k' l of Leaf -> t lt -> zig lt t | otherwise = case lookup k' r of Leaf -> t rt -> zag t rt -- | Locates the i^{th} element in BST order without splaying it. (!!) :: (Ord k) => SplayTree k v -> Int -> (k,v) (!!) Leaf _ = error "index out of bounds" (!!) (SplayTree k v d l r) n = if n > d then error "index out of bounds" else let l' = size l in if n == l' then (k,v) else if n <= l' then l !! n else r !! (n - l') -- | Splays the i^{th} element in BST order splay :: (Ord k) => SplayTree k v -> Int -> SplayTree k v splay Leaf _ = error "index out of bounds" splay t@(SplayTree _ _ d l r) n = if n > d then error "index out of bounds" else let l' = size l in if n == l' then t else if n <= l' then case splay l n of Leaf -> error "index out of bounds" lt -> zig lt t else case splay r (n - l') of Leaf -> error "index out of bounds" rt -> zag t rt -- | /O(1)/. zig rotates its first argument up zig :: (Ord k) => SplayTree k v -> SplayTree k v -> SplayTree k v zig Leaf _ = error "tree corruption" zig _ Leaf = error "tree corruption" zig (SplayTree k1 v1 _ l1 r1) (SplayTree k v d _ r) = SplayTree k1 v1 d l1 (SplayTree k v (d - size l1 - 1) r1 r) -- | /O(1)/. zig rotates its second argument up zag :: (Ord k) => SplayTree k v -> SplayTree k v -> SplayTree k v zag Leaf _ = error "tree corruption" zag _ Leaf = error "tree corruption" zag (SplayTree k v d l _) (SplayTree k1 v1 _ l1 r1) = SplayTree k1 v1 d (SplayTree k v (d - size r1 - 1) l l1) r1 -- | /Amortized O(lg n)/. Given a splay tree and a key-value pair, 'insert' places the the pair into the tree in BST order. This function is unsatisfying. insert :: (Ord k) => k -> v -> SplayTree k v -> SplayTree k v insert k v t = case lookup k t of Leaf -> (SplayTree k v 0 Leaf Leaf) (SplayTree k1 v1 d l r) -> if k1 < k then SplayTree k v (d + 1) (SplayTree k1 v1 (d - size r + 1) l Leaf) r else SplayTree k v (d + 1) l (SplayTree k1 v1 (d - size l + 1) Leaf r) -- | /O(1)/. 'head' returns the key-value pair of the root. head :: (Ord k) => SplayTree k v -> (k,v) head Leaf = error "head of empty tree" head (SplayTree k v _ _ _) = (k,v) -- | /Amortized O(lg n)/. 'tail' removes the root of the tree and merges its subtrees tail :: (Ord k) => SplayTree k v -> SplayTree k v tail Leaf = error "tail of empty tree" tail (SplayTree _ _ _ Leaf r) = r tail (SplayTree _ _ _ l Leaf) = l tail (SplayTree _ _ _ l r) = case splayRight l of (SplayTree k v d l1 Leaf) -> (SplayTree k v (d + size r) l1 r) _ -> error "splay tree corruption" delete :: (Ord k) => k -> SplayTree k v -> SplayTree k v delete _ Leaf = Leaf delete k t = case lookup k t of t'@(SplayTree k1 _ _ _ _) -> if k == k1 then tail t' else t' Leaf -> error "splay tree corruption" splayRight :: (Ord k) => SplayTree k v -> SplayTree k v splayRight Leaf = Leaf splayRight h@(SplayTree _ _ _ _ Leaf) = h splayRight (SplayTree k1 v1 d1 l1 (SplayTree k2 v2 _ l2 r2)) = splayRight (SplayTree k2 v2 d1 (SplayTree k1 v1 (d1 - size r2) l1 l2) r2) splayLeft :: (Ord k) => SplayTree k v -> SplayTree k v splayLeft Leaf = Leaf splayLeft h@(SplayTree _ _ _ Leaf _) = h splayLeft (SplayTree k1 v1 d1 (SplayTree k2 v2 _ l2 r2) r1) = splayLeft (SplayTree k2 v2 d1 l2 (SplayTree k1 v1 (d1 - size l2) r2 r1)) -- | /O(n lg n)/. Constructs a splay tree from an unsorted list of key-value pairs. fromList :: (Ord k) => [(k,v)] -> SplayTree k v fromList [] = Leaf fromList l = foldl (\ acc (k,v) -> insert k v acc) Leaf l -- | /O(n lg n)/. Constructs a splay tree from a list of key-value pairs sorted in ascending order. fromAscList :: (Ord k) => [(k,v)] -> SplayTree k v fromAscList = fromList -- | /O(n lg n)/. Converts a splay tree into a list of key-value pairs with no constraint on ordering. toList :: (Ord k) => SplayTree k v -> [(k,v)] toList = toAscList -- | /O(n lg n)/. 'toAscList' converts a splay tree to a list of key-value pairs sorted in ascending order. toAscList :: (Ord k) => SplayTree k v -> [(k,v)] toAscList h@(SplayTree _ _ _ Leaf _) = head h : toAscList (tail h) toAscList Leaf = [] toAscList h = toAscList $ splayLeft h