{-# LANGUAGE CPP #-}

-----------------------------------------------------------------------------
-- |
-- Module      :  Data.PQueue.Prio.Min
-- Copyright   :  (c) Louis Wasserman 2010
-- License     :  BSD-style
-- Maintainer  :  libraries@haskell.org
-- Stability   :  experimental
-- Portability :  portable
--
-- General purpose priority queue.
-- Each element is associated with a /key/, and the priority queue supports
-- viewing and extracting the element with the minimum key.
--
-- A worst-case bound is given for each operation. In some cases, an amortized
-- bound is also specified; these bounds hold even in a persistent context.
--
-- This implementation is based on a binomial heap augmented with a global root.
--
-- We do not guarantee stable behavior.
-- Ties are broken arbitrarily -- that is, if @k1 <= k2@ and @k2 <= k1@, then there
-- are no guarantees about the relative order in which @k1@, @k2@, and their associated
-- elements are returned. (Unlike Data.Map, we allow multiple elements with the
-- same key.)
--
-- 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.Prio.Min (
  MinPQueue,
  -- * Construction
  empty,
  singleton,
  insert,
  insertBehind,
  union,
  unions,
  -- * Query
  null,
  size,
  -- ** Minimum view
  findMin,
  getMin,
  deleteMin,
  deleteFindMin,
  adjustMin,
  adjustMinA,
  adjustMinWithKey,
  adjustMinWithKeyA,
  updateMin,
  updateMinA,
  updateMinWithKey,
  updateMinWithKeyA,
  minView,
  minViewWithKey,
  -- * Traversal
  -- ** Map
  map,
  mapWithKey,
  mapKeys,
  mapKeysMonotonic,
  -- ** Fold
  foldrWithKey,
  foldlWithKey,
  -- ** Traverse
  traverseWithKey,
  mapMWithKey,
  -- * Subsets
  -- ** Indexed
  take,
  drop,
  splitAt,
  -- ** Predicates
  takeWhile,
  takeWhileWithKey,
  dropWhile,
  dropWhileWithKey,
  span,
  spanWithKey,
  break,
  breakWithKey,
  -- *** Filter
  filter,
  filterWithKey,
  partition,
  partitionWithKey,
  mapMaybe,
  mapMaybeWithKey,
  mapEither,
  mapEitherWithKey,
  -- * List operations
  -- ** Conversion from lists
  fromList,
  fromAscList,
  fromDescList,
  -- ** Conversion to lists
  keys,
  elems,
  assocs,
  toAscList,
  toDescList,
  toList,
  -- * Unordered operations
  foldrU,
  foldMapWithKeyU,
  foldrWithKeyU,
  foldlU,
  foldlU',
  foldlWithKeyU,
  foldlWithKeyU',
  traverseU,
  traverseWithKeyU,
  keysU,
  elemsU,
  assocsU,
  toListU,
  -- * Helper methods
  seqSpine
  )
  where

import qualified Data.List as List
import Data.Maybe (fromMaybe)

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

import Data.PQueue.Prio.Internals

import Prelude hiding (map, filter, break, span, takeWhile, dropWhile, splitAt, take, drop, (!!), null)

#ifdef __GLASGOW_HASKELL__
import GHC.Exts (build)
#else
build :: ((a -> [a] -> [a]) -> [a] -> [a]) -> [a]
build f = f (:) []
#endif

(.:) :: (c -> d) -> (a -> b -> c) -> a -> b -> d
(c -> d
f .: :: forall c d a b. (c -> d) -> (a -> b -> c) -> a -> b -> d
.: a -> b -> c
g) a
x b
y = c -> d
f (a -> b -> c
g a
x b
y)

uncurry' :: (a -> b -> c) -> (a, b) -> c
uncurry' :: forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry' a -> b -> c
f (a
a, b
b) = a -> b -> c
f a
a b
b

infixr 8 .:

-- | \(O(1)\). The minimal (key, element) in the queue. Calls 'error' if empty.
findMin :: MinPQueue k a -> (k, a)
findMin :: forall k a. MinPQueue k a -> (k, a)
findMin = forall a. a -> Maybe a -> a
fromMaybe (forall a. HasCallStack => [Char] -> a
error [Char]
"Error: findMin called on an empty queue") forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall k a. MinPQueue k a -> Maybe (k, a)
getMin

