Copyright | (c) Daan Leijen 2002 (c) Andriy Palamarchuk 2008 |
---|---|

License | BSD-style |

Maintainer | libraries@haskell.org |

Stability | provisional |

Portability | portable |

Safe Haskell | Safe |

Language | Haskell98 |

An efficient implementation of maps from integer keys to values (dictionaries).

API of this module is strict in the keys, but lazy in the values.
If you need value-strict maps, use Data.IntMap.Strict instead.
The `IntMap`

type itself is shared between the lazy and strict modules,
meaning that the same `IntMap`

value can be passed to functions in
both modules (although that is rarely needed).

These modules are intended to be imported qualified, to avoid name clashes with Prelude functions, e.g.

import Data.IntMap.Lazy (IntMap) import qualified Data.IntMap.Lazy as IntMap

The implementation is based on *big-endian patricia trees*. This data
structure performs especially well on binary operations like `union`

and `intersection`

. However, my 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, http://citeseer.ist.psu.edu/okasaki98fast.html - D.R. Morrison, "/PATRICIA -- Practical Algorithm To Retrieve Information Coded In Alphanumeric/", Journal of the ACM, 15(4), October 1968, pages 514-534.

Operation comments contain the operation time complexity in
the Big-O notation http://en.wikipedia.org/wiki/Big_O_notation.
Many operations have a worst-case complexity of *O(min(n,W))*.
This means that the operation can become linear in the number of
elements with a maximum of *W* -- the number of bits in an `Int`

(32 or 64).

