containers-0.8: src/Data/IntMap/Internal.hs
{-# LANGUAGE CPP #-}
{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE PatternGuards #-}
#ifdef __GLASGOW_HASKELL__
{-# LANGUAGE DeriveLift #-}
{-# LANGUAGE MagicHash #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE Trustworthy #-}
#endif
{-# OPTIONS_HADDOCK not-home #-}
{-# OPTIONS_GHC -fno-warn-incomplete-uni-patterns #-}
#include "containers.h"
-----------------------------------------------------------------------------
-- |
-- Module : Data.IntMap.Internal
-- Copyright : (c) Daan Leijen 2002
-- (c) Andriy Palamarchuk 2008
-- (c) wren romano 2016
-- License : BSD-style
-- Maintainer : libraries@haskell.org
-- Portability : portable
--
-- = WARNING
--
-- This module is considered __internal__.
--
-- The Package Versioning Policy __does not apply__.
--
-- The contents of this module may change __in any way whatsoever__
-- and __without any warning__ between minor versions of this package.
--
-- Authors importing this module are expected to track development
-- closely.
--
--
-- = Finite Int Maps (lazy interface internals)
--
-- The @'IntMap' v@ type represents a finite map (sometimes called a dictionary)
-- from keys of type @Int@ to values of type @v@.
--
--
-- == Implementation
--
-- The implementation is based on /big-endian patricia trees/. This data
-- structure performs especially well on binary operations like 'union'
-- and 'intersection'. Additionally, benchmarks show that it is also
-- (much) faster on insertions and deletions when compared to a generic
-- size-balanced map implementation (see "Data.Map").
--
-- * Chris Okasaki and Andy Gill,
-- \"/Fast Mergeable Integer Maps/\",
-- Workshop on ML, September 1998, pages 77-86,
-- <https://web.archive.org/web/20150417234429/https://ittc.ku.edu/~andygill/papers/IntMap98.pdf>.
--
-- * D.R. Morrison,
-- \"/PATRICIA -- Practical Algorithm To Retrieve Information Coded In Alphanumeric/\",
-- Journal of the ACM, 15(4), October 1968, pages 514-534,
-- <https://doi.org/10.1145/321479.321481>.
--
-- @since 0.5.9
-----------------------------------------------------------------------------
-- [Note: Local 'go' functions and capturing]
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-- Care must be taken when using 'go' function which captures an argument.
-- Sometimes (for example when the argument is passed to a data constructor,
-- as in insert), GHC heap-allocates more than necessary. Therefore C-- code
-- must be checked for increased allocation when creating and modifying such
-- functions.
-- [Note: Order of constructors]
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-- The order of constructors of IntMap matters when considering performance.
-- Currently in GHC 7.0, when type has 3 constructors, they are matched from
-- the first to the last -- the best performance is achieved when the
-- constructors are ordered by frequency.
-- On GHC 7.0, reordering constructors from Nil | Tip | Bin to Bin | Tip | Nil
-- improves the benchmark by circa 10%.
--
module Data.IntMap.Internal (
-- * Map type
IntMap(..) -- instance Eq,Show
, Key
-- * Operators
, (!), (!?), (\\)
-- * Query
, null
, size
, member
, notMember
, lookup
, findWithDefault
, lookupLT
, lookupGT
, lookupLE
, lookupGE
, disjoint
-- * Construction
, empty
, singleton
-- ** Insertion
, insert
, insertWith
, insertWithKey
, insertLookupWithKey
-- ** Delete\/Update
, delete
, adjust
, adjustWithKey
, update
, updateWithKey
, updateLookupWithKey
, alter
, alterF
-- * Combine
-- ** Union
, union
, unionWith
, unionWithKey
, unions
, unionsWith
-- ** Difference
, difference
, differenceWith
, differenceWithKey
-- ** Intersection
, intersection
, intersectionWith
, intersectionWithKey
-- ** Symmetric difference
, symmetricDifference
-- ** Compose
, compose
-- ** General combining function
, SimpleWhenMissing
, SimpleWhenMatched
, runWhenMatched
, runWhenMissing
, merge
-- *** @WhenMatched@ tactics
, zipWithMaybeMatched
, zipWithMatched
-- *** @WhenMissing@ tactics
, mapMaybeMissing
, dropMissing
, preserveMissing
, mapMissing
, filterMissing
-- ** Applicative general combining function
, WhenMissing (..)
, WhenMatched (..)
, mergeA
-- *** @WhenMatched@ tactics
-- | The tactics described for 'merge' work for
-- 'mergeA' as well. Furthermore, the following
-- are available.
, zipWithMaybeAMatched
, zipWithAMatched
-- *** @WhenMissing@ tactics
-- | The tactics described for 'merge' work for
-- 'mergeA' as well. Furthermore, the following
-- are available.
, traverseMaybeMissing
, traverseMissing
, filterAMissing
-- ** Deprecated general combining function
, mergeWithKey
, mergeWithKey'
-- * Traversal
-- ** Map
, map
, mapWithKey
, traverseWithKey
, traverseMaybeWithKey
, mapAccum
, mapAccumWithKey
, mapAccumRWithKey
, mapKeys
, mapKeysWith
, mapKeysMonotonic
-- * Folds
, foldr
, foldl
, foldrWithKey
, foldlWithKey
, foldMapWithKey
-- ** Strict folds
, foldr'
, foldl'
, foldrWithKey'
, foldlWithKey'
-- * Conversion
, elems
, keys
, assocs
, keysSet
, fromSet
-- ** Lists
, toList
, fromList
, fromListWith
, fromListWithKey
-- ** Ordered lists
, toAscList
, toDescList
, fromAscList
, fromAscListWith
, fromAscListWithKey
, fromDistinctAscList
-- * Filter
, filter
, filterKeys
, filterWithKey
, restrictKeys
, withoutKeys
, partition
, partitionWithKey
, takeWhileAntitone
, dropWhileAntitone
, spanAntitone
, mapMaybe
, mapMaybeWithKey
, mapEither
, mapEitherWithKey
, split
, splitLookup
, splitRoot
-- * Submap
, isSubmapOf, isSubmapOfBy
, isProperSubmapOf, isProperSubmapOfBy
-- * Min\/Max
, lookupMin
, lookupMax
, findMin
, findMax
, deleteMin
, deleteMax
, deleteFindMin
, deleteFindMax
, updateMin
, updateMax
, updateMinWithKey
, updateMaxWithKey
, minView
, maxView
, minViewWithKey
, maxViewWithKey
-- * Debugging
, showTree
, showTreeWith
-- * Utility
, link
, linkKey
, linkWithMask
, bin
, binCheckLeft
, binCheckRight
-- * Used by "IntMap.Merge.Lazy" and "IntMap.Merge.Strict"
, mapWhenMissing
, mapWhenMatched
, lmapWhenMissing
, contramapFirstWhenMatched
, contramapSecondWhenMatched
, mapGentlyWhenMissing
, mapGentlyWhenMatched
) where
import Data.Functor.Identity (Identity (..))
import Data.Semigroup (Semigroup(stimes))
#if !(MIN_VERSION_base(4,11,0))
import Data.Semigroup (Semigroup((<>)))
#endif
import Data.Semigroup (stimesIdempotentMonoid)
import Data.Functor.Classes
import Control.DeepSeq (NFData(rnf),NFData1(liftRnf))
import Data.Bits
import qualified Data.Foldable as Foldable
import Data.Maybe (fromMaybe)
import Utils.Containers.Internal.Prelude hiding
(lookup, map, filter, foldr, foldl, foldl', null)
import Prelude ()
import qualified Data.IntSet.Internal as IntSet
import Data.IntSet.Internal.IntTreeCommons
( Key
, Prefix(..)
, nomatch
, left
, signBranch
, mask
, branchMask
, TreeTreeBranch(..)
, treeTreeBranch
, i2w
, Order(..)
)
import Utils.Containers.Internal.BitUtil (shiftLL, shiftRL, iShiftRL)
import Utils.Containers.Internal.StrictPair
#ifdef __GLASGOW_HASKELL__
import Data.Coerce
import Data.Data (Data(..), Constr, mkConstr, constrIndex,
DataType, mkDataType, gcast1)
import qualified Data.Data as Data
import GHC.Exts (build)
import qualified GHC.Exts as GHCExts
import Language.Haskell.TH.Syntax (Lift)
-- See Note [ Template Haskell Dependencies ]
import Language.Haskell.TH ()
#endif
#if defined(__GLASGOW_HASKELL__) || defined(__MHS__)
import Text.Read
#endif
import qualified Control.Category as Category
{--------------------------------------------------------------------
Types
--------------------------------------------------------------------}
-- | A map of integers to values @a@.
-- See Note: Order of constructors
data IntMap a = Bin {-# UNPACK #-} !Prefix
!(IntMap a)
!(IntMap a)
| Tip {-# UNPACK #-} !Key a
| Nil
--
-- Note [IntMap structure and invariants]
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
--
-- * Nil is never found as a child of Bin.
--
-- * The Prefix of a Bin indicates the common high-order bits that all keys in
-- the Bin share.
--
-- * The least significant set bit of the Int value of a Prefix is called the
-- mask bit.
--
-- * All the bits to the left of the mask bit are called the shared prefix. All
-- keys stored in the Bin begin with the shared prefix.
--
-- * All keys in the left child of the Bin have the mask bit unset, and all keys
-- in the right child have the mask bit set. It follows that
--
-- 1. The Int value of the Prefix of a Bin is the smallest key that can be
-- present in the right child of the Bin.
--
-- 2. All keys in the right child of a Bin are greater than keys in the
-- left child, with one exceptional situation. If the Bin separates
-- negative and non-negative keys, the mask bit is the sign bit and the
-- left child stores the non-negative keys while the right child stores the
-- negative keys.
--
-- * All bits to the right of the mask bit are set to 0 in a Prefix.
--
-- See Note [Okasaki-Gill] for how the implementation here relates to the one in
-- Okasaki and Gill's paper.
-- Some stuff from "Data.IntSet.Internal", for 'restrictKeys' and
-- 'withoutKeys' to use.
type IntSetPrefix = Int
type IntSetBitMap = Word
#ifdef __GLASGOW_HASKELL__
-- | @since 0.6.6
deriving instance Lift a => Lift (IntMap a)
#endif
bitmapOf :: Int -> IntSetBitMap
bitmapOf x = shiftLL 1 (x .&. IntSet.suffixBitMask)
{-# INLINE bitmapOf #-}
{--------------------------------------------------------------------
Operators
--------------------------------------------------------------------}
-- | \(O(\min(n,W))\). Find the value at a key.
-- Calls 'error' when the element can not be found.
--
-- > fromList [(5,'a'), (3,'b')] ! 1 Error: element not in the map
-- > fromList [(5,'a'), (3,'b')] ! 5 == 'a'
(!) :: IntMap a -> Key -> a
(!) m k = find k m
-- | \(O(\min(n,W))\). Find the value at a key.
-- Returns 'Nothing' when the element can not be found.
--
-- > fromList [(5,'a'), (3,'b')] !? 1 == Nothing
-- > fromList [(5,'a'), (3,'b')] !? 5 == Just 'a'
--
-- @since 0.5.11
(!?) :: IntMap a -> Key -> Maybe a
(!?) m k = lookup k m
-- | Same as 'difference'.
(\\) :: IntMap a -> IntMap b -> IntMap a
m1 \\ m2 = difference m1 m2
infixl 9 !?,\\{-This comment teaches CPP correct behaviour -}
{--------------------------------------------------------------------
Types
--------------------------------------------------------------------}
-- | @mempty@ = 'empty'
instance Monoid (IntMap a) where
mempty = empty
mconcat = unions
mappend = (<>)
-- | @(<>)@ = 'union'
--
-- @since 0.5.7
instance Semigroup (IntMap a) where
(<>) = union
stimes = stimesIdempotentMonoid
-- | Folds in order of increasing key.
instance Foldable.Foldable IntMap where
fold = go
where go Nil = mempty
go (Tip _ v) = v
go (Bin p l r)
| signBranch p = go r `mappend` go l
| otherwise = go l `mappend` go r
{-# INLINABLE fold #-}
foldr = foldr
{-# INLINE foldr #-}
foldl = foldl
{-# INLINE foldl #-}
foldMap f t = go t
where go Nil = mempty
go (Tip _ v) = f v
go (Bin p l r)
| signBranch p = go r `mappend` go l
| otherwise = go l `mappend` go r
{-# INLINE foldMap #-}
foldl' = foldl'
{-# INLINE foldl' #-}
foldr' = foldr'
{-# INLINE foldr' #-}
length = size
{-# INLINE length #-}
null = null
{-# INLINE null #-}
toList = elems -- NB: Foldable.toList /= IntMap.toList
{-# INLINE toList #-}
elem = go
where go !_ Nil = False
go x (Tip _ y) = x == y
go x (Bin _ l r) = go x l || go x r
{-# INLINABLE elem #-}
maximum = start
where start Nil = error "Data.Foldable.maximum (for Data.IntMap): empty map"
start (Tip _ y) = y
start (Bin p l r)
| signBranch p = go (start r) l
| otherwise = go (start l) r
go !m Nil = m
go m (Tip _ y) = max m y
go m (Bin _ l r) = go (go m l) r
{-# INLINABLE maximum #-}
minimum = start
where start Nil = error "Data.Foldable.minimum (for Data.IntMap): empty map"
start (Tip _ y) = y
start (Bin p l r)
| signBranch p = go (start r) l
| otherwise = go (start l) r
go !m Nil = m
go m (Tip _ y) = min m y
go m (Bin _ l r) = go (go m l) r
{-# INLINABLE minimum #-}
sum = foldl' (+) 0
{-# INLINABLE sum #-}
product = foldl' (*) 1
{-# INLINABLE product #-}
-- | Traverses in order of increasing key.
instance Traversable IntMap where
traverse f = traverseWithKey (\_ -> f)
{-# INLINE traverse #-}
instance NFData a => NFData (IntMap a) where
rnf Nil = ()
rnf (Tip _ v) = rnf v
rnf (Bin _ l r) = rnf l `seq` rnf r
-- | @since 0.8
instance NFData1 IntMap where
liftRnf rnfx = go
where
go Nil = ()
go (Tip _ v) = rnfx v
go (Bin _ l r) = go l `seq` go r
#if __GLASGOW_HASKELL__
{--------------------------------------------------------------------
A Data instance
--------------------------------------------------------------------}
-- This instance preserves data abstraction at the cost of inefficiency.
-- We provide limited reflection services for the sake of data abstraction.
instance Data a => Data (IntMap a) where
gfoldl f z im = z fromList `f` (toList im)
toConstr _ = fromListConstr
gunfold k z c = case constrIndex c of
1 -> k (z fromList)
_ -> error "gunfold"
dataTypeOf _ = intMapDataType
dataCast1 f = gcast1 f
fromListConstr :: Constr
fromListConstr = mkConstr intMapDataType "fromList" [] Data.Prefix
intMapDataType :: DataType
intMapDataType = mkDataType "Data.IntMap.Internal.IntMap" [fromListConstr]
#endif
{--------------------------------------------------------------------
Query
--------------------------------------------------------------------}
-- | \(O(1)\). Is the map empty?
--
-- > Data.IntMap.null (empty) == True
-- > Data.IntMap.null (singleton 1 'a') == False
null :: IntMap a -> Bool
null Nil = True
null _ = False
{-# INLINE null #-}
-- | \(O(n)\). Number of elements in the map.
--
-- > size empty == 0
-- > size (singleton 1 'a') == 1
-- > size (fromList([(1,'a'), (2,'c'), (3,'b')])) == 3
size :: IntMap a -> Int
size = go 0
where
go !acc (Bin _ l r) = go (go acc l) r
go acc (Tip _ _) = 1 + acc
go acc Nil = acc
-- | \(O(\min(n,W))\). Is the key a member of the map?
--
-- > member 5 (fromList [(5,'a'), (3,'b')]) == True
-- > member 1 (fromList [(5,'a'), (3,'b')]) == False
-- See Note: Local 'go' functions and capturing]
member :: Key -> IntMap a -> Bool
member !k = go
where
go (Bin p l r)
| nomatch k p = False
| left k p = go l
| otherwise = go r
go (Tip kx _) = k == kx
go Nil = False
-- | \(O(\min(n,W))\). Is the key not a member of the map?
--
-- > notMember 5 (fromList [(5,'a'), (3,'b')]) == False
-- > notMember 1 (fromList [(5,'a'), (3,'b')]) == True
notMember :: Key -> IntMap a -> Bool
notMember k m = not $ member k m
-- | \(O(\min(n,W))\). Look up the value at a key in the map. See also 'Data.Map.lookup'.
-- See Note: Local 'go' functions and capturing
lookup :: Key -> IntMap a -> Maybe a
lookup !k = go
where
go (Bin p l r) | left k p = go l
| otherwise = go r
go (Tip kx x) | k == kx = Just x
| otherwise = Nothing
go Nil = Nothing
-- See Note: Local 'go' functions and capturing]
find :: Key -> IntMap a -> a
find !k = go
where
go (Bin p l r) | left k p = go l
| otherwise = go r
go (Tip kx x) | k == kx = x
| otherwise = not_found
go Nil = not_found
not_found = error ("IntMap.!: key " ++ show k ++ " 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 'x' 1 (fromList [(5,'a'), (3,'b')]) == 'x'
-- > findWithDefault 'x' 5 (fromList [(5,'a'), (3,'b')]) == 'a'
-- See Note: Local 'go' functions and capturing]
findWithDefault :: a -> Key -> IntMap a -> a
findWithDefault def !k = go
where
go (Bin p l r) | nomatch k p = def
| left k p = go l
| otherwise = go r
go (Tip kx x) | k == kx = x
| otherwise = def
go Nil = def
-- | \(O(\min(n,W))\). Find largest key smaller than the given one and return the
-- corresponding (key, value) pair.
