{-# LANGUAGE CPP, NoBangPatterns, MagicHash, ScopedTypeVariables #-} ----------------------------------------------------------------------------- -- | -- Module : Data.IntMap -- Copyright : (c) Daan Leijen 2002 -- (c) Andriy Palamarchuk 2008 -- License : BSD-style -- Maintainer : libraries@haskell.org -- Stability : provisional -- Portability : portable -- -- An efficient implementation of maps from integer keys to values. -- -- Since many function names (but not the type name) clash with -- "Prelude" names, this module is usually imported @qualified@, e.g. -- -- > import Data.IntMap (IntMap) -- > import qualified Data.IntMap as IntMap -- -- The implementation is based on /big-endian patricia trees/. This data -- structure performs especially well on binary operations like 'union' -- and 'intersection'. However, my benchmarks show that it is also -- (much) faster on insertions and deletions when compared to a generic -- size-balanced map implementation (see "Data.Map"). -- -- * Chris Okasaki and Andy Gill, \"/Fast Mergeable Integer Maps/\", -- Workshop on ML, September 1998, pages 77-86, -- <http://citeseer.ist.psu.edu/okasaki98fast.html> -- -- * D.R. Morrison, \"/PATRICIA -- Practical Algorithm To Retrieve -- Information Coded In Alphanumeric/\", Journal of the ACM, 15(4), -- October 1968, pages 514-534. -- -- Operation comments contain the operation time complexity in -- the Big-O notation <http://en.wikipedia.org/wiki/Big_O_notation>. -- Many operations have a worst-case complexity of /O(min(n,W))/. -- This means that the operation can become linear in the number of -- elements with a maximum of /W/ -- the number of bits in an 'Int' -- (32 or 64). ----------------------------------------------------------------------------- -- It is essential that the bit fiddling functions like mask, zero, branchMask -- etc are inlined. If they do not, the memory allocation skyrockets. The GHC -- usually gets it right, but it is disastrous if it does not. Therefore we -- explicitly mark these functions INLINE. module Data.IntMap ( -- * Map type #if !defined(TESTING) IntMap, Key -- instance Eq,Show #else IntMap(..), Key -- instance Eq,Show #endif -- * Operators , (!), (\\) -- * Query , null , size , member , notMember , lookup , findWithDefault -- * Construction , empty , singleton -- ** Insertion , insert , insertWith , insertWith' , insertWithKey , insertWithKey' , insertLookupWithKey -- ** Delete\/Update , delete , adjust , adjustWithKey , update , updateWithKey , updateLookupWithKey , alter -- * Combine -- ** Union , union , unionWith , unionWithKey , unions , unionsWith -- ** Difference , difference , differenceWith , differenceWithKey -- ** Intersection , intersection , intersectionWith , intersectionWithKey -- * Traversal -- ** Map , map , mapWithKey , mapAccum , mapAccumWithKey , mapAccumRWithKey -- ** Fold , fold , foldWithKey -- * Conversion , elems , keys , keysSet , assocs -- ** Lists , toList , fromList , fromListWith , fromListWithKey -- ** Ordered lists , toAscList , fromAscList , fromAscListWith , fromAscListWithKey , fromDistinctAscList -- * Filter , filter , filterWithKey , partition , partitionWithKey , mapMaybe , mapMaybeWithKey , mapEither , mapEitherWithKey , split , splitLookup -- * Submap , isSubmapOf, isSubmapOfBy , isProperSubmapOf, isProperSubmapOfBy -- * Min\/Max , findMin , findMax , deleteMin , deleteMax , deleteFindMin , deleteFindMax , updateMin , updateMax , updateMinWithKey , updateMaxWithKey , minView , maxView , minViewWithKey , maxViewWithKey -- * Debugging , showTree , showTreeWith ) where import Prelude hiding (lookup,map,filter,foldr,foldl,null) import Data.Bits import qualified Data.IntSet as IntSet import Data.Monoid (Monoid(..)) import Data.Maybe (fromMaybe) import Data.Typeable import Data.Foldable (Foldable(foldMap)) import Data.Traversable (Traversable(traverse)) import Control.Applicative (Applicative(pure,(<*>)),(<$>)) import Control.Monad ( liftM ) {- -- just for testing import qualified Prelude import Test.QuickCheck import List (nub,sort) import qualified List -} #if __GLASGOW_HASKELL__ import Text.Read import Data.Data (Data(..), mkNoRepType) #endif #if __GLASGOW_HASKELL__ >= 503 import GHC.Exts ( Word(..), Int(..), shiftRL# ) #elif __GLASGOW_HASKELL__ import Word import GlaExts ( Word(..), Int(..), shiftRL# ) #else import Data.Word #endif infixl 9 \\{-This comment teaches CPP correct behaviour -} -- A "Nat" is a natural machine word (an unsigned Int) type Nat = Word natFromInt :: Key -> Nat natFromInt = fromIntegral {-# INLINE natFromInt #-} intFromNat :: Nat -> Key intFromNat = fromIntegral {-# INLINE intFromNat #-} shiftRL :: Nat -> Key -> Nat #if __GLASGOW_HASKELL__ {-------------------------------------------------------------------- GHC: use unboxing to get @shiftRL@ inlined. --------------------------------------------------------------------} shiftRL (W# x) (I# i) = W# (shiftRL# x i) #else shiftRL x i = shiftR x i {-# INLINE shiftRL #-} #endif {-------------------------------------------------------------------- Operators --------------------------------------------------------------------} -- | /O(min(n,W))/. Find the value at a key. -- Calls 'error' when the element can not be found. -- -- > fromList [(5,'a'), (3,'b')] ! 1 Error: element not in the map -- > fromList [(5,'a'), (3,'b')] ! 5 == 'a' (!) :: IntMap a -> Key -> a m ! k = find k m -- | Same as 'difference'. (\\) :: IntMap a -> IntMap b -> IntMap a m1 \\ m2 = difference m1 m2 {-------------------------------------------------------------------- Types --------------------------------------------------------------------} -- | A map of integers to values @a@. data IntMap a = Nil | Tip {-# UNPACK #-} !Key a | Bin {-# UNPACK #-} !Prefix {-# UNPACK #-} !Mask !(IntMap a) !(IntMap a) type Prefix = Int type Mask = Int type Key = Int instance Monoid (IntMap a) where mempty = empty mappend = union mconcat = unions instance Foldable IntMap where foldMap _ Nil = mempty foldMap f (Tip _k v) = f v foldMap f (Bin _ _ l r) = foldMap f l `mappend` foldMap f r instance Traversable IntMap where traverse _ Nil = pure Nil traverse f (Tip k v) = Tip k <$> f v traverse f (Bin p m l r) = Bin p m <$> traverse f l <*> traverse f r #if __GLASGOW_HASKELL__ {-------------------------------------------------------------------- A Data instance --------------------------------------------------------------------} -- This instance preserves data abstraction at the cost of inefficiency. -- We omit reflection services for the sake of data abstraction. instance Data a => Data (IntMap a) where gfoldl f z im = z fromList `f` (toList im) toConstr _ = error "toConstr" gunfold _ _ = error "gunfold" dataTypeOf _ = mkNoRepType "Data.IntMap.IntMap" dataCast1 f = gcast1 f #endif {-------------------------------------------------------------------- Query --------------------------------------------------------------------} -- | /O(1)/. Is the map empty? -- -- > Data.IntMap.null (empty) == True -- > Data.IntMap.null (singleton 1 'a') == False null :: IntMap a -> Bool null Nil = True null _ = False -- | /O(n)/. Number of elements in the map. -- -- > size empty == 0 -- > size (singleton 1 'a') == 1 -- > size (fromList([(1,'a'), (2,'c'), (3,'b')])) == 3 size :: IntMap a -> Int size t = case t of Bin _ _ l r -> size l + size r Tip _ _ -> 1 Nil -> 0 -- | /O(min(n,W))/. Is the key a member of the map? -- -- > member 5 (fromList [(5,'a'), (3,'b')]) == True -- > member 1 (fromList [(5,'a'), (3,'b')]) == False member :: Key -> IntMap a -> Bool member k m = case lookup k m of Nothing -> False Just _ -> True -- | /O(log n)/. Is the key not a member of the map? -- -- > notMember 5 (fromList [(5,'a'), (3,'b')]) == False -- > notMember 1 (fromList [(5,'a'), (3,'b')]) == True notMember :: Key -> IntMap a -> Bool notMember k m = not $ member k m -- The 'go' function in the lookup causes 10% speedup, but also an increased -- memory allocation. It does not cause speedup with other methods like insert -- and delete, so it is present only in lookup. -- | /O(min(n,W))/. Lookup the value at a key in the map. See also 'Data.Map.lookup'. lookup :: Key -> IntMap a -> Maybe a lookup k = k `seq` go where go (Bin _ m l r) | zero k m = go l | otherwise = go r go (Tip kx x) | k == kx = Just x | otherwise = Nothing go Nil = Nothing find :: Key -> IntMap a -> a find k m = case lookup k m of Nothing -> error ("IntMap.find: key " ++ show k ++ " is not an element of the map") Just x -> x -- | /O(min(n,W))/. The expression @('findWithDefault' def k map)@ -- returns the value at key @k@ or returns @def@ when the key is not an -- element of the map. -- -- > findWithDefault 'x' 1 (fromList [(5,'a'), (3,'b')]) == 'x' -- > findWithDefault 'x' 5 (fromList [(5,'a'), (3,'b')]) == 'a' findWithDefault :: a -> Key -> IntMap a -> a findWithDefault def k m = case lookup k m of Nothing -> def Just x -> x {-------------------------------------------------------------------- Construction --------------------------------------------------------------------} -- | /O(1)/. The empty map. -- -- > empty == fromList [] -- > size empty == 0 empty :: IntMap a empty = Nil -- | /O(1)/. A map of one element. -- -- > singleton 1 'a' == fromList [(1, 'a')] -- > size (singleton 1 'a') == 1 singleton :: Key -> a -> IntMap a singleton k x = Tip k x {-------------------------------------------------------------------- Insert --------------------------------------------------------------------} -- | /O(min(n,W))/. Insert a new key\/value pair in the map. -- If the key is already present in the map, the associated value is -- replaced with the supplied value, i.e. 'insert' is equivalent to -- @'insertWith' 'const'@. -- -- > insert 5 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'x')] -- > insert 7 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'a'), (7, 'x')] -- > insert 5 'x' empty == singleton 5 'x' insert :: Key -> a -> IntMap a -> IntMap a insert k x t = k `seq` case t of Bin p m l r | nomatch k p m -> join k (Tip k x) p t | zero k m -> Bin p m (insert k x l) r | otherwise -> Bin p m l (insert k x r) Tip ky _ | k==ky -> Tip k x | otherwise -> join k (Tip k x) ky t Nil -> Tip k x -- right-biased insertion, used by 'union' -- | /O(min(n,W))/. Insert with a combining function. -- @'insertWith' f key value mp@ -- will insert the pair (key, value) into @mp@ if key does -- not exist in the map. If the key does exist, the function will -- insert @f new_value old_value@. -- -- > insertWith (++) 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "xxxa")] -- > insertWith (++) 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")] -- > insertWith (++) 5 "xxx" empty == singleton 5 "xxx" insertWith :: (a -> a -> a) -> Key -> a -> IntMap a -> IntMap a insertWith f k x t = insertWithKey (\_ x' y' -> f x' y') k x t -- | Same as 'insertWith', but the combining function is applied strictly. insertWith' :: (a -> a -> a) -> Key -> a -> IntMap a -> IntMap a insertWith' f k x t = insertWithKey' (\_ x' y' -> f x' y') k x t -- | /O(min(n,W))/. Insert with a combining function. -- @'insertWithKey' f key value mp@ -- will insert the pair (key, value) into @mp@ if key does -- not exist in the map. If the key does exist, the function will -- insert @f key new_value old_value@. -- -- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value -- > insertWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:xxx|a")] -- > insertWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")] -- > insertWithKey f 5 "xxx" empty == singleton 5 "xxx" insertWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> IntMap a insertWithKey f k x t = k `seq` case t of Bin p m l r | nomatch k p m -> join k (Tip k x) p t | zero k m -> Bin p m (insertWithKey f k x l) r | otherwise -> Bin p m l (insertWithKey f k x r) Tip ky y | k==ky -> Tip k (f k x y) | otherwise -> join k (Tip k x) ky t Nil -> Tip k x -- | Same as 'insertWithKey', but the combining function is applied strictly. insertWithKey' :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> IntMap a insertWithKey' f k x t = k `seq` case t of Bin p m l r | nomatch k p m -> join k (Tip k x) p t | zero k m -> Bin p m (insertWithKey' f k x l) r | otherwise -> Bin p m l (insertWithKey' f k x r) Tip ky y | k==ky -> let x' = f k x y in seq x' (Tip k x') | otherwise -> join k (Tip k x) ky t Nil -> Tip k x -- | /O(min(n,W))/. The expression (@'insertLookupWithKey' f k x map@) -- is a pair where the first element is equal to (@'lookup' k map@) -- and the second element equal to (@'insertWithKey' f k x map@). -- -- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value -- > insertLookupWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:xxx|a")]) -- > insertLookupWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a"), (7, "xxx")]) -- > insertLookupWithKey f 5 "xxx" empty == (Nothing, singleton 5 "xxx") -- -- This is how to define @insertLookup@ using @insertLookupWithKey@: -- -- > let insertLookup kx x t = insertLookupWithKey (\_ a _ -> a) kx x t -- > insertLookup 5 "x" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "x")]) -- > insertLookup 7 "x" (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a"), (7, "x")]) insertLookupWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> (Maybe a, IntMap a) insertLookupWithKey f k x t = k `seq` case t of Bin p m l r | nomatch k p m -> (Nothing,join k (Tip k x) p t) | zero k m -> let (found,l') = insertLookupWithKey f k x l in (found,Bin p m l' r) | otherwise -> let (found,r') = insertLookupWithKey f k x r in (found,Bin p m l r') Tip ky y | k==ky -> (Just y,Tip k (f k x y)) | otherwise -> (Nothing,join k (Tip k x) ky t) Nil -> (Nothing,Tip k x) {-------------------------------------------------------------------- Deletion [delete] is the inlined version of [deleteWith (\k x -> Nothing)] --------------------------------------------------------------------} -- | /O(min(n,W))/. Delete a key and its value from the map. When the key is not -- a member of the map, the original map is returned. -- -- > delete 5 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" -- > delete 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] -- > delete 5 empty == empty delete :: Key -> IntMap a -> IntMap a delete k t = k `seq` case t of Bin p m l r | nomatch k p m -> t | zero k m -> bin p m (delete k l) r | otherwise -> bin p m l (delete k r) Tip ky _ | k==ky -> Nil | otherwise -> t Nil -> Nil -- | /O(min(n,W))/. Adjust a value at a specific key. When the key is not -- a member of the map, the original map is returned. -- -- > adjust ("new " ++) 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")] -- > adjust ("new " ++) 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] -- > adjust ("new " ++) 7 empty == empty adjust :: (a -> a) -> Key -> IntMap a -> IntMap a adjust f k m = adjustWithKey (\_ x -> f x) k m -- | /O(min(n,W))/. Adjust a value at a specific key. When the key is not -- a member of the map, the original map is returned. -- -- > let f key x = (show key) ++ ":new " ++ x -- > adjustWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")] -- > adjustWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] -- > adjustWithKey