{-# 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.
--
-- 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,
  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,
  foldlU',
  foldMapU,
  elemsU,
  toListU,
  -- * Miscellaneous operations
  keysQueue,
  seqSpine) where

import Control.DeepSeq (NFData(rnf))

import Data.Maybe (fromMaybe)

#if MIN_VERSION_base(4,9,0)
import Data.Semigroup (Semigroup(..), stimesMonoid)
#endif

import Data.Foldable (foldl')

import qualified Data.PQueue.Min as Min
import qualified Data.PQueue.Prio.Max.Internals as Prio
import Data.PQueue.Internals.Down (Down(..))

import Prelude hiding (null, map, 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 (MaxQueue a -> MaxQueue a -> Bool
forall a. Ord a => MaxQueue a -> MaxQueue a -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: MaxQueue a -> MaxQueue a -> Bool
$c/= :: forall a. Ord a => MaxQueue a -> MaxQueue a -> Bool
== :: MaxQueue a -> MaxQueue a -> Bool
$c== :: forall a. Ord a => MaxQueue a -> MaxQueue a -> Bool
Eq, MaxQueue a -> MaxQueue a -> Bool
MaxQueue a -> MaxQueue a -> Ordering
MaxQueue a -> MaxQueue a -> MaxQueue a
forall a.
Eq a
-> (a -> a -> Ordering)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> a)
-> (a -> a -> a)
-> Ord a
forall a. Ord a => Eq (MaxQueue a)
forall a. Ord a => MaxQueue a -> MaxQueue a -> Bool
forall a. Ord a => MaxQueue a -> MaxQueue a -> Ordering
forall a. Ord a => MaxQueue a -> MaxQueue a -> MaxQueue a
min :: MaxQueue a -> MaxQueue a -> MaxQueue a
$cmin :: forall a. Ord a => MaxQueue a -> MaxQueue a -> MaxQueue a
max :: MaxQueue a -> MaxQueue a -> MaxQueue a
$cmax :: forall a. Ord a => MaxQueue a -> MaxQueue a -> MaxQueue a
>= :: MaxQueue a -> MaxQueue a -> Bool
$c>= :: forall a. Ord a => MaxQueue a -> MaxQueue a -> Bool
> :: MaxQueue a -> MaxQueue a -> Bool
$c> :: forall a. Ord a => MaxQueue a -> MaxQueue a -> Bool
<= :: MaxQueue a -> MaxQueue a -> Bool
$c<= :: forall a. Ord a => MaxQueue a -> MaxQueue a -> Bool
< :: MaxQueue a -> MaxQueue a -> Bool
$c< :: forall a. Ord a => MaxQueue a -> MaxQueue a -> Bool
compare :: MaxQueue a -> MaxQueue a -> Ordering
$ccompare :: forall a. Ord a => MaxQueue a -> MaxQueue a -> Ordering
Ord, MaxQueue a -> DataType
MaxQueue a -> Constr
forall {a}. (Data a, Ord a) => Typeable (MaxQueue a)
forall a. (Data a, Ord a) => MaxQueue a -> DataType
forall a. (Data a, Ord a) => MaxQueue a -> Constr
forall a.
(Data a, Ord a) =>
(forall b. Data b => b -> b) -> MaxQueue a -> MaxQueue a
forall a u.
(Data a, Ord a) =>
Int -> (forall d. Data d => d -> u) -> MaxQueue a -> u
forall a u.
(Data a, Ord a) =>
(forall d. Data d => d -> u) -> MaxQueue a -> [u]
forall a r r'.
(Data a, Ord a) =>
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> MaxQueue a -> r
forall a r r'.
(Data a, Ord a) =>
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> MaxQueue a -> r
forall a (m :: * -> *).
(Data a, Ord a, Monad m) =>
(forall d. Data d => d -> m d) -> MaxQueue a -> m (MaxQueue a)
forall a (m :: * -> *).
(Data a, Ord a, MonadPlus m) =>
(forall d. Data d => d -> m d) -> MaxQueue a -> m (MaxQueue a)
forall a (c :: * -> *).
(Data a, Ord a) =>
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (MaxQueue a)
forall a (c :: * -> *).
(Data a, Ord a) =>
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> MaxQueue a -> c (MaxQueue a)
forall a (t :: * -> *) (c :: * -> *).
(Data a, Ord a, Typeable t) =>
(forall d. Data d => c (t d)) -> Maybe (c (MaxQueue a))
forall a (t :: * -> * -> *) (c :: * -> *).
(Data a, Ord a, Typeable t) =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c (MaxQueue a))
