{-# LANGUAGE CPP #-}
-----------------------------------------------------------------------------
-- |
-- Module : Data.PQueue.Max
-- Copyright : (c) Louis Wasserman 2010
-- License : BSD-style
-- Maintainer : libraries@haskell.org
-- Stability : experimental
-- Portability : portable
--
-- General purpose priority queue, supporting view-maximum operations.
--
-- An amortized running time is given for each operation, with /n/ referring
-- to the length of the sequence and /k/ being the integral index used by
-- some operations. These bounds hold even in a persistent (shared) setting.
--
-- This implementation is based on a binomial heap augmented with a global root.
-- The spine of the heap is maintained lazily. To force the spine of the heap,
-- use 'seqSpine'.
--
-- This implementation does not guarantee stable behavior.
--
-- This implementation offers a number of methods of the form @xxxU@, where @U@ stands for
-- unordered. No guarantees whatsoever are made on the execution or traversal order of
-- these functions.
-----------------------------------------------------------------------------
module Data.PQueue.Max (
MaxQueue,
-- * Basic operations
empty,
null,
size,
-- * Query operations
findMax,
getMax,
deleteMax,
deleteFindMax,
delete,
maxView,
-- * Construction operations
singleton,
insert,
insertBehind,
union,
unions,
-- * Subsets
-- ** Extracting subsets
(!!),
take,
drop,
splitAt,
-- ** Predicates
takeWhile,
dropWhile,
span,
break,
-- * Filter/Map
filter,
partition,
mapMaybe,
mapEither,
-- * Fold\/Functor\/Traversable variations
map,
foldrAsc,
foldlAsc,
foldrDesc,
foldlDesc,
-- * List operations
toList,
toAscList,
toDescList,
fromList,
fromAscList,
fromDescList,
-- * Unordered operations
mapU,
foldrU,
foldlU,
elemsU,
toListU,
-- * Miscellaneous operations
keysQueue,
seqSpine) where
import Control.DeepSeq (NFData(rnf))
import Data.Functor ((<$>))
import Data.Monoid (Monoid(mempty, mappend))
import Data.Maybe (fromMaybe)
import Data.Foldable (foldl, foldr)
import qualified Data.PQueue.Min as Min
import qualified Data.PQueue.Prio.Max.Internals as Prio
import Data.PQueue.Prio.Max.Internals (Down(..))
import Prelude hiding (null, foldr, foldl, take, drop, takeWhile, dropWhile, splitAt, span, break, (!!), filter)
#ifdef __GLASGOW_HASKELL__
import GHC.Exts (build)
import Text.Read (Lexeme(Ident), lexP, parens, prec,
readPrec, readListPrec, readListPrecDefault)
import Data.Data
#else
build :: ((a -> [a] -> [a]) -> [a] -> [a]) -> [a]
build f = f (:) []
#endif
-- | A priority queue with elements of type @a@. Supports extracting the maximum element.
-- Implemented as a wrapper around 'Min.MinQueue'.
newtype MaxQueue a = MaxQ (Min.MinQueue (Down a))
# if __GLASGOW_HASKELL__
deriving (Eq, Ord, Data, Typeable)
# else
deriving (Eq, Ord)
# endif
instance NFData a => NFData (MaxQueue a) where
rnf (MaxQ q) = rnf q
instance (Ord a, Show a) => Show (MaxQueue a) where
showsPrec p xs = showParen (p > 10) $
showString "fromDescList " . shows (toDescList xs)
instance Read a => Read (MaxQueue a) where
#ifdef __GLASGOW_HASKELL__
readPrec = parens $ prec 10 $ do
Ident "fromDescList" <- lexP
xs <- readPrec
return (fromDescList xs)
readListPrec = readListPrecDefault
#else
readsPrec p = readParen (p > 10) $ \ r -> do
("fromDescList",s) <- lex r
(xs,t) <- reads s
return (fromDescList xs,t)
#endif
instance Ord a => Monoid (MaxQueue a) where
mempty = empty
mappend = union
-- | /O(1)/. The empty priority queue.