-- | \(O(\log n)\). Deletes the minimal (key, element) in the queue. Returns an empty queue
-- if the queue is empty.
deleteMin :: Ord k => MinPQueue k a -> MinPQueue k a
deleteMin :: forall k a. Ord k => MinPQueue k a -> MinPQueue k a
deleteMin = forall k a.
Ord k =>
(a -> Maybe a) -> MinPQueue k a -> MinPQueue k a
updateMin (forall a b. a -> b -> a
const forall a. Maybe a
Nothing)

-- | \(O(\log n)\). Delete and find the element with the minimum key. Calls 'error' if empty.
deleteFindMin :: Ord k => MinPQueue k a -> ((k, a), MinPQueue k a)
deleteFindMin :: forall k a. Ord k => MinPQueue k a -> ((k, a), MinPQueue k a)
deleteFindMin = forall a. a -> Maybe a -> a
fromMaybe (forall a. HasCallStack => [Char] -> a
error [Char]
"Error: deleteFindMin called on an empty queue") forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall k a. Ord k => MinPQueue k a -> Maybe ((k, a), MinPQueue k a)
minViewWithKey

-- | \(O(1)\). Alter the value at the minimum key. If the queue is empty, does nothing.
adjustMin :: (a -> a) -> MinPQueue k a -> MinPQueue k a
adjustMin :: forall a k. (a -> a) -> MinPQueue k a -> MinPQueue k a
adjustMin = forall k a. (k -> a -> a) -> MinPQueue k a -> MinPQueue k a
adjustMinWithKey forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. a -> b -> a
const

-- | \(O(1)\). Alter the value at the minimum key in an 'Applicative' context. If
-- the queue is empty, does nothing.
--
-- @since 1.4.2
adjustMinA :: Applicative f => (a -> f a) -> MinPQueue k a -> f (MinPQueue k a)
adjustMinA :: forall (f :: * -> *) a k.
Applicative f =>
(a -> f a) -> MinPQueue k a -> f (MinPQueue k a)
adjustMinA = forall (f :: * -> *) k a.
Applicative f =>
(k -> a -> f a) -> MinPQueue k a -> f (MinPQueue k a)
adjustMinWithKeyA forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. a -> b -> a
const

-- | \(O(1)\) per operation. Alter the value at the minimum key in an 'Applicative' context. If the
-- queue is empty, does nothing.
--
-- @since 1.4.2
adjustMinWithKeyA :: Applicative f => (k -> a -> f a) -> MinPQueue k a -> f (MinPQueue k a)
adjustMinWithKeyA :: forall (f :: * -> *) k a.
Applicative f =>
(k -> a -> f a) -> MinPQueue k a -> f (MinPQueue k a)
adjustMinWithKeyA = forall (f :: * -> *) k a r.
Applicative f =>
(MinPQueue k a -> r) -> (k -> a -> f a) -> MinPQueue k a -> f r
adjustMinWithKeyA' forall a. a -> a
id

-- | \(O(\log n)\). (Actually \(O(1)\) if there's no deletion.) Update the value at the minimum key.
-- If the queue is empty, does nothing.
updateMin :: Ord k => (a -> Maybe a) -> MinPQueue k a -> MinPQueue k a
updateMin :: forall k a.
Ord k =>
(a -> Maybe a) -> MinPQueue k a -> MinPQueue k a
updateMin = forall k a.
Ord k =>
(k -> a -> Maybe a) -> MinPQueue k a -> MinPQueue k a
updateMinWithKey forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. a -> b -> a
const

-- | \(O(\log n)\) per operation. (Actually \(O(1)\) if there's no deletion.) Update
-- the value at the minimum key.  If the queue is empty, does nothing.
--
-- @since 1.4.2
updateMinA :: (Applicative f, Ord k) => (a -> f (Maybe a)) -> MinPQueue k a -> f (MinPQueue k a)
updateMinA :: forall (f :: * -> *) k a.
(Applicative f, Ord k) =>
(a -> f (Maybe a)) -> MinPQueue k a -> f (MinPQueue k a)
updateMinA = forall (f :: * -> *) k a.
(Applicative f, Ord k) =>
(k -> a -> f (Maybe a)) -> MinPQueue k a -> f (MinPQueue k a)
updateMinWithKeyA forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. a -> b -> a
const

