-{-# OPTIONS -cpp -fglasgow-exts #-}
+{-# OPTIONS -cpp -fglasgow-exts -fno-bang-patterns #-}
-----------------------------------------------------------------------------
+-- |
-- Module : Data.IntMap
-- Copyright : (c) Daan Leijen 2002
-- License : BSD-style
--
-- An efficient implementation of maps from integer keys to values.
--
--- 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.IntMap as Map
+-- > 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'
, null
, size
, member
+ , notMember
, lookup
, findWithDefault
, update
, updateWithKey
, updateLookupWithKey
+ , alter
-- * Combine
, partition
, partitionWithKey
+ , mapMaybe
+ , mapMaybeWithKey
+ , mapEither
+ , mapEitherWithKey
+
, split
, splitLookup
import Prelude hiding (lookup,map,filter,foldr,foldl,null)
import Data.Bits
import Data.Int
-import Data.Monoid
import qualified Data.IntSet as IntSet
+import Data.Monoid (Monoid(..))
import Data.Typeable
+import Data.Foldable (Foldable(foldMap))
{-
-- just for testing
-}
#if __GLASGOW_HASKELL__
+import Text.Read
import Data.Generics.Basics
import Data.Generics.Instances
#endif
Operators
--------------------------------------------------------------------}
--- | /O(min(n,W))/. Find the value of a key. Calls @error@ when the element can not be found.
+-- | /O(min(n,W))/. Find the value at a key.
+-- Calls 'error' when the element can not be found.
(!) :: IntMap a -> Key -> a
m ! k = find' k m
type Mask = Int
type Key = Int
+instance Monoid (IntMap a) where
+ mempty = empty
+ mappend = union
+ mconcat = unions
+
+instance Foldable IntMap where
+ foldMap f Nil = mempty
+ foldMap f (Tip _k v) = f v
+ foldMap f (Bin _ _ l r) = foldMap f l `mappend` foldMap f r
+
+#if __GLASGOW_HASKELL__
+
{--------------------------------------------------------------------
A Data instance
--------------------------------------------------------------------}
-#if __GLASGOW_HASKELL__
-
-- This instance preserves data abstraction at the cost of inefficiency.
-- We omit reflection services for the sake of data abstraction.
toConstr _ = error "toConstr"
gunfold _ _ = error "gunfold"
dataTypeOf _ = mkNorepType "Data.IntMap.IntMap"
+ dataCast1 f = gcast1 f
#endif
Nothing -> False
Just x -> True
--- | /O(min(n,W))/. Lookup the value of a key in the map.
-lookup :: Key -> IntMap a -> Maybe a
-lookup k t
+-- | /O(log n)/. Is the key not a member of the map?
+notMember :: Key -> IntMap a -> Bool
+notMember k m = not $ member k m
+
+-- | /O(min(n,W))/. Lookup the value at a key in the map.
+lookup :: (Monad m) => Key -> IntMap a -> m a
+lookup k t = case lookup' k t of
+ Just x -> return x
+ Nothing -> fail "Data.IntMap.lookup: Key not found"
+
+lookup' :: Key -> IntMap a -> Maybe a
+lookup' k t
= let nk = natFromInt k in seq nk (lookupN nk t)
lookupN :: Nat -> IntMap a -> Maybe a
Just x -> x
--- | /O(min(n,W))/. The expression @(findWithDefault def k map)@ returns the value of key @k@ or returns @def@ when
--- the key is not an element of the map.
+-- | /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 :: a -> Key -> IntMap a -> a
findWithDefault def k m
= case lookup k m of
{--------------------------------------------------------------------
Insert
- 'insert' is the inlined version of 'insertWith (\k x y -> x)'
--------------------------------------------------------------------}
--- | /O(min(n,W))/. Insert a new key\/value pair in the map. When the key
--- is already an element of the set, its value is replaced by the new value,
--- ie. 'insert' is left-biased.