empty :: MaxQueue a
empty = MaxQ Min.empty
-- | /O(1)/. Is this the empty priority queue?
null :: MaxQueue a -> Bool
null (MaxQ q) = Min.null q
-- | /O(1)/. The number of elements in the queue.
size :: MaxQueue a -> Int
size (MaxQ q) = Min.size q
-- | /O(1)/. Returns the maximum element of the queue. Throws an error on an empty queue.
findMax :: MaxQueue a -> a
findMax = fromMaybe (error "Error: findMax called on empty queue") . getMax
-- | /O(1)/. The top (maximum) element of the queue, if there is one.
getMax :: MaxQueue a -> Maybe a
getMax (MaxQ q) = unDown <$> Min.getMin q
-- | /O(log n)/. Deletes the maximum element of the queue. Does nothing on an empty queue.
deleteMax :: Ord a => MaxQueue a -> MaxQueue a
deleteMax (MaxQ q) = MaxQ (Min.deleteMin q)
-- | /O(log n)/. Extracts the maximum element of the queue. Throws an error on an empty queue.
deleteFindMax :: Ord a => MaxQueue a -> (a, MaxQueue a)
deleteFindMax = fromMaybe (error "Error: deleteFindMax called on empty queue") . maxView
-- | /O(log n)/. Extract the top (maximum) element of the sequence, if there is one.
maxView :: Ord a => MaxQueue a -> Maybe (a, MaxQueue a)
maxView (MaxQ q) = case Min.minView q of
Nothing -> Nothing
Just (Down x, q')
-> Just (x, MaxQ q')
-- | /O(log n)/. Delete the top (maximum) element of the sequence, if there is one.
delete :: Ord a => MaxQueue a -> Maybe (MaxQueue a)
delete = fmap snd . maxView
-- | /O(1)/. Construct a priority queue with a single element.
singleton :: a -> MaxQueue a
singleton = MaxQ . Min.singleton . Down
-- | /O(1)/. Insert an element into the priority queue.
insert :: Ord a => a -> MaxQueue a -> MaxQueue a
x `insert` MaxQ q = MaxQ (Down x `Min.insert` q)
-- | Amortized /O(1)/, worst-case /O(log n)/. Insert an element into the priority queue,
-- putting it behind elements that compare equal to the inserted one.
insertBehind :: Ord a => a -> MaxQueue a -> MaxQueue a
x `insertBehind` MaxQ q = MaxQ (Down x `Min.insertBehind` q)
-- | /O(log (min(n1,n2)))/. Take the union of two priority queues.
union :: Ord a => MaxQueue a -> MaxQueue a -> MaxQueue a
MaxQ q1 `union` MaxQ q2 = MaxQ (q1 `Min.union` q2)
-- | Takes the union of a list of priority queues. Equivalent to @'foldl' 'union' 'empty'@.
unions :: Ord a => [MaxQueue a] -> MaxQueue a
unions qs = MaxQ (Min.unions [q | MaxQ q <- qs])
-- | /O(k log n)/. Returns the @(k+1)@th largest element of the queue.
(!!) :: Ord a => MaxQueue a -> Int -> a
MaxQ q !! n = unDown ((Min.!!) q n)
{-# INLINE take #-}
-- | /O(k log n)/. Returns the list of the @k@ largest elements of the queue, in descending order, or
-- all elements of the queue, if @k >= n@.
take :: Ord a => Int -> MaxQueue a -> [a]
take k (MaxQ q) = [a | Down a <- Min.take k q]
-- | /O(k log n)/. Returns the queue with the @k@ largest elements deleted, or the empty queue if @k >= n@.