forall a.
Typeable a
-> (forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> a -> c a)
-> (forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c a)
-> (a -> Constr)
-> (a -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c a))
-> (forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a))
-> ((forall b. Data b => b -> b) -> a -> a)
-> (forall r r'.
    (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
-> (forall r r'.
    (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
-> (forall u. (forall d. Data d => d -> u) -> a -> [u])
-> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u)
-> (forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> Data a
forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (MaxQueue a)
forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> MaxQueue a -> c (MaxQueue a)
forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c (MaxQueue a))
gmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> MaxQueue a -> m (MaxQueue a)
$cgmapMo :: forall a (m :: * -> *).
(Data a, Ord a, MonadPlus m) =>
(forall d. Data d => d -> m d) -> MaxQueue a -> m (MaxQueue a)
gmapMp :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> MaxQueue a -> m (MaxQueue a)
$cgmapMp :: forall a (m :: * -> *).
(Data a, Ord a, MonadPlus m) =>
(forall d. Data d => d -> m d) -> MaxQueue a -> m (MaxQueue a)
gmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> MaxQueue a -> m (MaxQueue a)
$cgmapM :: forall a (m :: * -> *).
(Data a, Ord a, Monad m) =>
(forall d. Data d => d -> m d) -> MaxQueue a -> m (MaxQueue a)
gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> MaxQueue a -> u
$cgmapQi :: forall a u.
(Data a, Ord a) =>
Int -> (forall d. Data d => d -> u) -> MaxQueue a -> u
gmapQ :: forall u. (forall d. Data d => d -> u) -> MaxQueue a -> [u]
$cgmapQ :: forall a u.
(Data a, Ord a) =>
(forall d. Data d => d -> u) -> MaxQueue a -> [u]
gmapQr :: forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> MaxQueue a -> r
$cgmapQr :: forall a r r'.
(Data a, Ord a) =>
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> MaxQueue a -> r
gmapQl :: forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> MaxQueue a -> r
$cgmapQl :: forall a r r'.
(Data a, Ord a) =>
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> MaxQueue a -> r
gmapT :: (forall b. Data b => b -> b) -> MaxQueue a -> MaxQueue a
$cgmapT :: forall a.
(Data a, Ord a) =>
(forall b. Data b => b -> b) -> MaxQueue a -> MaxQueue a
dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c (MaxQueue a))
$cdataCast2 :: forall a (t :: * -> * -> *) (c :: * -> *).
(Data a, Ord a, Typeable t) =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c (MaxQueue a))
dataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c (MaxQueue a))
$cdataCast1 :: forall a (t :: * -> *) (c :: * -> *).
(Data a, Ord a, Typeable t) =>
(forall d. Data d => c (t d)) -> Maybe (c (MaxQueue a))
dataTypeOf :: MaxQueue a -> DataType
$cdataTypeOf :: forall a. (Data a, Ord a) => MaxQueue a -> DataType
toConstr :: MaxQueue a -> Constr
$ctoConstr :: forall a. (Data a, Ord a) => MaxQueue a -> Constr
gunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (MaxQueue a)
$cgunfold :: forall a (c :: * -> *).
(Data a, Ord a) =>
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (MaxQueue a)
gfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> MaxQueue a -> c (MaxQueue a)
$cgfoldl :: forall a (c :: * -> *).
(Data a, Ord a) =>
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> MaxQueue a -> c (MaxQueue a)
Data)
# else
  deriving (Eq, Ord)
# endif