-- | \(O(\log n)\) per operation. (Actually \(O(1)\) if there's no deletion.) Update
-- the value at the minimum key in an 'Applicative' context. If the queue is
-- empty, does nothing.
--
-- @since 1.4.2
updateMinWithKeyA :: (Applicative f, Ord k) => (k -> a -> f (Maybe a)) -> MinPQueue k a -> f (MinPQueue k a)
updateMinWithKeyA :: forall (f :: * -> *) k a.
(Applicative f, Ord k) =>
(k -> a -> f (Maybe a)) -> MinPQueue k a -> f (MinPQueue k a)
updateMinWithKeyA = forall (f :: * -> *) k a r.
(Applicative f, Ord k) =>
(MinPQueue k a -> r)
-> (k -> a -> f (Maybe a)) -> MinPQueue k a -> f r
updateMinWithKeyA' forall a. a -> a
id

-- | \(O(\log n)\). Retrieves the value associated with the minimal key of the queue, and the queue
-- stripped of that element, or 'Nothing' if passed an empty queue.
minView :: Ord k => MinPQueue k a -> Maybe (a, MinPQueue k a)
minView :: forall k a. Ord k => MinPQueue k a -> Maybe (a, MinPQueue k a)
minView MinPQueue k a
q = do  ((k
_, a
a), MinPQueue k a
q') <- forall k a. Ord k => MinPQueue k a -> Maybe ((k, a), MinPQueue k a)
minViewWithKey MinPQueue k a
q
                forall (m :: * -> *) a. Monad m => a -> m a
return (a
a, MinPQueue k a
q')

-- | \(O(n)\). Map a function over all values in the queue.
map :: (a -> b) -> MinPQueue k a -> MinPQueue k b
map :: forall a b k. (a -> b) -> MinPQueue k a -> MinPQueue k b
map = forall k a b. (k -> a -> b) -> MinPQueue k a -> MinPQueue k b
mapWithKey forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. a -> b -> a
const

-- | \(O(n)\). @'mapKeys' f q@ is the queue obtained by applying @f@ to each key of @q@.
mapKeys :: Ord k' => (k -> k') -> MinPQueue k a -> MinPQueue k' a
mapKeys :: forall k' k a.
Ord k' =>
(k -> k') -> MinPQueue k a -> MinPQueue k' a
mapKeys k -> k'
f MinPQueue k a
q = forall k a. Ord k => [(k, a)] -> MinPQueue k a
fromList [(k -> k'
f k
k, a
a) | (k
k, a
a) <- forall k a. MinPQueue k a -> [(k, a)]
toListU MinPQueue k a
q]

-- | \(O(n)\). Map values and collect the 'Just' results.
mapMaybe :: Ord k => (a -> Maybe b) -> MinPQueue k a -> MinPQueue k b
mapMaybe :: forall k a b.
Ord k =>
(a -> Maybe b) -> MinPQueue k a -> MinPQueue k b
mapMaybe = forall k a b.
Ord k =>
(k -> a -> Maybe b) -> MinPQueue k a -> MinPQueue k b
mapMaybeWithKey forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. a -> b -> a
const

-- | \(O(n)\). Map values and separate the 'Left' and 'Right' results.
mapEither :: Ord k => (a -> Either b c) -> MinPQueue k a -> (MinPQueue k b, MinPQueue k c)
mapEither :: forall k a b c.
Ord k =>
(a -> Either b c)
-> MinPQueue k a -> (MinPQueue k b, MinPQueue k c)
mapEither = forall k a b c.
Ord k =>
(k -> a -> Either b c)
-> MinPQueue k a -> (MinPQueue k b, MinPQueue k c)
mapEitherWithKey forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. a -> b -> a
const

-- | \(O(n)\). Filter all values that satisfy the predicate.
filter :: Ord k => (a -> Bool) -> MinPQueue k a -> MinPQueue k a
filter :: forall k a. Ord k => (a -> Bool) -> MinPQueue k a -> MinPQueue k a
filter = forall k a.
Ord k =>
(k -> a -> Bool) -> MinPQueue k a -> MinPQueue k a
filterWithKey forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. a -> b -> a
const

