X-Git-Url: http://git.megacz.com/?a=blobdiff_plain;f=Data%2FIntSet.hs;h=16226082b7f98e8f8475456341746321dc3fd8c5;hb=7c0b04fd273621130062418bb764809c79488dd2;hp=c41ed179f36336a4da9fc6538e3569611ac03520;hpb=a5d8b45865712ab237eee066f37c667f3574f7ac;p=haskell-directory.git

diff --git a/Data/IntSet.hs b/Data/IntSet.hs
index c41ed17..1622608 100644
--- a/Data/IntSet.hs
+++ b/Data/IntSet.hs
@@ -10,10 +10,11 @@
 --
 -- 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'
@@ -46,6 +47,7 @@ module Data.IntSet  (
             , null
             , size
             , member
+            , notMember
             , isSubsetOf
             , isProperSubsetOf
             
@@ -66,6 +68,16 @@ module Data.IntSet  (
             , split
             , splitMember
 
+            -- * Min\/Max
+            , findMin   
+            , findMax
+            , deleteMin
+            , deleteMax
+            , deleteFindMin
+            , deleteFindMax
+            , maxView
+            , minView
+
             -- * Map
 	    , map
 
@@ -91,9 +103,9 @@ module Data.IntSet  (
 
 import Prelude hiding (lookup,filter,foldr,foldl,null,map)
 import Data.Bits 
-import Data.Int
 
 import qualified Data.List as List
+import Data.Monoid (Monoid(..))
 import Data.Typeable
 
 {-
@@ -104,13 +116,12 @@ import qualified List
 -}
 
 #if __GLASGOW_HASKELL__
-import Text.Read (Lexeme(Ident), lexP, parens, prec, readPrec)
-import Data.Generics.Basics
-import Data.Generics.Instances
+import Text.Read
+import Data.Generics.Basics (Data(..), mkNorepType)
+import Data.Generics.Instances ()
 #endif
 
 #if __GLASGOW_HASKELL__ >= 503
-import GHC.Word
 import GHC.Exts ( Word(..), Int(..), shiftRL# )
 #elif __GLASGOW_HASKELL__
 import Word
@@ -155,10 +166,17 @@ m1 \\ m2 = difference m1 m2
 data IntSet = Nil
             | Tip {-# UNPACK #-} !Int
             | Bin {-# UNPACK #-} !Prefix {-# UNPACK #-} !Mask !IntSet !IntSet
+-- Invariant: Nil is never found as a child of Bin.
+
 
 type Prefix = Int
 type Mask   = Int
 
+instance Monoid IntSet where
+    mempty  = empty
+    mappend = union
+    mconcat = unions
+
 #if __GLASGOW_HASKELL__
 
 {--------------------------------------------------------------------
@@ -203,6 +221,10 @@ member x t
       Tip y -> (x==y)
       Nil   -> False
     
+-- | /O(min(n,W))/. 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
@@ -446,7 +468,7 @@ partition pred t
       Nil -> (Nil,Nil)
 
 
--- | /O(log n)/. The expression (@'split' x set@) is a pair @(set1,set2)@
+-- | /O(min(n,W))/. The expression (@'split' x set@) is a pair @(set1,set2)@
 -- where all elements in @set1@ are lower than @x@ and all elements in
 -- @set2@ larger than @x@.
 --
@@ -455,22 +477,54 @@ split :: Int -> IntSet -> (IntSet,IntSet)
 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)
         | otherwise -> (Nil,Nil)
       Nil -> (Nil,Nil)
 
--- | /O(log n)/. Performs a 'split' but also returns whether the pivot
+-- | /O(min(n,W))/. Performs a 'split' but also returns whether the pivot
 -- element was found in the original set.
 splitMember :: Int -> IntSet -> (IntSet,Bool,IntSet)
 splitMember x t
   = case t of
       Bin p m l r
-        | zero x m  -> let (lt,found,gt) = splitMember x l in (lt,found,union gt r)
-        | otherwise -> let (lt,found,gt) = splitMember x r in (union l lt,found,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       -> (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)
@@ -478,6 +532,80 @@ splitMember x t
       Nil -> (Nil,False,Nil)
 