instance NFData a => NFData (MaxQueue a) where
  rnf :: MaxQueue a -> ()
rnf (MaxQ MinQueue (Down a)
q) = forall a. NFData a => a -> ()
rnf MinQueue (Down a)
q

instance (Ord a, Show a) => Show (MaxQueue a) where
  showsPrec :: Int -> MaxQueue a -> ShowS
showsPrec Int
p MaxQueue a
xs = Bool -> ShowS -> ShowS
showParen (Int
p forall a. Ord a => a -> a -> Bool
> Int
10) forall a b. (a -> b) -> a -> b
$
    String -> ShowS
showString String
"fromDescList " forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Show a => a -> ShowS
shows (forall a. Ord a => MaxQueue a -> [a]
toDescList MaxQueue a
xs)

instance Read a => Read (MaxQueue a) where
#ifdef __GLASGOW_HASKELL__
  readPrec :: ReadPrec (MaxQueue a)
readPrec = forall a. ReadPrec a -> ReadPrec a
parens forall a b. (a -> b) -> a -> b
$ forall a. Int -> ReadPrec a -> ReadPrec a
prec Int
10 forall a b. (a -> b) -> a -> b
$ do
    Ident String
"fromDescList" <- ReadPrec Lexeme
lexP
    [a]
xs <- forall a. Read a => ReadPrec a
readPrec
    forall (m :: * -> *) a. Monad m => a -> m a
return (forall a. [a] -> MaxQueue a
fromDescList [a]
xs)

  readListPrec :: ReadPrec [MaxQueue a]
readListPrec = forall a. Read a => ReadPrec [a]
readListPrecDefault
#else
  readsPrec p = readParen (p > 10) $ \r -> do
    ("fromDescList",s) <- lex r
    (xs,t) <- reads s
    return (fromDescList xs,t)
#endif

#if MIN_VERSION_base(4,9,0)
instance Ord a => Semigroup (MaxQueue a) where
  <> :: MaxQueue a -> MaxQueue a -> MaxQueue a
(<>) = forall a. Ord a => MaxQueue a -> MaxQueue a -> MaxQueue a
union
  stimes :: forall b. Integral b => b -> MaxQueue a -> MaxQueue a
stimes = forall b a. (Integral b, Monoid a) => b -> a -> a
stimesMonoid
  {-# INLINABLE stimes #-}
#endif

instance Ord a => Monoid (MaxQueue a) where
  mempty :: MaxQueue a
mempty = forall a. MaxQueue a
empty
#if !MIN_VERSION_base(4,11,0)
  mappend = union
#endif
  mconcat :: [MaxQueue a] -> MaxQueue a
mconcat = forall a. Ord a => [MaxQueue a] -> MaxQueue a
unions

-- | \(O(1)\). The empty priority queue.
empty :: MaxQueue a
empty :: forall a. MaxQueue a
empty = forall a. MinQueue (Down a) -> MaxQueue a
MaxQ forall a. MinQueue a
Min.empty

-- | \(O(1)\). Is this the empty priority queue?
null :: MaxQueue a -> Bool
null :: forall a. MaxQueue a -> Bool
null (MaxQ MinQueue (Down a)
q) = forall a. MinQueue a -> Bool
Min.null MinQueue (Down a)
q

-- | \(O(1)\). The number of elements in the queue.
size :: MaxQueue a -> Int
size :: forall a. MaxQueue a -> Int
size (MaxQ MinQueue (Down a)
q) = forall a. MinQueue a -> Int
Min.size MinQueue (Down a)
q

-- | \(O(1)\). Returns the maximum element of the queue. Throws an error on an empty queue.
findMax :: MaxQueue a -> a
findMax :: forall a. MaxQueue a -> a
findMax = forall a. a -> Maybe a -> a
fromMaybe (forall a. HasCallStack => String -> a
error String
"Error: findMax called on empty queue") forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. MaxQueue a -> Maybe a
getMax

