containers-0.4.2.0: Assorted concrete container types

Data.IntMap

Description

An efficient implementation of maps from integer keys to values.

Since many function names (but not the type name) clash with Prelude names, this module is usually imported `qualified`, e.g.

```  import Data.IntMap (IntMap)
import qualified Data.IntMap 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).

Synopsis

# Map type

data IntMap a Source

A map of integers to values `a`.

Instances

 Functor IntMap Typeable1 IntMap Foldable IntMap Traversable IntMap 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) Monoid (IntMap a) NFData a => NFData (IntMap a)

type Key = IntSource

# Operators

(!) :: IntMap a -> Key -> aSource

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 -> IntMap b -> IntMap aSource

Same as `difference`.

# Query

null :: IntMap a -> BoolSource

O(1). Is the map empty?

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

size :: IntMap a -> IntSource

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 -> BoolSource

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 -> BoolSource

O(log n). 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 aSource

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

findWithDefault :: a -> Key -> IntMap a -> aSource

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'
```

# Construction

O(1). The empty map.

``` empty      == fromList []
size empty == 0
```

singleton :: Key -> a -> IntMap aSource

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 aSource

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 aSource

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"
```

insertWith' :: (a -> a -> a) -> Key -> a -> IntMap a -> IntMap aSource

Same as `insertWith`, but the combining function is applied strictly.

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

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"
```

insertWithKey' :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> IntMap aSource

Same as `insertWithKey`, but the combining function is applied strictly.

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

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")])
```

## Delete/Update

delete :: Key -> IntMap a -> IntMap aSource

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 aSource

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 aSource

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 aSource

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"
```

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

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"
```

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

O(min(n,W)). Lookup and update. The function returns 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")
```

alter :: (Maybe a -> Maybe a) -> Key -> IntMap a -> IntMap aSource

O(log n). 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)`.

# Combine

## Union

union :: IntMap a -> IntMap a -> IntMap aSource

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

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

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 aSource

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 aSource

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 aSource

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 aSource

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 aSource

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 aSource

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 (`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"
```

## Intersection

intersection :: IntMap a -> IntMap b -> IntMap aSource

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 cSource

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 cSource

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"
```

# Traversal

## Map

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

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 bSource

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")]
```

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

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")])
```

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

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")])
```

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

O(n). The function `mapAccumR` threads an accumulating argument through the map in descending order of keys.

# Folds

foldr :: (a -> b -> b) -> b -> IntMap a -> bSource

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
```

foldl :: (a -> b -> a) -> a -> IntMap b -> aSource

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
```

foldrWithKey :: (Int -> a -> b -> b) -> b -> IntMap a -> bSource

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)"
```

foldlWithKey :: (a -> Int -> b -> a) -> a -> IntMap b -> aSource

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)"
```

## Strict folds

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

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 -> aSource

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' :: (Int -> a -> b -> b) -> b -> IntMap a -> bSource

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 -> Int -> b -> a) -> a -> IntMap b -> aSource

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.

## Legacy folds

fold :: (a -> b -> b) -> b -> IntMap a -> bSource

O(n). Fold the values in the map using the given right-associative binary operator. This function is an equivalent of `foldr` and is present for compatibility only.

Please note that fold will be deprecated in the future and removed.

foldWithKey :: (Int -> a -> b -> b) -> b -> IntMap a -> bSource

O(n). Fold the keys and values in the map using the given right-associative binary operator. This function is an equivalent of `foldrWithKey` and is present for compatibility only.

Please note that foldWithKey will be deprecated in the future and removed.

# Conversion

elems :: IntMap a -> [a]Source

O(n). Return all elements of the map in the ascending order of their keys.

``` elems (fromList [(5,"a"), (3,"b")]) == ["b","a"]
elems empty == []
```

keys :: IntMap a -> [Key]Source

O(n). Return all keys of the map in ascending order.

``` keys (fromList [(5,"a"), (3,"b")]) == [3,5]
keys empty == []
```

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
```

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

O(n). Return all key/value pairs in the map in ascending key order.

``` assocs (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]
assocs empty == []
```

## Lists

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

O(n). Convert the map to a list of key/value pairs.

``` toList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]
toList empty == []
```

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

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 aSource

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 aSource

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)]Source

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

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

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

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 aSource

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 aSource

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 aSource

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 aSource

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 aSource

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)Source

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)Source

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 bSource

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 bSource

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)Source

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)Source

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)Source

O(log n). 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)
```

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

O(log n). 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)
```

# Submap

isSubmapOf :: Eq a => IntMap a -> IntMap a -> BoolSource

O(n+m). Is this a submap? Defined as (`isSubmapOf = isSubmapOfBy (==)`).

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

O(n+m). 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)])
```

isProperSubmapOf :: Eq a => IntMap a -> IntMap a -> BoolSource

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 -> BoolSource

O(n+m). Is this a proper submap? (ie. a submap but not equal). The expression (`isProperSubmapOfBy f m1 m2`) returns `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

findMin :: IntMap a -> (Key, a)Source

O(log n). The minimal key of the map.

findMax :: IntMap a -> (Key, a)Source

O(log n). The maximal key of the map.

deleteMin :: IntMap a -> IntMap aSource

O(log n). Delete the minimal key. An error is thrown if the IntMap is already empty. Note, this is not the same behavior Map.

deleteMax :: IntMap a -> IntMap aSource

O(log n). Delete the maximal key. An error is thrown if the IntMap is already empty. Note, this is not the same behavior Map.

deleteFindMin :: IntMap a -> (a, IntMap a)Source

O(log n). Delete and find the minimal element.

deleteFindMax :: IntMap a -> (a, IntMap a)Source

O(log n). Delete and find the maximal element.

updateMin :: (a -> a) -> IntMap a -> IntMap aSource

O(log n). 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 -> a) -> IntMap a -> IntMap aSource

O(log n). 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 -> a) -> IntMap a -> IntMap aSource

O(log n). 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 -> a) -> IntMap a -> IntMap aSource

O(log n). 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)Source

O(log n). 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)Source

O(log n). 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)Source

O(log n). 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)Source

O(log n). 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 -> StringSource

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 -> StringSource

O(n). 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.