+-- | /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 :: Key -> a -> IntMap a -> IntMap a
insert k x t
= case t of
-- 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 :: (a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
insertWith f k x t
= insertWithKey (\k 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@.
insertWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
insertWithKey f k x t
= case t of
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@).
+-- | /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@).
insertLookupWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> (Maybe a, IntMap a)
insertLookupWithKey f k x t
= case t of
adjustWithKey f k m
= updateWithKey (\k x -> Just (f k x)) k m
--- | /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@.
+-- | /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@.
update :: (a -> Maybe a) -> Key -> IntMap a -> IntMap a
update f k m
= updateWithKey (\k x -> f x) k m
--- | /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@.
+-- | /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@.
updateWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> IntMap a
updateWithKey f k t
= case t of
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 a 'Map'.
+-- In short : @'lookup' k ('alter' f k m) = f ('lookup' k m)@
+alter f k t
+ = 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
--------------------------------------------------------------------}
unionsWith f ts
= foldlStrict (unionWith f) empty ts
--- | /O(n+m)/. The (left-biased) union of two sets.
+-- | /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 :: IntMap a -> IntMap a -> IntMap a
union t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
| shorter m1 m2 = union1
-- | /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@.
+-- 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@.
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
Submap
--------------------------------------------------------------------}
-- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
--- Defined as (@isProperSubmapOf = isProperSubmapOfBy (==)@).
+-- 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
+ 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
+ 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@.
+ 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@:
+ 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)])
submapCmp pred Nil Nil = EQ
submapCmp pred Nil t = LT
--- | /O(n+m)/. Is this a submap? Defined as (@isSubmapOf = isSubmapOfBy (==)@).
+-- | /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
+ 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@.
+ 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@:
+ But the following are all 'False':
> isSubmapOfBy (==) (fromList [(1,2)]) (fromList [(1,1),(2,2)])
> isSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
Tip k x -> Tip k (f k x)
Nil -> Nil
--- | /O(n)/. The function @mapAccum@ threads an accumulating
--- argument through the map in an unspecified order.
+-- | /O(n)/. The function @'mapAccum'@ threads an accumulating
+-- argument through the map in ascending order of keys.
mapAccum :: (a -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
mapAccum f a m
= mapAccumWithKey (\a k x -> f a x) a m
--- | /O(n)/. The function @mapAccumWithKey@ threads an accumulating
--- argument through the map in an unspecified order.
+-- | /O(n)/. The function @'mapAccumWithKey'@ threads an accumulating
+-- argument through the map in ascending order of keys.
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 pre-order.
+-- | /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
Nil -> (a,Nil)
--- | /O(n)/. The function @mapAccumR@ threads an accumulating
--- argument throught the map in post-order.
+-- | /O(n)/. The function @'mapAccumR'@ threads an accumulating
+-- argument throught the map in descending order of keys.
mapAccumR :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
mapAccumR f a t
= case t of
| otherwise -> (Nil,t)
Nil -> (Nil,Nil)
-
--- | /O(log n)/. The expression (@split k map@) is a pair @(map1,map2)@
+-- | /O(n)/. Map values and collect the 'Just' results.
+mapMaybe :: (a -> Maybe b) -> IntMap a -> IntMap b
+mapMaybe f m
+ = mapMaybeWithKey (\k x -> f x) m
+
+-- | /O(n)/. Map keys\/values and collect the 'Just' results.
+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 f Nil = Nil
+
+-- | /O(n)/. Map values and separate the 'Left' and 'Right' results.
+mapEither :: (a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)
+mapEither f m
+ = mapEitherWithKey (\k x -> f x) m
+
+-- | /O(n)/. Map keys\/values and separate the 'Left' and 'Right' results.
+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 f 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 :: Key -> IntMap a -> (IntMap a,IntMap a)
split k t
= case t of
+ Bin p 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 y
+ | 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 y
-- | /O(log n)/. Performs a 'split' but also returns whether the pivot
-- key was found in the original map.