-- | \(O(1)\). The top (maximum) element of the queue, if there is one.
getMax :: MaxQueue a -> Maybe a
getMax :: forall a. MaxQueue a -> Maybe a
getMax (MaxQ MinQueue (Down a)
q) = forall a. Down a -> a
unDown forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> forall a. MinQueue a -> Maybe a
Min.getMin MinQueue (Down a)
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 :: forall a. Ord a => MaxQueue a -> MaxQueue a
deleteMax (MaxQ MinQueue (Down a)
q) = forall a. MinQueue (Down a) -> MaxQueue a
MaxQ (forall a. Ord a => MinQueue a -> MinQueue a
Min.deleteMin MinQueue (Down a)
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 :: forall a. Ord a => MaxQueue a -> (a, MaxQueue a)
deleteFindMax = forall a. a -> Maybe a -> a
fromMaybe (forall a. HasCallStack => String -> a
error String
"Error: deleteFindMax called on empty queue") forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Ord a => MaxQueue a -> Maybe (a, MaxQueue a)
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 :: forall a. Ord a => MaxQueue a -> Maybe (a, MaxQueue a)
maxView (MaxQ MinQueue (Down a)
q) = case forall a. Ord a => MinQueue a -> Maybe (a, MinQueue a)
Min.minView MinQueue (Down a)
q of
  Maybe (Down a, MinQueue (Down a))
Nothing -> forall a. Maybe a
Nothing
  Just (Down a
x, MinQueue (Down a)
q')
          -> forall a. a -> Maybe a
Just (a
x, forall a. MinQueue (Down a) -> MaxQueue a
MaxQ MinQueue (Down a)
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 :: forall a. Ord a => MaxQueue a -> Maybe (MaxQueue a)
delete = forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap forall a b. (a, b) -> b
snd forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Ord a => MaxQueue a -> Maybe (a, MaxQueue a)
maxView

-- | \(O(1)\). Construct a priority queue with a single element.
singleton :: a -> MaxQueue a
singleton :: forall a. a -> MaxQueue a
singleton = forall a. MinQueue (Down a) -> MaxQueue a
MaxQ forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. a -> MinQueue a
Min.singleton forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. a -> Down a
Down

-- | \(O(1)\). Insert an element into the priority queue.
insert :: Ord a => a -> MaxQueue a -> MaxQueue a
a
x insert :: forall a. Ord a => a -> MaxQueue a -> MaxQueue a
`insert` MaxQ MinQueue (Down a)
q = forall a. MinQueue (Down a) -> MaxQueue a
MaxQ (forall a. a -> Down a
Down a
x forall a. Ord a => a -> MinQueue a -> MinQueue a
`Min.insert` MinQueue (Down a)
q)

-- | \(O(\log min(n_1,n_2))\). Take the union of two priority queues.
union :: Ord a => MaxQueue a -> MaxQueue a -> MaxQueue a
MaxQ MinQueue (Down a)
q1 union :: forall a. Ord a => MaxQueue a -> MaxQueue a -> MaxQueue a
`union` MaxQ MinQueue (Down a)
q2 = forall a. MinQueue (Down a) -> MaxQueue a
MaxQ (MinQueue (Down a)
q1 forall a. Ord a => MinQueue a -> MinQueue a -> MinQueue a
`Min.union` MinQueue (Down a)
q2)

-- | Takes the union of a list of priority queues. Equivalent to @'foldl' 'union' 'empty'@.
unions :: Ord a => [MaxQueue a] -> MaxQueue a
unions :: forall a. Ord a => [MaxQueue a] -> MaxQueue a
unions [MaxQueue a]
qs = forall a. MinQueue (Down a) -> MaxQueue a
MaxQ (forall a. Ord a => [MinQueue a] -> MinQueue a
Min.unions [MinQueue (Down a)
q | MaxQ MinQueue (Down a)
q <- [MaxQueue a]
qs])