drop :: Ord a => Int -> MaxQueue a -> MaxQueue a
drop k (MaxQ q) = MaxQ (Min.drop k q)
-- | /O(k log n)/. Equivalent to @(take k queue, drop k queue)@.
splitAt :: Ord a => Int -> MaxQueue a -> ([a], MaxQueue a)
splitAt k (MaxQ q) = (map unDown xs, MaxQ q') where
(xs, q') = Min.splitAt k q
-- | 'takeWhile', applied to a predicate @p@ and a queue @queue@, returns the
-- longest prefix (possibly empty) of @queue@ of elements that satisfy @p@.
takeWhile :: Ord a => (a -> Bool) -> MaxQueue a -> [a]
takeWhile p (MaxQ q) = map unDown (Min.takeWhile (p . unDown) q)
-- | 'dropWhile' @p queue@ returns the queue remaining after 'takeWhile' @p queue@.
dropWhile :: Ord a => (a -> Bool) -> MaxQueue a -> MaxQueue a
dropWhile p (MaxQ q) = MaxQ (Min.dropWhile (p . unDown) q)
-- | 'span', applied to a predicate @p@ and a queue @queue@, returns a tuple where
-- first element is longest prefix (possibly empty) of @queue@ of elements that
-- satisfy @p@ and second element is the remainder of the queue.
--
span :: Ord a => (a -> Bool) -> MaxQueue a -> ([a], MaxQueue a)
span p (MaxQ q) = (map unDown xs, MaxQ q') where
(xs, q') = Min.span (p . unDown) q
-- | 'break', applied to a predicate @p@ and a queue @queue@, returns a tuple where
-- first element is longest prefix (possibly empty) of @queue@ of elements that
-- /do not satisfy/ @p@ and second element is the remainder of the queue.
break :: Ord a => (a -> Bool) -> MaxQueue a -> ([a], MaxQueue a)
break p = span (not . p)
-- | /O(n)/. Returns a queue of those elements which satisfy the predicate.
filter :: Ord a => (a -> Bool) -> MaxQueue a -> MaxQueue a
filter p (MaxQ q) = MaxQ (Min.filter (p . unDown) q)
-- | /O(n)/. Returns a pair of queues, where the left queue contains those elements that satisfy the predicate,
-- and the right queue contains those that do not.
partition :: Ord a => (a -> Bool) -> MaxQueue a -> (MaxQueue a, MaxQueue a)
partition p (MaxQ q) = (MaxQ q0, MaxQ q1)
where (q0, q1) = Min.partition (p . unDown) q
-- | /O(n)/. Maps a function over the elements of the queue, and collects the 'Just' values.
mapMaybe :: Ord b => (a -> Maybe b) -> MaxQueue a -> MaxQueue b
mapMaybe f (MaxQ q) = MaxQ (Min.mapMaybe (\ (Down x) -> Down <$> f x) q)
-- | /O(n)/. Maps a function over the elements of the queue, and separates the 'Left' and 'Right' values.
mapEither :: (Ord b, Ord c) => (a -> Either b c) -> MaxQueue a -> (MaxQueue b, MaxQueue c)
mapEither f (MaxQ q) = (MaxQ q0, MaxQ q1)
where (q0, q1) = Min.mapEither (either (Left . Down) (Right . Down) . f . unDown) q
-- | /O(n)/. Assumes that the function it is given is monotonic, and applies this function to every element of the priority queue.