--
-- > lookupLT 3 (fromList [(3,'a'), (5,'b')]) == Nothing
-- > lookupLT 4 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a')
-- See Note: Local 'go' functions and capturing.
lookupLT :: Key -> IntMap a -> Maybe (Key, a)
lookupLT !k t = case t of
Bin p l r | signBranch p -> if k >= 0 then go r l else go Nil r
_ -> go Nil t
where
go def (Bin p l r)
| nomatch k p = if k < unPrefix p then unsafeFindMax def else unsafeFindMax r
| left k p = go def l
| otherwise = go l r
go def (Tip ky y)
| k <= ky = unsafeFindMax def
| otherwise = Just (ky, y)
go def Nil = unsafeFindMax def
-- | \(O(\min(n,W))\). Find smallest key greater than the given one and return the
-- corresponding (key, value) pair.
--
-- > lookupGT 4 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b')
-- > lookupGT 5 (fromList [(3,'a'), (5,'b')]) == Nothing
-- See Note: Local 'go' functions and capturing.
lookupGT :: Key -> IntMap a -> Maybe (Key, a)
lookupGT !k t = case t of
Bin p l r | signBranch p -> if k >= 0 then go Nil l else go l r
_ -> go Nil t
where
go def (Bin p l r)
| nomatch k p = if k < unPrefix p then unsafeFindMin l else unsafeFindMin def
| left k p = go r l
| otherwise = go def r
go def (Tip ky y)
| k >= ky = unsafeFindMin def
| otherwise = Just (ky, y)
go def Nil = unsafeFindMin def
-- | \(O(\min(n,W))\). Find largest key smaller or equal to the given one and return
-- the corresponding (key, value) pair.
--
-- > lookupLE 2 (fromList [(3,'a'), (5,'b')]) == Nothing
-- > lookupLE 4 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a')
-- > lookupLE 5 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b')
-- See Note: Local 'go' functions and capturing.
lookupLE :: Key -> IntMap a -> Maybe (Key, a)
lookupLE !k t = case t of
Bin p l r | signBranch p -> if k >= 0 then go r l else go Nil r
_ -> go Nil t
where
go def (Bin p l r)
| nomatch k p = if k < unPrefix p then unsafeFindMax def else unsafeFindMax r
| left k p = go def l
| otherwise = go l r
go def (Tip ky y)
| k < ky = unsafeFindMax def
| otherwise = Just (ky, y)
go def Nil = unsafeFindMax def
-- | \(O(\min(n,W))\). Find smallest key greater or equal to the given one and return
-- the corresponding (key, value) pair.
--
-- > lookupGE 3 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a')
-- > lookupGE 4 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b')
-- > lookupGE 6 (fromList [(3,'a'), (5,'b')]) == Nothing
-- See Note: Local 'go' functions and capturing.
lookupGE :: Key -> IntMap a -> Maybe (Key, a)
lookupGE !k t = case t of
Bin p l r | signBranch p -> if k >= 0 then go Nil l else go l r
_ -> go Nil t
where
go def (Bin p l r)
| nomatch k p = if k < unPrefix p then unsafeFindMin l else unsafeFindMin def
| left k p = go r l
| otherwise = go def r
go def (Tip ky y)
| k > ky = unsafeFindMin def
| otherwise = Just (ky, y)
go def Nil = unsafeFindMin def
-- Helper function for lookupGE and lookupGT. It assumes that if a Bin node is
-- given, it has m > 0.
unsafeFindMin :: IntMap a -> Maybe (Key, a)
unsafeFindMin Nil = Nothing
unsafeFindMin (Tip ky y) = Just (ky, y)
unsafeFindMin (Bin _ l _) = unsafeFindMin l
-- Helper function for lookupLE and lookupLT. It assumes that if a Bin node is
-- given, it has m > 0.
unsafeFindMax :: IntMap a -> Maybe (Key, a)
unsafeFindMax Nil = Nothing
unsafeFindMax (Tip ky y) = Just (ky, y)
unsafeFindMax (Bin _ _ r) = unsafeFindMax r
{--------------------------------------------------------------------
Disjoint
--------------------------------------------------------------------}
-- | \(O(\min(n, m \log \frac{2^W}{m})), m \leq n\).
-- Check whether the key sets of two maps are disjoint
-- (i.e. their 'intersection' is empty).
--
-- > disjoint (fromList [(2,'a')]) (fromList [(1,()), (3,())]) == True
-- > disjoint (fromList [(2,'a')]) (fromList [(1,'a'), (2,'b')]) == False
-- > disjoint (fromList []) (fromList []) == True
--
-- > disjoint a b == null (intersection a b)
--
-- @since 0.6.2.1
disjoint :: IntMap a -> IntMap b -> Bool
disjoint Nil _ = True
disjoint _ Nil = True
disjoint (Tip kx _) ys = notMember kx ys
disjoint xs (Tip ky _) = notMember ky xs
disjoint t1@(Bin p1 l1 r1) t2@(Bin p2 l2 r2) = case treeTreeBranch p1 p2 of
ABL -> disjoint l1 t2
ABR -> disjoint r1 t2
BAL -> disjoint t1 l2
BAR -> disjoint t1 r2
EQL -> disjoint l1 l2 && disjoint r1 r2
NOM -> True
{--------------------------------------------------------------------
Compose
--------------------------------------------------------------------}
-- | Relate the keys of one map to the values of
-- the other, by using the values of the former as keys for lookups
-- in the latter.
--
-- Complexity: \( O(n * \min(m,W)) \), where \(m\) is the size of the first argument
--
-- > compose (fromList [('a', "A"), ('b', "B")]) (fromList [(1,'a'),(2,'b'),(3,'z')]) = fromList [(1,"A"),(2,"B")]
--
-- @
-- ('compose' bc ab '!?') = (bc '!?') <=< (ab '!?')
-- @
--
-- __Note:__ Prior to v0.6.4, "Data.IntMap.Strict" exposed a version of
-- 'compose' that forced the values of the output 'IntMap'. This version does
-- not force these values.
--
-- @since 0.6.3.1
compose :: IntMap c -> IntMap Int -> IntMap c
compose bc !ab
| null bc = empty
| otherwise = mapMaybe (bc !?) ab
{--------------------------------------------------------------------
Construction
--------------------------------------------------------------------}
-- | \(O(1)\). The empty map.
--
-- > empty == fromList []
-- > size empty == 0
empty :: IntMap a
empty
= Nil
{-# INLINE empty #-}
-- | \(O(1)\). A map of one element.
--
-- > singleton 1 'a' == fromList [(1, 'a')]
-- > size (singleton 1 'a') == 1
singleton :: Key -> a -> IntMap a
singleton k x
= Tip k x
{-# INLINE singleton #-}
{--------------------------------------------------------------------
Insert
--------------------------------------------------------------------}
-- | \(O(\min(n,W))\). 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 5 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'x')]
-- > insert 7 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'a'), (7, 'x')]
-- > insert 5 'x' empty == singleton 5 'x'
insert :: Key -> a -> IntMap a -> IntMap a
insert !k x t@(Bin p l r)
| nomatch k p = linkKey k (Tip k x) p t
| left k p = Bin p (insert k x l) r
| otherwise = Bin p l (insert k x r)
insert k x t@(Tip ky _)
| k==ky = Tip k x
| otherwise = link k (Tip k x) ky t
insert k x Nil = Tip k x
-- 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 (++) 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "xxxa")]
-- > insertWith (++) 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")]
-- > insertWith (++) 5 "xxx" empty == singleton 5 "xxx"
--
-- Also see the performance note on 'fromListWith'.
insertWith :: (a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
insertWith f k x t
= insertWithKey (\_ 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@.
--
-- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value
-- > insertWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:xxx|a")]
-- > insertWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")]
-- > insertWithKey f 5 "xxx" empty == singleton 5 "xxx"
--
-- Also see the performance note on 'fromListWith'.
insertWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
insertWithKey f !k x t@(Bin p l r)
| nomatch k p = linkKey k (Tip k x) p t
| left k p = Bin p (insertWithKey f k x l) r
| otherwise = Bin p l (insertWithKey f k x r)
insertWithKey f k x t@(Tip ky y)
| k == ky = Tip k (f k x y)
| otherwise = link k (Tip k x) ky t
insertWithKey _ k x 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@).
--
-- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value
-- > insertLookupWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:xxx|a")])
-- > insertLookupWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a"), (7, "xxx")])
-- > insertLookupWithKey f 5 "xxx" empty == (Nothing, singleton 5 "xxx")
--
-- This is how to define @insertLookup@ using @insertLookupWithKey@:
--
-- > let insertLookup kx x t = insertLookupWithKey (\_ a _ -> a) kx x t
-- > insertLookup 5 "x" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "x")])
-- > insertLookup 7 "x" (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a"), (7, "x")])
--
-- Also see the performance note on 'fromListWith'.
insertLookupWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> (Maybe a, IntMap a)
insertLookupWithKey f !k x t@(Bin p l r)
| nomatch k p = (Nothing,linkKey k (Tip k x) p t)
| left k p = let (found,l') = insertLookupWithKey f k x l
in (found,Bin p l' r)
| otherwise = let (found,r') = insertLookupWithKey f k x r
in (found,Bin p l r')
insertLookupWithKey f k x t@(Tip ky y)
| k == ky = (Just y,Tip k (f k x y))
| otherwise = (Nothing,link k (Tip k x) ky t)
insertLookupWithKey _ k x Nil = (Nothing,Tip k x)
{--------------------------------------------------------------------
Deletion
--------------------------------------------------------------------}
-- | \(O(\min(n,W))\). Delete a key and its value from the map. When the key is not
-- a member of the map, the original map is returned.
--
-- > delete 5 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
-- > delete 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
-- > delete 5 empty == empty
delete :: Key -> IntMap a -> IntMap a
delete !k t@(Bin p l r)
| nomatch k p = t
| left k p = binCheckLeft p (delete k l) r
| otherwise = binCheckRight p l (delete k r)
delete k t@(Tip ky _)
| k == ky = Nil
| otherwise = t
delete _k Nil = Nil
-- | \(O(\min(n,W))\). Adjust a value at a specific key. When the key is not
-- a member of the map, the original map is returned.
--
-- > adjust ("new " ++) 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")]
-- > adjust ("new " ++) 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
-- > adjust ("new " ++) 7 empty == empty
adjust :: (a -> a) -> Key -> IntMap a -> IntMap a
adjust f k m
= adjustWithKey (\_ x -> f x) k m
-- | \(O(\min(n,W))\). Adjust a value at a specific key. When the key is not
-- a member of the map, the original map is returned.
--
-- > let f key x = (show key) ++ ":new " ++ x
-- > adjustWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")]
-- > adjustWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
-- > adjustWithKey f 7 empty == empty
adjustWithKey :: (Key -> a -> a) -> Key -> IntMap a -> IntMap a
adjustWithKey f !k (Bin p l r)
| left k p = Bin p (adjustWithKey f k l) r
| otherwise = Bin p l (adjustWithKey f k r)
adjustWithKey f k t@(Tip ky y)
| k == ky = Tip ky (f k y)
| otherwise = t
adjustWithKey _ _ Nil = Nil
-- | \(O(\min(n,W))\). 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@.
--
-- > let f x = if x == "a" then Just "new a" else Nothing
-- > update f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")]
-- > update f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
-- > update f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
update :: (a -> Maybe a) -> Key -> IntMap a -> IntMap a
update f
= updateWithKey (\_ x -> f x)
-- | \(O(\min(n,W))\). 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@.
--
-- > let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing
-- > updateWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")]
-- > updateWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
-- > updateWithKey f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
updateWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> IntMap a
updateWithKey f !k (Bin p l r)
| left k p = binCheckLeft p (updateWithKey f k l) r
| otherwise = binCheckRight p l (updateWithKey f k r)
updateWithKey f k t@(Tip ky y)
| k == ky = case (f k y) of
Just y' -> Tip ky y'
Nothing -> Nil
| otherwise = t
updateWithKey _ _ Nil = Nil
-- | \(O(\min(n,W))\). Look up and update.
-- This function returns the original value, if it is updated.
-- This is different behavior than 'Data.Map.updateLookupWithKey'.
-- Returns the original key value if the map entry is deleted.
--
-- > let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing
-- > updateLookupWithKey f 5 (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:new a")])
-- > updateLookupWithKey f 7 (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a")])
-- > updateLookupWithKey f 3 (fromList [(5,"a"), (3,"b")]) == (Just "b", singleton 5 "a")
updateLookupWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> (Maybe a,IntMap a)
updateLookupWithKey f !k (Bin p l r)
| left k p = let !(found,l') = updateLookupWithKey f k l
in (found,binCheckLeft p l' r)
| otherwise = let !(found,r') = updateLookupWithKey f k r
in (found,binCheckRight p l r')
updateLookupWithKey f k t@(Tip ky y)
| k==ky = case (f k y) of
Just y' -> (Just y,Tip ky y')
Nothing -> (Just y,Nil)
| otherwise = (Nothing,t)
updateLookupWithKey _ _ Nil = (Nothing,Nil)
-- | \(O(\min(n,W))\). 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 an 'IntMap'.
-- In short : @'lookup' k ('alter' f k m) = f ('lookup' k m)@.
alter :: (Maybe a -> Maybe a) -> Key -> IntMap a -> IntMap a
alter f !k t@(Bin p l r)
| nomatch k p = case f Nothing of
Nothing -> t
Just x -> linkKey k (Tip k x) p t
| left k p = binCheckLeft p (alter f k l) r
| otherwise = binCheckRight p l (alter f k r)
alter f k t@(Tip ky y)
| k==ky = case f (Just y) of
Just x -> Tip ky x
Nothing -> Nil
| otherwise = case f Nothing of
Just x -> link k (Tip k x) ky t
Nothing -> Tip ky y
alter f k Nil = case f Nothing of
Just x -> Tip k x
Nothing -> Nil
-- | \(O(\min(n,W))\). The expression (@'alterF' f k map@) alters the value @x@ at
-- @k@, or absence thereof. 'alterF' can be used to inspect, insert, delete,
-- or update a value in an 'IntMap'. In short : @'lookup' k \<$\> 'alterF' f k m = f
-- ('lookup' k m)@.
--
-- Example:
--
-- @
-- interactiveAlter :: Int -> IntMap String -> IO (IntMap String)
-- interactiveAlter k m = alterF f k m where
-- f Nothing = do
-- putStrLn $ show k ++
-- " was not found in the map. Would you like to add it?"
-- getUserResponse1 :: IO (Maybe String)
-- f (Just old) = do
-- putStrLn $ "The key is currently bound to " ++ show old ++
-- ". Would you like to change or delete it?"
-- getUserResponse2 :: IO (Maybe String)
-- @
--
-- 'alterF' is the most general operation for working with an individual
-- key that may or may not be in a given map.
--
-- Note: 'alterF' is a flipped version of the @at@ combinator from
-- @Control.Lens.At@.
--
-- @since 0.5.8
alterF :: Functor f
=> (Maybe a -> f (Maybe a)) -> Key -> IntMap a -> f (IntMap a)
-- This implementation was stolen from 'Control.Lens.At'.
alterF f k m = (<$> f mv) $ \fres ->
case fres of
Nothing -> maybe m (const (delete k m)) mv
Just v' -> insert k v' m
where mv = lookup k m
{--------------------------------------------------------------------
Union
--------------------------------------------------------------------}
-- | The union of a list of maps.
--
-- > unions [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])]
-- > == fromList [(3, "b"), (5, "a"), (7, "C")]
-- > unions [(fromList [(5, "A3"), (3, "B3")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "a"), (3, "b")])]
-- > == fromList [(3, "B3"), (5, "A3"), (7, "C")]
unions :: Foldable f => f (IntMap a) -> IntMap a
unions xs
= Foldable.foldl' union empty xs
-- | The union of a list of maps, with a combining operation.
--
-- > unionsWith (++) [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])]
-- > == fromList [(3, "bB3"), (5, "aAA3"), (7, "C")]
unionsWith :: Foldable f => (a->a->a) -> f (IntMap a) -> IntMap a
unionsWith f ts
= Foldable.foldl' (unionWith f) empty ts
-- | \(O(\min(n, m \log \frac{2^W}{m})), m \leq n\).
-- The (left-biased) union of two maps.
-- It prefers the first map when duplicate keys are encountered,
-- i.e. (@'union' == 'unionWith' 'const'@).
--
-- > union (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "a"), (7, "C")]
union :: IntMap a -> IntMap a -> IntMap a
union m1 m2
= mergeWithKey' Bin const id id m1 m2
-- | \(O(\min(n, m \log \frac{2^W}{m})), m \leq n\).
-- The union with a combining function.
--
-- > unionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "aA"), (7, "C")]
--
-- Also see the performance note on 'fromListWith'.
unionWith :: (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
unionWith f m1 m2
= unionWithKey (\_ x y -> f x y) m1 m2
-- | \(O(\min(n, m \log \frac{2^W}{m})), m \leq n\).
-- The union with a combining function.
--
-- > let f key left_value right_value = (show key) ++ ":" ++ left_value ++ "|" ++ right_value
-- > unionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "5:a|A"), (7, "C")]
--
-- Also see the performance note on 'fromListWith'.
unionWithKey :: (Key -> a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
unionWithKey f m1 m2
= mergeWithKey' Bin (\(Tip k1 x1) (Tip _k2 x2) -> Tip k1 (f k1 x1 x2)) id id m1 m2
{--------------------------------------------------------------------
Difference
--------------------------------------------------------------------}
-- | \(O(\min(n, m \log \frac{2^W}{m})), m \leq n\).
-- Difference between two maps (based on keys).
--
-- > difference (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 3 "b"
difference :: IntMap a -> IntMap b -> IntMap a
difference m1 m2
= mergeWithKey (\_ _ _ -> Nothing) id (const Nil) m1 m2
-- | \(O(\min(n, m \log \frac{2^W}{m})), m \leq n\).
-- Difference with a combining function.
--
-- > let f al ar = if al == "b" then Just (al ++ ":" ++ ar) else Nothing
-- > differenceWith f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (7, "C")])
-- > == singleton 3 "b:B"
differenceWith :: (a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
differenceWith f m1 m2
= differenceWithKey (\_ x y -> f x y) m1 m2
-- | \(O(\min(n, m \log \frac{2^W}{m})), m \leq n\).
