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 Copyright (c) 2009 Brendan Hickey  http://bhickey.net
 Simplified BSD License (see http://www.opensource.org/licenses/bsdlicense.php)

module Data.Tree.Splay
(SplayTree, head, tail, singleton, empty, null, fromList, fromAscList, toList, toAscList, insert, lookup)
where
import Prelude hiding (head, tail, lookup, null)
data (Ord k) => SplayTree k v =
Leaf
 SplayTree k v (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 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
  /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) => SplayTree k v > k > SplayTree k v
lookup Leaf _ = Leaf
lookup n@(SplayTree k v l r) sk =
if sk == k
then n
else if k > sk
then case lookup l sk of
Leaf > n
(SplayTree k1 v1 l1 r1) > (SplayTree k1 v1 l1 (SplayTree k v r1 r))
else case lookup r sk of
Leaf > n
(SplayTree k1 v1 l1 r1) > (SplayTree k1 v1 (SplayTree k v l l1) r1)
  /Amortized O(lg n)/. Given a splay tree and a keyvalue pair, 'insert' places the the pair into the tree in BST order.
insert :: (Ord k) => SplayTree k v > (k,v) > SplayTree k v
insert t (k,v) =
case lookup t k of
Leaf > (SplayTree k v Leaf Leaf)
(SplayTree k1 v1 l r) >
if k1 < k
then (SplayTree k v (SplayTree k1 v1 l Leaf) r)
else (SplayTree k v l (SplayTree k1 v1 Leaf r))
  /O(1)/. 'head' returns the keyvalue 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 l1 Leaf) > (SplayTree k v l1 r)
_ > 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 l1 (SplayTree k2 v2 l2 r2)) = splayRight $ (SplayTree k2 v2 (SplayTree k1 v1 l1 l2) r2)
splayLeft :: (Ord k) => SplayTree k v > SplayTree k v
splayLeft Leaf = Leaf
splayLeft h@(SplayTree _ _ Leaf _) = h
splayLeft (SplayTree k1 v1 (SplayTree k2 v2 l2 r2) r1) = splayLeft $ (SplayTree k2 v2 l2 (SplayTree k1 v1 r2 r1))
  /O(n lg n)/. Constructs a splay tree from an unsorted list of keyvalue pairs.
fromList :: (Ord k) => [(k,v)] > SplayTree k v
fromList [] = Leaf
fromList l = foldl (\ acc x > insert acc x) Leaf l
  /O(n lg n)/. Constructs a splay tree from a list of keyvalue 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 keyvalue 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 keyvalue 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