- data IntMap a
- type Key = Int
- (!) :: IntMap a -> Key -> a
- (\\) :: IntMap a -> IntMap b -> IntMap a
- null :: IntMap a -> Bool
- size :: IntMap a -> Int
- member :: Key -> IntMap a -> Bool
- notMember :: Key -> IntMap a -> Bool
- lookup :: Key -> IntMap a -> Maybe a
- findWithDefault :: a -> Key -> IntMap a -> a
- lookupLT :: Key -> IntMap a -> Maybe (Key, a)
- lookupGT :: Key -> IntMap a -> Maybe (Key, a)
- lookupLE :: Key -> IntMap a -> Maybe (Key, a)
- lookupGE :: Key -> IntMap a -> Maybe (Key, a)
- empty :: IntMap a
- singleton :: Key -> a -> IntMap a
- insert :: Key -> a -> IntMap a -> IntMap a
- insertWith :: (a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
- insertWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
- insertLookupWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> (Maybe a, IntMap a)
- delete :: Key -> IntMap a -> IntMap a
- adjust :: (a -> a) -> Key -> IntMap a -> IntMap a
- adjustWithKey :: (Key -> a -> a) -> Key -> IntMap a -> IntMap a
- update :: (a -> Maybe a) -> Key -> IntMap a -> IntMap a
- updateWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> IntMap a
- updateLookupWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> (Maybe a, IntMap a)
- alter :: (Maybe a -> Maybe a) -> Key -> IntMap a -> IntMap a
- union :: IntMap a -> IntMap a -> IntMap a
- unionWith :: (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
- unionWithKey :: (Key -> a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
- unions :: [IntMap a] -> IntMap a
- unionsWith :: (a -> a -> a) -> [IntMap a] -> IntMap a
- difference :: IntMap a -> IntMap b -> IntMap a
- differenceWith :: (a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
- differenceWithKey :: (Key -> a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
- intersection :: IntMap a -> IntMap b -> IntMap a
- intersectionWith :: (a -> b -> c) -> IntMap a -> IntMap b -> IntMap c
- intersectionWithKey :: (Key -> a -> b -> c) -> IntMap a -> IntMap b -> IntMap c
- mergeWithKey :: (Key -> a -> b -> Maybe c) -> (IntMap a -> IntMap c) -> (IntMap b -> IntMap c) -> IntMap a -> IntMap b -> IntMap c
- map :: (a -> b) -> IntMap a -> IntMap b
- mapWithKey :: (Key -> a -> b) -> IntMap a -> IntMap b
- traverseWithKey :: Applicative t => (Key -> a -> t b) -> IntMap a -> t (IntMap b)
- mapAccum :: (a -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
- mapAccumWithKey :: (a -> Key -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
- mapAccumRWithKey :: (a -> Key -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
- mapKeys :: (Key -> Key) -> IntMap a -> IntMap a
- mapKeysWith :: (a -> a -> a) -> (Key -> Key) -> IntMap a -> IntMap a
- mapKeysMonotonic :: (Key -> Key) -> IntMap a -> IntMap a
- foldr :: (a -> b -> b) -> b -> IntMap a -> b
- foldl :: (a -> b -> a) -> a -> IntMap b -> a
- foldrWithKey :: (Key -> a -> b -> b) -> b -> IntMap a -> b
- foldlWithKey :: (a -> Key -> b -> a) -> a -> IntMap b -> a
- foldMapWithKey :: Monoid m => (Key -> a -> m) -> IntMap a -> m
- foldr' :: (a -> b -> b) -> b -> IntMap a -> b
- foldl' :: (a -> b -> a) -> a -> IntMap b -> a
- foldrWithKey' :: (Key -> a -> b -> b) -> b -> IntMap a -> b
- foldlWithKey' :: (a -> Key -> b -> a) -> a -> IntMap b -> a
- elems :: IntMap a -> [a]
- keys :: IntMap a -> [Key]
- assocs :: IntMap a -> [(Key, a)]
- keysSet :: IntMap a -> IntSet
- fromSet :: (Key -> a) -> IntSet -> IntMap a
- toList :: IntMap a -> [(Key, a)]
- fromList :: [(Key, a)] -> IntMap a
- fromListWith :: (a -> a -> a) -> [(Key, a)] -> IntMap a
- fromListWithKey :: (Key -> a -> a -> a) -> [(Key, a)] -> IntMap a
- toAscList :: IntMap a -> [(Key, a)]
- toDescList :: IntMap a -> [(Key, a)]
- fromAscList :: [(Key, a)] -> IntMap a
- fromAscListWith :: (a -> a -> a) -> [(Key, a)] -> IntMap a
- fromAscListWithKey :: (Key -> a -> a -> a) -> [(Key, a)] -> IntMap a
- fromDistinctAscList :: forall a. [(Key, a)] -> IntMap a
- filter :: (a -> Bool) -> IntMap a -> IntMap a
- filterWithKey :: (Key -> a -> Bool) -> IntMap a -> IntMap a
- partition :: (a -> Bool) -> IntMap a -> (IntMap a, IntMap a)
- partitionWithKey :: (Key -> a -> Bool) -> IntMap a -> (IntMap a, IntMap a)
- mapMaybe :: (a -> Maybe b) -> IntMap a -> IntMap b
- mapMaybeWithKey :: (Key -> a -> Maybe b) -> IntMap a -> IntMap b
- mapEither :: (a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)
- mapEitherWithKey :: (Key -> a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)
- split :: Key -> IntMap a -> (IntMap a, IntMap a)
- splitLookup :: Key -> IntMap a -> (IntMap a, Maybe a, IntMap a)
- splitRoot :: IntMap a -> [IntMap a]
- isSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
- isSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
- isProperSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
- isProperSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
- findMin :: IntMap a -> (Key, a)
- findMax :: IntMap a -> (Key, a)
- deleteMin :: IntMap a -> IntMap a
- deleteMax :: IntMap a -> IntMap a
- deleteFindMin :: IntMap a -> ((Key, a), IntMap a)
- deleteFindMax :: IntMap a -> ((Key, a), IntMap a)
- updateMin :: (a -> Maybe a) -> IntMap a -> IntMap a
- updateMax :: (a -> Maybe a) -> IntMap a -> IntMap a
- updateMinWithKey :: (Key -> a -> Maybe a) -> IntMap a -> IntMap a
- updateMaxWithKey :: (Key -> a -> Maybe a) -> IntMap a -> IntMap a
- minView :: IntMap a -> Maybe (a, IntMap a)
- maxView :: IntMap a -> Maybe (a, IntMap a)
- minViewWithKey :: IntMap a -> Maybe ((Key, a), IntMap a)
- maxViewWithKey :: IntMap a -> Maybe ((Key, a), IntMap a)
- showTree :: Show a => IntMap a -> String
- showTreeWith :: Show a => Bool -> Bool -> IntMap a -> String

# Strictness properties

This module satisfies the following strictness property:

- Key arguments are evaluated to WHNF

Here are some examples that illustrate the property:

insertWith (\ new old -> old) undefined v m == undefined insertWith (\ new old -> old) k undefined m == OK delete undefined m == undefined

# Map type

A map of integers to values `a`

.

Functor IntMap # | |

Foldable IntMap # | |

Traversable IntMap # | |

IsList (IntMap a) # | |

Eq a => Eq (IntMap a) # | |

Data a => Data (IntMap a) # | |

Ord a => Ord (IntMap a) # | |

Read e => Read (IntMap e) # | |

Show a => Show (IntMap a) # | |

Semigroup (IntMap a) # | |

Monoid (IntMap a) # | |

NFData a => NFData (IntMap a) # | |

type Item (IntMap a) # | |

# 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'

# Query

*O(1)*. Is the map empty?