-- 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@.
--
-- > let f k al ar = if al == "b" then Just ((show k) ++ ":" ++ al ++ "|" ++ ar) else Nothing
-- > differenceWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (10, "C")])
-- > == singleton 3 "3:b|B"
differenceWithKey :: (Key -> a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
differenceWithKey f m1 m2
= mergeWithKey f id (const Nil) m1 m2
-- | \(O(\min(n, m \log \frac{2^W}{m})), m \leq n\).
-- Remove all the keys in a given set from a map.
--
-- @
-- m \`withoutKeys\` s = 'filterWithKey' (\\k _ -> k ``IntSet.notMember`` s) m
-- @
--
-- @since 0.5.8
withoutKeys :: IntMap a -> IntSet.IntSet -> IntMap a
withoutKeys t1@(Bin p1 l1 r1) t2@(IntSet.Bin p2 l2 r2) = case treeTreeBranch p1 p2 of
ABL -> binCheckLeft p1 (withoutKeys l1 t2) r1
ABR -> binCheckRight p1 l1 (withoutKeys r1 t2)
BAL -> withoutKeys t1 l2
BAR -> withoutKeys t1 r2
EQL -> bin p1 (withoutKeys l1 l2) (withoutKeys r1 r2)
NOM -> t1
where
withoutKeys t1@(Bin p1 _ _) (IntSet.Tip p2 bm2) =
let px1 = unPrefix p1
minbit = bitmapOf (px1 .&. (px1-1))
lt_minbit = minbit - 1
maxbit = bitmapOf (px1 .|. (px1-1))
gt_maxbit = (-maxbit) `xor` maxbit
-- TODO(wrengr): should we manually inline/unroll 'updatePrefix'
-- and 'withoutBM' here, in order to avoid redundant case analyses?
in updatePrefix p2 t1 $ withoutBM (bm2 .|. lt_minbit .|. gt_maxbit)
withoutKeys t1@(Bin _ _ _) IntSet.Nil = t1
withoutKeys t1@(Tip k1 _) t2
| k1 `IntSet.member` t2 = Nil
| otherwise = t1
withoutKeys Nil _ = Nil
updatePrefix
:: IntSetPrefix -> IntMap a -> (IntMap a -> IntMap a) -> IntMap a
updatePrefix !kp t@(Bin p l r) f
| unPrefix p .&. IntSet.suffixBitMask /= 0 =
if unPrefix p .&. IntSet.prefixBitMask == kp then f t else t
| nomatch kp p = t
| left kp p = binCheckLeft p (updatePrefix kp l f) r
| otherwise = binCheckRight p l (updatePrefix kp r f)
updatePrefix kp t@(Tip kx _) f
| kx .&. IntSet.prefixBitMask == kp = f t
| otherwise = t
updatePrefix _ Nil _ = Nil
withoutBM :: IntSetBitMap -> IntMap a -> IntMap a
withoutBM 0 t = t
withoutBM bm (Bin p l r) =
let leftBits = bitmapOf (unPrefix p) - 1
bmL = bm .&. leftBits
bmR = bm `xor` bmL -- = (bm .&. complement leftBits)
in bin p (withoutBM bmL l) (withoutBM bmR r)
withoutBM bm t@(Tip k _)
-- TODO(wrengr): need we manually inline 'IntSet.Member' here?
| k `IntSet.member` IntSet.Tip (k .&. IntSet.prefixBitMask) bm = Nil
| otherwise = t
withoutBM _ Nil = Nil
{--------------------------------------------------------------------
Intersection
--------------------------------------------------------------------}
-- | \(O(\min(n, m \log \frac{2^W}{m})), m \leq n\).
-- The (left-biased) intersection of two maps (based on keys).
--
-- > intersection (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "a"
intersection :: IntMap a -> IntMap b -> IntMap a
intersection m1 m2
= mergeWithKey' bin const (const Nil) (const Nil) m1 m2
-- | \(O(\min(n, m \log \frac{2^W}{m})), m \leq n\).
-- The restriction of a map to the keys in a set.
--
-- @
-- m \`restrictKeys\` s = 'filterWithKey' (\\k _ -> k ``IntSet.member`` s) m
-- @
--
-- @since 0.5.8
restrictKeys :: IntMap a -> IntSet.IntSet -> IntMap a
restrictKeys t1@(Bin p1 l1 r1) t2@(IntSet.Bin p2 l2 r2) = case treeTreeBranch p1 p2 of
ABL -> restrictKeys l1 t2
ABR -> restrictKeys r1 t2
BAL -> restrictKeys t1 l2
BAR -> restrictKeys t1 r2
EQL -> bin p1 (restrictKeys l1 l2) (restrictKeys r1 r2)
NOM -> Nil
restrictKeys t1@(Bin p1 _ _) (IntSet.Tip p2 bm2) =
let px1 = unPrefix p1
minbit = bitmapOf (px1 .&. (px1-1))
ge_minbit = complement (minbit - 1)
maxbit = bitmapOf (px1 .|. (px1-1))
le_maxbit = maxbit .|. (maxbit - 1)
-- TODO(wrengr): should we manually inline/unroll 'lookupPrefix'
-- and 'restrictBM' here, in order to avoid redundant case analyses?
in restrictBM (bm2 .&. ge_minbit .&. le_maxbit) (lookupPrefix p2 t1)
restrictKeys (Bin _ _ _) IntSet.Nil = Nil
restrictKeys t1@(Tip k1 _) t2
| k1 `IntSet.member` t2 = t1
| otherwise = Nil
restrictKeys Nil _ = Nil
-- | \(O(\min(n,W))\). Restrict to the sub-map with all keys matching
-- a key prefix.
lookupPrefix :: IntSetPrefix -> IntMap a -> IntMap a
lookupPrefix !kp t@(Bin p l r)
| unPrefix p .&. IntSet.suffixBitMask /= 0 =
if unPrefix p .&. IntSet.prefixBitMask == kp then t else Nil
| nomatch kp p = Nil
| left kp p = lookupPrefix kp l
| otherwise = lookupPrefix kp r
lookupPrefix kp t@(Tip kx _)
| (kx .&. IntSet.prefixBitMask) == kp = t
| otherwise = Nil
lookupPrefix _ Nil = Nil
restrictBM :: IntSetBitMap -> IntMap a -> IntMap a
restrictBM 0 _ = Nil
restrictBM bm (Bin p l r) =
let leftBits = bitmapOf (unPrefix p) - 1
bmL = bm .&. leftBits
bmR = bm `xor` bmL -- = (bm .&. complement leftBits)
in bin p (restrictBM bmL l) (restrictBM bmR r)
restrictBM bm t@(Tip k _)
-- TODO(wrengr): need we manually inline 'IntSet.Member' here?
| k `IntSet.member` IntSet.Tip (k .&. IntSet.prefixBitMask) bm = t
| otherwise = Nil
restrictBM _ Nil = Nil
-- | \(O(\min(n, m \log \frac{2^W}{m})), m \leq n\).
-- The intersection with a combining function.
--
-- > intersectionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "aA"
intersectionWith :: (a -> b -> c) -> IntMap a -> IntMap b -> IntMap c
intersectionWith f m1 m2
= intersectionWithKey (\_ x y -> f x y) m1 m2
-- | \(O(\min(n, m \log \frac{2^W}{m})), m \leq n\).
-- The intersection with a combining function.
--
-- > let f k al ar = (show k) ++ ":" ++ al ++ "|" ++ ar
-- > intersectionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "5:a|A"
intersectionWithKey :: (Key -> a -> b -> c) -> IntMap a -> IntMap b -> IntMap c
intersectionWithKey f m1 m2
= mergeWithKey' bin (\(Tip k1 x1) (Tip _k2 x2) -> Tip k1 (f k1 x1 x2)) (const Nil) (const Nil) m1 m2
{--------------------------------------------------------------------
Symmetric difference
--------------------------------------------------------------------}
-- | \(O(\min(n, m \log \frac{2^W}{m})), m \leq n\).
-- The symmetric difference of two maps.
--
-- The result contains entries whose keys appear in exactly one of the two maps.
--
-- @
-- symmetricDifference
-- (fromList [(0,\'q\'),(2,\'b\'),(4,\'w\'),(6,\'o\')])
-- (fromList [(0,\'e\'),(3,\'r\'),(6,\'t\'),(9,\'s\')])
-- ==
-- fromList [(2,\'b\'),(3,\'r\'),(4,\'w\'),(9,\'s\')]
-- @
--
-- @since 0.8
symmetricDifference :: IntMap a -> IntMap a -> IntMap a
symmetricDifference t1@(Bin p1 l1 r1) t2@(Bin p2 l2 r2) =
case treeTreeBranch p1 p2 of
ABL -> bin p1 (symmetricDifference l1 t2) r1
ABR -> bin p1 l1 (symmetricDifference r1 t2)
BAL -> bin p2 (symmetricDifference t1 l2) r2
BAR -> bin p2 l2 (symmetricDifference t1 r2)
EQL -> bin p1 (symmetricDifference l1 l2) (symmetricDifference r1 r2)
NOM -> link (unPrefix p1) t1 (unPrefix p2) t2
symmetricDifference t1@(Bin _ _ _) t2@(Tip k2 _) = symDiffTip t2 k2 t1
symmetricDifference t1@(Bin _ _ _) Nil = t1
symmetricDifference t1@(Tip k1 _) t2 = symDiffTip t1 k1 t2
symmetricDifference Nil t2 = t2
symDiffTip :: IntMap a -> Int -> IntMap a -> IntMap a
symDiffTip !t1 !k1 = go
where
go t2@(Bin p2 l2 r2)
| nomatch k1 p2 = linkKey k1 t1 p2 t2
| left k1 p2 = bin p2 (go l2) r2
| otherwise = bin p2 l2 (go r2)
go t2@(Tip k2 _)
| k1 == k2 = Nil
| otherwise = link k1 t1 k2 t2
go Nil = t1
{--------------------------------------------------------------------
MergeWithKey
--------------------------------------------------------------------}
-- | \(O(\min(n, m \log \frac{2^W}{m})), m \leq n\).
-- A high-performance universal combining function. Using
-- 'mergeWithKey', all combining functions can be defined without any loss of
-- efficiency (with exception of 'union', 'difference' and 'intersection',
-- where sharing of some nodes is lost with 'mergeWithKey').
--
-- __Warning__: Please make sure you know what is going on when using 'mergeWithKey',
-- otherwise you can be surprised by unexpected code growth or even
-- corruption of the data structure.
--
-- When 'mergeWithKey' is given three arguments, it is inlined to the call
-- site. You should therefore use 'mergeWithKey' only to define your custom
-- combining functions. For example, you could define 'unionWithKey',
-- 'differenceWithKey' and 'intersectionWithKey' as
--
-- > myUnionWithKey f m1 m2 = mergeWithKey (\k x1 x2 -> Just (f k x1 x2)) id id m1 m2
-- > myDifferenceWithKey f m1 m2 = mergeWithKey f id (const empty) m1 m2
-- > myIntersectionWithKey f m1 m2 = mergeWithKey (\k x1 x2 -> Just (f k x1 x2)) (const empty) (const empty) m1 m2
--
-- When calling @'mergeWithKey' combine only1 only2@, a function combining two
-- 'IntMap's is created, such that
--
-- * if a key is present in both maps, it is passed with both corresponding
-- values to the @combine@ function. Depending on the result, the key is either
-- present in the result with specified value, or is left out;
--
-- * a nonempty subtree present only in the first map is passed to @only1@ and
-- the output is added to the result;
--
-- * a nonempty subtree present only in the second map is passed to @only2@ and
-- the output is added to the result.
--
-- The @only1@ and @only2@ methods /must return a map with a subset (possibly empty) of the keys of the given map/.
-- The values can be modified arbitrarily. Most common variants of @only1@ and
-- @only2@ are 'id' and @'const' 'empty'@, but for example @'map' f@ or
-- @'filterWithKey' f@ could be used for any @f@.
-- See Note [IntMap merge complexity]
mergeWithKey :: (Key -> a -> b -> Maybe c) -> (IntMap a -> IntMap c) -> (IntMap b -> IntMap c)
-> IntMap a -> IntMap b -> IntMap c
mergeWithKey f g1 g2 = mergeWithKey' bin combine g1 g2
where -- We use the lambda form to avoid non-exhaustive pattern matches warning.
combine = \(Tip k1 x1) (Tip _k2 x2) ->
case f k1 x1 x2 of
Nothing -> Nil
Just x -> Tip k1 x
{-# INLINE combine #-}
{-# INLINE mergeWithKey #-}
-- Slightly more general version of mergeWithKey. It differs in the following:
--
-- * the combining function operates on maps instead of keys and values. The
-- reason is to enable sharing in union, difference and intersection.
--
-- * mergeWithKey' is given an equivalent of bin. The reason is that in union*,
-- Bin constructor can be used, because we know both subtrees are nonempty.
mergeWithKey' :: (Prefix -> IntMap c -> IntMap c -> IntMap c)
-> (IntMap a -> IntMap b -> IntMap c) -> (IntMap a -> IntMap c) -> (IntMap b -> IntMap c)
-> IntMap a -> IntMap b -> IntMap c
mergeWithKey' bin' f g1 g2 = go
where
go t1@(Bin p1 l1 r1) t2@(Bin p2 l2 r2) = case treeTreeBranch p1 p2 of
ABL -> bin' p1 (go l1 t2) (g1 r1)
ABR -> bin' p1 (g1 l1) (go r1 t2)
BAL -> bin' p2 (go t1 l2) (g2 r2)
BAR -> bin' p2 (g2 l2) (go t1 r2)
EQL -> bin' p1 (go l1 l2) (go r1 r2)
NOM -> maybe_link (unPrefix p1) (g1 t1) (unPrefix p2) (g2 t2)
go t1'@(Bin _ _ _) t2'@(Tip k2' _) = merge0 t2' k2' t1'
where
merge0 t2 k2 t1@(Bin p1 l1 r1)
| nomatch k2 p1 = maybe_link (unPrefix p1) (g1 t1) k2 (g2 t2)
| left k2 p1 = bin' p1 (merge0 t2 k2 l1) (g1 r1)
| otherwise = bin' p1 (g1 l1) (merge0 t2 k2 r1)
merge0 t2 k2 t1@(Tip k1 _)
| k1 == k2 = f t1 t2
| otherwise = maybe_link k1 (g1 t1) k2 (g2 t2)
merge0 t2 _ Nil = g2 t2
go t1@(Bin _ _ _) Nil = g1 t1
go t1'@(Tip k1' _) t2' = merge0 t1' k1' t2'
where
merge0 t1 k1 t2@(Bin p2 l2 r2)
| nomatch k1 p2 = maybe_link k1 (g1 t1) (unPrefix p2) (g2 t2)
| left k1 p2 = bin' p2 (merge0 t1 k1 l2) (g2 r2)
| otherwise = bin' p2 (g2 l2) (merge0 t1 k1 r2)
merge0 t1 k1 t2@(Tip k2 _)
| k1 == k2 = f t1 t2
| otherwise = maybe_link k1 (g1 t1) k2 (g2 t2)
merge0 t1 _ Nil = g1 t1
go Nil Nil = Nil
go Nil t2 = g2 t2
maybe_link _ Nil _ t2 = t2
maybe_link _ t1 _ Nil = t1
maybe_link k1 t1 k2 t2 = link k1 t1 k2 t2
{-# INLINE maybe_link #-}
{-# INLINE mergeWithKey' #-}
{--------------------------------------------------------------------
mergeA
--------------------------------------------------------------------}
-- | A tactic for dealing with keys present in one map but not the
-- other in 'merge' or 'mergeA'.
--
-- A tactic of type @WhenMissing f k x z@ is an abstract representation
-- of a function of type @Key -> x -> f (Maybe z)@.
--
-- @since 0.5.9
data WhenMissing f x y = WhenMissing
{ missingSubtree :: IntMap x -> f (IntMap y)
, missingKey :: Key -> x -> f (Maybe y)}
-- | @since 0.5.9
instance (Applicative f, Monad f) => Functor (WhenMissing f x) where
fmap = mapWhenMissing
{-# INLINE fmap #-}
-- | @since 0.5.9
instance (Applicative f, Monad f) => Category.Category (WhenMissing f)
where
id = preserveMissing
f . g =
traverseMaybeMissing $ \ k x -> do
y <- missingKey g k x
case y of
Nothing -> pure Nothing
Just q -> missingKey f k q
{-# INLINE id #-}
{-# INLINE (.) #-}
-- | Equivalent to @ReaderT k (ReaderT x (MaybeT f))@.
--
-- @since 0.5.9
instance (Applicative f, Monad f) => Applicative (WhenMissing f x) where
pure x = mapMissing (\ _ _ -> x)
f <*> g =
traverseMaybeMissing $ \k x -> do
res1 <- missingKey f k x
case res1 of
Nothing -> pure Nothing
Just r -> (pure $!) . fmap r =<< missingKey g k x
{-# INLINE pure #-}
{-# INLINE (<*>) #-}
-- | Equivalent to @ReaderT k (ReaderT x (MaybeT f))@.
--
-- @since 0.5.9
instance (Applicative f, Monad f) => Monad (WhenMissing f x) where
m >>= f =
traverseMaybeMissing $ \k x -> do
res1 <- missingKey m k x
case res1 of
Nothing -> pure Nothing
Just r -> missingKey (f r) k x
{-# INLINE (>>=) #-}
-- | Map covariantly over a @'WhenMissing' f x@.
