+{-# OPTIONS_GHC -fno-bang-patterns #-}
+
-----------------------------------------------------------------------------
-- |
-- Module : Data.Map
--
-- An efficient implementation of maps from keys to values (dictionaries).
--
--- 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.Map as Map
+-- > import Data.Map (Map)
+-- > import qualified Data.Map as Map
--
-- The implementation of 'Map' is based on /size balanced/ binary trees (or
-- trees of /bounded balance/) as described by:
-- * J. Nievergelt and E.M. Reingold,
-- \"/Binary search trees of bounded balance/\",
-- SIAM journal of computing 2(1), March 1973.
+--
+-- Note that the implementation is /left-biased/ -- the elements of a
+-- first argument are always preferred to the second, for example in
+-- 'union' or 'insert'.
-----------------------------------------------------------------------------
module Data.Map (
, null
, size
, member
+ , notMember
, lookup
, findWithDefault
-- ** Insertion
, insert
, insertWith, insertWithKey, insertLookupWithKey
+ , insertWith', insertWithKey'
-- ** Delete\/Update
, delete
, update
, updateWithKey
, updateLookupWithKey
+ , alter
-- * Combine
, partition
, partitionWithKey
+ , mapMaybe
+ , mapMaybeWithKey
+ , mapEither
+ , mapEitherWithKey
+
, split
, splitLookup
, updateMax
, updateMinWithKey
, updateMaxWithKey
+ , minView
+ , maxView
+ , minViewWithKey
+ , maxViewWithKey
-- * Debugging
, showTree
import qualified Data.List as List
import Data.Monoid (Monoid(..))
import Data.Typeable
+import Control.Applicative (Applicative(..), (<$>))
+import Data.Traversable (Traversable(traverse))
+import Data.Foldable (Foldable(foldMap))
{-
-- for quick check
toConstr _ = error "toConstr"
gunfold _ _ = error "gunfold"
dataTypeOf _ = mkNorepType "Data.Map.Map"
+ dataCast2 f = gcast2 f
#endif
Bin sz k x l r -> sz
--- | /O(log n)/. Lookup the value at a key in the map.
+-- | /O(log n)/. Lookup the value at a key in the map.
+--
+-- The function will
+-- @return@ the result in the monad or @fail@ in it the key isn't in the
+-- map. Often, the monad to use is 'Maybe', so you get either
+-- @('Just' result)@ or @'Nothing'@.
lookup :: (Monad m,Ord k) => k -> Map k a -> m a
lookup k t = case lookup' k t of
Just x -> return x
GT -> lookup' k r
EQ -> Just x
+lookupAssoc :: Ord k => k -> Map k a -> Maybe (k,a)
+lookupAssoc k t
+ = case t of
+ Tip -> Nothing
+ Bin sz kx x l r
+ -> case compare k kx of
+ LT -> lookupAssoc k l
+ GT -> lookupAssoc k r
+ EQ -> Just (kx,x)
+
-- | /O(log n)/. Is the key a member of the map?
member :: Ord k => k -> Map k a -> Bool
member k m
Nothing -> False
Just x -> True
+-- | /O(log n)/. Is the key not a member of the map?
+notMember :: Ord k => k -> Map k a -> Bool
+notMember k m = not $ member k m
+
-- | /O(log n)/. Find the value at a key.
-- Calls 'error' when the element can not be found.
find :: Ord k => k -> Map k a -> a
EQ -> Bin sz kx x l r
-- | /O(log n)/. 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 the pair @(key, f new_value old_value)@.
insertWith :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
insertWith f k x m
= insertWithKey (\k x y -> f x y) k x m
+-- | Same as 'insertWith', but the combining function is applied strictly.
+insertWith' :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
+insertWith' f k x m
+ = insertWithKey' (\k x y -> f x y) k x m
+
+
-- | /O(log n)/. 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 the pair @(key,f key new_value old_value)@.
+-- Note that the key passed to f is the same key passed to 'insertWithKey'.
insertWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
insertWithKey f kx x t
= case t of
-> case compare kx ky of
LT -> balance ky y (insertWithKey f kx x l) r
GT -> balance ky y l (insertWithKey f kx x r)
- EQ -> Bin sy ky (f ky x y) l r
+ EQ -> Bin sy kx (f kx x y) l r
+
+-- | Same as 'insertWithKey', but the combining function is applied strictly.