f 7 empty == empty adjustWithKey :: (Key -> a -> a) -> Key -> IntMap a -> IntMap a adjustWithKey f = updateWithKey (\k' x -> Just (f k' x)) -- | /O(min(n,W))/. The expression (@'update' f k map@) updates the value @x@ -- at @k@ (if it is in the map). If (@f x@) is 'Nothing', the element is -- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y@. -- -- > let f x = if x == "a" then Just "new a" else Nothing -- > update f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")] -- > update f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] -- > update f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" update :: (a -> Maybe a) -> Key -> IntMap a -> IntMap a update f = updateWithKey (\_ x -> f x) -- | /O(min(n,W))/. The expression (@'update' f k map@) updates the value @x@ -- at @k@ (if it is in the map). If (@f k x@) is 'Nothing', the element is -- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y@. -- -- > let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing -- > updateWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")] -- > updateWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] -- > updateWithKey f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" updateWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> IntMap a updateWithKey f k t = k `seq` case t of Bin p m l r | nomatch k p m -> t | zero k m -> bin p m (updateWithKey f k l) r | otherwise -> bin p m l (updateWithKey f k r) Tip ky y | k==ky -> case (f k y) of Just y' -> Tip ky y' Nothing -> Nil | otherwise -> t Nil -> Nil -- | /O(min(n,W))/. Lookup and update. -- The function returns original value, if it is updated. -- This is different behavior than 'Data.Map.updateLookupWithKey'. -- Returns the original key value if the map entry is deleted. -- -- > let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing -- > updateLookupWithKey f 5 (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:new a")]) -- > updateLookupWithKey f 7 (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a")]) -- > updateLookupWithKey f 3 (fromList [(5,"a"), (3,"b")]) == (Just "b", singleton 5 "a") updateLookupWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> (Maybe a,IntMap a) updateLookupWithKey f k t = k `seq` case t of Bin p m l r | nomatch k p m -> (Nothing,t) | zero k m -> let (found,l') = updateLookupWithKey f k l in (found,bin p m l' r) | otherwise -> let (found,r') = updateLookupWithKey f k r in (found,bin p m l r') Tip ky y | k==ky -> case (f k y) of Just y' -> (Just y,Tip ky y') Nothing -> (Just y,Nil) | otherwise -> (Nothing,t) Nil -> (Nothing,Nil) -- | /O(log n)/. The expression (@'alter' f k map@) alters the value @x@ at @k@, or absence thereof. -- 'alter' can be used to insert, delete, or update a value in an 'IntMap'. -- In short : @'lookup' k ('alter' f k m) = f ('lookup' k m)@. alter :: (Maybe a -> Maybe a) -> Key -> IntMap a -> IntMap a alter f k t = k `seq` case t of Bin p m l r | nomatch k p m -> case f Nothing of Nothing -> t Just x -> join k (Tip k x) p t | zero k m -> bin p m (alter f k l) r | otherwise -> bin p m l (alter f k r) Tip ky y | k==ky -> case f (Just y) of Just x -> Tip ky x Nothing -> Nil | otherwise -> case f Nothing of Just x -> join k (Tip k x) ky t Nothing -> Tip ky y Nil -> case f Nothing of Just x -> Tip k x Nothing -> Nil {-------------------------------------------------------------------- Union --------------------------------------------------------------------} -- | The union of a list of maps. -- -- > unions [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])] -- > == fromList [(3, "b"), (5, "a"), (7, "C")] -- > unions [(fromList [(5, "A3"), (3, "B3")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "a"), (3, "b")])] -- > == fromList [(3, "B3"), (5, "A3"), (7, "C")] unions :: [IntMap a] -> IntMap a unions xs = foldlStrict union empty xs -- | The union of a list of maps, with a combining operation. -- -- > unionsWith (++) [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])] -- > == fromList [(3, "bB3"), (5, "aAA3"), (7, "C")] unionsWith :: (a->a->a) -> [IntMap a] -> IntMap a unionsWith f ts = foldlStrict (unionWith f) empty ts -- | /O(n+m)/. The (left-biased) union of two maps. -- It prefers the first map when duplicate keys are encountered, -- i.e. (@'union' == 'unionWith' 'const'@). -- -- > union (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "a"), (7, "C")] union :: IntMap a -> IntMap a -> IntMap a union t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2) | shorter m1 m2 = union1 | shorter m2 m1 = union2 | p1 == p2 = Bin p1 m1 (union l1 l2) (union r1 r2) | otherwise = join p1 t1 p2 t2 where union1 | nomatch p2 p1 m1 = join p1 t1 p2 t2 | zero p2 m1 = Bin p1 m1 (union l1 t2) r1 | otherwise = Bin p1 m1 l1 (union r1 t2) union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2 | zero p1 m2 = Bin p2 m2 (union t1 l2) r2 | otherwise = Bin p2 m2 l2 (union t1 r2) union (Tip k x) t = insert k x t union t (Tip k x) = insertWith (\_ y -> y) k x t -- right bias union Nil t = t union t Nil = t -- | /O(n+m)/. The union with a combining function. -- -- > unionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "aA"), (7, "C")] unionWith :: (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a unionWith f m1 m2 = unionWithKey (\_ x y -> f x y) m1 m2 -- | /O(n+m)/. The union with a combining function. -- -- > let f key left_value right_value = (show key) ++ ":" ++ left_value ++ "|" ++ right_value -- > unionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "5:a|A"), (7, "C")] unionWithKey :: (Key -> a -> a -> a) -> IntMap a -> IntMap a -> IntMap a unionWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2) | shorter m1 m2 = union1 | shorter m2 m1 = union2 | p1 == p2 = Bin p1 m1 (unionWithKey f l1 l2) (unionWithKey f r1 r2) | otherwise = join p1 t1 p2 t2 where union1 | nomatch p2 p1 m1 = join p1 t1 p2 t2 | zero p2 m1 = Bin p1 m1 (unionWithKey f l1 t2) r1 | otherwise = Bin p1 m1 l1 (unionWithKey f r1 t2) union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2 | zero p1 m2 = Bin p2 m2 (unionWithKey f t1 l2) r2 | otherwise = Bin p2 m2 l2 (unionWithKey f t1 r2) unionWithKey f (Tip k x) t = insertWithKey f k x t unionWithKey f t (Tip k x) = insertWithKey (\k' x' y' -> f k' y' x') k x t -- right bias unionWithKey _ Nil t = t unionWithKey _ t Nil = t {-------------------------------------------------------------------- Difference --------------------------------------------------------------------} -- | /O(n+m)/. Difference between two maps (based on keys). -- -- > difference (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 3 "b" difference :: IntMap a -> IntMap b -> IntMap a difference t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2) | shorter m1 m2 = difference1 | shorter m2 m1 = difference2 | p1 == p2 = bin p1 m1 (difference l1 l2) (difference r1 r2) | otherwise = t1 where difference1 | nomatch p2 p1 m1 = t1 | zero p2 m1 = bin p1 m1 (difference l1 t2) r1 | otherwise = bin p1 m1 l1 (difference r1 t2) difference2 | nomatch p1 p2 m2 = t1 | zero p1 m2 = difference t1 l2 | otherwise = difference t1 r2 difference t1@(Tip k _) t2 | member k t2 = Nil | otherwise = t1 difference Nil _ = Nil difference t (Tip k _) = delete k t difference t Nil = t -- | /O(n+m)/. Difference with a combining function. -- -- > let f al ar = if al == "b" then Just (al ++ ":" ++ ar) else Nothing -- > differenceWith f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (7, "C")]) -- > == singleton 3 "b:B" differenceWith :: (a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a differenceWith f m1 m2 = differenceWithKey (\_ x y -> f x y) m1 m2 -- | /O(n+m)/. Difference with a combining function. When two equal keys are -- encountered, the combining function is applied to the key and both values. -- If it returns 'Nothing', the element is discarded (proper set difference). -- If it returns (@'Just' y@), the element is updated with a new value @y@. -- -- > let f k al ar = if al == "b" then Just ((show k) ++ ":" ++ al ++ "|" ++ ar) else Nothing -- > differenceWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (10, "C")]) -- > == singleton 3 "3:b|B" differenceWithKey :: (Key -> a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a differenceWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2) | shorter m1 m2 = difference1 | shorter m2 m1 = difference2 | p1 == p2 = bin p1 m1 (differenceWithKey f l1 l2) (differenceWithKey f r1 r2) | otherwise = t1 where difference1 | nomatch p2 p1 m1 = t1 | zero p2 m1 = bin p1 m1 (differenceWithKey f l1 t2) r1 | otherwise = bin p1 m1 l1 (differenceWithKey f r1 t2) difference2 | nomatch p1 p2 m2 = t1 | zero p1 m2 = differenceWithKey f t1 l2 | otherwise = differenceWithKey f t1 r2 differenceWithKey f t1@(Tip k x) t2 = case lookup k t2 of Just y -> case f k x y of Just y' -> Tip k y' Nothing -> Nil Nothing -> t1 differenceWithKey _ Nil _ = Nil differenceWithKey f t (Tip k y) = updateWithKey (\k' x -> f k' x y) k t differenceWithKey _ t Nil = t {-------------------------------------------------------------------- Intersection --------------------------------------------------------------------} -- | /O(n+m)/. The (left-biased) intersection of two maps (based on keys). -- -- > intersection (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "a" intersection :: IntMap a -> IntMap b -> IntMap a intersection t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2) | shorter m1 m2 = intersection1 | shorter m2 m1 = intersection2 | p1 == p2 = bin p1 m1 (intersection l1 l2) (intersection r1 r2) | otherwise = Nil where intersection1 | nomatch p2 p1 m1 = Nil | zero p2 m1 = intersection l1 t2 | otherwise = intersection r1 t2 intersection2 | nomatch p1 p2 m2 = Nil | zero p1 m2 = intersection t1 l2 | otherwise = intersection t1 r2 intersection t1@(Tip k _) t2 | member k t2 = t1 | otherwise = Nil intersection t (Tip k _) = case lookup k t of Just y -> Tip k y Nothing -> Nil intersection Nil _ = Nil intersection _ Nil = Nil -- | /O(n+m)/. The intersection with a combining function. -- -- > intersectionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "aA" intersectionWith :: (a -> b -> c) -> IntMap a -> IntMap b -> IntMap c intersectionWith f m1 m2 = intersectionWithKey (\_ x y -> f x y) m1 m2 -- | /O(n+m)/. The intersection with a combining function. -- -- > let f k al ar = (show k) ++ ":" ++ al ++ "|" ++ ar -- > intersectionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "5:a|A" intersectionWithKey :: (Key -> a -> b -> c) -> IntMap a -> IntMap b -> IntMap c intersectionWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2) | shorter m1 m2 = intersection1 | shorter m2 m1 = intersection2 | p1 == p2 = bin p1 m1 (intersectionWithKey f l1 l2) (intersectionWithKey f r1 r2) | otherwise = Nil where intersection1 | nomatch p2 p1 m1 = Nil | zero p2 m1 = intersectionWithKey f l1 t2 | otherwise = intersectionWithKey f r1 t2 intersection2 | nomatch p1 p2 m2 = Nil | zero p1 m2 = intersectionWithKey f t1 l2 | otherwise = intersectionWithKey f t1 r2 intersectionWithKey f (Tip k x) t2 = case lookup k t2 of Just y -> Tip k (f k x y) Nothing -> Nil intersectionWithKey f t1 (Tip k y) = case lookup k t1 of Just x -> Tip k (f k x y) Nothing -> Nil intersectionWithKey _ Nil _ = Nil intersectionWithKey _ _ Nil = Nil {-------------------------------------------------------------------- Min\/Max --------------------------------------------------------------------} -- | /O(log n)/. Update the value at the minimal key. -- -- > updateMinWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"3:b"), (5,"a")] -- > updateMinWithKey (\ _ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" updateMinWithKey :: (Key -> a -> a) -> IntMap a -> IntMap a updateMinWithKey f t = case t of Bin p m l r | m < 0 -> let t' = updateMinWithKeyUnsigned f r in Bin p m l t' Bin p m l r -> let t' = updateMinWithKeyUnsigned f l in Bin p m t' r Tip k y -> Tip k (f k y) Nil -> error "maxView: empty map has no maximal element" updateMinWithKeyUnsigned :: (Key -> a -> a) -> IntMap a -> IntMap a updateMinWithKeyUnsigned f t = case t of Bin p m l r -> let t' = updateMinWithKeyUnsigned f l in Bin p m t' r Tip k y -> Tip k (f k y) Nil -> error "updateMinWithKeyUnsigned Nil" -- | /O(log n)/. Update the value at the maximal key. -- -- > updateMaxWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"b"), (5,"5:a")] -- > updateMaxWithKey (\ _ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" updateMaxWithKey :: (Key -> a -> a) -> IntMap a -> IntMap a updateMaxWithKey f t = case t of Bin p m l r | m < 0 -> let t' = updateMaxWithKeyUnsigned f l in Bin p m t' r Bin p m l r -> let t' = updateMaxWithKeyUnsigned f r in Bin p m l t' Tip k y -> Tip k (f k y) Nil -> error "maxView: empty map has no maximal element" updateMaxWithKeyUnsigned :: (Key -> a -> a) -> IntMap a -> IntMap a updateMaxWithKeyUnsigned f t = case t of Bin p m l r -> let t' = updateMaxWithKeyUnsigned f r in Bin p m l t' Tip k y -> Tip k (f k y) Nil -> error "updateMaxWithKeyUnsigned Nil" -- | /O(log n)/. Retrieves the maximal (key,value) pair of the map, and -- the map stripped of that element, or 'Nothing' if passed an empty map. -- -- > maxViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((5,"a"), singleton 3 "b") -- > maxViewWithKey empty == Nothing maxViewWithKey :: IntMap a -> Maybe ((Key, a), IntMap a) maxViewWithKey t = case t of Bin p m l r | m < 0 -> let (result, t') = maxViewUnsigned l in Just (result, bin p m t' r) Bin p m l r -> let (result, t') = maxViewUnsigned r in Just (result, bin p m l t') Tip k y -> Just ((k,y), Nil) Nil -> Nothing maxViewUnsigned :: IntMap a -> ((Key, a), IntMap a) maxViewUnsigned t = case t of Bin p m l r -> let (result,t') = maxViewUnsigned r in (result,bin p m l t') Tip k y -> ((k,y), Nil) Nil -> error "maxViewUnsigned Nil" -- | /O(log n)/. Retrieves the minimal (key,value) pair of the map, and -- the map stripped of that element, or 'Nothing' if passed an empty map. -- -- > minViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((3,"b"), singleton 5 "a") -- > minViewWithKey empty == Nothing minViewWithKey :: IntMap a -> Maybe ((Key, a), IntMap a) minViewWithKey t = case t of Bin p m l r | m < 0 -> let (result, t') = minViewUnsigned r in Just (result, bin p m l t') Bin p m l r -> let (result, t') = minViewUnsigned l in Just (result, bin p m t' r) Tip k y -> Just ((k,y),Nil) Nil -> Nothing minViewUnsigned :: IntMap a -> ((Key, a), IntMap a) minViewUnsigned t = case t of Bin p m l r -> let (result,t') = minViewUnsigned l in (result,bin p m t' r) Tip k y -> ((k,y),Nil) Nil -> error "minViewUnsigned Nil" -- | /O(log n)/. Update the value at the maximal key. -- -- > updateMax (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "Xa")] -- > updateMax (\ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" updateMax :: (a -> a) -> IntMap a -> IntMap a updateMax f = updateMaxWithKey (const f) -- | /O(log n)/. Update the value at the minimal key. -- -- > updateMin (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "Xb"), (5, "a")] -- > updateMin (\ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" updateMin :: (a -> a) -> IntMap a -> IntMap a updateMin f = updateMinWithKey (const f) -- Similar to the Arrow instance. first :: (a -> c) -> (a, b) -> (c, b) first f (x,y) = (f x,y) -- | /O(log n)/. Retrieves the maximal key of the map, and the map -- stripped of that element, or 'Nothing' if passed an empty map. maxView :: IntMap a -> Maybe (a, IntMap a) maxView t = liftM (first snd) (maxViewWithKey t) -- | /O(log n)/. Retrieves the minimal key of the map, and the map -- stripped of that element, or 'Nothing' if passed an empty map. minView :: IntMap a -> Maybe (a, IntMap a) minView t = liftM (first snd) (minViewWithKey t) -- | /O(log n)/. Delete and find the maximal element. deleteFindMax :: IntMap a -> (a, IntMap a) deleteFindMax = fromMaybe (error "deleteFindMax: empty map has no maximal element") . maxView -- | /O(log n)/. Delete and find the minimal element. deleteFindMin :: IntMap a -> (a, IntMap a) deleteFindMin = fromMaybe (error "deleteFindMin: empty map has no minimal element") . minView -- | /O(log n)/. The minimal key of the map. findMin :: IntMap a -> (Key, a) findMin Nil = error $ "findMin: empty map has no minimal element" findMin (Tip k v) = (k,v) findMin (Bin _ m l r) | m < 0 = go r | otherwise = go l where go (Tip k v) = (k,v) go (Bin _ _ l' _) = go l' go Nil = error "findMax Nil" -- | /O(log n)/. The maximal key of the map. findMax :: IntMap a -> (Key, a) findMax Nil = error $ "findMax: empty map has no maximal element" findMax (Tip k v) = (k,v) findMax (Bin _ m l r) | m < 0 = go l | otherwise = go r where go (Tip k v) = (k,v) go (Bin _ _ _ r') = go r' go Nil = error "findMax Nil" -- | /O(log n)/. Delete the minimal key. An error is thrown if the IntMap is already empty. -- Note, this is not the same behavior Map. deleteMin :: IntMap a -> IntMap a deleteMin = maybe (error "deleteMin: empty map has no minimal element") snd . minView -- | /O(log n)/. Delete the maximal key. An error is thrown if the IntMap is already empty. -- Note, this is not the same behavior Map. deleteMax :: IntMap a -> IntMap a deleteMax = maybe (error "deleteMax: empty map has no maximal element") snd . maxView {-------------------------------------------------------------------- Submap --------------------------------------------------------------------} -- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal). -- Defined as (@'isProperSubmapOf' = 'isProperSubmapOfBy' (==)@). isProperSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool isProperSubmapOf m1 m2 = isProperSubmapOfBy (==) m1 m2 {- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal). The expression (@'isProperSubmapOfBy' f m1 m2@) returns 'True' when @m1@ and @m2@ are not equal, all keys in @m1@ are in @m2@, and when @f@ returns 'True' when applied to their respective values. For example, the following expressions are all 'True': > isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) > isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) But the following are all 'False': > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)]) > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)]) > isProperSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) -} isProperSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool isProperSubmapOfBy predicate t1 t2 = case submapCmp predicate t1 t2 of LT -> True _ -> False submapCmp :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Ordering submapCmp predicate t1@(Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2) | shorter m1 m2 = GT | shorter m2 m1 = submapCmpLt | p1 == p2 = submapCmpEq | otherwise = GT -- disjoint where submapCmpLt | nomatch p1 p2 m2 = GT | zero p1 m2 = submapCmp predicate t1 l2 | otherwise = submapCmp predicate t1 r2 submapCmpEq = case (submapCmp predicate l1 l2, submapCmp predicate r1 r2) of (GT,_ ) -> GT (_ ,GT) -> GT (EQ,EQ) -> EQ _ -> LT submapCmp _ (Bin _ _ _ _) _ = GT submapCmp predicate (Tip kx x) (Tip ky y) | (kx == ky) && predicate x y = EQ | otherwise = GT -- disjoint submapCmp predicate (Tip k x) t = case lookup k t of Just y | predicate x y -> LT _ -> GT -- disjoint submapCmp _ Nil Nil = EQ submapCmp _ Nil _ = LT -- | /O(n+m)/. Is this a submap? -- Defined as (@'isSubmapOf' = 'isSubmapOfBy' (==)@). isSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool isSubmapOf m1 m2 = isSubmapOfBy (==) m1 m2 {- | /O(n+m)/. The expression (@'isSubmapOfBy' f m1 m2@) returns 'True' if all keys in @m1@ are in @m2@, and when @f@ returns 'True' when applied to their respective values. For example, the following expressions are all 'True': > isSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) > isSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)]) But the following are all 'False': > isSubmapOfBy (==) (fromList [(1,2)]) (fromList [(1,1),(2,2)]) > isSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)]) -} isSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool isSubmapOfBy predicate t1@(Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2) | shorter m1 m2 = False | shorter m2 m1 = match p1 p2 m2 && (if zero p1 m2 then isSubmapOfBy predicate t1 l2 else isSubmapOfBy predicate t1 r2) | otherwise = (p1==p2) && isSubmapOfBy predicate l1 l2 && isSubmapOfBy predicate r1 r2 isSubmapOfBy _ (Bin _ _ _ _) _ = False isSubmapOfBy predicate (Tip k x) t = case lookup k t of Just y -> predicate x y Nothing -> False isSubmapOfBy _ Nil _ = True {-------------------------------------------------------------------- Mapping --------------------------------------------------------------------} -- | /O(n)/. Map a function over all values in the map. -- -- > map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")] map :: (a -> b) -> IntMap a -> IntMap b map f = mapWithKey (\_ x -> f x) -- | /O(n)/. Map a function over all values in the map. -- -- > let f key x = (show key) ++ ":" ++ x -- > mapWithKey f (fromList [(5,"a"), (3,"b")]) == fromList [(3, "3:b"), (5, "5:a")] mapWithKey :: (Key -> a -> b) -> IntMap a -> IntMap b mapWithKey f t = case t of Bin p m l r -> Bin p m (mapWithKey f l) (mapWithKey f r) Tip k x -> Tip k (f k x) Nil -> Nil -- | /O(n)/. The function @'mapAccum'@ threads an accumulating -- argument through the map in ascending order of keys. -- -- > let f a b = (a ++ b, b ++ "X") -- > mapAccum f "Everything: " (fromList [(5,"a"), (3,"b")]) == ("Everything: ba", fromList [(3, "bX"), (5, "aX")]) mapAccum :: (a -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c) mapAccum f = mapAccumWithKey (\a' _ x -> f a' x) -- | /O(n)/. The function @'mapAccumWithKey'@ threads an accumulating -- argument through the map in ascending order of keys. -- -- > let f a k b = (a ++ " " ++ (show k) ++ "-" ++ b, b ++ "X") -- > mapAccumWithKey f "Everything:" (fromList [(5,"a"), (3,"b")]) == ("Everything: 3-b 5-a", fromList [(3, "bX"), (5, "aX")]) mapAccumWithKey :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c) mapAccumWithKey f a t = mapAccumL f a t -- | /O(n)/. The function @'mapAccumL'@ threads an accumulating -- argument through the map in ascending order of keys. mapAccumL :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c) mapAccumL f a t = case t of Bin p m l r -> let (a1,l') = mapAccumL f a l (a2,r') = mapAccumL f a1 r in (a2,Bin p m l' r') Tip k x -> let (a',x') = f a k x in (a',Tip k x') Nil -> (a,Nil) -- | /O(n)/. The function @'mapAccumR'@ threads an accumulating -- argument through the map in descending order of keys. mapAccumRWithKey :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c) mapAccumRWithKey