--
-- @since 0.5.9
mapWhenMissing
:: (Applicative f, Monad f)
=> (a -> b)
-> WhenMissing f x a
-> WhenMissing f x b
mapWhenMissing f t = WhenMissing
{ missingSubtree = \m -> missingSubtree t m >>= \m' -> pure $! fmap f m'
, missingKey = \k x -> missingKey t k x >>= \q -> (pure $! fmap f q) }
{-# INLINE mapWhenMissing #-}
-- | Map covariantly over a @'WhenMissing' f x@, using only a
-- 'Functor f' constraint.
mapGentlyWhenMissing
:: Functor f
=> (a -> b)
-> WhenMissing f x a
-> WhenMissing f x b
mapGentlyWhenMissing f t = WhenMissing
{ missingSubtree = \m -> fmap f <$> missingSubtree t m
, missingKey = \k x -> fmap f <$> missingKey t k x }
{-# INLINE mapGentlyWhenMissing #-}
-- | Map covariantly over a @'WhenMatched' f k x@, using only a
-- 'Functor f' constraint.
mapGentlyWhenMatched
:: Functor f
=> (a -> b)
-> WhenMatched f x y a
-> WhenMatched f x y b
mapGentlyWhenMatched f t =
zipWithMaybeAMatched $ \k x y -> fmap f <$> runWhenMatched t k x y
{-# INLINE mapGentlyWhenMatched #-}
-- | Map contravariantly over a @'WhenMissing' f _ x@.
--
-- @since 0.5.9
lmapWhenMissing :: (b -> a) -> WhenMissing f a x -> WhenMissing f b x
lmapWhenMissing f t = WhenMissing
{ missingSubtree = \m -> missingSubtree t (fmap f m)
, missingKey = \k x -> missingKey t k (f x) }
{-# INLINE lmapWhenMissing #-}
-- | Map contravariantly over a @'WhenMatched' f _ y z@.
--
-- @since 0.5.9
contramapFirstWhenMatched
:: (b -> a)
-> WhenMatched f a y z
-> WhenMatched f b y z
contramapFirstWhenMatched f t =
WhenMatched $ \k x y -> runWhenMatched t k (f x) y
{-# INLINE contramapFirstWhenMatched #-}
-- | Map contravariantly over a @'WhenMatched' f x _ z@.
--
-- @since 0.5.9
contramapSecondWhenMatched
:: (b -> a)
-> WhenMatched f x a z
-> WhenMatched f x b z
contramapSecondWhenMatched f t =
WhenMatched $ \k x y -> runWhenMatched t k x (f y)
{-# INLINE contramapSecondWhenMatched #-}
-- | A tactic for dealing with keys present in one map but not the
-- other in 'merge'.
--
-- A tactic of type @SimpleWhenMissing x z@ is an abstract
-- representation of a function of type @Key -> x -> Maybe z@.
--
-- @since 0.5.9
type SimpleWhenMissing = WhenMissing Identity
-- | A tactic for dealing with keys present in both maps in 'merge'
-- or 'mergeA'.
--
-- A tactic of type @WhenMatched f x y z@ is an abstract representation
-- of a function of type @Key -> x -> y -> f (Maybe z)@.
--
-- @since 0.5.9
newtype WhenMatched f x y z = WhenMatched
{ matchedKey :: Key -> x -> y -> f (Maybe z) }
-- | Along with zipWithMaybeAMatched, witnesses the isomorphism
-- between @WhenMatched f x y z@ and @Key -> x -> y -> f (Maybe z)@.
--
-- @since 0.5.9
runWhenMatched :: WhenMatched f x y z -> Key -> x -> y -> f (Maybe z)
runWhenMatched = matchedKey
{-# INLINE runWhenMatched #-}
-- | Along with traverseMaybeMissing, witnesses the isomorphism
-- between @WhenMissing f x y@ and @Key -> x -> f (Maybe y)@.
--
-- @since 0.5.9
runWhenMissing :: WhenMissing f x y -> Key-> x -> f (Maybe y)
runWhenMissing = missingKey
{-# INLINE runWhenMissing #-}
-- | @since 0.5.9
instance Functor f => Functor (WhenMatched f x y) where
fmap = mapWhenMatched
{-# INLINE fmap #-}
-- | @since 0.5.9
instance (Monad f, Applicative f) => Category.Category (WhenMatched f x)
where
id = zipWithMatched (\_ _ y -> y)
f . g =
zipWithMaybeAMatched $ \k x y -> do
res <- runWhenMatched g k x y
case res of
Nothing -> pure Nothing
Just r -> runWhenMatched f k x r
{-# INLINE id #-}
{-# INLINE (.) #-}
-- | Equivalent to @ReaderT Key (ReaderT x (ReaderT y (MaybeT f)))@
--
-- @since 0.5.9
instance (Monad f, Applicative f) => Applicative (WhenMatched f x y) where
pure x = zipWithMatched (\_ _ _ -> x)
fs <*> xs =
zipWithMaybeAMatched $ \k x y -> do
res <- runWhenMatched fs k x y
case res of
Nothing -> pure Nothing
Just r -> (pure $!) . fmap r =<< runWhenMatched xs k x y
{-# INLINE pure #-}
{-# INLINE (<*>) #-}
-- | Equivalent to @ReaderT Key (ReaderT x (ReaderT y (MaybeT f)))@
--
-- @since 0.5.9
instance (Monad f, Applicative f) => Monad (WhenMatched f x y) where
m >>= f =
zipWithMaybeAMatched $ \k x y -> do
res <- runWhenMatched m k x y
case res of
Nothing -> pure Nothing
Just r -> runWhenMatched (f r) k x y
{-# INLINE (>>=) #-}
-- | Map covariantly over a @'WhenMatched' f x y@.
--
-- @since 0.5.9
mapWhenMatched
:: Functor f
=> (a -> b)
-> WhenMatched f x y a
-> WhenMatched f x y b
mapWhenMatched f (WhenMatched g) =
WhenMatched $ \k x y -> fmap (fmap f) (g k x y)
{-# INLINE mapWhenMatched #-}
-- | A tactic for dealing with keys present in both maps in 'merge'.
--
-- A tactic of type @SimpleWhenMatched x y z@ is an abstract
-- representation of a function of type @Key -> x -> y -> Maybe z@.
--
-- @since 0.5.9
type SimpleWhenMatched = WhenMatched Identity
-- | When a key is found in both maps, apply a function to the key
-- and values and use the result in the merged map.
--
-- > zipWithMatched
-- > :: (Key -> x -> y -> z)
-- > -> SimpleWhenMatched x y z
--
-- @since 0.5.9
zipWithMatched
:: Applicative f
=> (Key -> x -> y -> z)
-> WhenMatched f x y z
zipWithMatched f = WhenMatched $ \ k x y -> pure . Just $ f k x y
{-# INLINE zipWithMatched #-}
-- | When a key is found in both maps, apply a function to the key
-- and values to produce an action and use its result in the merged
-- map.
--
-- @since 0.5.9
zipWithAMatched
:: Applicative f
=> (Key -> x -> y -> f z)
-> WhenMatched f x y z
zipWithAMatched f = WhenMatched $ \ k x y -> Just <$> f k x y
{-# INLINE zipWithAMatched #-}
-- | When a key is found in both maps, apply a function to the key
-- and values and maybe use the result in the merged map.
--
-- > zipWithMaybeMatched
-- > :: (Key -> x -> y -> Maybe z)
-- > -> SimpleWhenMatched x y z
--
-- @since 0.5.9
zipWithMaybeMatched
:: Applicative f
=> (Key -> x -> y -> Maybe z)
-> WhenMatched f x y z
zipWithMaybeMatched f = WhenMatched $ \ k x y -> pure $ f k x y
{-# INLINE zipWithMaybeMatched #-}
-- | When a key is found in both maps, apply a function to the key
-- and values, perform the resulting action, and maybe use the
-- result in the merged map.
--
-- This is the fundamental 'WhenMatched' tactic.
--
-- @since 0.5.9
zipWithMaybeAMatched
:: (Key -> x -> y -> f (Maybe z))
-> WhenMatched f x y z
zipWithMaybeAMatched f = WhenMatched $ \ k x y -> f k x y
{-# INLINE zipWithMaybeAMatched #-}
-- | Drop all the entries whose keys are missing from the other
-- map.
--
-- > dropMissing :: SimpleWhenMissing x y
--
-- prop> dropMissing = mapMaybeMissing (\_ _ -> Nothing)
--
-- but @dropMissing@ is much faster.
--
-- @since 0.5.9
dropMissing :: Applicative f => WhenMissing f x y
dropMissing = WhenMissing
{ missingSubtree = const (pure Nil)
, missingKey = \_ _ -> pure Nothing }
{-# INLINE dropMissing #-}
-- | Preserve, unchanged, the entries whose keys are missing from
-- the other map.
--
-- > preserveMissing :: SimpleWhenMissing x x
--
-- prop> preserveMissing = Merge.Lazy.mapMaybeMissing (\_ x -> Just x)
--
-- but @preserveMissing@ is much faster.
--
-- @since 0.5.9
preserveMissing :: Applicative f => WhenMissing f x x
preserveMissing = WhenMissing
{ missingSubtree = pure
, missingKey = \_ v -> pure (Just v) }
{-# INLINE preserveMissing #-}
-- | Map over the entries whose keys are missing from the other map.
--
-- > mapMissing :: (k -> x -> y) -> SimpleWhenMissing x y
--
-- prop> mapMissing f = mapMaybeMissing (\k x -> Just $ f k x)
--
-- but @mapMissing@ is somewhat faster.
--
-- @since 0.5.9
mapMissing :: Applicative f => (Key -> x -> y) -> WhenMissing f x y
mapMissing f = WhenMissing
{ missingSubtree = \m -> pure $! mapWithKey f m
, missingKey = \k x -> pure $ Just (f k x) }
{-# INLINE mapMissing #-}
-- | Map over the entries whose keys are missing from the other
-- map, optionally removing some. This is the most powerful
-- 'SimpleWhenMissing' tactic, but others are usually more efficient.
--
-- > mapMaybeMissing :: (Key -> x -> Maybe y) -> SimpleWhenMissing x y
--
-- prop> mapMaybeMissing f = traverseMaybeMissing (\k x -> pure (f k x))
--
-- but @mapMaybeMissing@ uses fewer unnecessary 'Applicative'
-- operations.
--
-- @since 0.5.9
mapMaybeMissing
:: Applicative f => (Key -> x -> Maybe y) -> WhenMissing f x y
mapMaybeMissing f = WhenMissing
{ missingSubtree = \m -> pure $! mapMaybeWithKey f m
, missingKey = \k x -> pure $! f k x }
{-# INLINE mapMaybeMissing #-}
-- | Filter the entries whose keys are missing from the other map.
--
-- > filterMissing :: (k -> x -> Bool) -> SimpleWhenMissing x x
--
-- prop> filterMissing f = Merge.Lazy.mapMaybeMissing $ \k x -> guard (f k x) *> Just x
--
-- but this should be a little faster.
--
-- @since 0.5.9
filterMissing
:: Applicative f => (Key -> x -> Bool) -> WhenMissing f x x
filterMissing f = WhenMissing
{ missingSubtree = \m -> pure $! filterWithKey f m
, missingKey = \k x -> pure $! if f k x then Just x else Nothing }
{-# INLINE filterMissing #-}
-- | Filter the entries whose keys are missing from the other map
-- using some 'Applicative' action.
--
-- > filterAMissing f = Merge.Lazy.traverseMaybeMissing $
-- > \k x -> (\b -> guard b *> Just x) <$> f k x
--
-- but this should be a little faster.
--
-- @since 0.5.9
filterAMissing
:: Applicative f => (Key -> x -> f Bool) -> WhenMissing f x x
filterAMissing f = WhenMissing
{ missingSubtree = \m -> filterWithKeyA f m
, missingKey = \k x -> bool Nothing (Just x) <$> f k x }
{-# INLINE filterAMissing #-}
-- | \(O(n)\). Filter keys and values using an 'Applicative' predicate.
filterWithKeyA
:: Applicative f => (Key -> a -> f Bool) -> IntMap a -> f (IntMap a)
filterWithKeyA _ Nil = pure Nil
filterWithKeyA f t@(Tip k x) = (\b -> if b then t else Nil) <$> f k x
filterWithKeyA f (Bin p l r)
| signBranch p = liftA2 (flip (bin p)) (filterWithKeyA f r) (filterWithKeyA f l)
| otherwise = liftA2 (bin p) (filterWithKeyA f l) (filterWithKeyA f r)
-- | This wasn't in Data.Bool until 4.7.0, so we define it here
bool :: a -> a -> Bool -> a
bool f _ False = f
bool _ t True = t
-- | Traverse over the entries whose keys are missing from the other
-- map.
--
-- @since 0.5.9
traverseMissing
:: Applicative f => (Key -> x -> f y) -> WhenMissing f x y
traverseMissing f = WhenMissing
{ missingSubtree = traverseWithKey f
, missingKey = \k x -> Just <$> f k x }
{-# INLINE traverseMissing #-}
-- | Traverse over the entries whose keys are missing from the other
-- map, optionally producing values to put in the result. This is
-- the most powerful 'WhenMissing' tactic, but others are usually
-- more efficient.
--
-- @since 0.5.9
traverseMaybeMissing
:: Applicative f => (Key -> x -> f (Maybe y)) -> WhenMissing f x y
traverseMaybeMissing f = WhenMissing
{ missingSubtree = traverseMaybeWithKey f
, missingKey = f }
{-# INLINE traverseMaybeMissing #-}
-- | \(O(n)\). Traverse keys\/values and collect the 'Just' results.
--
-- @since 0.6.4
traverseMaybeWithKey
:: Applicative f => (Key -> a -> f (Maybe b)) -> IntMap a -> f (IntMap b)
traverseMaybeWithKey f = go
where
go Nil = pure Nil
go (Tip k x) = maybe Nil (Tip k) <$> f k x
go (Bin p l r)
| signBranch p = liftA2 (flip (bin p)) (go r) (go l)
| otherwise = liftA2 (bin p) (go l) (go r)
-- | Merge two maps.
--
-- 'merge' takes two 'WhenMissing' tactics, a 'WhenMatched' tactic
-- and two maps. It uses the tactics to merge the maps. Its behavior
-- is best understood via its fundamental tactics, 'mapMaybeMissing'
-- and 'zipWithMaybeMatched'.
--
-- Consider
--
-- @
-- merge (mapMaybeMissing g1)
-- (mapMaybeMissing g2)
-- (zipWithMaybeMatched f)
-- m1 m2
-- @
--
-- Take, for example,
--
-- @
-- m1 = [(0, \'a\'), (1, \'b\'), (3, \'c\'), (4, \'d\')]
-- m2 = [(1, "one"), (2, "two"), (4, "three")]
-- @
--
-- 'merge' will first \"align\" these maps by key:
--
-- @
-- m1 = [(0, \'a\'), (1, \'b\'), (3, \'c\'), (4, \'d\')]
-- m2 = [(1, "one"), (2, "two"), (4, "three")]
-- @
--
-- It will then pass the individual entries and pairs of entries
-- to @g1@, @g2@, or @f@ as appropriate:
--
-- @
-- maybes = [g1 0 \'a\', f 1 \'b\' "one", g2 2 "two", g1 3 \'c\', f 4 \'d\' "three"]
-- @
--
-- This produces a 'Maybe' for each key:
--
-- @
-- keys = 0 1 2 3 4
-- results = [Nothing, Just True, Just False, Nothing, Just True]
-- @
--
-- Finally, the @Just@ results are collected into a map:
--
-- @
-- return value = [(1, True), (2, False), (4, True)]
-- @
--
-- The other tactics below are optimizations or simplifications of
-- 'mapMaybeMissing' for special cases. Most importantly,
--
-- * 'dropMissing' drops all the keys.
-- * 'preserveMissing' leaves all the entries alone.
--
-- When 'merge' is given three arguments, it is inlined at the call
-- site. To prevent excessive inlining, you should typically use
-- 'merge' to define your custom combining functions.
--
--
-- Examples:
--
-- prop> unionWithKey f = merge preserveMissing preserveMissing (zipWithMatched f)
-- prop> intersectionWithKey f = merge dropMissing dropMissing (zipWithMatched f)
-- prop> differenceWith f = merge diffPreserve diffDrop f
-- prop> symmetricDifference = merge diffPreserve diffPreserve (\ _ _ _ -> Nothing)
-- prop> mapEachPiece f g h = merge (diffMapWithKey f) (diffMapWithKey g)
--
-- @since 0.5.9
merge
:: SimpleWhenMissing a c -- ^ What to do with keys in @m1@ but not @m2@
-> SimpleWhenMissing b c -- ^ What to do with keys in @m2@ but not @m1@
-> SimpleWhenMatched a b c -- ^ What to do with keys in both @m1@ and @m2@
-> IntMap a -- ^ Map @m1@
-> IntMap b -- ^ Map @m2@
-> IntMap c
merge g1 g2 f m1 m2 =
runIdentity $ mergeA g1 g2 f m1 m2
{-# INLINE merge #-}
-- | An applicative version of 'merge'.
--
-- 'mergeA' takes two 'WhenMissing' tactics, a 'WhenMatched'
-- tactic and two maps. It uses the tactics to merge the maps.
-- Its behavior is best understood via its fundamental tactics,
-- 'traverseMaybeMissing' and 'zipWithMaybeAMatched'.
--
-- Consider
--
-- @
-- mergeA (traverseMaybeMissing g1)
-- (traverseMaybeMissing g2)
-- (zipWithMaybeAMatched f)
-- m1 m2
-- @
--
-- Take, for example,
--
-- @
-- m1 = [(0, \'a\'), (1, \'b\'), (3,\'c\'), (4, \'d\')]
-- m2 = [(1, "one"), (2, "two"), (4, "three")]
-- @
--
-- 'mergeA' will first \"align\" these maps by key:
--
-- @
-- m1 = [(0, \'a\'), (1, \'b\'), (3, \'c\'), (4, \'d\')]
-- m2 = [(1, "one"), (2, "two"), (4, "three")]
-- @
--
-- It will then pass the individual entries and pairs of entries
-- to @g1@, @g2@, or @f@ as appropriate:
--
-- @
-- actions = [g1 0 \'a\', f 1 \'b\' "one", g2 2 "two", g1 3 \'c\', f 4 \'d\' "three"]
-- @
--
-- Next, it will perform the actions in the @actions@ list in order from
-- left to right.