-- | \(O(k \log n)\)/. Returns the @(k+1)@th largest element of the queue.
(!!) :: Ord a => MaxQueue a -> Int -> a
MaxQ MinQueue (Down a)
q !! :: forall a. Ord a => MaxQueue a -> Int -> a
!! Int
n = forall a. Down a -> a
unDown (forall a. Ord a => MinQueue a -> Int -> a
(Min.!!) MinQueue (Down a)
q Int
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 :: forall a. Ord a => Int -> MaxQueue a -> [a]
take Int
k (MaxQ MinQueue (Down a)
q) = [a
a | Down a
a <- forall a. Ord a => Int -> MinQueue a -> [a]
Min.take Int
k MinQueue (Down a)
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 :: forall a. Ord a => Int -> MaxQueue a -> MaxQueue a
drop Int
k (MaxQ MinQueue (Down a)
q) = forall a. MinQueue (Down a) -> MaxQueue a
MaxQ (forall a. Ord a => Int -> MinQueue a -> MinQueue a
Min.drop Int
k MinQueue (Down a)
q)

-- | \(O(k \log n)\)/. Equivalent to @(take k queue, drop k queue)@.
splitAt :: Ord a => Int -> MaxQueue a -> ([a], MaxQueue a)
splitAt :: forall a. Ord a => Int -> MaxQueue a -> ([a], MaxQueue a)
splitAt Int
k (MaxQ MinQueue (Down a)
q) = (forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap forall a. Down a -> a
unDown [Down a]
xs, forall a. MinQueue (Down a) -> MaxQueue a
MaxQ MinQueue (Down a)
q') where
  ([Down a]
xs, MinQueue (Down a)
q') = forall a. Ord a => Int -> MinQueue a -> ([a], MinQueue a)
Min.splitAt Int
k MinQueue (Down a)
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 :: forall a. Ord a => (a -> Bool) -> MaxQueue a -> [a]
takeWhile a -> Bool
p (MaxQ MinQueue (Down a)
q) = forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap forall a. Down a -> a
unDown (forall a. Ord a => (a -> Bool) -> MinQueue a -> [a]
Min.takeWhile (a -> Bool
p forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Down a -> a
unDown) MinQueue (Down a)
q)

-- | 'dropWhile' @p queue@ returns the queue remaining after 'takeWhile' @p queue@.
dropWhile :: Ord a => (a -> Bool) -> MaxQueue a -> MaxQueue a
dropWhile :: forall a. Ord a => (a -> Bool) -> MaxQueue a -> MaxQueue a
dropWhile a -> Bool
p (MaxQ MinQueue (Down a)
q) = forall a. MinQueue (Down a) -> MaxQueue a
MaxQ (forall a. Ord a => (a -> Bool) -> MinQueue a -> MinQueue a
Min.dropWhile (a -> Bool
p forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Down a -> a
unDown) MinQueue (Down a)
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 :: forall a. Ord a => (a -> Bool) -> MaxQueue a -> ([a], MaxQueue a)
span a -> Bool
p (MaxQ MinQueue (Down a)
q) = (forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap forall a. Down a -> a
unDown [Down a]
xs, forall a. MinQueue (Down a) -> MaxQueue a
MaxQ MinQueue (Down a)
q') where
  ([Down a]
xs, MinQueue (Down a)
q') = forall a. Ord a => (a -> Bool) -> MinQueue a -> ([a], MinQueue a)
Min.span (a -> Bool
p forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Down a -> a
unDown) MinQueue (Down a)
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 :: forall a. Ord a => (a -> Bool) -> MaxQueue a -> ([a], MaxQueue a)
break a -> Bool
p = forall a. Ord a => (a -> Bool) -> MaxQueue a -> ([a], MaxQueue a)
span (Bool -> Bool
not forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> Bool
p)