 {----------------------------------------------------------------------
+  Min/Max
+----------------------------------------------------------------------}
+
+-- | /O(min(n,W))/. Retrieves the maximal key of the set, and the set stripped from that element
+-- @fail@s (in the monad) when passed an empty set.
+maxView :: (Monad m) => IntSet -> m (Int, IntSet)
+maxView t
+    = case t of
+        Bin p m l r | m < 0 -> let (result,t') = maxViewUnsigned l in return (result, bin p m t' r)
+        Bin p m l r         -> let (result,t') = maxViewUnsigned r in return (result, bin p m l t')            
+        Tip y -> return (y,Nil)
+        Nil -> fail "maxView: empty set has no maximal element"
+
+maxViewUnsigned :: IntSet -> (Int, IntSet)
+maxViewUnsigned t 
+    = case t of
+        Bin p m l r -> let (result,t') = maxViewUnsigned r in (result, bin p m l t')
+        Tip y -> (y, Nil)
+
+-- | /O(min(n,W))/. Retrieves the minimal key of the set, and the set stripped from that element
+-- @fail@s (in the monad) when passed an empty set.
+minView :: (Monad m) => IntSet -> m (Int, IntSet)
+minView t
+    = case t of
+        Bin p m l r | m < 0 -> let (result,t') = minViewUnsigned r in return (result, bin p m l t')            
+        Bin p m l r         -> let (result,t') = minViewUnsigned l in return (result, bin p m t' r)
+        Tip y -> return (y, Nil)
+        Nil -> fail "minView: empty set has no minimal element"
+
+minViewUnsigned :: IntSet -> (Int, IntSet)
+minViewUnsigned t 
+    = case t of
+        Bin p m l r -> let (result,t') = minViewUnsigned l in (result, bin p m t' r)
+        Tip y -> (y, Nil)
+
+
+-- Duplicate the Identity monad here because base < mtl.
+newtype Identity a = Identity { runIdentity :: a }
+instance Monad Identity where
+	return a = Identity a
+	m >>= k  = k (runIdentity m)
+
+
+-- | /O(min(n,W))/. Delete and find the minimal element.
+-- 
+-- > deleteFindMin set = (findMin set, deleteMin set)
+deleteFindMin :: IntSet -> (Int, IntSet)
+deleteFindMin = runIdentity . minView
+
+-- | /O(min(n,W))/. Delete and find the maximal element.
+-- 
+-- > deleteFindMax set = (findMax set, deleteMax set)
+deleteFindMax :: IntSet -> (Int, IntSet)
+deleteFindMax = runIdentity . maxView
+
+-- | /O(min(n,W))/. The minimal element of a set.
+findMin :: IntSet -> Int
+findMin = fst . runIdentity . minView
+
+-- | /O(min(n,W))/. The maximal element of a set.
+findMax :: IntSet -> Int
+findMax = fst . runIdentity . maxView
+
+-- | /O(min(n,W))/. Delete the minimal element.
+deleteMin :: IntSet -> IntSet
+deleteMin = snd . runIdentity . minView
+
+-- | /O(min(n,W))/. Delete the maximal element.
+deleteMax :: IntSet -> IntSet
+deleteMax = snd . runIdentity . maxView
+
+
+
+{----------------------------------------------------------------------
   Map
 ----------------------------------------------------------------------}
 
@@ -499,7 +627,12 @@ map f = fromList . List.map f . toList
 -- > 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
@@ -526,9 +659,7 @@ toList 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
@@ -604,10 +735,12 @@ instance Read IntSet where
     Ident "fromList" <- lexP
     xs <- readPrec
     return (fromList xs)
+
+  readListPrec = readListPrecDefault
 #else
   readsPrec p = readParen (p > 10) $ \ r -> do
-    ("fromList",s) <- lex
-    (xs,t) <- reads
+    ("fromList",s) <- lex r
+    (xs,t) <- reads s
     return (fromList xs,t)
 #endif