Data.IntMap.null (empty) == True Data.IntMap.null (singleton 1 'a') == False

*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

member :: Key -> IntMap a -> Bool #

*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

notMember :: Key -> IntMap a -> Bool #

*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

lookup :: Key -> IntMap a -> Maybe a #

*O(min(n,W))*. Lookup the value at a key in the map. See also `lookup`

.

findWithDefault :: a -> Key -> IntMap a -> a #

*O(min(n,W))*. The expression `(`

returns the value at key `findWithDefault`

def k map)`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'

lookupLT :: Key -> IntMap a -> Maybe (Key, a) #

*O(log n)*. 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')

lookupGT :: Key -> IntMap a -> Maybe (Key, a) #

*O(log n)*. 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

lookupLE :: Key -> IntMap a -> Maybe (Key, a) #

*O(log n)*. 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')

lookupGE :: Key -> IntMap a -> Maybe (Key, a) #

*O(log n)*. 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

# Construction

singleton :: Key -> a -> IntMap a #

*O(1)*. A map of one element.

singleton 1 'a' == fromList [(1, 'a')] size (singleton 1 'a') == 1

## Insertion

insert :: Key -> a -> IntMap a -> IntMap a #

*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'

insertWith :: (a -> a -> a) -> Key -> a -> IntMap a -> IntMap a #

*O(min(n,W))*. Insert with a combining function.

will insert the pair (key, value) into `insertWith`

f key value mp`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"

insertWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> IntMap a #

*O(min(n,W))*. Insert with a combining function.

will insert the pair (key, value) into `insertWithKey`

f key value mp`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"

insertLookupWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> (Maybe a, IntMap a) #

*O(min(n,W))*. The expression (

)
is a pair where the first element is equal to (`insertLookupWithKey`

f k x map

)
and the second element equal to (`lookup`

k map

).`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")])

## Delete/Update

delete :: Key -> IntMap a -> IntMap a #

*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

adjust :: (a -> a) -> Key -> IntMap a -> IntMap a #

*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

adjustWithKey :: (Key -> a -> a) -> Key -> IntMap a -> IntMap a #

*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

update :: (a -> Maybe a) -> Key -> IntMap a -> IntMap a #

*O(min(n,W))*. The expression (

) updates the value `update`

f k map`x`

at `k`

(if it is in the map). If (`f x`

) is `Nothing`

, the element is
deleted. If it is (

), the key `Just`

y`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"

updateWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> IntMap a #

*O(min(n,W))*. The expression (

) updates the value `update`

f k map`x`

at `k`

(if it is in the map). If (`f k x`

) is `Nothing`

, the element is
deleted. If it is (

), the key `Just`

y`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"

updateLookupWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> (Maybe a, IntMap a) #

*O(min(n,W))*. Lookup and update.
The function returns original value, if it is updated.
This is different behavior than `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")

# Combine

## Union

unionWith :: (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a #

*O(n+m)*. The union with a combining function.

unionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "aA"), (7, "C")]

unionWithKey :: (Key -> a -> a -> a) -> IntMap a -> IntMap a -> IntMap a #

*O(n+m)*. 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")]

unions :: [IntMap a] -> IntMap a #

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")]

unionsWith :: (a -> a -> a) -> [IntMap a] -> IntMap a #

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")]

## Difference

difference :: IntMap a -> IntMap b -> IntMap a #

*O(n+m)*. Difference between two maps (based on keys).

difference (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 3 "b"

differenceWith :: (a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a #

*O(n+m)*. 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"

differenceWithKey :: (Key -> a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a #

*O(n+m)*. 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 (

), the element is updated with a new value `Just`

y`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"

## Intersection

intersection :: IntMap a -> IntMap b -> IntMap a #

*O(n+m)*. The (left-biased) intersection of two maps (based on keys).

intersection (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "a"

intersectionWith :: (a -> b -> c) -> IntMap a -> IntMap b -> IntMap c #

*O(n+m)*. The intersection with a combining function.

intersectionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "aA"

intersectionWithKey :: (Key -> a -> b -> c) -> IntMap a -> IntMap b -> IntMap c #

*O(n+m)*. 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"

## Universal combining function

mergeWithKey :: (Key -> a -> b -> Maybe c) -> (IntMap a -> IntMap c) -> (IntMap b -> IntMap c) -> IntMap a -> IntMap b -> IntMap c #

*O(n+m)*. 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`

).