-- | \(O(n)\). Returns a queue of those elements which satisfy the predicate.
filter :: Ord a => (a -> Bool) -> MaxQueue a -> MaxQueue a
filter :: forall a. Ord a => (a -> Bool) -> MaxQueue a -> MaxQueue a
filter a -> Bool
p (MaxQ MinQueue (Down a)
q) = forall a. MinQueue (Down a) -> MaxQueue a
MaxQ (forall a. Ord a => (a -> Bool) -> MinQueue a -> MinQueue a
Min.filter (a -> Bool
p forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Down a -> a
unDown) MinQueue (Down a)
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 :: forall a.
Ord a =>
(a -> Bool) -> MaxQueue a -> (MaxQueue a, MaxQueue a)
partition a -> Bool
p (MaxQ MinQueue (Down a)
q) = (forall a. MinQueue (Down a) -> MaxQueue a
MaxQ MinQueue (Down a)
q0, forall a. MinQueue (Down a) -> MaxQueue a
MaxQ MinQueue (Down a)
q1)
  where  (MinQueue (Down a)
q0, MinQueue (Down a)
q1) = forall a.
Ord a =>
(a -> Bool) -> MinQueue a -> (MinQueue a, MinQueue a)
Min.partition (a -> Bool
p forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Down a -> a
unDown) MinQueue (Down a)
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 :: forall b a. Ord b => (a -> Maybe b) -> MaxQueue a -> MaxQueue b
mapMaybe a -> Maybe b
f (MaxQ MinQueue (Down a)
q) = forall a. MinQueue (Down a) -> MaxQueue a
MaxQ (forall b a. Ord b => (a -> Maybe b) -> MinQueue a -> MinQueue b
Min.mapMaybe (\(Down a
x) -> forall a. a -> Down a
Down forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> Maybe b
f a
x) MinQueue (Down a)
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 :: forall b c a.
(Ord b, Ord c) =>
(a -> Either b c) -> MaxQueue a -> (MaxQueue b, MaxQueue c)
mapEither a -> Either b c
f (MaxQ MinQueue (Down a)
q) = (forall a. MinQueue (Down a) -> MaxQueue a
MaxQ MinQueue (Down b)
q0, forall a. MinQueue (Down a) -> MaxQueue a
MaxQ MinQueue (Down c)
q1)
  where  (MinQueue (Down b)
q0, MinQueue (Down c)
q1) = forall b c a.
(Ord b, Ord c) =>
(a -> Either b c) -> MinQueue a -> (MinQueue b, MinQueue c)
Min.mapEither (forall a c b. (a -> c) -> (b -> c) -> Either a b -> c
either (forall a b. a -> Either a b
Left forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. a -> Down a
Down) (forall a b. b -> Either a b
Right forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. a -> Down a
Down) forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> Either b c
f forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Down a -> a
unDown) MinQueue (Down a)
q

-- | \(O(n)\). Creates a new priority queue containing the images of the elements of this queue.
-- Equivalent to @'fromList' . 'Data.List.map' f . toList@.
map :: Ord b => (a -> b) -> MaxQueue a -> MaxQueue b
map :: forall b a. Ord b => (a -> b) -> MaxQueue a -> MaxQueue b
map a -> b
f (MaxQ MinQueue (Down a)
q) = forall a. MinQueue (Down a) -> MaxQueue a
MaxQ (forall b a. Ord b => (a -> b) -> MinQueue a -> MinQueue b
Min.map (\(Down a
x) -> forall a. a -> Down a
Down (a -> b
f a
x)) MinQueue (Down a)
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 :: forall a b. (a -> b) -> MaxQueue a -> MaxQueue b
mapU a -> b
f (MaxQ MinQueue (Down a)
q) = forall a. MinQueue (Down a) -> MaxQueue a
MaxQ (forall a b. (a -> b) -> MinQueue a -> MinQueue b
Min.mapU (\(Down a
a) -> forall a. a -> Down a
Down (a -> b
f a
a)) MinQueue (Down a)
q)