-splitLookup :: Key -> IntMap a -> (Maybe a,IntMap a,IntMap a)
+splitLookup :: Key -> IntMap a -> (IntMap a,Maybe a,IntMap a)
splitLookup k t
= case t of
Bin p m l r
- | zero k m -> let (found,lt,gt) = splitLookup k l in (found,lt,union gt r)
- | otherwise -> let (found,lt,gt) = splitLookup k r in (found,union l lt,gt)
+ | 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 -> (Nothing,t,Nil)
- | k<ky -> (Nothing,Nil,t)
- | otherwise -> (Just y,Nil,Nil)
- Nil -> (Nothing,Nil,Nil)
+ | 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 over the elements of a map in an unspecified order.
+-- | /O(n)/. Fold the values in the map, such that
+-- @'fold' f z == 'Prelude.foldr' f z . 'elems'@.
+-- For example,
--
--- > sum map = fold (+) 0 map
-- > elems map = fold (:) [] map
+--
fold :: (a -> b -> b) -> b -> IntMap a -> b
fold f z t
= foldWithKey (\k x y -> f x y) z t
--- | /O(n)/. Fold over the elements of a map in an unspecified order.
+-- | /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
+--
foldWithKey :: (Key -> a -> b -> b) -> b -> IntMap a -> b
foldWithKey f z t
= foldr f z t
foldr :: (Key -> a -> b -> b) -> b -> IntMap a -> b
foldr f z t
= case t of
- Bin p m l r -> foldr f (foldr f z r) l
+ Bin 0 m l r | m < 0 -> foldr' f (foldr' f z l) r -- put negative numbers before.
+ Bin _ _ _ _ -> foldr' f z t
Tip k x -> f k x z
Nil -> z
+foldr' :: (Key -> a -> b -> b) -> b -> IntMap a -> b
+foldr' f z t
+ = case t of
+ Bin p m l r -> foldr' f (foldr' f z r) l
+ Tip k x -> f k x z
+ Nil -> z
+
+
+
{--------------------------------------------------------------------
List variations
--------------------------------------------------------------------}
--- | /O(n)/. Return all elements of the map.
+-- | /O(n)/.
+-- Return all elements of the map in the ascending order of their keys.
elems :: IntMap a -> [a]
elems m
= foldWithKey (\k x xs -> x:xs) [] m
--- | /O(n)/. Return all keys of the map.
+-- | /O(n)/. Return all keys of the map in ascending order.
keys :: IntMap a -> [Key]
keys m
= foldWithKey (\k x ks -> k:ks) [] m
keysSet m = IntSet.fromDistinctAscList (keys m)
--- | /O(n)/. Return all key\/value pairs in the map.
+-- | /O(n)/. Return all key\/value pairs in the map in ascending key order.
assocs :: IntMap a -> [(Key,a)]
assocs m
= toList m
fmap = map
{--------------------------------------------------------------------
- Monoid
---------------------------------------------------------------------}
-
-instance Ord a => Monoid (IntMap a) where
- mempty = empty
- mappend = union
- mconcat = unions
-
-{--------------------------------------------------------------------
Show
--------------------------------------------------------------------}
instance Show a => Show (IntMap a) where
- showsPrec d t = showMap (toList t)
-
+ showsPrec d m = showParen (d > 10) $
+ showString "fromList " . shows (toList m)
showMap :: (Show a) => [(Key,a)] -> ShowS
showMap []
showTail (x:xs) = showChar ',' . showElem x . showTail xs
showElem (k,x) = shows k . showString ":=" . shows x
-
+
+{--------------------------------------------------------------------
+ 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
--------------------------------------------------------------------}
= showTreeWith True False s
-{- | /O(n)/. The expression (@showTreeWith hang wide map@) shows
+{- | /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.
+ '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