+insertWithKey' :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
+insertWithKey' f kx x t
+ = case t of
+ Tip -> singleton kx x
+ Bin sy ky y l r
+ -> case compare kx ky of
+ LT -> balance ky y (insertWithKey' f kx x l) r
+ GT -> balance ky y l (insertWithKey' f kx x r)
+ EQ -> let x' = f kx x y in seq x' (Bin sy kx x' l r)
+
-- | /O(log n)/. The expression (@'insertLookupWithKey' f k x map@)
-- is a pair where the first element is equal to (@'lookup' k map@)
-> case compare kx ky of
LT -> let (found,l') = insertLookupWithKey f kx x l in (found,balance ky y l' r)
GT -> let (found,r') = insertLookupWithKey f kx x r in (found,balance ky y l r')
- EQ -> (Just y, Bin sy ky (f ky x y) l r)
+ EQ -> (Just y, Bin sy kx (f kx x y) l r)
{--------------------------------------------------------------------
Deletion
Just x' -> (Just x',Bin sx kx x' l r)
Nothing -> (Just x,glue l r)
+-- | /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 :: Ord k => (Maybe a -> Maybe a) -> k -> Map k a -> Map k a
+alter f k t
+ = case t of
+ Tip -> case f Nothing of
+ Nothing -> Tip
+ Just x -> singleton k x
+ Bin sx kx x l r
+ -> case compare k kx of
+ LT -> balance kx x (alter f k l) r
+ GT -> balance kx x l (alter f k r)
+ EQ -> case f (Just x) of
+ Just x' -> Bin sx kx x' l r
+ Nothing -> glue l r
+
{--------------------------------------------------------------------
Indexing
--------------------------------------------------------------------}
findMin :: Map k a -> (k,a)
findMin (Bin _ kx x Tip r) = (kx,x)
findMin (Bin _ kx x l r) = findMin l
-findMin Tip = error "Map.findMin: empty tree has no minimal element"
+findMin Tip = error "Map.findMin: empty map has no minimal element"
-- | /O(log n)/. The maximal key of the map.
findMax :: Map k a -> (k,a)
findMax (Bin _ kx x l Tip) = (kx,x)
findMax (Bin _ kx x l r) = findMax r
-findMax Tip = error "Map.findMax: empty tree has no maximal element"
+findMax Tip = error "Map.findMax: empty map has no maximal element"
-- | /O(log n)/. Delete the minimal key.
deleteMin :: Map k a -> Map k a
Bin sx kx x l r -> balance kx x l (updateMaxWithKey f r)
Tip -> Tip
+-- | /O(log n)/. Retrieves the minimal (key,value) pair of the map, and the map stripped from that element
+-- @fail@s (in the monad) when passed an empty map.
+minViewWithKey :: Monad m => Map k a -> m ((k,a), Map k a)
+minViewWithKey Tip = fail "Map.minView: empty map"
+minViewWithKey x = return (deleteFindMin x)
+
+-- | /O(log n)/. Retrieves the maximal (key,value) pair of the map, and the map stripped from that element
+-- @fail@s (in the monad) when passed an empty map.
+maxViewWithKey :: Monad m => Map k a -> m ((k,a), Map k a)
+maxViewWithKey Tip = fail "Map.maxView: empty map"
+maxViewWithKey x = return (deleteFindMax x)
+
+-- | /O(log n)/. Retrieves the minimal key\'s value of the map, and the map stripped from that element
+-- @fail@s (in the monad) when passed an empty map.
+minView :: Monad m => Map k a -> m (a, Map k a)
+minView Tip = fail "Map.minView: empty map"
+minView x = return (first snd $ deleteFindMin x)
+
+-- | /O(log n)/. Retrieves the maximal key\'s value of the map, and the map stripped from that element
+-- @fail@s (in the monad) when passed an empty map.
+maxView :: Monad m => Map k a -> m (a, Map k a)
+maxView Tip = fail "Map.maxView: empty map"
+maxView x = return (first snd $ deleteFindMax x)
+
+-- Update the 1st component of a tuple (special case of Control.Arrow.first)
+first :: (a -> b) -> (a,c) -> (b,c)
+first f (x,y) = (f x, y)
{--------------------------------------------------------------------
Union.
-- It prefers @t1@ when duplicate keys are encountered,
-- i.e. (@'union' == 'unionWith' 'const'@).
-- The implementation uses the efficient /hedge-union/ algorithm.
--- Hedge-union is more efficient on (bigset `union` smallset)?