-- | \(O(n)\). Unordered right fold on a priority queue.
foldrU :: (a -> b -> b) -> b -> MaxQueue a -> b
foldrU :: forall a b. (a -> b -> b) -> b -> MaxQueue a -> b
foldrU a -> b -> b
f b
z (MaxQ MinQueue (Down a)
q) = forall a b. (a -> b -> b) -> b -> MinQueue a -> b
Min.foldrU (forall a b c. (a -> b -> c) -> b -> a -> c
flip (forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr a -> b -> b
f)) b
z MinQueue (Down a)
q

-- | \(O(n)\). Unordered monoidal fold on a priority queue.
--
-- @since 1.4.2
foldMapU :: Monoid m => (a -> m) -> MaxQueue a -> m
foldMapU :: forall m a. Monoid m => (a -> m) -> MaxQueue a -> m
foldMapU a -> m
f (MaxQ MinQueue (Down a)
q) = forall m a. Monoid m => (a -> m) -> MinQueue a -> m
Min.foldMapU (a -> m
f forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Down a -> a
unDown) MinQueue (Down a)
q

-- | \(O(n)\). Unordered left fold on a priority queue. This is rarely
-- what you want; 'foldrU' and 'foldlU'' are more likely to perform
-- well.
foldlU :: (b -> a -> b) -> b -> MaxQueue a -> b
foldlU :: forall b a. (b -> a -> b) -> b -> MaxQueue a -> b
foldlU b -> a -> b
f b
z (MaxQ MinQueue (Down a)
q) = forall b a. (b -> a -> b) -> b -> MinQueue a -> b
Min.foldlU (forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
foldl b -> a -> b
f) b
z MinQueue (Down a)
q

-- | \(O(n)\). Unordered strict left fold on a priority queue.
--
-- @since 1.4.2
foldlU' :: (b -> a -> b) -> b -> MaxQueue a -> b
foldlU' :: forall b a. (b -> a -> b) -> b -> MaxQueue a -> b
foldlU' b -> a -> b
f b
z (MaxQ MinQueue (Down a)
q) = forall b a. (b -> a -> b) -> b -> MinQueue a -> b
Min.foldlU' (forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
foldl' b -> a -> b
f) b
z MinQueue (Down a)
q

{-# INLINE elemsU #-}
-- | Equivalent to 'toListU'.
elemsU :: MaxQueue a -> [a]
elemsU :: forall a. MaxQueue a -> [a]
elemsU = forall a. MaxQueue a -> [a]
toListU

{-# INLINE toListU #-}
-- | \(O(n)\). Returns a list of the elements of the priority queue, in no particular order.
toListU :: MaxQueue a -> [a]
toListU :: forall a. MaxQueue a -> [a]
toListU (MaxQ MinQueue (Down a)
q) = forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap forall a. Down a -> a
unDown (forall a. MinQueue a -> [a]
Min.toListU MinQueue (Down a)
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 :: forall a b. Ord a => (a -> b -> b) -> b -> MaxQueue a -> b
foldrAsc = forall a b. Ord a => (b -> a -> b) -> b -> MaxQueue a -> b
foldlDesc forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b c. (a -> b -> c) -> b -> a -> c
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 :: forall a b. Ord a => (b -> a -> b) -> b -> MaxQueue a -> b
foldlAsc = forall a b. Ord a => (a -> b -> b) -> b -> MaxQueue a -> b
foldrDesc forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b c. (a -> b -> c) -> b -> a -> c
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 :: forall a b. Ord a => (a -> b -> b) -> b -> MaxQueue a -> b
foldrDesc a -> b -> b
f b
z (MaxQ MinQueue (Down a)
q) = forall a b. Ord a => (a -> b -> b) -> b -> MinQueue a -> b
Min.foldrAsc (forall a b c. (a -> b -> c) -> b -> a -> c
flip (forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr a -> b -> b
f)) b
z MinQueue (Down a)
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 :: forall a b. Ord a => (b -> a -> b) -> b -> MaxQueue a -> b
foldlDesc b -> a -> b
f b
z (MaxQ MinQueue (Down a)
q) = forall a b. Ord a => (b -> a -> b) -> b -> MinQueue a -> b
Min.foldlAsc (forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
foldl b -> a -> b
f) b
z MinQueue (Down a)
q