-- /Does not check the precondition/.
mapU :: (a -> b) -> MaxQueue a -> MaxQueue b
mapU f (MaxQ q) = MaxQ (Min.mapU (\ (Down a) -> Down (f a)) q)
-- | /O(n)/. Unordered right fold on a priority queue.
foldrU :: (a -> b -> b) -> b -> MaxQueue a -> b
foldrU f z (MaxQ q) = Min.foldrU (flip (foldr f)) z q
-- | /O(n)/. Unordered left fold on a priority queue.
foldlU :: (b -> a -> b) -> b -> MaxQueue a -> b
foldlU f z (MaxQ q) = Min.foldlU (foldl f) z q
{-# INLINE elemsU #-}
-- | Equivalent to 'toListU'.
elemsU :: MaxQueue a -> [a]
elemsU = toListU
{-# INLINE toListU #-}
-- | /O(n)/. Returns a list of the elements of the priority queue, in no particular order.
toListU :: MaxQueue a -> [a]
toListU (MaxQ q) = map unDown (Min.toListU q)
-- | /O(n log n)/. Performs a right-fold on the elements of a priority queue in ascending order.
-- @'foldrAsc' f z q == 'foldlDesc' (flip f) z q@.
foldrAsc :: Ord a => (a -> b -> b) -> b -> MaxQueue a -> b
foldrAsc = foldlDesc . flip
-- | /O(n log n)/. Performs a left-fold on the elements of a priority queue in descending order.
-- @'foldlAsc' f z q == 'foldrDesc' (flip f) z q@.
foldlAsc :: Ord a => (b -> a -> b) -> b -> MaxQueue a -> b
foldlAsc = foldrDesc . flip
-- | /O(n log n)/. Performs a right-fold on the elements of a priority queue in descending order.
foldrDesc :: Ord a => (a -> b -> b) -> b -> MaxQueue a -> b
foldrDesc f z (MaxQ q) = Min.foldrAsc (flip (foldr f)) z q
-- | /O(n log n)/. Performs a left-fold on the elements of a priority queue in descending order.
foldlDesc :: Ord a => (b -> a -> b) -> b -> MaxQueue a -> b
foldlDesc f z (MaxQ q) = Min.foldlAsc (foldl f) z q
{-# INLINE toAscList #-}
-- | /O(n log n)/. Extracts the elements of the priority queue in ascending order.
toAscList :: Ord a => MaxQueue a -> [a]
toAscList q = build (\ c nil -> foldrAsc c nil q)
-- I can see no particular reason this does not simply forward to Min.toDescList. (lsp, 2016)
{-# INLINE toDescList #-}
-- | /O(n log n)/. Extracts the elements of the priority queue in descending order.
toDescList :: Ord a => MaxQueue a -> [a]
toDescList q = build (\ c nil -> foldrDesc c nil q)
-- I can see no particular reason this does not simply forward to Min.toAscList. (lsp, 2016)
{-# INLINE toList #-}
-- | /O(n log n)/. Returns the elements of the priority queue in ascending order. Equivalent to 'toDescList'.
--
-- If the order of the elements is irrelevant, consider using 'toListU'.
toList :: Ord a => MaxQueue a -> [a]
toList (MaxQ q) = map unDown (Min.toList q)
{-# INLINE fromAscList #-}
-- | /O(n)/. Constructs a priority queue from an ascending list. /Warning/: Does not check the precondition.
fromAscList :: [a] -> MaxQueue a
fromAscList = MaxQ . Min.fromDescList . map Down
{-# INLINE fromDescList #-}
-- | /O(n)/. Constructs a priority queue from a descending list. /Warning/: Does not check the precondition.
fromDescList :: [a] -> MaxQueue a
fromDescList = MaxQ . Min.fromAscList . map Down
{-# INLINE fromList #-}
-- | /O(n log n)/. Constructs a priority queue from an unordered list.
fromList :: Ord a => [a] -> MaxQueue a
fromList = foldr insert empty
-- | /O(n)/. Constructs a priority queue from the keys of a 'Prio.MaxPQueue'.
keysQueue :: Prio.MaxPQueue k a -> MaxQueue k
keysQueue (Prio.MaxPQ q) = MaxQ (Min.keysQueue q)
-- | /O(log n)/. Forces the spine of the heap.
seqSpine :: MaxQueue a -> b -> b
seqSpine (MaxQ q) = Min.seqSpine q