+-- Hedge-union is more efficient on (bigset `union` smallset)
union :: Ord k => Map k a -> Map k a -> Map k a
union Tip t2 = t2
union t1 Tip = t1
-union t1 t2
- | size t1 >= size t2 = hedgeUnionL (const LT) (const GT) t1 t2
- | otherwise = hedgeUnionR (const LT) (const GT) t2 t1
+union t1 t2 = hedgeUnionL (const LT) (const GT) t1 t2
-- left-biased hedge union
hedgeUnionL cmplo cmphi t1 Tip
(found,gt) = trimLookupLo kx cmphi t2
newx = case found of
Nothing -> x
- Just y -> y
+ Just (_,y) -> y
{--------------------------------------------------------------------
Union with a combining function
unionWithKey :: Ord k => (k -> a -> a -> a) -> Map k a -> Map k a -> Map k a
unionWithKey f Tip t2 = t2
unionWithKey f t1 Tip = t1
-unionWithKey f t1 t2
- | size t1 >= size t2 = hedgeUnionWithKey f (const LT) (const GT) t1 t2
- | otherwise = hedgeUnionWithKey flipf (const LT) (const GT) t2 t1
- where
- flipf k x y = f k y x
+unionWithKey f t1 t2 = hedgeUnionWithKey f (const LT) (const GT) t1 t2
hedgeUnionWithKey f cmplo cmphi t1 Tip
= t1
(found,gt) = trimLookupLo kx cmphi t2
newx = case found of
Nothing -> x
- Just y -> f kx x y
+ Just (_,y) -> f kx x y
{--------------------------------------------------------------------
Difference
hedgeDiffWithKey f cmplo cmphi t (Bin _ kx x l r)
= case found of
Nothing -> merge tl tr
- Just y -> case f kx y x of
- Nothing -> merge tl tr
- Just z -> join kx z tl tr
+ Just (ky,y) ->
+ case f ky y x of
+ Nothing -> merge tl tr
+ Just z -> join ky z tl tr
where
cmpkx k = compare kx k
lt = trim cmplo cmpkx t
-- | /O(n+m)/. Intersection with a combining function.
-- Intersection is more efficient on (bigset `intersection` smallset)
+--intersectionWithKey :: Ord k => (k -> a -> b -> c) -> Map k a -> Map k b -> Map k c
+--intersectionWithKey f Tip t = Tip
+--intersectionWithKey f t Tip = Tip
+--intersectionWithKey f t1 t2 = intersectWithKey f t1 t2
+--
+--intersectWithKey f Tip t = Tip
+--intersectWithKey f t Tip = Tip
+--intersectWithKey f t (Bin _ kx x l r)
+-- = case found of
+-- Nothing -> merge tl tr
+-- Just y -> join kx (f kx y x) tl tr
+-- where
+-- (lt,found,gt) = splitLookup kx t
+-- tl = intersectWithKey f lt l
+-- tr = intersectWithKey f gt r
+
+
intersectionWithKey :: Ord k => (k -> a -> b -> c) -> Map k a -> Map k b -> Map k c
intersectionWithKey f Tip t = Tip
intersectionWithKey f t Tip = Tip
-intersectionWithKey f t1 t2
- | size t1 >= size t2 = intersectWithKey f t1 t2
- | otherwise = intersectWithKey flipf t2 t1
- where
- flipf k x y = f k y x
-
-intersectWithKey f Tip t = Tip
-intersectWithKey f t Tip = Tip
-intersectWithKey f t (Bin _ kx x l r)
- = case found of
+intersectionWithKey f t1@(Bin s1 k1 x1 l1 r1) t2@(Bin s2 k2 x2 l2 r2) =
+ if s1 >= s2 then
+ let (lt,found,gt) = splitLookupWithKey k2 t1
+ tl = intersectionWithKey f lt l2
+ tr = intersectionWithKey f gt r2
+ in case found of
+ Just (k,x) -> join k (f k x x2) tl tr
+ Nothing -> merge tl tr
+ else let (lt,found,gt) = splitLookup k1 t2
+ tl = intersectionWithKey f l1 lt
+ tr = intersectionWithKey f r1 gt
+ in case found of
+ Just x -> join k1 (f k1 x1 x) tl tr
Nothing -> merge tl tr
- Just y -> join kx (f kx y x) tl tr
- where
- (lt,found,gt) = splitLookup kx t
- tl = intersectWithKey f lt l
- tr = intersectWithKey f gt r
(l1,l2) = partitionWithKey p l
(r1,r2) = partitionWithKey p r
+-- | /O(n)/. Map values and collect the 'Just' results.