--
-- @
-- keys = 0 1 2 3 4
-- results = [Nothing, Just True, Just False, Nothing, Just True]
-- @
--
-- Finally, the @Just@ results are collected into a map:
--
-- @
-- return value = [(1, True), (2, False), (4, True)]
-- @
--
-- The other tactics below are optimizations or simplifications of
-- 'traverseMaybeMissing' for special cases. Most importantly,
--
-- * 'dropMissing' drops all the keys.
-- * 'preserveMissing' leaves all the entries alone.
-- * 'mapMaybeMissing' does not use the 'Applicative' context.
--
-- When 'mergeA' is given three arguments, it is inlined at the call
-- site. To prevent excessive inlining, you should generally only use
-- 'mergeA' to define custom combining functions.
--
-- @since 0.5.9
mergeA
:: (Applicative f)
=> WhenMissing f a c -- ^ What to do with keys in @m1@ but not @m2@
-> WhenMissing f b c -- ^ What to do with keys in @m2@ but not @m1@
-> WhenMatched f a b c -- ^ What to do with keys in both @m1@ and @m2@
-> IntMap a -- ^ Map @m1@
-> IntMap b -- ^ Map @m2@
-> f (IntMap c)
mergeA
WhenMissing{missingSubtree = g1t, missingKey = g1k}
WhenMissing{missingSubtree = g2t, missingKey = g2k}
WhenMatched{matchedKey = f}
= go
where
go t1 Nil = g1t t1
go Nil t2 = g2t t2
-- This case is already covered below.
-- go (Tip k1 x1) (Tip k2 x2) = mergeTips k1 x1 k2 x2
go (Tip k1 x1) t2' = merge2 t2'
where
merge2 t2@(Bin p2 l2 r2)
| nomatch k1 p2 = linkA k1 (subsingletonBy g1k k1 x1) (unPrefix p2) (g2t t2)
| left k1 p2 = binA p2 (merge2 l2) (g2t r2)
| otherwise = binA p2 (g2t l2) (merge2 r2)
merge2 (Tip k2 x2) = mergeTips k1 x1 k2 x2
merge2 Nil = subsingletonBy g1k k1 x1
go t1' (Tip k2 x2) = merge1 t1'
where
merge1 t1@(Bin p1 l1 r1)
| nomatch k2 p1 = linkA (unPrefix p1) (g1t t1) k2 (subsingletonBy g2k k2 x2)
| left k2 p1 = binA p1 (merge1 l1) (g1t r1)
| otherwise = binA p1 (g1t l1) (merge1 r1)
merge1 (Tip k1 x1) = mergeTips k1 x1 k2 x2
merge1 Nil = subsingletonBy g2k k2 x2
go t1@(Bin p1 l1 r1) t2@(Bin p2 l2 r2) = case treeTreeBranch p1 p2 of
ABL -> binA p1 (go l1 t2) (g1t r1)
ABR -> binA p1 (g1t l1) (go r1 t2)
BAL -> binA p2 (go t1 l2) (g2t r2)
BAR -> binA p2 (g2t l2) (go t1 r2)
EQL -> binA p1 (go l1 l2) (go r1 r2)
NOM -> linkA (unPrefix p1) (g1t t1) (unPrefix p2) (g2t t2)
subsingletonBy :: Functor f => (Key -> a -> f (Maybe c)) -> Key -> a -> f (IntMap c)
subsingletonBy gk k x = maybe Nil (Tip k) <$> gk k x
{-# INLINE subsingletonBy #-}
mergeTips k1 x1 k2 x2
| k1 == k2 = maybe Nil (Tip k1) <$> f k1 x1 x2
| k1 < k2 = liftA2 (subdoubleton k1 k2) (g1k k1 x1) (g2k k2 x2)
{-
= link_ k1 k2 <$> subsingletonBy g1k k1 x1 <*> subsingletonBy g2k k2 x2
-}
| otherwise = liftA2 (subdoubleton k2 k1) (g2k k2 x2) (g1k k1 x1)
{-# INLINE mergeTips #-}
subdoubleton _ _ Nothing Nothing = Nil
subdoubleton _ k2 Nothing (Just y2) = Tip k2 y2
subdoubleton k1 _ (Just y1) Nothing = Tip k1 y1
subdoubleton k1 k2 (Just y1) (Just y2) = link k1 (Tip k1 y1) k2 (Tip k2 y2)
{-# INLINE subdoubleton #-}
-- | A variant of 'link_' which makes sure to execute side-effects
-- in the right order.
linkA
:: Applicative f
=> Int -> f (IntMap a)
-> Int -> f (IntMap a)
-> f (IntMap a)
linkA k1 t1 k2 t2
| i2w k1 < i2w k2 = binA p t1 t2
| otherwise = binA p t2 t1
where
m = branchMask k1 k2
p = Prefix (mask k1 m .|. m)
{-# INLINE linkA #-}
-- A variant of 'bin' that ensures that effects for negative keys are executed
-- first.
binA
:: Applicative f
=> Prefix
-> f (IntMap a)
-> f (IntMap a)
-> f (IntMap a)
binA p a b
| signBranch p = liftA2 (flip (bin p)) b a
| otherwise = liftA2 (bin p) a b
{-# INLINE binA #-}
{-# INLINE mergeA #-}
{--------------------------------------------------------------------
Min\/Max
--------------------------------------------------------------------}
-- | \(O(\min(n,W))\). Update the value at the minimal key.
--
-- > updateMinWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"3:b"), (5,"a")]
-- > updateMinWithKey (\ _ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
updateMinWithKey :: (Key -> a -> Maybe a) -> IntMap a -> IntMap a
updateMinWithKey f t =
case t of Bin p l r | signBranch p -> binCheckRight p l (go f r)
_ -> go f t
where
go f' (Bin p l r) = binCheckLeft p (go f' l) r
go f' (Tip k y) = case f' k y of
Just y' -> Tip k y'
Nothing -> Nil
go _ Nil = Nil
-- | \(O(\min(n,W))\). Update the value at the maximal key.
--
-- > updateMaxWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"b"), (5,"5:a")]
-- > updateMaxWithKey (\ _ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
updateMaxWithKey :: (Key -> a -> Maybe a) -> IntMap a -> IntMap a
updateMaxWithKey f t =
case t of Bin p l r | signBranch p -> binCheckLeft p (go f l) r
_ -> go f t
where
go f' (Bin p l r) = binCheckRight p l (go f' r)
go f' (Tip k y) = case f' k y of
Just y' -> Tip k y'
Nothing -> Nil
go _ Nil = Nil
data View a = View {-# UNPACK #-} !Key a !(IntMap a)
-- | \(O(\min(n,W))\). Retrieves the maximal (key,value) pair of the map, and
-- the map stripped of that element, or 'Nothing' if passed an empty map.
--
-- > maxViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((5,"a"), singleton 3 "b")
-- > maxViewWithKey empty == Nothing
maxViewWithKey :: IntMap a -> Maybe ((Key, a), IntMap a)
maxViewWithKey t = case t of
Nil -> Nothing
_ -> Just $ case maxViewWithKeySure t of
View k v t' -> ((k, v), t')
{-# INLINE maxViewWithKey #-}
maxViewWithKeySure :: IntMap a -> View a
maxViewWithKeySure t =
case t of
Nil -> error "maxViewWithKeySure Nil"
Bin p l r | signBranch p ->
case go l of View k a l' -> View k a (binCheckLeft p l' r)
_ -> go t
where
go (Bin p l r) =
case go r of View k a r' -> View k a (binCheckRight p l r')
go (Tip k y) = View k y Nil
go Nil = error "maxViewWithKey_go Nil"
-- See note on NOINLINE at minViewWithKeySure
{-# NOINLINE maxViewWithKeySure #-}
-- | \(O(\min(n,W))\). Retrieves the minimal (key,value) pair of the map, and
-- the map stripped of that element, or 'Nothing' if passed an empty map.
--
-- > minViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((3,"b"), singleton 5 "a")
-- > minViewWithKey empty == Nothing
minViewWithKey :: IntMap a -> Maybe ((Key, a), IntMap a)
minViewWithKey t =
case t of
Nil -> Nothing
_ -> Just $ case minViewWithKeySure t of
View k v t' -> ((k, v), t')
-- We inline this to give GHC the best possible chance of
-- getting rid of the Maybe, pair, and Int constructors, as
-- well as a thunk under the Just. That is, we really want to
-- be certain this inlines!
{-# INLINE minViewWithKey #-}
minViewWithKeySure :: IntMap a -> View a
minViewWithKeySure t =
case t of
Nil -> error "minViewWithKeySure Nil"
Bin p l r | signBranch p ->
case go r of
View k a r' -> View k a (binCheckRight p l r')
_ -> go t
where
go (Bin p l r) =
case go l of View k a l' -> View k a (binCheckLeft p l' r)
go (Tip k y) = View k y Nil
go Nil = error "minViewWithKey_go Nil"
-- There's never anything significant to be gained by inlining
-- this. Sufficiently recent GHC versions will inline the wrapper
-- anyway, which should be good enough.
{-# NOINLINE minViewWithKeySure #-}
-- | \(O(\min(n,W))\). Update the value at the maximal key.
--
-- > updateMax (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "Xa")]
-- > updateMax (\ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
updateMax :: (a -> Maybe a) -> IntMap a -> IntMap a
updateMax f = updateMaxWithKey (const f)
-- | \(O(\min(n,W))\). Update the value at the minimal key.
--
-- > updateMin (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "Xb"), (5, "a")]
-- > updateMin (\ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
updateMin :: (a -> Maybe a) -> IntMap a -> IntMap a
updateMin f = updateMinWithKey (const f)
-- | \(O(\min(n,W))\). Retrieves the maximal key of the map, and the map
-- stripped of that element, or 'Nothing' if passed an empty map.
maxView :: IntMap a -> Maybe (a, IntMap a)
maxView t = fmap (\((_, x), t') -> (x, t')) (maxViewWithKey t)
-- | \(O(\min(n,W))\). Retrieves the minimal key of the map, and the map
-- stripped of that element, or 'Nothing' if passed an empty map.
minView :: IntMap a -> Maybe (a, IntMap a)
minView t = fmap (\((_, x), t') -> (x, t')) (minViewWithKey t)
-- | \(O(\min(n,W))\). Delete and find the maximal element.
-- This function throws an error if the map is empty. Use 'maxViewWithKey'
-- if the map may be empty.
deleteFindMax :: IntMap a -> ((Key, a), IntMap a)
deleteFindMax = fromMaybe (error "deleteFindMax: empty map has no maximal element") . maxViewWithKey
-- | \(O(\min(n,W))\). Delete and find the minimal element.
-- This function throws an error if the map is empty. Use 'minViewWithKey'
-- if the map may be empty.
deleteFindMin :: IntMap a -> ((Key, a), IntMap a)
deleteFindMin = fromMaybe (error "deleteFindMin: empty map has no minimal element") . minViewWithKey
-- The KeyValue type is used when returning a key-value pair and helps with
-- GHC optimizations.
--
-- For lookupMinSure, if the return type is (Int, a), GHC compiles it to a
-- worker $wlookupMinSure :: IntMap a -> (# Int, a #). If the return type is
-- KeyValue a instead, the worker does not box the int and returns
-- (# Int#, a #).
-- For a modern enough GHC (>=9.4), this measure turns out to be unnecessary in
-- this instance. We still use it for older GHCs and to make our intent clear.
data KeyValue a = KeyValue {-# UNPACK #-} !Key a
kvToTuple :: KeyValue a -> (Key, a)
kvToTuple (KeyValue k x) = (k, x)
{-# INLINE kvToTuple #-}
lookupMinSure :: IntMap a -> KeyValue a
lookupMinSure (Tip k v) = KeyValue k v
lookupMinSure (Bin _ l _) = lookupMinSure l
lookupMinSure Nil = error "lookupMinSure Nil"
-- | \(O(\min(n,W))\). The minimal key of the map. Returns 'Nothing' if the map is empty.
lookupMin :: IntMap a -> Maybe (Key, a)
lookupMin Nil = Nothing
lookupMin (Tip k v) = Just (k,v)
lookupMin (Bin p l r) =
Just $! kvToTuple (lookupMinSure (if signBranch p then r else l))
{-# INLINE lookupMin #-} -- See Note [Inline lookupMin] in Data.Set.Internal
-- | \(O(\min(n,W))\). The minimal key of the map. Calls 'error' if the map is empty.
findMin :: IntMap a -> (Key, a)
findMin t
| Just r <- lookupMin t = r
| otherwise = error "findMin: empty map has no minimal element"
lookupMaxSure :: IntMap a -> KeyValue a
lookupMaxSure (Tip k v) = KeyValue k v
lookupMaxSure (Bin _ _ r) = lookupMaxSure r
lookupMaxSure Nil = error "lookupMaxSure Nil"
-- | \(O(\min(n,W))\). The maximal key of the map. Returns 'Nothing' if the map is empty.
lookupMax :: IntMap a -> Maybe (Key, a)
lookupMax Nil = Nothing
lookupMax (Tip k v) = Just (k,v)
lookupMax (Bin p l r) =
Just $! kvToTuple (lookupMaxSure (if signBranch p then l else r))
{-# INLINE lookupMax #-} -- See Note [Inline lookupMin] in Data.Set.Internal
-- | \(O(\min(n,W))\). The maximal key of the map. Calls 'error' if the map is empty.
findMax :: IntMap a -> (Key, a)
findMax t
| Just r <- lookupMax t = r
| otherwise = error "findMax: empty map has no maximal element"
-- | \(O(\min(n,W))\). Delete the minimal key. Returns an empty map if the map is empty.
--
-- Note that this is a change of behaviour for consistency with 'Data.Map.Map' –
-- versions prior to 0.5 threw an error if the 'IntMap' was already empty.
deleteMin :: IntMap a -> IntMap a
deleteMin = maybe Nil snd . minView
-- | \(O(\min(n,W))\). Delete the maximal key. Returns an empty map if the map is empty.
--
-- Note that this is a change of behaviour for consistency with 'Data.Map.Map' –
-- versions prior to 0.5 threw an error if the 'IntMap' was already empty.
deleteMax :: IntMap a -> IntMap a
deleteMax = maybe Nil snd . maxView
{--------------------------------------------------------------------
Submap
--------------------------------------------------------------------}
-- | \(O(\min(n, m \log \frac{2^W}{m})), m \leq n\).
-- Is this a proper submap? (ie. a submap but not equal).
-- Defined as (@'isProperSubmapOf' = 'isProperSubmapOfBy' (==)@).
isProperSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
isProperSubmapOf m1 m2
= isProperSubmapOfBy (==) m1 m2
{- | \(O(\min(n, m \log \frac{2^W}{m})), m \leq n\).
Is this a proper submap? (ie. a submap but not equal).
The expression (@'isProperSubmapOfBy' f m1 m2@) returns 'True' when
@keys m1@ and @keys m2@ are not equal,
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':
> isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
> isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
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)])
> isProperSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
-}
isProperSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
isProperSubmapOfBy predicate t1 t2
= case submapCmp predicate t1 t2 of
LT -> True
_ -> False
submapCmp :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Ordering
submapCmp predicate t1@(Bin p1 l1 r1) (Bin p2 l2 r2) = case treeTreeBranch p1 p2 of
ABL -> GT
ABR -> GT
BAL -> submapCmpLt l2
BAR -> submapCmpLt r2
EQL -> submapCmpEq
NOM -> GT -- disjoint
where
submapCmpLt t = case submapCmp predicate t1 t of
GT -> GT
_ -> LT
submapCmpEq = case (submapCmp predicate l1 l2, submapCmp predicate r1 r2) of
(GT,_ ) -> GT
(_ ,GT) -> GT
(EQ,EQ) -> EQ
_ -> LT
submapCmp _ (Bin _ _ _) _ = GT
submapCmp predicate (Tip kx x) (Tip ky y)
| (kx == ky) && predicate x y = EQ
| otherwise = GT -- disjoint
submapCmp predicate (Tip k x) t
= case lookup k t of
Just y | predicate x y -> LT
_ -> GT -- disjoint
submapCmp _ Nil Nil = EQ
submapCmp _ Nil _ = LT
-- | \(O(\min(n, m \log \frac{2^W}{m})), m \leq n\).
-- Is this a submap?
-- Defined as (@'isSubmapOf' = 'isSubmapOfBy' (==)@).
isSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
isSubmapOf m1 m2
= isSubmapOfBy (==) m1 m2
{- | \(O(\min(n, m \log \frac{2^W}{m})), m \leq n\).
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':
> 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':
> isSubmapOfBy (==) (fromList [(1,2)]) (fromList [(1,1),(2,2)])
> isSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
> isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
-}
isSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
isSubmapOfBy predicate t1@(Bin p1 l1 r1) (Bin p2 l2 r2) = case treeTreeBranch p1 p2 of
ABL -> False
ABR -> False
BAL -> isSubmapOfBy predicate t1 l2
BAR -> isSubmapOfBy predicate t1 r2
EQL -> isSubmapOfBy predicate l1 l2 && isSubmapOfBy predicate r1 r2
NOM -> False
isSubmapOfBy _ (Bin _ _ _) _ = False
isSubmapOfBy predicate (Tip k x) t = case lookup k t of
Just y -> predicate x y
Nothing -> False
isSubmapOfBy _ Nil _ = True
{--------------------------------------------------------------------
Mapping
--------------------------------------------------------------------}
-- | \(O(n)\). Map a function over all values in the map.
--
-- > map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")]
map :: (a -> b) -> IntMap a -> IntMap b
map f = go
where
go (Bin p l r) = Bin p (go l) (go r)
go (Tip k x) = Tip k (f x)
go Nil = Nil
#ifdef __GLASGOW_HASKELL__
{-# NOINLINE [1] map #-}
{-# RULES
"map/map" forall f g xs . map f (map g xs) = map (f . g) xs
"map/coerce" map coerce = coerce
#-}
#endif
-- | \(O(n)\). Map a function over all values in the map.