{-# INLINE toAscList #-}
-- | \(O(n \log n)\). Extracts the elements of the priority queue in ascending order.
toAscList :: Ord a => MaxQueue a -> [a]
toAscList :: forall a. Ord a => MaxQueue a -> [a]
toAscList MaxQueue a
q = forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
build (\a -> b -> b
c b
nil -> forall a b. Ord a => (a -> b -> b) -> b -> MaxQueue a -> b
foldrAsc a -> b -> b
c b
nil MaxQueue a
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 :: forall a. Ord a => MaxQueue a -> [a]
toDescList MaxQueue a
q = forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
build (\a -> b -> b
c b
nil -> forall a b. Ord a => (a -> b -> b) -> b -> MaxQueue a -> b
foldrDesc a -> b -> b
c b
nil MaxQueue a
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 :: forall a. Ord a => MaxQueue a -> [a]
toList (MaxQ MinQueue (Down a)
q) = forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap forall a. Down a -> a
unDown (forall a. Ord a => MinQueue a -> [a]
Min.toList MinQueue (Down a)
q)

{-# INLINE fromAscList #-}
-- | \(O(n)\). Constructs a priority queue from an ascending list. /Warning/: Does not check the precondition.
fromAscList :: [a] -> MaxQueue a
fromAscList :: forall a. [a] -> MaxQueue a
fromAscList = forall a. MinQueue (Down a) -> MaxQueue a
MaxQ forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. [a] -> MinQueue a
Min.fromDescList forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap forall a. a -> Down a
Down

{-# INLINE fromDescList #-}
-- | \(O(n)\). Constructs a priority queue from a descending list. /Warning/: Does not check the precondition.
fromDescList :: [a] -> MaxQueue a
fromDescList :: forall a. [a] -> MaxQueue a
fromDescList = forall a. MinQueue (Down a) -> MaxQueue a
MaxQ forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. [a] -> MinQueue a
Min.fromAscList forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap forall a. a -> Down a
Down

{-# INLINE fromList #-}
-- | \(O(n \log n)\). Constructs a priority queue from an unordered list.
fromList :: Ord a => [a] -> MaxQueue a
fromList :: forall a. Ord a => [a] -> MaxQueue a
fromList = forall a. MinQueue (Down a) -> MaxQueue a
MaxQ forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Ord a => [a] -> MinQueue a
Min.fromList forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap forall a. a -> Down a
Down

-- | \(O(n)\). Constructs a priority queue from the keys of a 'Prio.MaxPQueue'.
keysQueue :: Prio.MaxPQueue k a -> MaxQueue k
keysQueue :: forall k a. MaxPQueue k a -> MaxQueue k
keysQueue (Prio.MaxPQ MinPQueue (Down k) a
q) = forall a. MinQueue (Down a) -> MaxQueue a
MaxQ (forall k a. MinPQueue k a -> MinQueue k
Min.keysQueue MinPQueue (Down k) a
q)

-- | \(O(\log n)\). @seqSpine q r@ forces the spine of @q@ and returns @r@.
--
-- Note: The spine of a 'MaxQueue' is stored somewhat lazily. Most operations
-- take great care to prevent chains of thunks from accumulating along the
-- spine to the detriment of performance. However, 'mapU' can leave expensive
-- thunks in the structure and repeated applications of that function can
-- create thunk chains.
seqSpine :: MaxQueue a -> b -> b
seqSpine :: forall a b. MaxQueue a -> b -> b
seqSpine (MaxQ MinQueue (Down a)
q) = forall a b. MinQueue a -> b -> b
Min.seqSpine MinQueue (Down a)
q