f a t = case t of Bin p m l r -> let (a1,r') = mapAccumRWithKey f a r (a2,l') = mapAccumRWithKey f a1 l in (a2,Bin p m l' r') Tip k x -> let (a',x') = f a k x in (a',Tip k x') Nil -> (a,Nil) {-------------------------------------------------------------------- Filter --------------------------------------------------------------------} -- | /O(n)/. Filter all values that satisfy some predicate. -- -- > filter (> "a") (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" -- > filter (> "x") (fromList [(5,"a"), (3,"b")]) == empty -- > filter (< "a") (fromList [(5,"a"), (3,"b")]) == empty filter :: (a -> Bool) -> IntMap a -> IntMap a filter p m = filterWithKey (\_ x -> p x) m -- | /O(n)/. Filter all keys\/values that satisfy some predicate. -- -- > filterWithKey (\k _ -> k > 4) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" filterWithKey :: (Key -> a -> Bool) -> IntMap a -> IntMap a filterWithKey predicate t = case t of Bin p m l r -> bin p m (filterWithKey predicate l) (filterWithKey predicate r) Tip k x | predicate k x -> t | otherwise -> Nil Nil -> Nil -- | /O(n)/. Partition the map according to some predicate. The first -- map contains all elements that satisfy the predicate, the second all -- elements that fail the predicate. See also 'split'. -- -- > partition (> "a") (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a") -- > partition (< "x") (fromList [(5,"a"), (3,"b")]) == (fromList [(3, "b"), (5, "a")], empty) -- > partition (> "x") (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3, "b"), (5, "a")]) partition :: (a -> Bool) -> IntMap a -> (IntMap a,IntMap a) partition p m = partitionWithKey (\_ x -> p x) m -- | /O(n)/. Partition the map according to some predicate. The first -- map contains all elements that satisfy the predicate, the second all -- elements that fail the predicate. See also 'split'. -- -- > partitionWithKey (\ k _ -> k > 3) (fromList [(5,"a"), (3,"b")]) == (singleton 5 "a", singleton 3 "b") -- > partitionWithKey (\ k _ -> k < 7) (fromList [(5,"a"), (3,"b")]) == (fromList [(3, "b"), (5, "a")], empty) -- > partitionWithKey (\ k _ -> k > 7) (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3, "b"), (5, "a")]) partitionWithKey :: (Key -> a -> Bool) -> IntMap a -> (IntMap a,IntMap a) partitionWithKey predicate t = case t of Bin p m l r -> let (l1,l2) = partitionWithKey predicate l (r1,r2) = partitionWithKey predicate r in (bin p m l1 r1, bin p m l2 r2) Tip k x | predicate k x -> (t,Nil) | otherwise -> (Nil,t) Nil -> (Nil,Nil) -- | /O(n)/. Map values and collect the 'Just' results. -- -- > let f x = if x == "a" then Just "new a" else Nothing -- > mapMaybe f (fromList [(5,"a"), (3,"b")]) == singleton 5 "new a" mapMaybe :: (a -> Maybe b) -> IntMap a -> IntMap b mapMaybe f = mapMaybeWithKey (\_ x -> f x) -- | /O(n)/. Map keys\/values and collect the 'Just' results. -- -- > let f k _ = if k < 5 then Just ("key : " ++ (show k)) else Nothing -- > mapMaybeWithKey f (fromList [(5,"a"), (3,"b")]) == singleton 3 "key : 3" mapMaybeWithKey :: (Key -> a -> Maybe b) -> IntMap a -> IntMap b mapMaybeWithKey f (Bin p m l r) = bin p m (mapMaybeWithKey f l) (mapMaybeWithKey f r) mapMaybeWithKey f (Tip k x) = case f k x of Just y -> Tip k y Nothing -> Nil mapMaybeWithKey _ Nil = Nil -- | /O(n)/. Map values and separate the 'Left' and 'Right' results. -- -- > let f a = if a < "c" then Left a else Right a -- > mapEither f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) -- > == (fromList [(3,"b"), (5,"a")], fromList [(1,"x"), (7,"z")]) -- > -- > mapEither (\ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) -- > == (empty, fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) mapEither :: (a -> Either b c) -> IntMap a -> (IntMap b, IntMap c) mapEither f m = mapEitherWithKey (\_ x -> f x) m -- | /O(n)/. Map keys\/values and separate the 'Left' and 'Right' results. -- -- > let f k a = if k < 5 then Left (k * 2) else Right (a ++ a) -- > mapEitherWithKey f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) -- > == (fromList [(1,2), (3,6)], fromList [(5,"aa"), (7,"zz")]) -- > -- > mapEitherWithKey (\_ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) -- > == (empty, fromList [(1,"x"), (3,"b"), (5,"a"), (7,"z")]) mapEitherWithKey :: (Key -> a -> Either b c) -> IntMap a -> (IntMap b, IntMap c) mapEitherWithKey f (Bin p m l r) = (bin p m l1 r1, bin p m l2 r2) where (l1,l2) = mapEitherWithKey f l (r1,r2) = mapEitherWithKey f r mapEitherWithKey f (Tip k x) = case f k x of Left y -> (Tip k y, Nil) Right z -> (Nil, Tip k z) mapEitherWithKey _ Nil = (Nil, Nil) -- | /O(log n)/. The expression (@'split' k map@) is a pair @(map1,map2)@ -- where all keys in @map1@ are lower than @k@ and all keys in -- @map2@ larger than @k@. Any key equal to @k@ is found in neither @map1@ nor @map2@. -- -- > split 2 (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3,"b"), (5,"a")]) -- > split 3 (fromList [(5,"a"), (3,"b")]) == (empty, singleton 5 "a") -- > split 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a") -- > split 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", empty) -- > split 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], empty) split :: Key -> IntMap a -> (IntMap a,IntMap a) split k t = case t of Bin _ m l r | m < 0 -> (if k >= 0 -- handle negative numbers. then let (lt,gt) = split' k l in (union r lt, gt) else let (lt,gt) = split' k r in (lt, union gt l)) | otherwise -> split' k t Tip ky _ | k>ky -> (t,Nil) | k<ky -> (Nil,t) | otherwise -> (Nil,Nil) Nil -> (Nil,Nil) split' :: Key -> IntMap a -> (IntMap a,IntMap a) split' k t = case t of Bin p m l r | nomatch k p m -> if k>p then (t,Nil) else (Nil,t) | zero k m -> let (lt,gt) = split k l in (lt,union gt r) | otherwise -> let (lt,gt) = split k r in (union l lt,gt) Tip ky _ | k>ky -> (t,Nil) | k<ky -> (Nil,t) | otherwise -> (Nil,Nil) Nil -> (Nil,Nil) -- | /O(log n)/. Performs a 'split' but also returns whether the pivot -- key was found in the original map. -- -- > splitLookup 2 (fromList [(5,"a"), (3,"b")]) == (empty, Nothing, fromList [(3,"b"), (5,"a")]) -- > splitLookup 3 (fromList [(5,"a"), (3,"b")]) == (empty, Just "b", singleton 5 "a") -- > splitLookup 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Nothing, singleton 5 "a") -- > splitLookup 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Just "a", empty) -- > splitLookup 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], Nothing, empty) splitLookup :: Key -> IntMap a -> (IntMap a,Maybe a,IntMap a) splitLookup k t = case t of Bin _ m l r | m < 0 -> (if k >= 0 -- handle negative numbers. then let (lt,found,gt) = splitLookup' k l in (union r lt,found, gt) else let (lt,found,gt) = splitLookup' k r in (lt,found, union gt l)) | otherwise -> splitLookup' k t Tip ky y | k>ky -> (t,Nothing,Nil) | k<ky -> (Nil,Nothing,t) | otherwise -> (Nil,Just y,Nil) Nil -> (Nil,Nothing,Nil) splitLookup' :: Key -> IntMap a -> (IntMap a,Maybe a,IntMap a) splitLookup' k t = case t of Bin p m l r | nomatch k p m -> if k>p then (t,Nothing,Nil) else (Nil,Nothing,t) | zero k m -> let (lt,found,gt) = splitLookup k l in (lt,found,union gt r) | otherwise -> let (lt,found,gt) = splitLookup k r in (union l lt,found,gt) Tip ky y | k>ky -> (t,Nothing,Nil) | k<ky -> (Nil,Nothing,t) | otherwise -> (Nil,Just y,Nil) Nil -> (Nil,Nothing,Nil) {-------------------------------------------------------------------- Fold --------------------------------------------------------------------} -- | /O(n)/. Fold the values in the map, such that -- @'fold' f z == 'Prelude.foldr' f z . 