--
-- > let f key x = (show key) ++ ":" ++ x
-- > mapWithKey f (fromList [(5,"a"), (3,"b")]) == fromList [(3, "3:b"), (5, "5:a")]
mapWithKey :: (Key -> a -> b) -> IntMap a -> IntMap b
mapWithKey f t
= case t of
Bin p l r -> Bin p (mapWithKey f l) (mapWithKey f r)
Tip k x -> Tip k (f k x)
Nil -> Nil
#ifdef __GLASGOW_HASKELL__
{-# NOINLINE [1] mapWithKey #-}
{-# RULES
"mapWithKey/mapWithKey" forall f g xs . mapWithKey f (mapWithKey g xs) =
mapWithKey (\k a -> f k (g k a)) xs
"mapWithKey/map" forall f g xs . mapWithKey f (map g xs) =
mapWithKey (\k a -> f k (g a)) xs
"map/mapWithKey" forall f g xs . map f (mapWithKey g xs) =
mapWithKey (\k a -> f (g k a)) xs
#-}
#endif
-- | \(O(n)\).
-- @'traverseWithKey' f s == 'fromList' <$> 'traverse' (\(k, v) -> (,) k <$> f k v) ('toList' m)@
-- That is, behaves exactly like a regular 'traverse' except that the traversing
-- function also has access to the key associated with a value.
--
-- > traverseWithKey (\k v -> if odd k then Just (succ v) else Nothing) (fromList [(1, 'a'), (5, 'e')]) == Just (fromList [(1, 'b'), (5, 'f')])
-- > traverseWithKey (\k v -> if odd k then Just (succ v) else Nothing) (fromList [(2, 'c')]) == Nothing
traverseWithKey :: Applicative t => (Key -> a -> t b) -> IntMap a -> t (IntMap b)
traverseWithKey f = go
where
go Nil = pure Nil
go (Tip k v) = Tip k <$> f k v
go (Bin p l r)
| signBranch p = liftA2 (flip (Bin p)) (go r) (go l)
| otherwise = liftA2 (Bin p) (go l) (go r)
{-# INLINE traverseWithKey #-}
-- | \(O(n)\). The function @'mapAccum'@ threads an accumulating
-- argument through the map in ascending order of keys.
--
-- > let f a b = (a ++ b, b ++ "X")
-- > mapAccum f "Everything: " (fromList [(5,"a"), (3,"b")]) == ("Everything: ba", fromList [(3, "bX"), (5, "aX")])
mapAccum :: (a -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
mapAccum f = mapAccumWithKey (\a' _ x -> f a' x)
-- | \(O(n)\). The function @'mapAccumWithKey'@ threads an accumulating
-- argument through the map in ascending order of keys.
--
-- > let f a k b = (a ++ " " ++ (show k) ++ "-" ++ b, b ++ "X")
-- > mapAccumWithKey f "Everything:" (fromList [(5,"a"), (3,"b")]) == ("Everything: 3-b 5-a", fromList [(3, "bX"), (5, "aX")])
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 ascending order of keys.
mapAccumL :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
mapAccumL f a t
= case t of
Bin p l r
| signBranch p ->
let (a1,r') = mapAccumL f a r
(a2,l') = mapAccumL f a1 l
in (a2,Bin p l' r')
| otherwise ->
let (a1,l') = mapAccumL f a l
(a2,r') = mapAccumL f a1 r
in (a2,Bin p l' r')
Tip k x -> let (a',x') = f a k x in (a',Tip k x')
Nil -> (a,Nil)
-- | \(O(n)\). The function @'mapAccumRWithKey'@ threads an accumulating
-- argument through the map in descending order of keys.
mapAccumRWithKey :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
mapAccumRWithKey f a t
= case t of
Bin p l r
| signBranch p ->
let (a1,l') = mapAccumRWithKey f a l
(a2,r') = mapAccumRWithKey f a1 r
in (a2,Bin p l' r')
| otherwise ->
let (a1,r') = mapAccumRWithKey f a r
(a2,l') = mapAccumRWithKey f a1 l
in (a2,Bin p l' r')
Tip k x -> let (a',x') = f a k x in (a',Tip k x')
Nil -> (a,Nil)
-- | \(O(n \min(n,W))\).
-- @'mapKeys' f s@ is the map obtained by applying @f@ to each key of @s@.
--
-- The size of the result may be smaller if @f@ maps two or more distinct
-- keys to the same new key. In this case the value at the greatest of the
-- original keys is retained.
--
-- > mapKeys (+ 1) (fromList [(5,"a"), (3,"b")]) == fromList [(4, "b"), (6, "a")]
-- > mapKeys (\ _ -> 1) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 1 "c"
-- > mapKeys (\ _ -> 3) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 3 "c"
mapKeys :: (Key->Key) -> IntMap a -> IntMap a
mapKeys f = fromList . foldrWithKey (\k x xs -> (f k, x) : xs) []
-- | \(O(n \min(n,W))\).
-- @'mapKeysWith' c f s@ is the map obtained by applying @f@ to each key of @s@.
--
-- The size of the result may be smaller if @f@ maps two or more distinct
-- keys to the same new key. In this case the associated values will be
-- combined using @c@.
--
-- > mapKeysWith (++) (\ _ -> 1) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 1 "cdab"
-- > mapKeysWith (++) (\ _ -> 3) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 3 "cdab"
--
-- Also see the performance note on 'fromListWith'.
mapKeysWith :: (a -> a -> a) -> (Key->Key) -> IntMap a -> IntMap a
mapKeysWith c f
= fromListWith c . foldrWithKey (\k x xs -> (f k, x) : xs) []
-- | \(O(n)\).
-- @'mapKeysMonotonic' f s == 'mapKeys' f s@, but works only when @f@
-- is strictly monotonic.
-- That is, for any values @x@ and @y@, if @x@ < @y@ then @f x@ < @f y@.
-- Semi-formally, we have:
--
-- > and [x < y ==> f x < f y | x <- ls, y <- ls]
-- > ==> mapKeysMonotonic f s == mapKeys f s
-- > where ls = keys s
--
-- This means that @f@ maps distinct original keys to distinct resulting keys.
-- This function has slightly better performance than 'mapKeys'.
--
-- __Warning__: This function should be used only if @f@ is monotonically
-- strictly increasing. This precondition is not checked. Use 'mapKeys' if the
-- precondition may not hold.
--
-- > mapKeysMonotonic (\ k -> k * 2) (fromList [(5,"a"), (3,"b")]) == fromList [(6, "b"), (10, "a")]
mapKeysMonotonic :: (Key->Key) -> IntMap a -> IntMap a
mapKeysMonotonic f
= fromDistinctAscList . foldrWithKey (\k x xs -> (f k, x) : xs) []
{--------------------------------------------------------------------
Filter
--------------------------------------------------------------------}
-- | \(O(n)\). Filter all values that satisfy some predicate.
--
-- > filter (> "a") (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
-- > filter (> "x") (fromList [(5,"a"), (3,"b")]) == empty
-- > filter (< "a") (fromList [(5,"a"), (3,"b")]) == empty
filter :: (a -> Bool) -> IntMap a -> IntMap a
filter p m
= filterWithKey (\_ x -> p x) m
-- | \(O(n)\). Filter all keys that satisfy some predicate.
--
-- @
-- filterKeys p = 'filterWithKey' (\\k _ -> p k)
-- @
--
-- > filterKeys (> 4) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
--
-- @since 0.8
filterKeys :: (Key -> Bool) -> IntMap a -> IntMap a
filterKeys predicate = filterWithKey (\k _ -> predicate k)
-- | \(O(n)\). Filter all keys\/values that satisfy some predicate.
--
-- > filterWithKey (\k _ -> k > 4) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
filterWithKey :: (Key -> a -> Bool) -> IntMap a -> IntMap a
filterWithKey predicate = go
where
go Nil = Nil
go t@(Tip k x) = if predicate k x then t else Nil
go (Bin p l r) = bin p (go l) (go r)
-- | \(O(n)\). Partition the map according to some predicate. The first
-- map contains all elements that satisfy the predicate, the second all
-- elements that fail the predicate. See also 'split'.
--
-- > partition (> "a") (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a")
-- > partition (< "x") (fromList [(5,"a"), (3,"b")]) == (fromList [(3, "b"), (5, "a")], empty)
-- > partition (> "x") (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3, "b"), (5, "a")])
partition :: (a -> Bool) -> IntMap a -> (IntMap a,IntMap a)
partition p m
= partitionWithKey (\_ x -> p x) m
-- | \(O(n)\). Partition the map according to some predicate. The first
-- map contains all elements that satisfy the predicate, the second all
-- elements that fail the predicate. See also 'split'.
--
-- > partitionWithKey (\ k _ -> k > 3) (fromList [(5,"a"), (3,"b")]) == (singleton 5 "a", singleton 3 "b")
-- > partitionWithKey (\ k _ -> k < 7) (fromList [(5,"a"), (3,"b")]) == (fromList [(3, "b"), (5, "a")], empty)
-- > partitionWithKey (\ k _ -> k > 7) (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3, "b"), (5, "a")])
partitionWithKey :: (Key -> a -> Bool) -> IntMap a -> (IntMap a,IntMap a)
partitionWithKey predicate0 t0 = toPair $ go predicate0 t0
where
go predicate t =
case t of
Bin p l r ->
let (l1 :*: l2) = go predicate l
(r1 :*: r2) = go predicate r
in bin p l1 r1 :*: bin p l2 r2
Tip k x
| predicate k x -> (t :*: Nil)
| otherwise -> (Nil :*: t)
Nil -> (Nil :*: Nil)
-- | \(O(\min(n,W))\). Take while a predicate on the keys holds.
-- The user is responsible for ensuring that for all @Int@s, @j \< k ==\> p j \>= p k@.
-- See note at 'spanAntitone'.
--
-- @
-- takeWhileAntitone p = 'fromDistinctAscList' . 'Data.List.takeWhile' (p . fst) . 'toList'
-- takeWhileAntitone p = 'filterWithKey' (\\k _ -> p k)
-- @
--
-- @since 0.6.7
takeWhileAntitone :: (Key -> Bool) -> IntMap a -> IntMap a
takeWhileAntitone predicate t =
case t of
Bin p l r
| signBranch p ->
if predicate 0 -- handle negative numbers.
then bin p (go predicate l) r
else go predicate r
_ -> go predicate t
where
go predicate' (Bin p l r)
| predicate' (unPrefix p) = bin p l (go predicate' r)
| otherwise = go predicate' l
go predicate' t'@(Tip ky _)
| predicate' ky = t'
| otherwise = Nil
go _ Nil = Nil
-- | \(O(\min(n,W))\). Drop while a predicate on the keys holds.
-- The user is responsible for ensuring that for all @Int@s, @j \< k ==\> p j \>= p k@.
-- See note at 'spanAntitone'.
--
-- @
-- dropWhileAntitone p = 'fromDistinctAscList' . 'Data.List.dropWhile' (p . fst) . 'toList'
-- dropWhileAntitone p = 'filterWithKey' (\\k _ -> not (p k))
-- @
--
-- @since 0.6.7
dropWhileAntitone :: (Key -> Bool) -> IntMap a -> IntMap a
dropWhileAntitone predicate t =
case t of
Bin p l r
| signBranch p ->
if predicate 0 -- handle negative numbers.
then go predicate l
else bin p l (go predicate r)
_ -> go predicate t
where
go predicate' (Bin p l r)
| predicate' (unPrefix p) = go predicate' r
| otherwise = bin p (go predicate' l) r
go predicate' t'@(Tip ky _)
| predicate' ky = Nil
| otherwise = t'
go _ Nil = Nil
-- | \(O(\min(n,W))\). Divide a map at the point where a predicate on the keys stops holding.
-- The user is responsible for ensuring that for all @Int@s, @j \< k ==\> p j \>= p k@.
--
-- @
-- spanAntitone p xs = ('takeWhileAntitone' p xs, 'dropWhileAntitone' p xs)
-- spanAntitone p xs = 'partitionWithKey' (\\k _ -> p k) xs
-- @
--
-- Note: if @p@ is not actually antitone, then @spanAntitone@ will split the map
-- at some /unspecified/ point.
--
-- @since 0.6.7
spanAntitone :: (Key -> Bool) -> IntMap a -> (IntMap a, IntMap a)
spanAntitone predicate t =
case t of
Bin p l r
| signBranch p ->
if predicate 0 -- handle negative numbers.
then
case go predicate l of
(lt :*: gt) ->
let !lt' = bin p lt r
in (lt', gt)
else
case go predicate r of
(lt :*: gt) ->
let !gt' = bin p l gt
in (lt, gt')
_ -> case go predicate t of
(lt :*: gt) -> (lt, gt)
where
go predicate' (Bin p l r)
| predicate' (unPrefix p)
= case go predicate' r of (lt :*: gt) -> bin p l lt :*: gt
| otherwise
= case go predicate' l of (lt :*: gt) -> lt :*: bin p gt r
go predicate' t'@(Tip ky _)
| predicate' ky = (t' :*: Nil)
| otherwise = (Nil :*: t')
go _ Nil = (Nil :*: Nil)
-- | \(O(n)\). Map values and collect the 'Just' results.
--
-- > let f x = if x == "a" then Just "new a" else Nothing
-- > mapMaybe f (fromList [(5,"a"), (3,"b")]) == singleton 5 "new a"
mapMaybe :: (a -> Maybe b) -> IntMap a -> IntMap b
mapMaybe f = mapMaybeWithKey (\_ x -> f x)
-- | \(O(n)\). Map keys\/values and collect the 'Just' results.
--
-- > let f k _ = if k < 5 then Just ("key : " ++ (show k)) else Nothing
-- > mapMaybeWithKey f (fromList [(5,"a"), (3,"b")]) == singleton 3 "key : 3"
mapMaybeWithKey :: (Key -> a -> Maybe b) -> IntMap a -> IntMap b
mapMaybeWithKey f (Bin p l r)
= bin p (mapMaybeWithKey f l) (mapMaybeWithKey f r)
mapMaybeWithKey f (Tip k x) = case f k x of
Just y -> Tip k y
Nothing -> Nil
mapMaybeWithKey _ Nil = Nil
-- | \(O(n)\). Map values and separate the 'Left' and 'Right' results.
--
-- > let f a = if a < "c" then Left a else Right a
-- > mapEither f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
-- > == (fromList [(3,"b"), (5,"a")], fromList [(1,"x"), (7,"z")])
-- >
-- > mapEither (\ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
-- > == (empty, fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
mapEither :: (a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)
mapEither f m
= mapEitherWithKey (\_ x -> f x) m
-- | \(O(n)\). Map keys\/values and separate the 'Left' and 'Right' results.
--
-- > let f k a = if k < 5 then Left (k * 2) else Right (a ++ a)
-- > mapEitherWithKey f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
-- > == (fromList [(1,2), (3,6)], fromList [(5,"aa"), (7,"zz")])
-- >
-- > mapEitherWithKey (\_ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
-- > == (empty, fromList [(1,"x"), (3,"b"), (5,"a"), (7,"z")])
mapEitherWithKey :: (Key -> a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)
mapEitherWithKey f0 t0 = toPair $ go f0 t0
where
go f (Bin p l r) =
bin p l1 r1 :*: bin p l2 r2
where
(l1 :*: l2) = go f l
(r1 :*: r2) = go f r
go f (Tip k x) = case f k x of
Left y -> (Tip k y :*: Nil)
Right z -> (Nil :*: Tip k z)
go _ Nil = (Nil :*: Nil)
-- | \(O(\min(n,W))\). 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 2 (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3,"b"), (5,"a")])
-- > split 3 (fromList [(5,"a"), (3,"b")]) == (empty, singleton 5 "a")
-- > split 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a")
-- > split 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", empty)
-- > split 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], empty)
split :: Key -> IntMap a -> (IntMap a, IntMap a)
split k t =
case t of
Bin p l r
| signBranch p ->
if k >= 0 -- handle negative numbers.
then
case go k l of
(lt :*: gt) ->
let !lt' = bin p lt r
in (lt', gt)
else
case go k r of
(lt :*: gt) ->
let !gt' = bin p l gt
in (lt, gt')
_ -> case go k t of
(lt :*: gt) -> (lt, gt)
where
go !k' t'@(Bin p l r)
| nomatch k' p = if k' < unPrefix p then Nil :*: t' else t' :*: Nil
| left k' p = case go k' l of (lt :*: gt) -> lt :*: bin p gt r
| otherwise = case go k' r of (lt :*: gt) -> bin p l lt :*: gt
go k' t'@(Tip ky _)
| k' > ky = (t' :*: Nil)
| k' < ky = (Nil :*: t')
| otherwise = (Nil :*: Nil)
go _ Nil = (Nil :*: Nil)
data SplitLookup a = SplitLookup !(IntMap a) !(Maybe a) !(IntMap a)
mapLT :: (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
mapLT f (SplitLookup lt fnd gt) = SplitLookup (f lt) fnd gt
{-# INLINE mapLT #-}
mapGT :: (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
mapGT f (SplitLookup lt fnd gt) = SplitLookup lt fnd (f gt)
{-# INLINE mapGT #-}
-- | \(O(\min(n,W))\). Performs a 'split' but also returns whether the pivot
-- key was found in the original map.
--
-- > splitLookup 2 (fromList [(5,"a"), (3,"b")]) == (empty, Nothing, fromList [(3,"b"), (5,"a")])
-- > splitLookup 3 (fromList [(5,"a"), (3,"b")]) == (empty, Just "b", singleton 5 "a")
-- > splitLookup 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Nothing, singleton 5 "a")
-- > splitLookup 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Just "a", empty)
-- > splitLookup 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], Nothing, empty)
splitLookup :: Key -> IntMap a -> (IntMap a, Maybe a, IntMap a)
splitLookup k t =
case
case t of
Bin p l r
| signBranch p ->
if k >= 0 -- handle negative numbers.
then mapLT (flip (bin p) r) (go k l)
else mapGT (bin p l) (go k r)
_ -> go k t
of SplitLookup lt fnd gt -> (lt, fnd, gt)
where
go !k' t'@(Bin p l r)
| nomatch k' p =
if k' < unPrefix p
then SplitLookup Nil Nothing t'
else SplitLookup t' Nothing Nil
| left k' p = mapGT (flip (bin p) r) (go k' l)
| otherwise = mapLT (bin p l) (go k' r)
go k' t'@(Tip ky y)
| k' > ky = SplitLookup t' Nothing Nil
| k' < ky = SplitLookup Nil Nothing t'
| otherwise = SplitLookup Nil (Just y) Nil
go _ Nil = SplitLookup Nil Nothing Nil
{--------------------------------------------------------------------
Fold
--------------------------------------------------------------------}
-- | \(O(n)\). Fold the values in the map using the given right-associative
-- binary operator, such that @'foldr' f z == 'Prelude.foldr' f z . 'elems'@.