-- | \(O(n)\). Filter all values that satisfy the predicate.
filterWithKey :: Ord k => (k -> a -> Bool) -> MinPQueue k a -> MinPQueue k a
filterWithKey :: forall k a.
Ord k =>
(k -> a -> Bool) -> MinPQueue k a -> MinPQueue k a
filterWithKey k -> a -> Bool
p = forall k a b.
Ord k =>
(k -> a -> Maybe b) -> MinPQueue k a -> MinPQueue k b
mapMaybeWithKey (\k
k a
a -> if k -> a -> Bool
p k
k a
a then forall a. a -> Maybe a
Just a
a else forall a. Maybe a
Nothing)

-- | \(O(n)\). Partition the queue according to a predicate. The first queue contains all elements
-- which satisfy the predicate, the second all elements that fail the predicate.
partition :: Ord k => (a -> Bool) -> MinPQueue k a -> (MinPQueue k a, MinPQueue k a)
partition :: forall k a.
Ord k =>
(a -> Bool) -> MinPQueue k a -> (MinPQueue k a, MinPQueue k a)
partition = forall k a.
Ord k =>
(k -> a -> Bool) -> MinPQueue k a -> (MinPQueue k a, MinPQueue k a)
partitionWithKey forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. a -> b -> a
const

-- | \(O(n)\). Partition the queue according to a predicate. The first queue contains all elements
-- which satisfy the predicate, the second all elements that fail the predicate.
partitionWithKey :: Ord k => (k -> a -> Bool) -> MinPQueue k a -> (MinPQueue k a, MinPQueue k a)
partitionWithKey :: forall k a.
Ord k =>
(k -> a -> Bool) -> MinPQueue k a -> (MinPQueue k a, MinPQueue k a)
partitionWithKey k -> a -> Bool
p = forall k a b c.
Ord k =>
(k -> a -> Either b c)
-> MinPQueue k a -> (MinPQueue k b, MinPQueue k c)
mapEitherWithKey (\k
k a
a -> if k -> a -> Bool
p k
k a
a then forall a b. a -> Either a b
Left a
a else forall a b. b -> Either a b
Right a
a)

{-# INLINE take #-}
-- | \(O(k \log n)\)/. Takes the first @k@ (key, value) pairs in the queue, or the first @n@ if @k >= n@.
-- (@'take' k q == 'List.take' k ('toAscList' q)@)
take :: Ord k => Int -> MinPQueue k a -> [(k, a)]
take :: forall k a. Ord k => Int -> MinPQueue k a -> [(k, a)]
take Int
n = forall a. Int -> [a] -> [a]
List.take Int
n forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall k a. Ord k => MinPQueue k a -> [(k, a)]
toAscList

-- | \(O(k \log n)\)/. Deletes the first @k@ (key, value) pairs in the queue, or returns an empty queue if @k >= n@.
drop :: Ord k => Int -> MinPQueue k a -> MinPQueue k a
drop :: forall k a. Ord k => Int -> MinPQueue k a -> MinPQueue k a
drop Int
n0 MinPQueue k a
q0
  | Int
n0 forall a. Ord a => a -> a -> Bool
<= Int
0  = MinPQueue k a
q0
  | Int
n0 forall a. Ord a => a -> a -> Bool
>= forall k a. MinPQueue k a -> Int
size MinPQueue k a
q0  = forall k a. MinPQueue k a
empty
  | Bool
otherwise  = forall {t} {k} {a}.
(Num t, Ord k, Eq t) =>
t -> MinPQueue k a -> MinPQueue k a
drop' Int
n0 MinPQueue k a
q0
  where
    drop' :: t -> MinPQueue k a -> MinPQueue k a
drop' t
n MinPQueue k a
q
      | t
n forall a. Eq a => a -> a -> Bool
== t
0    = MinPQueue k a
q
      | Bool
otherwise = t -> MinPQueue k a -> MinPQueue k a
drop' (t
n forall a. Num a => a -> a -> a
- t
1) (forall k a. Ord k => MinPQueue k a -> MinPQueue k a
deleteMin MinPQueue k a
q)