'elems'@. -- For example, -- -- > elems map = fold (:) [] map -- -- > let f a len = len + (length a) -- > fold f 0 (fromList [(5,"a"), (3,"bbb")]) == 4 fold :: (a -> b -> b) -> b -> IntMap a -> b fold f = foldWithKey (\_ x y -> f x y) {-# INLINE fold #-} -- | /O(n)/. Fold the keys and values in the map, such that -- @'foldWithKey' f z == 'Prelude.foldr' ('uncurry' f) z . 'toAscList'@. -- For example, -- -- > keys map = foldWithKey (\k x ks -> k:ks) [] map -- -- > let f k a result = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")" -- > foldWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (5:a)(3:b)" foldWithKey :: (Key -> a -> b -> b) -> b -> IntMap a -> b foldWithKey = foldr {-# INLINE foldWithKey #-} foldr :: (Key -> a -> b -> b) -> b -> IntMap a -> b foldr f z t = case t of Bin 0 m l r | m < 0 -> go (go z l) r -- put negative numbers before. Bin _ _ _ _ -> go z t Tip k x -> f k x z Nil -> z where go z' (Bin _ _ l r) = go (go z' r) l go z' (Tip k x) = f k x z' go z' Nil = z' {-# INLINE foldr #-} {-------------------------------------------------------------------- List variations --------------------------------------------------------------------} -- | /O(n)/. -- Return all elements of the map in the ascending order of their keys. -- -- > elems (fromList [(5,"a"), (3,"b")]) == ["b","a"] -- > elems empty == [] elems :: IntMap a -> [a] elems = foldWithKey (\_ x xs -> x:xs) [] -- | /O(n)/. Return all keys of the map in ascending order. -- -- > keys (fromList [(5,"a"), (3,"b")]) == [3,5] -- > keys empty == [] keys :: IntMap a -> [Key] keys = foldWithKey (\k _ ks -> k:ks) [] -- | /O(n*min(n,W))/. The set of all keys of the map. -- -- > keysSet (fromList [(5,"a"), (3,"b")]) == Data.IntSet.fromList [3,5] -- > keysSet empty == Data.IntSet.empty keysSet :: IntMap a -> IntSet.IntSet keysSet m = IntSet.fromDistinctAscList (keys m) -- | /O(n)/. Return all key\/value pairs in the map in ascending key order. -- -- > assocs (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")] -- > assocs empty == [] assocs :: IntMap a -> [(Key,a)] assocs m = toList m {-------------------------------------------------------------------- Lists --------------------------------------------------------------------} -- | /O(n)/. Convert the map to a list of key\/value pairs. -- -- > toList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")] -- > toList empty == [] toList :: IntMap a -> [(Key,a)] toList = foldWithKey (\k x xs -> (k,x):xs) [] -- | /O(n)/. Convert the map to a list of key\/value pairs where the -- keys are in ascending order. -- -- > toAscList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")] toAscList :: IntMap a -> [(Key,a)] toAscList t = -- NOTE: the following algorithm only works for big-endian trees let (pos,neg) = span (\(k,_) -> k >=0) (foldr (\k x xs -> (k,x):xs) [] t) in neg ++ pos -- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs. -- -- > fromList [] == empty -- > fromList [(5,"a"), (3,"b"), (5, "c")] == fromList [(5,"c"), (3,"b")] -- > fromList [(5,"c"), (3,"b"), (5, "a")] == fromList [(5,"a"), (3,"b")] fromList :: [(Key,a)] -> IntMap a fromList xs = foldlStrict ins empty xs where ins t (k,x) = insert k x t -- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs with a combining function. See also 'fromAscListWith'. -- -- > fromListWith (++) [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"a")] == fromList [(3, "ab"), (5, "aba")] -- > fromListWith (++) [] == empty fromListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a fromListWith f xs = fromListWithKey (\_ x y -> f x y) xs -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs with a combining function. See also fromAscListWithKey'. -- -- > fromListWith (++) [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"a")] == fromList [(3, "ab"), (5, "aba")] -- > fromListWith (++) [] == empty fromListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a fromListWithKey f xs = foldlStrict ins empty xs where ins t (k,x) = insertWithKey f k x t -- | /O(n)/. Build a map from a list of key\/value pairs where -- the keys are in ascending order. -- -- > fromAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")] -- > fromAscList [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "b")] fromAscList :: [(Key,a)] -> IntMap a fromAscList xs = fromAscListWithKey (\_ x _ -> x) xs -- | /O(n)/. Build a map from a list of key\/value pairs where -- the keys are in ascending order, with a combining function on equal keys. -- /The precondition (input list is ascending) is not checked./ -- -- > fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "ba")] fromAscListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a fromAscListWith f xs = fromAscListWithKey (\_ x y -> f x y) xs -- | /O(n)/. Build a map from a list of key\/value pairs where -- the keys are in ascending order, with a combining function on equal keys. -- /The precondition (input list is ascending) is not checked./ -- -- > fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "ba")] fromAscListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a fromAscListWithKey _ [] = Nil fromAscListWithKey f (x0 : xs0) = fromDistinctAscList (combineEq x0 xs0) where -- [combineEq f xs] combines equal elements with function [f] in an ordered list [xs] combineEq z [] = [z] combineEq z@(kz,zz) (x@(kx,xx):xs) | kx==kz = let yy = f kx xx zz in combineEq (kx,yy) xs | otherwise = z:combineEq x xs -- | /O(n)/. Build a map from a list of key\/value pairs where -- the keys are in ascending order and all distinct. -- /The precondition (input list is strictly ascending) is not checked./ -- -- > fromDistinctAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")] #ifdef __GLASGOW_HASKELL__ fromDistinctAscList :: forall a. [(Key,a)] -> IntMap a #else fromDistinctAscList :: [(Key,a)] -> IntMap a #endif fromDistinctAscList [] = Nil fromDistinctAscList (z0 : zs0) = work z0 zs0 Nada where work (kx,vx) [] stk = finish kx (Tip kx vx) stk work (kx,vx) (z@(kz,_):zs) stk = reduce z zs (branchMask kx kz) kx (Tip kx vx) stk #ifdef __GLASGOW_HASKELL__ reduce :: (Key,a) -> [(Key,a)] -> Mask -> Prefix -> IntMap a -> Stack a -> IntMap a #endif reduce z zs _ px tx Nada = work z zs (Push px tx Nada) reduce z zs m px tx stk@(Push py ty stk') = let mxy = branchMask px py pxy = mask px mxy in if shorter m mxy then reduce z zs m pxy (Bin pxy mxy ty tx) stk' else work z zs (Push px tx stk) finish _ t Nada = t finish px tx (Push py ty stk) = finish p (join py ty px tx) stk where m = branchMask px py p = mask px m data Stack a = Push {-# UNPACK #-} !Prefix !(IntMap a) !