--
-- An efficient implementation of integer sets.
--
--- This module is intended to be imported @qualified@, to avoid name
--- clashes with "Prelude" functions. eg.
+-- Since many function names (but not the type name) clash with
+-- "Prelude" names, this module is usually imported @qualified@, e.g.
--
--- > import Data.IntSet as Set
+-- > import Data.IntSet (IntSet)
+-- > import qualified Data.IntSet as IntSet
--
-- The implementation is based on /big-endian patricia trees/. This data
-- structure performs especially well on binary operations like 'union'
, null
, size
, member
+ , notMember
, isSubsetOf
, isProperSubsetOf
import Data.Int
import qualified Data.List as List
-import Data.Monoid
+import Data.Monoid (Monoid(..))
import Data.Typeable
{-
-}
#if __GLASGOW_HASKELL__
+import Text.Read
import Data.Generics.Basics
import Data.Generics.Instances
#endif
type Prefix = Int
type Mask = Int
+instance Monoid IntSet where
+ mempty = empty
+ mappend = union
+ mconcat = unions
+
#if __GLASGOW_HASKELL__
{--------------------------------------------------------------------
Tip y -> (x==y)
Nil -> False
+-- | /O(log n)/. Is the element not in the set?
+notMember :: Int -> IntSet -> Bool
+notMember k = not . member k
+
-- 'lookup' is used by 'intersection' for left-biasing
lookup :: Int -> IntSet -> Maybe Int
lookup k t
split x t
= case t of
Bin p m l r
- | zero x m -> let (lt,gt) = split x l in (lt,union gt r)
- | otherwise -> let (lt,gt) = split x r in (union l lt,gt)
+ | m < 0 -> if x >= 0 then let (lt,gt) = split' x l in (union r lt, gt)
+ else let (lt,gt) = split' x r in (lt, union gt l)
+ -- handle negative numbers.
+ | otherwise -> split' x t
+ Tip y
+ | x>y -> (t,Nil)
+ | x<y -> (Nil,t)
+ | otherwise -> (Nil,Nil)
+ Nil -> (Nil, Nil)
+
+split' :: Int -> IntSet -> (IntSet,IntSet)
+split' x t
+ = case t of
+ Bin p m l r
+ | match x p m -> if zero x m then let (lt,gt) = split' x l in (lt,union gt r)
+ else let (lt,gt) = split' x r in (union l lt,gt)
+ | otherwise -> if x < p then (Nil, t)
+ else (t, Nil)
Tip y
| x>y -> (t,Nil)
| x<y -> (Nil,t)
-- | /O(log n)/. Performs a 'split' but also returns whether the pivot
-- element was found in the original set.
-splitMember :: Int -> IntSet -> (Bool,IntSet,IntSet)
+splitMember :: Int -> IntSet -> (IntSet,Bool,IntSet)
splitMember x t
= case t of
Bin p m l r
- | zero x m -> let (found,lt,gt) = splitMember x l in (found,lt,union gt r)
- | otherwise -> let (found,lt,gt) = splitMember x r in (found,union l lt,gt)
+ | m < 0 -> if x >= 0 then let (lt,found,gt) = splitMember' x l in (union r lt, found, gt)
+ else let (lt,found,gt) = splitMember' x r in (lt, found, union gt l)
+ -- handle negative numbers.
+ | otherwise -> splitMember' x t
Tip y
- | x>y -> (False,t,Nil)
- | x<y -> (False,Nil,t)
- | otherwise -> (True,Nil,Nil)
- Nil -> (False,Nil,Nil)
+ | x>y -> (t,False,Nil)
+ | x<y -> (Nil,False,t)
+ | otherwise -> (Nil,True,Nil)
+ Nil -> (Nil,False,Nil)
+
+splitMember' :: Int -> IntSet -> (IntSet,Bool,IntSet)
+splitMember' x t
+ = case t of
+ Bin p m l r
+ | match x p m -> if zero x m then let (lt,found,gt) = splitMember x l in (lt,found,union gt r)
+ else let (lt,found,gt) = splitMember x r in (union l lt,found,gt)
+ | otherwise -> if x < p then (Nil, False, t)
+ else (t, False, Nil)
+ Tip y
+ | x>y -> (t,False,Nil)
+ | x<y -> (Nil,False,t)
+ | otherwise -> (Nil,True,Nil)
+ Nil -> (Nil,False,Nil)
{----------------------------------------------------------------------
Map
-- > elems set == fold (:) [] set
fold :: (Int -> b -> b) -> b -> IntSet -> b
fold f z t
- = foldr f z t
+ = case t of
+ Bin 0 m l r | m < 0 -> foldr f (foldr f z l) r
+ -- put negative numbers before.
+ Bin p m l r -> foldr f z t
+ Tip x -> f x z
+ Nil -> z
foldr :: (Int -> b -> b) -> b -> IntSet -> b
foldr f z t
-- | /O(n)/. Convert the set to an ascending list of elements.
toAscList :: IntSet -> [Int]
-toAscList t
- = -- NOTE: the following algorithm only works for big-endian trees
- let (pos,neg) = span (>=0) (foldr (:) [] t) in neg ++ pos
+toAscList t = toList t
-- | /O(n*min(n,W))/. Create a set from a list of integers.
fromList :: [Int] -> IntSet
-- tentative implementation. See if more efficient exists.
{--------------------------------------------------------------------
- Monoid
---------------------------------------------------------------------}
-
-instance Monoid IntSet where
- mempty = empty
- mappend = union
- mconcat = unions
-
-{--------------------------------------------------------------------
Show
--------------------------------------------------------------------}
instance Show IntSet where
- showsPrec d s = showSet (toList s)
+ showsPrec p xs = showParen (p > 10) $
+ showString "fromList " . shows (toList xs)
showSet :: [Int] -> ShowS
showSet []
showTail (x:xs) = showChar ',' . shows x . showTail xs
{--------------------------------------------------------------------
+ Read
+--------------------------------------------------------------------}
+instance Read IntSet where
+#ifdef __GLASGOW_HASKELL__
+ readPrec = parens $ prec 10 $ do
+ Ident "fromList" <- lexP
+ xs <- readPrec
+ return (fromList xs)
+
+ readListPrec = readListPrecDefault
+#else
+ readsPrec p = readParen (p > 10) $ \ r -> do
+ ("fromList",s) <- lex r
+ (xs,t) <- reads s
+ return (fromList xs,t)
+#endif
+
+{--------------------------------------------------------------------
Typeable
--------------------------------------------------------------------}
projects / haskell-directory.git / blobdiff