-- | \(O(k \log n)\)/. Equivalent to @('take' k q, 'drop' k q)@.
splitAt :: Ord k => Int -> MinPQueue k a -> ([(k, a)], MinPQueue k a)
splitAt :: forall k a.
Ord k =>
Int -> MinPQueue k a -> ([(k, a)], MinPQueue k a)
splitAt Int
n MinPQueue k a
q
  | Int
n forall a. Ord a => a -> a -> Bool
<= Int
0     = ([], MinPQueue k a
q)
  | Bool
otherwise  = Int
n seq :: forall a b. a -> b -> b
`seq` case forall k a. Ord k => MinPQueue k a -> Maybe ((k, a), MinPQueue k a)
minViewWithKey MinPQueue k a
q of
      Just ((k, a)
ka, MinPQueue k a
q') -> let ([(k, a)]
kas, MinPQueue k a
q'') = forall k a.
Ord k =>
Int -> MinPQueue k a -> ([(k, a)], MinPQueue k a)
splitAt (Int
n forall a. Num a => a -> a -> a
- Int
1) MinPQueue k a
q' in ((k, a)
ka forall a. a -> [a] -> [a]
: [(k, a)]
kas, MinPQueue k a
q'')
      Maybe ((k, a), MinPQueue k a)
_             -> ([], MinPQueue k a
q)

{-# INLINE takeWhile #-}
-- | Takes the longest possible prefix of elements satisfying the predicate.
-- (@'takeWhile' p q == 'List.takeWhile' (p . 'snd') ('toAscList' q)@)
takeWhile :: Ord k => (a -> Bool) -> MinPQueue k a -> [(k, a)]
takeWhile :: forall k a. Ord k => (a -> Bool) -> MinPQueue k a -> [(k, a)]
takeWhile = forall k a. Ord k => (k -> a -> Bool) -> MinPQueue k a -> [(k, a)]
takeWhileWithKey forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. a -> b -> a
const

{-# INLINE takeWhileWithKey #-}
-- | Takes the longest possible prefix of elements satisfying the predicate.
-- (@'takeWhile' p q == 'List.takeWhile' (uncurry p) ('toAscList' q)@)
takeWhileWithKey :: Ord k => (k -> a -> Bool) -> MinPQueue k a -> [(k, a)]
takeWhileWithKey :: forall k a. Ord k => (k -> a -> Bool) -> MinPQueue k a -> [(k, a)]
takeWhileWithKey k -> a -> Bool
p0 = forall {t :: * -> *} {a}. Foldable t => (a -> Bool) -> t a -> [a]
takeWhileFB (forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry' k -> a -> Bool
p0) forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall k a. Ord k => MinPQueue k a -> [(k, a)]
toAscList where
  takeWhileFB :: (a -> Bool) -> t a -> [a]
takeWhileFB a -> Bool
p t a
xs = forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
build (\a -> b -> b
c b
n -> forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr (\a
x b
z -> if a -> Bool
p a
x then a
x a -> b -> b
`c` b
z else b
n) b
n t a
xs)

-- | Removes the longest possible prefix of elements satisfying the predicate.
dropWhile :: Ord k => (a -> Bool) -> MinPQueue k a -> MinPQueue k a
dropWhile :: forall k a. Ord k => (a -> Bool) -> MinPQueue k a -> MinPQueue k a
dropWhile = forall k a.
Ord k =>
(k -> a -> Bool) -> MinPQueue k a -> MinPQueue k a
dropWhileWithKey forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. a -> b -> a
const

-- | Removes the longest possible prefix of elements satisfying the predicate.
dropWhileWithKey :: Ord k => (k -> a -> Bool) -> MinPQueue k a -> MinPQueue k a
dropWhileWithKey :: forall k a.
Ord k =>
(k -> a -> Bool) -> MinPQueue k a -> MinPQueue k a
dropWhileWithKey k -> a -> Bool
p MinPQueue k a
q = case forall k a. Ord k => MinPQueue k a -> Maybe ((k, a), MinPQueue k a)
minViewWithKey MinPQueue k a
q of
  Just ((k
k, a
a), MinPQueue k a
q')
    | k -> a -> Bool
p k
k a
a -> forall k a.
Ord k =>
(k -> a -> Bool) -> MinPQueue k a -> MinPQueue k a
dropWhileWithKey k -> a -> Bool
p MinPQueue k a
q'
  Maybe ((k, a), MinPQueue k a)
_         -> MinPQueue k a
q