(Stack a) | Nada {-------------------------------------------------------------------- Eq --------------------------------------------------------------------} instance Eq a => Eq (IntMap a) where t1 == t2 = equal t1 t2 t1 /= t2 = nequal t1 t2 equal :: Eq a => IntMap a -> IntMap a -> Bool equal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2) = (m1 == m2) && (p1 == p2) && (equal l1 l2) && (equal r1 r2) equal (Tip kx x) (Tip ky y) = (kx == ky) && (x==y) equal Nil Nil = True equal _ _ = False nequal :: Eq a => IntMap a -> IntMap a -> Bool nequal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2) = (m1 /= m2) || (p1 /= p2) || (nequal l1 l2) || (nequal r1 r2) nequal (Tip kx x) (Tip ky y) = (kx /= ky) || (x/=y) nequal Nil Nil = False nequal _ _ = True {-------------------------------------------------------------------- Ord --------------------------------------------------------------------} instance Ord a => Ord (IntMap a) where compare m1 m2 = compare (toList m1) (toList m2) {-------------------------------------------------------------------- Functor --------------------------------------------------------------------} instance Functor IntMap where fmap = map {-------------------------------------------------------------------- Show --------------------------------------------------------------------} instance Show a => Show (IntMap a) where showsPrec d m = showParen (d > 10) $ showString "fromList " . shows (toList m) {- XXX unused code showMap :: (Show a) => [(Key,a)] -> ShowS showMap [] = showString "{}" showMap (x:xs) = showChar '{' . showElem x . showTail xs where showTail [] = showChar '}' showTail (x':xs') = showChar ',' . showElem x' . showTail xs' showElem (k,v) = shows k . showString ":=" . shows v -} {-------------------------------------------------------------------- Read --------------------------------------------------------------------} instance (Read e) => Read (IntMap e) 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 --------------------------------------------------------------------} #include "Typeable.h" INSTANCE_TYPEABLE1(IntMap,intMapTc,"IntMap") {-------------------------------------------------------------------- Debugging --------------------------------------------------------------------} -- | /O(n)/. Show the tree that implements the map. The tree is shown -- in a compressed, hanging format. showTree :: Show a => IntMap a -> String showTree s = showTreeWith True False s {- | /O(n)/. The expression (@'showTreeWith' hang wide map@) shows the tree that implements the map. If @hang@ is 'True', a /hanging/ tree is shown otherwise a rotated tree is shown. If @wide@ is 'True', an extra wide version is shown. -} showTreeWith :: Show a => Bool -> Bool -> IntMap a -> String showTreeWith hang wide t | hang = (showsTreeHang wide [] t) "" | otherwise = (showsTree wide [] [] t) "" showsTree :: Show a => Bool -> [String] -> [String] -> IntMap a -> ShowS showsTree wide lbars rbars t = case t of Bin p m l r -> showsTree wide (withBar rbars) (withEmpty rbars) r . showWide wide rbars . showsBars lbars . showString (showBin p m) . showString "\n" . showWide wide lbars . showsTree wide (withEmpty lbars) (withBar lbars) l Tip k x -> showsBars lbars . showString " " . shows k . showString ":=" . shows x . showString "\n" Nil -> showsBars lbars . showString "|\n" showsTreeHang :: Show a => Bool -> [String] -> IntMap a -> ShowS showsTreeHang wide bars t = case t of Bin p m l r -> showsBars bars . showString (showBin p m) . showString "\n" . showWide wide bars . showsTreeHang wide (withBar bars) l . showWide wide bars . showsTreeHang wide (withEmpty bars) r Tip k x -> showsBars bars . showString " " . shows k . showString ":=" . shows x . showString "\n" Nil -> showsBars bars . showString "|\n" showBin :: Prefix -> Mask -> String showBin _ _ = "*" -- ++ show (p,m) showWide :: Bool -> [String] -> String -> String showWide wide bars | wide = showString (concat (reverse bars)) . showString "|\n" | otherwise = id showsBars :: [String] -> ShowS showsBars bars = case bars of [] -> id _ -> showString (concat (reverse (tail bars))) . showString node node :: String node = "+--" withBar, withEmpty :: [String] -> [String] withBar bars = "| ":bars withEmpty bars = " ":bars {-------------------------------------------------------------------- Helpers --------------------------------------------------------------------} {-------------------------------------------------------------------- Join --------------------------------------------------------------------} join :: Prefix -> IntMap a -> Prefix -> IntMap a -> IntMap a join p1 t1 p2 t2 | zero p1 m = Bin p m t1 t2 | otherwise = Bin p m t2 t1 where m = branchMask p1 p2 p = mask p1 m {-# INLINE join #-} {-------------------------------------------------------------------- @bin@ assures that we never have empty trees within a tree. --------------------------------------------------------------------} bin :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a bin _ _ l Nil = l bin _ _ Nil r = r bin p m l r = Bin p m l r {-# INLINE bin #-} {-------------------------------------------------------------------- Endian independent bit twiddling --------------------------------------------------------------------} zero :: Key -> Mask -> Bool zero i m = (natFromInt i) .&. (natFromInt m) == 0 {-# INLINE zero #-} nomatch,match :: Key -> Prefix -> Mask -> Bool nomatch i p m = (mask i m) /= p {-# INLINE nomatch #-} match i p m = (mask i m) == p {-# INLINE match #-} mask :: Key -> Mask -> Prefix mask i m = maskW (natFromInt i) (natFromInt m) {-# INLINE mask #-} {-------------------------------------------------------------------- Big endian operations --------------------------------------------------------------------} maskW :: Nat -> Nat -> Prefix maskW i m = intFromNat (i .&. (complement (m-1) `xor` m)) {-# INLINE maskW #-} shorter :: Mask -> Mask -> Bool shorter m1 m2 = (natFromInt m1) > (natFromInt m2) {-# INLINE shorter #-} branchMask :: Prefix -> Prefix -> Mask branchMask p1 p2 = intFromNat (highestBitMask (natFromInt p1 `xor` natFromInt p2)) {-# INLINE branchMask #-} {---------------------------------------------------------------------- Finding the highest bit (mask) in a word [x] can be done efficiently in three ways: * convert to a floating point value and the mantissa tells us the [log2(x)] that corresponds with the highest bit position. The mantissa is retrieved either via the standard C function [frexp] or by some bit twiddling on IEEE compatible numbers (float). Note that one needs to use at least [double] precision for an accurate mantissa of 32 bit numbers. * use bit twiddling, a logarithmic sequence of bitwise or's and shifts (bit). * use processor specific assembler instruction (asm). The most portable way would be [bit], but is it efficient enough? I have measured the cycle counts of the different methods on an AMD Athlon-XP 1800 (~ Pentium III 1.8Ghz) using the RDTSC instruction: highestBitMask: method cycles -------------- frexp 200 float 33 bit 11 asm 12 highestBit: method cycles -------------- frexp 195 float 33 bit 11 asm 11 Wow, the bit twiddling is on today's RISC like machines even faster than a single CISC instruction (BSR)! ----------------------------------------------------------------------} {---------------------------------------------------------------------- [highestBitMask] returns a word where only the highest bit is set. It is found by first setting all bits in lower positions than the highest bit and than taking an exclusive or with the original value. Allthough the function may look expensive, GHC compiles this into excellent C code that subsequently compiled into highly efficient machine code. The algorithm is derived from Jorg Arndt's FXT library. ----------------------------------------------------------------------} highestBitMask :: Nat -> Nat highestBitMask x0 = case (x0 .|. shiftRL x0 1) of x1 -> case (x1 .|. shiftRL x1 2) of x2 -> case (x2 .|. shiftRL x2 4) of x3 -> case (x3 .|. shiftRL x3 8) of x4 -> case (x4 .|. shiftRL x4 16) of x5 -> case (x5 .|. shiftRL x5 32) of -- for 64 bit platforms x6 -> (x6 `xor` (shiftRL x6 1)) {-# INLINE highestBitMask #-} {-------------------------------------------------------------------- Utilities --------------------------------------------------------------------} foldlStrict :: (a -> b -> a) -> a -> [b] -> a foldlStrict f = go where go z [] = z go z (x:xs) = let z' = f z x in z' `seq` go z' xs {-# INLINE foldlStrict #-}