+mapMaybe :: Ord k => (a -> Maybe b) -> Map k a -> Map k b
+mapMaybe f m
+ = mapMaybeWithKey (\k x -> f x) m
+
+-- | /O(n)/. Map keys\/values and collect the 'Just' results.
+mapMaybeWithKey :: Ord k => (k -> a -> Maybe b) -> Map k a -> Map k b
+mapMaybeWithKey f Tip = Tip
+mapMaybeWithKey f (Bin _ kx x l r) = case f kx x of
+ Just y -> join kx y (mapMaybeWithKey f l) (mapMaybeWithKey f r)
+ Nothing -> merge (mapMaybeWithKey f l) (mapMaybeWithKey f r)
+
+-- | /O(n)/. Map values and separate the 'Left' and 'Right' results.
+mapEither :: Ord k => (a -> Either b c) -> Map k a -> (Map k b, Map k c)
+mapEither f m
+ = mapEitherWithKey (\k x -> f x) m
+
+-- | /O(n)/. Map keys\/values and separate the 'Left' and 'Right' results.
+mapEitherWithKey :: Ord k =>
+ (k -> a -> Either b c) -> Map k a -> (Map k b, Map k c)
+mapEitherWithKey f Tip = (Tip, Tip)
+mapEitherWithKey f (Bin _ kx x l r) = case f kx x of
+ Left y -> (join kx y l1 r1, merge l2 r2)
+ Right z -> (merge l1 r1, join kx z l2 r2)
+ where
+ (l1,l2) = mapEitherWithKey f l
+ (r1,r2) = mapEitherWithKey f r
{--------------------------------------------------------------------
Mapping
le -> trim cmplo cmphi l
ge -> trim cmplo cmphi r
-trimLookupLo :: Ord k => k -> (k -> Ordering) -> Map k a -> (Maybe a, Map k a)
+trimLookupLo :: Ord k => k -> (k -> Ordering) -> Map k a -> (Maybe (k,a), Map k a)
trimLookupLo lo cmphi Tip = (Nothing,Tip)
trimLookupLo lo cmphi t@(Bin sx kx x l r)
= case compare lo kx of
LT -> case cmphi kx of
- GT -> (lookup lo t, t)
+ GT -> (lookupAssoc lo t, t)
le -> trimLookupLo lo cmphi l
GT -> trimLookupLo lo cmphi r
- EQ -> (Just x,trim (compare lo) cmphi r)
+ EQ -> (Just (kx,x),trim (compare lo) cmphi r)
{--------------------------------------------------------------------
GT -> let (lt,z,gt) = splitLookup k r in (join kx x l lt,z,gt)
EQ -> (l,Just x,r)
+-- | /O(log n)/.
+splitLookupWithKey :: Ord k => k -> Map k a -> (Map k a,Maybe (k,a),Map k a)
+splitLookupWithKey k Tip = (Tip,Nothing,Tip)
+splitLookupWithKey k (Bin sx kx x l r)
+ = case compare k kx of
+ LT -> let (lt,z,gt) = splitLookupWithKey k l in (lt,z,join kx x gt r)
+ GT -> let (lt,z,gt) = splitLookupWithKey k r in (join kx x l lt,z,gt)
+ EQ -> (l,Just (kx, x),r)
+
+-- | /O(log n)/. Performs a 'split' but also returns whether the pivot
+-- element was found in the original set.
+splitMember :: Ord k => k -> Map k a -> (Map k a,Bool,Map k a)
+splitMember x t = let (l,m,r) = splitLookup x t in
+ (l,maybe False (const True) m,r)
+
+
{--------------------------------------------------------------------
Utility functions that maintain the balance properties of the tree.
All constructors assume that all values in [l] < [k] and all values
instance Functor (Map k) where
fmap f m = map f m
+instance Traversable (Map k) where
+ traverse f Tip = pure Tip
+ traverse f (Bin s k v l r)
+ = flip (Bin s k) <$> traverse f l <*> f v <*> traverse f r
+
+instance Foldable (Map k) where
+ foldMap _f Tip = mempty
+ foldMap f (Bin _s _k v l r)
+ = foldMap f l `mappend` f v `mappend` foldMap f r
+
{--------------------------------------------------------------------
Read
--------------------------------------------------------------------}
projects / haskell-directory.git / blobdiff