-- | Equivalent to @('takeWhile' p q, 'dropWhile' p q)@.
span :: Ord k => (a -> Bool) -> MinPQueue k a -> ([(k, a)], MinPQueue k a)
span :: forall k a.
Ord k =>
(a -> Bool) -> MinPQueue k a -> ([(k, a)], MinPQueue k a)
span = forall k a.
Ord k =>
(k -> a -> Bool) -> MinPQueue k a -> ([(k, a)], MinPQueue k a)
spanWithKey forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. a -> b -> a
const

-- | Equivalent to @'span' ('not' . p)@.
break :: Ord k => (a -> Bool) -> MinPQueue k a -> ([(k, a)], MinPQueue k a)
break :: forall k a.
Ord k =>
(a -> Bool) -> MinPQueue k a -> ([(k, a)], MinPQueue k a)
break a -> Bool
p = forall k a.
Ord k =>
(a -> Bool) -> MinPQueue k a -> ([(k, a)], MinPQueue k a)
span (Bool -> Bool
not forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> Bool
p)

-- | Equivalent to @('takeWhileWithKey' p q, 'dropWhileWithKey' p q)@.
spanWithKey :: Ord k => (k -> a -> Bool) -> MinPQueue k a -> ([(k, a)], MinPQueue k a)
spanWithKey :: forall k a.
Ord k =>
(k -> a -> Bool) -> MinPQueue k a -> ([(k, a)], MinPQueue k a)
spanWithKey k -> a -> Bool
p MinPQueue k a
q = case forall k a. Ord k => MinPQueue k a -> Maybe ((k, a), MinPQueue k a)
minViewWithKey MinPQueue k a
q of
  Just (t :: (k, a)
t@(k
k, a
a), MinPQueue k a
q')
    | k -> a -> Bool
p k
k a
a -> let ([(k, a)]
kas, MinPQueue k a
q'') = forall k a.
Ord k =>
(k -> a -> Bool) -> MinPQueue k a -> ([(k, a)], MinPQueue k a)
spanWithKey k -> a -> Bool
p MinPQueue k a
q' in ((k, a)
t forall a. a -> [a] -> [a]
: [(k, a)]
kas, MinPQueue k a
q'')
  Maybe ((k, a), MinPQueue k a)
_         -> ([], MinPQueue k a
q)

-- | Equivalent to @'spanWithKey' (\ k a -> 'not' (p k a)) q@.
breakWithKey :: Ord k => (k -> a -> Bool) -> MinPQueue k a -> ([(k, a)], MinPQueue k a)
breakWithKey :: forall k a.
Ord k =>
(k -> a -> Bool) -> MinPQueue k a -> ([(k, a)], MinPQueue k a)
breakWithKey k -> a -> Bool
p = forall k a.
Ord k =>
(k -> a -> Bool) -> MinPQueue k a -> ([(k, a)], MinPQueue k a)
spanWithKey (Bool -> Bool
not forall c d a b. (c -> d) -> (a -> b -> c) -> a -> b -> d
.: k -> a -> Bool
p)

-- | \(O(n)\). Build a priority queue from a descending list of (key, value) pairs. /The precondition is not checked./
fromDescList :: [(k, a)] -> MinPQueue k a
{-# INLINE fromDescList #-}
fromDescList :: forall k a. [(k, a)] -> MinPQueue k a
fromDescList [(k, a)]
xs = forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
List.foldl' (\MinPQueue k a
q (k
k, a
a) -> forall k a. k -> a -> MinPQueue k a -> MinPQueue k a
insertMin' k
k a
a MinPQueue k a
q) forall k a. MinPQueue k a
empty [(k, a)]
xs

{-# INLINE keys #-}
-- | \(O(n \log n)\). Return all keys of the queue in ascending order.
keys :: Ord k => MinPQueue k a -> [k]
keys :: forall k a. Ord k => MinPQueue k a -> [k]
keys = forall a b. (a -> b) -> [a] -> [b]
List.map forall a b. (a, b) -> a
fst forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall k a. Ord k => MinPQueue k a -> [(k, a)]
toAscList