--
-- For example,
--
-- > elems map = foldr (:) [] map
--
-- > let f a len = len + (length a)
-- > foldr f 0 (fromList [(5,"a"), (3,"bbb")]) == 4
foldr :: (a -> b -> b) -> b -> IntMap a -> b
foldr f z = \t -> -- Use lambda t to be inlinable with two arguments only.
case t of
Bin p l r
| signBranch p -> go (go z l) r -- put negative numbers before
| otherwise -> go (go z r) l
_ -> go z t
where
go z' Nil = z'
go z' (Tip _ x) = f x z'
go z' (Bin _ l r) = go (go z' r) l
{-# INLINE foldr #-}
-- | \(O(n)\). A strict version of 'foldr'. Each application of the operator is
-- evaluated before using the result in the next application. This
-- function is strict in the starting value.
foldr' :: (a -> b -> b) -> b -> IntMap a -> b
foldr' f z = \t -> -- Use lambda t to be inlinable with two arguments only.
case t of
Bin p l r
| signBranch p -> go (go z l) r -- put negative numbers before
| otherwise -> go (go z r) l
_ -> go z t
where
go !z' Nil = z'
go z' (Tip _ x) = f x z'
go z' (Bin _ l r) = go (go z' r) l
{-# INLINE foldr' #-}
-- | \(O(n)\). Fold the values in the map using the given left-associative
-- binary operator, such that @'foldl' f z == 'Prelude.foldl' f z . 'elems'@.
--
-- For example,
--
-- > elems = reverse . foldl (flip (:)) []
--
-- > let f len a = len + (length a)
-- > foldl f 0 (fromList [(5,"a"), (3,"bbb")]) == 4
foldl :: (a -> b -> a) -> a -> IntMap b -> a
foldl f z = \t -> -- Use lambda t to be inlinable with two arguments only.
case t of
Bin p l r
| signBranch p -> go (go z r) l -- put negative numbers before
| otherwise -> go (go z l) r
_ -> go z t
where
go z' Nil = z'
go z' (Tip _ x) = f z' x
go z' (Bin _ l r) = go (go z' l) r
{-# INLINE foldl #-}
-- | \(O(n)\). A strict version of 'foldl'. Each application of the operator is
-- evaluated before using the result in the next application. This
-- function is strict in the starting value.
foldl' :: (a -> b -> a) -> a -> IntMap b -> a
foldl' f z = \t -> -- Use lambda t to be inlinable with two arguments only.
case t of
Bin p l r
| signBranch p -> go (go z r) l -- put negative numbers before
| otherwise -> go (go z l) r
_ -> go z t
where
go !z' Nil = z'
go z' (Tip _ x) = f z' x
go z' (Bin _ l r) = go (go z' l) r
{-# INLINE foldl' #-}
-- | \(O(n)\). Fold the keys and values in the map using the given right-associative
-- binary operator, such that
-- @'foldrWithKey' f z == 'Prelude.foldr' ('uncurry' f) z . 'toAscList'@.
--
-- For example,
--
-- > keys map = foldrWithKey (\k x ks -> k:ks) [] map
--
-- > let f k a result = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")"
-- > foldrWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (5:a)(3:b)"
foldrWithKey :: (Key -> a -> b -> b) -> b -> IntMap a -> b
foldrWithKey f z = \t -> -- Use lambda t to be inlinable with two arguments only.
case t of
Bin p l r
| signBranch p -> go (go z l) r -- put negative numbers before
| otherwise -> go (go z r) l
_ -> go z t
where
go z' Nil = z'
go z' (Tip kx x) = f kx x z'
go z' (Bin _ l r) = go (go z' r) l
{-# INLINE foldrWithKey #-}
-- | \(O(n)\). A strict version of 'foldrWithKey'. Each application of the operator is
-- evaluated before using the result in the next application. This
-- function is strict in the starting value.
foldrWithKey' :: (Key -> a -> b -> b) -> b -> IntMap a -> b
foldrWithKey' f z = \t -> -- Use lambda t to be inlinable with two arguments only.
case t of
Bin p l r
| signBranch p -> go (go z l) r -- put negative numbers before
| otherwise -> go (go z r) l
_ -> go z t
where
go !z' Nil = z'
go z' (Tip kx x) = f kx x z'
go z' (Bin _ l r) = go (go z' r) l
{-# INLINE foldrWithKey' #-}
-- | \(O(n)\). Fold the keys and values in the map using the given left-associative
-- binary operator, such that
-- @'foldlWithKey' f z == 'Prelude.foldl' (\\z' (kx, x) -> f z' kx x) z . 'toAscList'@.
--
-- For example,
--
-- > keys = reverse . foldlWithKey (\ks k x -> k:ks) []
--
-- > let f result k a = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")"
-- > foldlWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (3:b)(5:a)"
foldlWithKey :: (a -> Key -> b -> a) -> a -> IntMap b -> a
foldlWithKey f z = \t -> -- Use lambda t to be inlinable with two arguments only.
case t of
Bin p l r
| signBranch p -> go (go z r) l -- put negative numbers before
| otherwise -> go (go z l) r
_ -> go z t
where
go z' Nil = z'
go z' (Tip kx x) = f z' kx x
go z' (Bin _ l r) = go (go z' l) r
{-# INLINE foldlWithKey #-}
-- | \(O(n)\). A strict version of 'foldlWithKey'. Each application of the operator is
-- evaluated before using the result in the next application. This
-- function is strict in the starting value.
foldlWithKey' :: (a -> Key -> b -> a) -> a -> IntMap b -> a
foldlWithKey' f z = \t -> -- Use lambda t to be inlinable with two arguments only.
case t of
Bin p l r
| signBranch p -> go (go z r) l -- put negative numbers before
| otherwise -> go (go z l) r
_ -> go z t
where
go !z' Nil = z'
go z' (Tip kx x) = f z' kx x
go z' (Bin _ l r) = go (go z' l) r
{-# INLINE foldlWithKey' #-}
-- | \(O(n)\). Fold the keys and values in the map using the given monoid, such that
--
-- @'foldMapWithKey' f = 'Prelude.fold' . 'mapWithKey' f@
--
-- This can be an asymptotically faster than 'foldrWithKey' or 'foldlWithKey' for some monoids.
--
-- @since 0.5.4
foldMapWithKey :: Monoid m => (Key -> a -> m) -> IntMap a -> m
foldMapWithKey f = go
where
go Nil = mempty
go (Tip kx x) = f kx x
go (Bin p l r)
| signBranch p = go r `mappend` go l
| otherwise = go l `mappend` go r
{-# INLINE foldMapWithKey #-}
{--------------------------------------------------------------------
List variations
--------------------------------------------------------------------}
-- | \(O(n)\).
-- Return all elements of the map in the ascending order of their keys.
-- Subject to list fusion.
--
-- > elems (fromList [(5,"a"), (3,"b")]) == ["b","a"]
-- > elems empty == []
elems :: IntMap a -> [a]
elems = foldr (:) []
-- | \(O(n)\). Return all keys of the map in ascending order. Subject to list
-- fusion.
--
-- > keys (fromList [(5,"a"), (3,"b")]) == [3,5]
-- > keys empty == []
keys :: IntMap a -> [Key]
keys = foldrWithKey (\k _ ks -> k : ks) []
-- | \(O(n)\). An alias for 'toAscList'. Returns all key\/value pairs in the
-- map in ascending key order. Subject to list fusion.
--
-- > assocs (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]
-- > assocs empty == []
assocs :: IntMap a -> [(Key,a)]
assocs = toAscList
-- | \(O(n)\). The set of all keys of the map.
--
-- > keysSet (fromList [(5,"a"), (3,"b")]) == Data.IntSet.fromList [3,5]
-- > keysSet empty == Data.IntSet.empty
keysSet :: IntMap a -> IntSet.IntSet
keysSet Nil = IntSet.Nil
keysSet (Tip kx _) = IntSet.singleton kx
keysSet (Bin p l r)
| unPrefix p .&. IntSet.suffixBitMask == 0
= IntSet.Bin p (keysSet l) (keysSet r)
| otherwise
= IntSet.Tip (unPrefix p .&. IntSet.prefixBitMask) (computeBm (computeBm 0 l) r)
where computeBm !acc (Bin _ l' r') = computeBm (computeBm acc l') r'
computeBm acc (Tip kx _) = acc .|. IntSet.bitmapOf kx
computeBm _ Nil = error "Data.IntSet.keysSet: Nil"
-- | \(O(n)\). Build a map from a set of keys and a function which for each key
-- computes its value.
--
-- > fromSet (\k -> replicate k 'a') (Data.IntSet.fromList [3, 5]) == fromList [(5,"aaaaa"), (3,"aaa")]
-- > fromSet undefined Data.IntSet.empty == empty
fromSet :: (Key -> a) -> IntSet.IntSet -> IntMap a
fromSet _ IntSet.Nil = Nil
fromSet f (IntSet.Bin p l r) = Bin p (fromSet f l) (fromSet f r)
fromSet f (IntSet.Tip kx bm) = buildTree f kx bm (IntSet.suffixBitMask + 1)
where
-- This is slightly complicated, as we to convert the dense
-- representation of IntSet into tree representation of IntMap.
--
-- We are given a nonzero bit mask 'bmask' of 'bits' bits with
-- prefix 'prefix'. We split bmask into halves corresponding
-- to left and right subtree. If they are both nonempty, we
-- create a Bin node, otherwise exactly one of them is nonempty
-- and we construct the IntMap from that half.
buildTree g !prefix !bmask bits = case bits of
0 -> Tip prefix (g prefix)
_ -> case bits `iShiftRL` 1 of
bits2
| bmask .&. ((1 `shiftLL` bits2) - 1) == 0 ->
buildTree g (prefix + bits2) (bmask `shiftRL` bits2) bits2
| (bmask `shiftRL` bits2) .&. ((1 `shiftLL` bits2) - 1) == 0 ->
buildTree g prefix bmask bits2
| otherwise ->
Bin (Prefix (prefix .|. bits2))
(buildTree g prefix bmask bits2)
(buildTree g (prefix + bits2) (bmask `shiftRL` bits2) bits2)
{--------------------------------------------------------------------
Lists
--------------------------------------------------------------------}
#ifdef __GLASGOW_HASKELL__
-- | @since 0.5.6.2
instance GHCExts.IsList (IntMap a) where
type Item (IntMap a) = (Key,a)
fromList = fromList
toList = toList
#endif
-- | \(O(n)\). Convert the map to a list of key\/value pairs. Subject to list
-- fusion.
--
-- > toList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]
-- > toList empty == []
toList :: IntMap a -> [(Key,a)]
toList = toAscList
-- | \(O(n)\). Convert the map to a list of key\/value pairs where the
-- keys are in ascending order. Subject to list fusion.
--
-- > toAscList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]
toAscList :: IntMap a -> [(Key,a)]
toAscList = foldrWithKey (\k x xs -> (k,x):xs) []
-- | \(O(n)\). Convert the map to a list of key\/value pairs where the keys
-- are in descending order. Subject to list fusion.
--
-- > toDescList (fromList [(5,"a"), (3,"b")]) == [(5,"a"), (3,"b")]
toDescList :: IntMap a -> [(Key,a)]
toDescList = foldlWithKey (\xs k x -> (k,x):xs) []
-- List fusion for the list generating functions.
#if __GLASGOW_HASKELL__
-- The foldrFB and foldlFB are fold{r,l}WithKey equivalents, used for list fusion.
-- They are important to convert unfused methods back, see mapFB in prelude.
foldrFB :: (Key -> a -> b -> b) -> b -> IntMap a -> b
foldrFB = foldrWithKey
{-# INLINE[0] foldrFB #-}
foldlFB :: (a -> Key -> b -> a) -> a -> IntMap b -> a
foldlFB = foldlWithKey
{-# INLINE[0] foldlFB #-}
-- Inline assocs and toList, so that we need to fuse only toAscList.
{-# INLINE assocs #-}
{-# INLINE toList #-}
-- The fusion is enabled up to phase 2 included. If it does not succeed,
-- convert in phase 1 the expanded elems,keys,to{Asc,Desc}List calls back to
-- elems,keys,to{Asc,Desc}List. In phase 0, we inline fold{lr}FB (which were
-- used in a list fusion, otherwise it would go away in phase 1), and let compiler
-- do whatever it wants with elems,keys,to{Asc,Desc}List -- it was forbidden to
-- inline it before phase 0, otherwise the fusion rules would not fire at all.
{-# NOINLINE[0] elems #-}
{-# NOINLINE[0] keys #-}
{-# NOINLINE[0] toAscList #-}
{-# NOINLINE[0] toDescList #-}
{-# RULES "IntMap.elems" [~1] forall m . elems m = build (\c n -> foldrFB (\_ x xs -> c x xs) n m) #-}
{-# RULES "IntMap.elemsBack" [1] foldrFB (\_ x xs -> x : xs) [] = elems #-}
{-# RULES "IntMap.keys" [~1] forall m . keys m = build (\c n -> foldrFB (\k _ xs -> c k xs) n m) #-}
{-# RULES "IntMap.keysBack" [1] foldrFB (\k _ xs -> k : xs) [] = keys #-}
{-# RULES "IntMap.toAscList" [~1] forall m . toAscList m = build (\c n -> foldrFB (\k x xs -> c (k,x) xs) n m) #-}
{-# RULES "IntMap.toAscListBack" [1] foldrFB (\k x xs -> (k, x) : xs) [] = toAscList #-}
{-# RULES "IntMap.toDescList" [~1] forall m . toDescList m = build (\c n -> foldlFB (\xs k x -> c (k,x) xs) n m) #-}
{-# RULES "IntMap.toDescListBack" [1] foldlFB (\xs k x -> (k, x) : xs) [] = toDescList #-}
#endif
-- | \(O(n \min(n,W))\). Create a map from a list of key\/value pairs.
--
-- > fromList [] == empty
-- > fromList [(5,"a"), (3,"b"), (5, "c")] == fromList [(5,"c"), (3,"b")]
-- > fromList [(5,"c"), (3,"b"), (5, "a")] == fromList [(5,"a"), (3,"b")]
fromList :: [(Key,a)] -> IntMap a
fromList xs
= Foldable.foldl' ins empty xs
where
ins t (k,x) = insert k x t
-- | \(O(n \min(n,W))\). Build a map from a list of key\/value pairs with a combining function. See also 'fromAscListWith'.
--
-- > fromListWith (++) [(5,"a"), (5,"b"), (3,"x"), (5,"c")] == fromList [(3, "x"), (5, "cba")]
-- > fromListWith (++) [] == empty
--
-- Note the reverse ordering of @"cba"@ in the example.
--
-- The symmetric combining function @f@ is applied in a left-fold over the list, as @f new old@.
--
-- === Performance
--
-- You should ensure that the given @f@ is fast with this order of arguments.
--
-- Symmetric functions may be slow in one order, and fast in another.
-- For the common case of collecting values of matching keys in a list, as above:
--
-- The complexity of @(++) a b@ is \(O(a)\), so it is fast when given a short list as its first argument.
-- Thus:
--
-- > fromListWith (++) (replicate 1000000 (3, "x")) -- O(n), fast
-- > fromListWith (flip (++)) (replicate 1000000 (3, "x")) -- O(n²), extremely slow
--
-- because they evaluate as, respectively:
--
-- > fromList [(3, "x" ++ ("x" ++ "xxxxx..xxxxx"))] -- O(n)
-- > fromList [(3, ("xxxxx..xxxxx" ++ "x") ++ "x")] -- O(n²)
--
-- Thus, to get good performance with an operation like @(++)@ while also preserving
-- the same order as in the input list, reverse the input:
--
-- > fromListWith (++) (reverse [(5,"a"), (5,"b"), (5,"c")]) == fromList [(5, "abc")]
--
-- and it is always fast to combine singleton-list values @[v]@ with @fromListWith (++)@, as in:
--
-- > fromListWith (++) $ reverse $ map (\(k, v) -> (k, [v])) someListOfTuples
fromListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a
fromListWith f xs
= fromListWithKey (\_ x y -> f x y) xs
-- | \(O(n \min(n,W))\). Build a map from a list of key\/value pairs with a combining function. See also fromAscListWithKey'.
--
-- > let f key new_value old_value = show key ++ ":" ++ new_value ++ "|" ++ old_value
-- > fromListWithKey f [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"c")] == fromList [(3, "3:a|b"), (5, "5:c|5:b|a")]
-- > fromListWithKey f [] == empty
--
-- Also see the performance note on 'fromListWith'.
fromListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a
fromListWithKey f xs
= Foldable.foldl' ins empty xs
where
ins t (k,x) = insertWithKey f k x t
-- | \(O(n)\). Build a map from a list of key\/value pairs where
-- the keys are in ascending order.
--
-- __Warning__: This function should be used only if the keys are in
-- non-decreasing order. This precondition is not checked. Use 'fromList' if the
-- precondition may not hold.
--
-- > fromAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")]
-- > fromAscList [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "b")]
fromAscList :: [(Key,a)] -> IntMap a
fromAscList = fromMonoListWithKey Nondistinct (\_ x _ -> x)
{-# NOINLINE fromAscList #-}
-- | \(O(n)\). Build a map from a list of key\/value pairs where
-- the keys are in ascending order, with a combining function on equal keys.
--
-- __Warning__: This function should be used only if the keys are in
-- non-decreasing order. This precondition is not checked. Use 'fromListWith' if
-- the precondition may not hold.