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

, a function combining two
`mergeWithKey`

combine only1 only2`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

, but for example `const`

`empty`

or
`map`

f

could be used for any `filterWithKey`

f`f`

.

# Traversal

## Map

map :: (a -> b) -> IntMap a -> IntMap b #

*O(n)*. Map a function over all values in the map.

map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")]

mapWithKey :: (Key -> a -> b) -> IntMap a -> IntMap b #

*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")]

traverseWithKey :: Applicative t => (Key -> a -> t b) -> IntMap a -> t (IntMap b) #

*O(n)*.

That is, behaves exactly like a regular `traverseWithKey`

f s == `fromList`

$ `traverse`

((k, v) -> (,) k $ f k v) (`toList`

m)`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

mapAccum :: (a -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c) #

*O(n)*. The function

threads an accumulating
argument through the map in ascending order of keys.`mapAccum`

let f a b = (a ++ b, b ++ "X") mapAccum f "Everything: " (fromList [(5,"a"), (3,"b")]) == ("Everything: ba", fromList [(3, "bX"), (5, "aX")])

mapAccumWithKey :: (a -> Key -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c) #

*O(n)*. The function

threads an accumulating
argument through the map in ascending order of keys.`mapAccumWithKey`

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")])

mapAccumRWithKey :: (a -> Key -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c) #

*O(n)*. The function

threads an accumulating
argument through the map in descending order of keys.`mapAccumR`

mapKeys :: (Key -> Key) -> IntMap a -> IntMap a #

*O(n*min(n,W))*.

is the map obtained by applying `mapKeys`

f s`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"

mapKeysWith :: (a -> a -> a) -> (Key -> Key) -> IntMap a -> IntMap a #

*O(n*min(n,W))*.

is the map obtained by applying `mapKeysWith`

c f s`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"

mapKeysMonotonic :: (Key -> Key) -> IntMap a -> IntMap a #

*O(n*min(n,W))*.

, but works only when `mapKeysMonotonic`

f s == `mapKeys`

f s`f`

is strictly monotonic.
That is, for any values `x`

and `y`

, if `x`

< `y`

then `f x`

< `f y`

.
*The precondition is not checked.*
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`

.

mapKeysMonotonic (\ k -> k * 2) (fromList [(5,"a"), (3,"b")]) == fromList [(6, "b"), (10, "a")]

# Folds

foldrWithKey :: (Key -> a -> b -> b) -> b -> IntMap a -> b #

*O(n)*. Fold the keys and values in the map using the given right-associative
binary operator, such that

.`foldrWithKey`

f z == `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)"

foldlWithKey :: (a -> Key -> b -> a) -> a -> IntMap b -> a #

*O(n)*. Fold the keys and values in the map using the given left-associative
binary operator, such that

.`foldlWithKey`

f z == `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)"

foldMapWithKey :: Monoid m => (Key -> a -> m) -> IntMap a -> m #

*O(n)*. Fold the keys and values in the map using the given monoid, such that

`foldMapWithKey`

f =`fold`

.`mapWithKey`

f

This can be an asymptotically faster than `foldrWithKey`

or `foldlWithKey`

for some monoids.

## Strict folds

foldr' :: (a -> b -> b) -> b -> IntMap a -> b #

*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.

foldl' :: (a -> b -> a) -> a -> IntMap b -> a #

*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.

foldrWithKey' :: (Key -> a -> b -> b) -> b -> IntMap a -> b #

*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.

foldlWithKey' :: (a -> Key -> b -> a) -> a -> IntMap b -> a #

*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.

# Conversion

*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 == []

*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 == []

assocs :: IntMap a -> [(Key, a)] #

*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 == []

keysSet :: IntMap a -> IntSet #

*O(n*min(n,W))*. The set of all keys of the map.

keysSet (fromList [(5,"a"), (3,"b")]) == Data.IntSet.fromList [3,5] keysSet empty == Data.IntSet.empty

fromSet :: (Key -> a) -> IntSet -> IntMap a #

*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

## Lists

toList :: IntMap a -> [(Key, a)] #

*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 == []

fromList :: [(Key, a)] -> IntMap a #

*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")]

fromListWith :: (a -> a -> a) -> [(Key, a)] -> IntMap a #

*O(n*min(n,W))*. Create a map from a list of key/value pairs with a combining function. See also `fromAscListWith`

.