{-# INLINE elems #-}
-- | \(O(n \log n)\). Return all elements of the queue in ascending order by key.
elems :: Ord k => MinPQueue k a -> [a]
elems :: forall k a. Ord k => MinPQueue k a -> [a]
elems = forall a b. (a -> b) -> [a] -> [b]
List.map forall a b. (a, b) -> b
snd forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall k a. Ord k => MinPQueue k a -> [(k, a)]
toAscList

{-# INLINE toList #-}
-- | \(O(n \log n)\). Equivalent to 'toAscList'.
--
-- If the traversal order is irrelevant, consider using 'toListU'.
toList :: Ord k => MinPQueue k a -> [(k, a)]
toList :: forall k a. Ord k => MinPQueue k a -> [(k, a)]
toList = forall k a. Ord k => MinPQueue k a -> [(k, a)]
toAscList

{-# INLINE assocs #-}
-- | \(O(n \log n)\). Equivalent to 'toAscList'.
assocs :: Ord k => MinPQueue k a -> [(k, a)]
assocs :: forall k a. Ord k => MinPQueue k a -> [(k, a)]
assocs = forall k a. Ord k => MinPQueue k a -> [(k, a)]
toAscList

{-# INLINE keysU #-}
-- | \(O(n)\). Return all keys of the queue in no particular order.
keysU :: MinPQueue k a -> [k]
keysU :: forall k a. MinPQueue k a -> [k]
keysU = forall a b. (a -> b) -> [a] -> [b]
List.map forall a b. (a, b) -> a
fst forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall k a. MinPQueue k a -> [(k, a)]
toListU

{-# INLINE elemsU #-}
-- | \(O(n)\). Return all elements of the queue in no particular order.
elemsU :: MinPQueue k a -> [a]
elemsU :: forall k a. MinPQueue k a -> [a]
elemsU = forall a b. (a -> b) -> [a] -> [b]
List.map forall a b. (a, b) -> b
snd forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall k a. MinPQueue k a -> [(k, a)]
toListU

{-# INLINE assocsU #-}
-- | \(O(n)\). Equivalent to 'toListU'.
assocsU :: MinPQueue k a -> [(k, a)]
assocsU :: forall k a. MinPQueue k a -> [(k, a)]
assocsU = forall k a. MinPQueue k a -> [(k, a)]
toListU

-- | \(O(n)\). An unordered left fold over the elements of the queue, in no
-- particular order. This is rarely what you want; 'foldrU' and 'foldlU'' are
-- more likely to perform well.
foldlU :: (b -> a -> b) -> b -> MinPQueue k a -> b
foldlU :: forall b a k. (b -> a -> b) -> b -> MinPQueue k a -> b
foldlU b -> a -> b
f = forall b k a. (b -> k -> a -> b) -> b -> MinPQueue k a -> b
foldlWithKeyU (forall a b. a -> b -> a
const forall b c a. (b -> c) -> (a -> b) -> a -> c
. b -> a -> b
f)

-- | \(O(n)\). An unordered strict left fold over the elements of the queue, in no
-- particular order.
--
-- @since 1.4.2
foldlU' :: (b -> a -> b) -> b -> MinPQueue k a -> b
foldlU' :: forall b a k. (b -> a -> b) -> b -> MinPQueue k a -> b
foldlU' b -> a -> b
f = forall b k a. (b -> k -> a -> b) -> b -> MinPQueue k a -> b
foldlWithKeyU' (forall a b. a -> b -> a
const forall b c a. (b -> c) -> (a -> b) -> a -> c
. b -> a -> b
f)

-- | \(O(n)\). An unordered traversal over a priority queue, in no particular order.
-- While there is no guarantee in which order the elements are traversed, the resulting
-- priority queue will be perfectly valid.
traverseU :: (Applicative f) => (a -> f b) -> MinPQueue k a -> f (MinPQueue k b)
traverseU :: forall (f :: * -> *) a b k.
Applicative f =>
(a -> f b) -> MinPQueue k a -> f (MinPQueue k b)
traverseU = forall (f :: * -> *) k a b.
Applicative f =>
(k -> a -> f b) -> MinPQueue k a -> f (MinPQueue k b)
traverseWithKeyU forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. a -> b -> a
const