--
-- > fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "ba")]
--
-- Also see the performance note on 'fromListWith'.
fromAscListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a
fromAscListWith f = fromMonoListWithKey Nondistinct (\_ x y -> f x y)
{-# NOINLINE fromAscListWith #-}
-- | \(O(n)\). Build a map from a list of key\/value pairs where
-- the keys are in ascending order, with a combining function on equal keys.
--
-- __Warning__: This function should be used only if the keys are in
-- non-decreasing order. This precondition is not checked. Use 'fromListWithKey'
-- if the precondition may not hold.
--
-- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value
-- > fromAscListWithKey f [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "5:b|a")]
--
-- Also see the performance note on 'fromListWith'.
fromAscListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a
fromAscListWithKey f = fromMonoListWithKey Nondistinct f
{-# NOINLINE fromAscListWithKey #-}
-- | \(O(n)\). Build a map from a list of key\/value pairs where
-- the keys are in ascending order and all distinct.
--
-- __Warning__: This function should be used only if the keys are in
-- strictly increasing order. This precondition is not checked. Use 'fromList'
-- if the precondition may not hold.
--
-- > fromDistinctAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")]
fromDistinctAscList :: [(Key,a)] -> IntMap a
fromDistinctAscList = fromMonoListWithKey Distinct (\_ x _ -> x)
{-# NOINLINE fromDistinctAscList #-}
-- | \(O(n)\). Build a map from a list of key\/value pairs with monotonic keys
-- and a combining function.
--
-- The precise conditions under which this function works are subtle:
-- For any branch mask, keys with the same prefix w.r.t. the branch
-- mask must occur consecutively in the list.
--
-- Also see the performance note on 'fromListWith'.
fromMonoListWithKey :: Distinct -> (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a
fromMonoListWithKey distinct f = go
where
go [] = Nil
go ((kx,vx) : zs1) = addAll' kx vx zs1
-- `addAll'` collects all keys equal to `kx` into a single value,
-- and then proceeds with `addAll`.
addAll' !kx vx []
= Tip kx vx
addAll' !kx vx ((ky,vy) : zs)
| Nondistinct <- distinct, kx == ky
= let v = f kx vy vx in addAll' ky v zs
-- inlined: | otherwise = addAll kx (Tip kx vx) (ky : zs)
| m <- branchMask kx ky
, Inserted ty zs' <- addMany' m ky vy zs
= addAll kx (linkWithMask m ky ty kx (Tip kx vx)) zs'
-- for `addAll` and `addMany`, kx is /a/ key inside the tree `tx`
-- `addAll` consumes the rest of the list, adding to the tree `tx`
addAll !_kx !tx []
= tx
addAll !kx !tx ((ky,vy) : zs)
| m <- branchMask kx ky
, Inserted ty zs' <- addMany' m ky vy zs
= addAll kx (linkWithMask m ky ty kx tx) zs'
-- `addMany'` is similar to `addAll'`, but proceeds with `addMany'`.
addMany' !_m !kx vx []
= Inserted (Tip kx vx) []
addMany' !m !kx vx zs0@((ky,vy) : zs)
| Nondistinct <- distinct, kx == ky
= let v = f kx vy vx in addMany' m ky v zs
-- inlined: | otherwise = addMany m kx (Tip kx vx) (ky : zs)
| mask kx m /= mask ky m
= Inserted (Tip kx vx) zs0
| mxy <- branchMask kx ky
, Inserted ty zs' <- addMany' mxy ky vy zs
= addMany m kx (linkWithMask mxy ky ty kx (Tip kx vx)) zs'
-- `addAll` adds to `tx` all keys whose prefix w.r.t. `m` agrees with `kx`.
addMany !_m !_kx tx []
= Inserted tx []
addMany !m !kx tx zs0@((ky,vy) : zs)
| mask kx m /= mask ky m
= Inserted tx zs0
| mxy <- branchMask kx ky
, Inserted ty zs' <- addMany' mxy ky vy zs
= addMany m kx (linkWithMask mxy ky ty kx tx) zs'
{-# INLINE fromMonoListWithKey #-}
data Inserted a = Inserted !(IntMap a) ![(Key,a)]
data Distinct = Distinct | Nondistinct
{--------------------------------------------------------------------
Eq
--------------------------------------------------------------------}
instance Eq a => Eq (IntMap a) where
(==) = equal
equal :: Eq a => IntMap a -> IntMap a -> Bool
equal (Bin p1 l1 r1) (Bin p2 l2 r2)
= (p1 == p2) && (equal l1 l2) && (equal r1 r2)
equal (Tip kx x) (Tip ky y)
= (kx == ky) && (x==y)
equal Nil Nil = True
equal _ _ = False
{-# INLINABLE equal #-}
-- | @since 0.5.9
instance Eq1 IntMap where
liftEq eq = go
where
go (Bin p1 l1 r1) (Bin p2 l2 r2) = p1 == p2 && go l1 l2 && go r1 r2
go (Tip kx x) (Tip ky y) = kx == ky && eq x y
go Nil Nil = True
go _ _ = False
{-# INLINE liftEq #-}
{--------------------------------------------------------------------
Ord
--------------------------------------------------------------------}
instance Ord a => Ord (IntMap a) where
compare m1 m2 = liftCmp compare m1 m2
{-# INLINABLE compare #-}
-- | @since 0.5.9
instance Ord1 IntMap where
liftCompare = liftCmp
liftCmp :: (a -> b -> Ordering) -> IntMap a -> IntMap b -> Ordering
liftCmp cmp m1 m2 = case (splitSign m1, splitSign m2) of
((l1, r1), (l2, r2)) -> case go l1 l2 of
A_LT_B -> LT
A_Prefix_B -> if null r1 then LT else GT
A_EQ_B -> case go r1 r2 of
A_LT_B -> LT
A_Prefix_B -> LT
A_EQ_B -> EQ
B_Prefix_A -> GT
A_GT_B -> GT
B_Prefix_A -> if null r2 then GT else LT
A_GT_B -> GT
where
go t1@(Bin p1 l1 r1) t2@(Bin p2 l2 r2) = case treeTreeBranch p1 p2 of
ABL -> case go l1 t2 of
A_Prefix_B -> A_GT_B
A_EQ_B -> B_Prefix_A
o -> o
ABR -> A_LT_B
BAL -> case go t1 l2 of
A_EQ_B -> A_Prefix_B
B_Prefix_A -> A_LT_B
o -> o
BAR -> A_GT_B
EQL -> case go l1 l2 of
A_Prefix_B -> A_GT_B
A_EQ_B -> go r1 r2
B_Prefix_A -> A_LT_B
o -> o
NOM -> if unPrefix p1 < unPrefix p2 then A_LT_B else A_GT_B
go (Bin _ l1 _) (Tip k2 x2) = case lookupMinSure l1 of
KeyValue k1 x1 -> case compare k1 k2 <> cmp x1 x2 of
LT -> A_LT_B
EQ -> B_Prefix_A
GT -> A_GT_B
go (Tip k1 x1) (Bin _ l2 _) = case lookupMinSure l2 of
KeyValue k2 x2 -> case compare k1 k2 <> cmp x1 x2 of
LT -> A_LT_B
EQ -> A_Prefix_B
GT -> A_GT_B
go (Tip k1 x1) (Tip k2 x2) = case compare k1 k2 <> cmp x1 x2 of
LT -> A_LT_B
EQ -> A_EQ_B
GT -> A_GT_B
go Nil Nil = A_EQ_B
go Nil _ = A_Prefix_B
go _ Nil = B_Prefix_A
{-# INLINE liftCmp #-}
-- Split into negative and non-negative
splitSign :: IntMap a -> (IntMap a, IntMap a)
splitSign t@(Bin p l r)
| signBranch p = (r, l)
| unPrefix p < 0 = (t, Nil)
| otherwise = (Nil, t)
splitSign t@(Tip k _)
| k < 0 = (t, Nil)
| otherwise = (Nil, t)
splitSign Nil = (Nil, Nil)
{-# INLINE splitSign #-}
{--------------------------------------------------------------------
Functor
--------------------------------------------------------------------}
instance Functor IntMap where
fmap = map
#ifdef __GLASGOW_HASKELL__
a <$ Bin p l r = Bin p (a <$ l) (a <$ r)
a <$ Tip k _ = Tip k a
_ <$ Nil = Nil
#endif
{--------------------------------------------------------------------
Show
--------------------------------------------------------------------}
instance Show a => Show (IntMap a) where
showsPrec d m = showParen (d > 10) $
showString "fromList " . shows (toList m)
-- | @since 0.5.9
instance Show1 IntMap where
liftShowsPrec sp sl d m =
showsUnaryWith (liftShowsPrec sp' sl') "fromList" d (toList m)
where
sp' = liftShowsPrec sp sl
sl' = liftShowList sp sl
{--------------------------------------------------------------------
Read
--------------------------------------------------------------------}
instance (Read e) => Read (IntMap e) where
#if defined(__GLASGOW_HASKELL__) || defined(__MHS__)
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
-- | @since 0.5.9
instance Read1 IntMap where
liftReadsPrec rp rl = readsData $
readsUnaryWith (liftReadsPrec rp' rl') "fromList" fromList
where
rp' = liftReadsPrec rp rl
rl' = liftReadList rp rl
{--------------------------------------------------------------------
Helpers
--------------------------------------------------------------------}
{--------------------------------------------------------------------
Link
--------------------------------------------------------------------}
-- | Link two @IntMap@s. The maps must not be empty. The @Prefix@es of the two
-- maps must be different. @k1@ must share the prefix of @t1@. @p2@ must be the
-- prefix of @t2@.
linkKey :: Key -> IntMap a -> Prefix -> IntMap a -> IntMap a
linkKey k1 t1 p2 t2 = link k1 t1 (unPrefix p2) t2
{-# INLINE linkKey #-}
-- | Link two @IntMap@s. The maps must not be empty. The @Prefix@es of the two
-- maps must be different. @k1@ must share the prefix of @t1@ and @k2@ must
-- share the prefix of @t2@.
link :: Int -> IntMap a -> Int -> IntMap a -> IntMap a
link k1 t1 k2 t2 = linkWithMask (branchMask k1 k2) k1 t1 k2 t2
{-# INLINE link #-}
-- `linkWithMask` is useful when the `branchMask` has already been computed
linkWithMask :: Int -> Key -> IntMap a -> Key -> IntMap a -> IntMap a
linkWithMask m k1 t1 k2 t2
| i2w k1 < i2w k2 = Bin p t1 t2
| otherwise = Bin p t2 t1
where
p = Prefix (mask k1 m .|. m)
{-# INLINE linkWithMask #-}
{--------------------------------------------------------------------
@bin@ assures that we never have empty trees within a tree.
--------------------------------------------------------------------}
bin :: Prefix -> IntMap a -> IntMap a -> IntMap a
bin _ l Nil = l
bin _ Nil r = r
bin p l r = Bin p l r
{-# INLINE bin #-}
-- binCheckLeft only checks that the left subtree is non-empty
binCheckLeft :: Prefix -> IntMap a -> IntMap a -> IntMap a
binCheckLeft _ Nil r = r
binCheckLeft p l r = Bin p l r
{-# INLINE binCheckLeft #-}
-- binCheckRight only checks that the right subtree is non-empty
binCheckRight :: Prefix -> IntMap a -> IntMap a -> IntMap a
binCheckRight _ l Nil = l
binCheckRight p l r = Bin p l r
{-# INLINE binCheckRight #-}
{--------------------------------------------------------------------
Utilities
--------------------------------------------------------------------}
-- | \(O(1)\). Decompose a map into pieces based on the structure
-- of the underlying tree. This function is useful for consuming a
-- map in parallel.
--
-- No guarantee is made as to the sizes of the pieces; an internal, but
-- deterministic process determines this. However, it is guaranteed that the
-- pieces returned will be in ascending order (all elements in the first submap
-- less than all elements in the second, and so on).
--
-- Examples:
--
-- > splitRoot (fromList (zip [1..6::Int] ['a'..])) ==
-- > [fromList [(1,'a'),(2,'b'),(3,'c')],fromList [(4,'d'),(5,'e'),(6,'f')]]
--
-- > splitRoot empty == []
--
-- Note that the current implementation does not return more than two submaps,
-- but you should not depend on this behaviour because it can change in the
-- future without notice.
splitRoot :: IntMap a -> [IntMap a]
splitRoot orig =
case orig of
Nil -> []
x@(Tip _ _) -> [x]
Bin p l r
| signBranch p -> [r, l]
| otherwise -> [l, r]
{-# INLINE splitRoot #-}
{--------------------------------------------------------------------
Debugging
--------------------------------------------------------------------}
-- | \(O(n \min(n,W))\). Show the tree that implements the map. The tree is shown
-- in a compressed, hanging format.
showTree :: Show a => IntMap a -> String
showTree s
= showTreeWith True False s
{- | \(O(n \min(n,W))\). 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.
-}
showTreeWith :: Show a => Bool -> Bool -> IntMap a -> String
showTreeWith hang wide t
| hang = (showsTreeHang wide [] t) ""
| otherwise = (showsTree wide [] [] t) ""
showsTree :: Show a => Bool -> [String] -> [String] -> IntMap a -> ShowS
showsTree wide lbars rbars t = case t of
Bin p l r ->
showsTree wide (withBar rbars) (withEmpty rbars) r .
showWide wide rbars .
showsBars lbars . showString (showBin p) . showString "\n" .
showWide wide lbars .
showsTree wide (withEmpty lbars) (withBar lbars) l
Tip k x ->
showsBars lbars .
showString " " . shows k . showString ":=" . shows x . showString "\n"
Nil -> showsBars lbars . showString "|\n"
showsTreeHang :: Show a => Bool -> [String] -> IntMap a -> ShowS
showsTreeHang wide bars t = case t of
Bin p l r ->
showsBars bars . showString (showBin p) . showString "\n" .
showWide wide bars .
showsTreeHang wide (withBar bars) l .
showWide wide bars .
showsTreeHang wide (withEmpty bars) r
Tip k x ->
showsBars bars .
showString " " . shows k . showString ":=" . shows x . showString "\n"
Nil -> showsBars bars . showString "|\n"
showBin :: Prefix -> String
showBin _
= "*" -- ++ show (p,m)
showWide :: Bool -> [String] -> String -> String
showWide wide bars
| wide = showString (concat (reverse bars)) . showString "|\n"
| otherwise = id
showsBars :: [String] -> ShowS
showsBars bars
= case bars of
[] -> id
_ : tl -> showString (concat (reverse tl)) . showString node
node :: String
node = "+--"
withBar, withEmpty :: [String] -> [String]
withBar bars = "| ":bars
withEmpty bars = " ":bars
{--------------------------------------------------------------------
Notes
--------------------------------------------------------------------}
-- Note [Okasaki-Gill]
-- ~~~~~~~~~~~~~~~~~~~
--
-- The IntMap structure is based on the map described in the paper "Fast
-- Mergeable Integer Maps" by Chris Okasaki and Andy Gill, with some
-- differences.
--
-- The paper spends most of its time describing a little-endian tree, where the
-- branching is done first on low bits then high bits. It then briefly describes
-- a big-endian tree. The implementation here is big-endian.
--
-- The definition of Okasaki and Gill's map would be written in Haskell as
--
-- data Dict a
-- = Empty
-- | Lf !Int a
-- | Br !Int !Int !(Dict a) !(Dict a)
--
-- Empty is the same as IntMap's Nil, and Lf is the same as Tip.
--
-- In Br, the first Int is the shared prefix and the second is the mask bit by
-- itself. For the big-endian map, the paper suggests that the prefix be the
-- common prefix, followed by a 0-bit, followed by all 1-bits. This is so that
-- the prefix value can be used as a point of split for binary search.
--
-- IntMap's Bin corresponds to Br, but is different because it has only one
-- Int (newtyped as Prefix). This describes both prefix and mask, so it is not
-- necessary to store them separately. This value is, in fact, one plus the
-- value suggested for the prefix in the paper. This representation is chosen
-- because it saves one word per Bin without detriment to the efficiency of
-- operations.
--
-- The implementation of operations such as lookup, insert, union, follow
-- the described implementations on Dict and split into the same cases. For
-- instance, for insert, the three cases on a Br are whether the key belongs
-- outside the map, or it belongs in the left child, or it belongs in the
-- right child. We have the same three cases for a Bin. However, the bitwise
-- operations we use to determine the case is naturally different due to the
-- difference in representation.
-- Note [IntMap merge complexity]
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-- The merge algorithm (used for union, intersection, etc.) is adopted from
-- Okasaki-Gill who give the complexity as O(m+n), where m and n are the sizes
-- of the two input maps. This is correct, since we visit all constructors in
-- both maps in the worst case, but we can try to find a tighter bound.
--
-- Consider that m<=n, i.e. m is the size of the smaller map and n is the size
-- of the larger. It does not matter which map is the first argument.
--
-- Now we have O(n) as one upper bound for our complexity, since O(n) is the
-- same as O(m+n) for m<=n.
--
-- Next, consider the smaller map. For this map, we will visit some
-- constructors, plus all the Bins of the larger map that lie in our way.
-- For the former, the worst case is that we visit all constructors, which is
-- O(m).
-- For the latter, the worst case is that we encounter Bins at every point
-- possible. This happens when for every key in the smaller map, the path to
-- that key's Tip in the larger map has a full length of W, with a Bin at every
-- bit position. To maximize the total number of Bins, the paths should be as
-- disjoint as possible. But even if the paths are spread out, at least O(m)
-- Bins are unavoidably shared, which extend up to a depth of lg(m) from the
-- root. Beyond this, the paths may be disjoint. This gives us a total of
-- O(m + m (W - lg m)) = O(m log (2^W / m)).
-- The number of Bins we encounter is also bounded by the total number of Bins,
-- which is n-1, but we already have O(n) as an upper bound.
--
-- Combining our bounds, we have the final complexity as
-- O(min(n, m log (2^W / m))).
--
-- Note that
-- * This is similar to the Map merge complexity, which is O(m log (n/m)).
-- * When m is a small constant the term simplifies to O(min(n, W)), which is
-- just the complexity we expect for single operations like insert and delete.