fromListWith (++) [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"c")] == fromList [(3, "ab"), (5, "cba")] fromListWith (++) [] == empty

fromListWithKey :: (Key -> a -> a -> a) -> [(Key, a)] -> IntMap a #

*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

## Ordered lists

toAscList :: IntMap a -> [(Key, a)] #

*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")]

toDescList :: IntMap a -> [(Key, a)] #

*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")]

fromAscList :: [(Key, a)] -> IntMap a #

*O(n)*. Build a map from a list of key/value pairs where
the keys are in ascending order.

fromAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")] fromAscList [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "b")]

fromAscListWith :: (a -> a -> a) -> [(Key, a)] -> IntMap a #

*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.
*The precondition (input list is ascending) is not checked.*

fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "ba")]

fromAscListWithKey :: (Key -> a -> a -> a) -> [(Key, a)] -> IntMap a #

*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.
*The precondition (input list is ascending) is not checked.*

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")]

fromDistinctAscList :: forall a. [(Key, a)] -> IntMap a #

*O(n)*. Build a map from a list of key/value pairs where
the keys are in ascending order and all distinct.
*The precondition (input list is strictly ascending) is not checked.*

fromDistinctAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")]

# Filter

filter :: (a -> Bool) -> IntMap a -> IntMap a #

*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

filterWithKey :: (Key -> a -> Bool) -> IntMap a -> IntMap a #

*O(n)*. Filter all keys/values that satisfy some predicate.

filterWithKey (\k _ -> k > 4) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"

partition :: (a -> Bool) -> IntMap a -> (IntMap a, IntMap a) #

*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")])

partitionWithKey :: (Key -> a -> Bool) -> IntMap a -> (IntMap a, IntMap a) #

*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")])

mapMaybe :: (a -> Maybe b) -> IntMap a -> IntMap b #

*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"

mapMaybeWithKey :: (Key -> a -> Maybe b) -> IntMap a -> IntMap b #

*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"

mapEither :: (a -> Either b c) -> IntMap a -> (IntMap b, IntMap c) #

*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")])

mapEitherWithKey :: (Key -> a -> Either b c) -> IntMap a -> (IntMap b, IntMap c) #

*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")])

split :: Key -> IntMap a -> (IntMap a, IntMap a) #

*O(min(n,W))*. The expression (

) is a pair `split`

k map`(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)

splitLookup :: Key -> IntMap a -> (IntMap a, Maybe a, IntMap a) #

*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)

splitRoot :: IntMap a -> [IntMap a] #

*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.

# Submap

isSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool #

*O(n+m)*. Is this a submap?
Defined as (

).`isSubmapOf`

= `isSubmapOfBy`

(==)

isSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool #

*O(n+m)*.
The expression (

) returns `isSubmapOfBy`

f m1 m2`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)])

isProperSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool #

*O(n+m)*. Is this a proper submap? (ie. a submap but not equal).
Defined as (

).`isProperSubmapOf`

= `isProperSubmapOfBy`

(==)

isProperSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool #

*O(n+m)*. Is this a proper submap? (ie. a submap but not equal).
The expression (

) returns `isProperSubmapOfBy`

f m1 m2`True`

when
`m1`

and `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)])

# Min/Max

deleteFindMin :: IntMap a -> ((Key, a), IntMap a) #

*O(min(n,W))*. Delete and find the minimal element.

deleteFindMax :: IntMap a -> ((Key, a), IntMap a) #

*O(min(n,W))*. Delete and find the maximal element.

updateMin :: (a -> Maybe a) -> IntMap a -> IntMap a #

*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"

updateMax :: (a -> Maybe a) -> IntMap a -> IntMap a #

*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"

updateMinWithKey :: (Key -> a -> Maybe a) -> IntMap a -> IntMap a #

*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"

updateMaxWithKey :: (Key -> a -> Maybe a) -> IntMap a -> IntMap a #

*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"

minView :: IntMap a -> Maybe (a, IntMap a) #

*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.

maxView :: IntMap a -> Maybe (a, IntMap a) #

*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.

minViewWithKey :: IntMap a -> Maybe ((Key, a), IntMap a) #

*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

maxViewWithKey :: IntMap a -> Maybe ((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

# Debugging

showTree :: Show a => IntMap a -> String #

*O(n)*. Show the tree that implements the map. The tree is shown
in a compressed, hanging format.

showTreeWith :: Show a => Bool -> Bool -> IntMap a -> String #

*O(n)*. The expression (

) shows
the tree that implements the map. If `showTreeWith`

hang wide map`hang`

is
`True`

, a *hanging* tree is shown otherwise a rotated tree is shown. If
`wide`

is `True`

, an extra wide version is shown.