UU.DData.Map

Map type

data Map k a

A Map from keys k and values a.

Instances

Functor (Map k)

(Eq k, Eq a) => Eq (Map k a)

(Show k, Show a) => Show (Map k a)

Operators

(!) :: Ord k => Map k a -> k -> a

O(log n). See find.

(\\) :: Ord k => Map k a -> Map k a -> Map k a

O(n+m). See difference.

Query

isEmpty :: Map k a -> Bool

O(1). Is the map empty?

size :: Map k a -> Int

O(1). The number of elements in the map.

member :: Ord k => k -> Map k a -> Bool

O(log n). Is the key a member of the map?

lookup :: Ord k => k -> Map k a -> Maybe a

O(log n). Lookup the value of key in the map.

find :: Ord k => k -> Map k a -> a

O(log n). Find the value of a key. Calls error when the element can not be found.

findWithDefault :: Ord k => a -> k -> Map k a -> a

O(log n). The expression (findWithDefault def k map) returns the value of key k or returns def when the key is not in the map.

Construction

empty :: Map k a

O(1). Create an empty map.

single :: k -> a -> Map k a

O(1). Create a map with a single element.

Insertion

insert :: Ord k => k -> a -> Map k a -> Map k a

O(log n). Insert a new key and value in the map.

insertWith :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a

O(log n). Insert with a combining function.

insertWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a

O(log n). Insert with a combining function.

insertLookupWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> (Maybe a, Map k a)

O(log n). 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).

Delete/Update

delete :: Ord k => k -> Map k a -> Map k a

O(log n). Delete a key and its value from the map. When the key is not a member of the map, the original map is returned.

adjust :: Ord k => (a -> a) -> k -> Map k a -> Map k a

O(log n). Adjust a value at a specific key. When the key is not a member of the map, the original map is returned.

adjustWithKey :: Ord k => (k -> a -> a) -> k -> Map k a -> Map k a

O(log n). Adjust a value at a specific key. When the key is not a member of the map, the original map is returned.

update :: Ord k => (a -> Maybe a) -> k -> Map k a -> Map k a

O(log n). 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.

updateWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> Map k a

O(log n). 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.

updateLookupWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> (Maybe a, Map k a)

O(log n). Lookup and update.

Combine

Union

union :: Ord k => Map k a -> Map k a -> Map k a

O(n+m). The expression (union t1 t2) takes the left-biased union of t1 and t2. It prefers t1 when duplicate keys are encountered, ie. (union == unionWith const). The implementation uses the efficient hedge-union algorithm.

unionWith :: Ord k => (a -> a -> a) -> Map k a -> Map k a -> Map k a

O(n+m). Union with a combining function. The implementation uses the efficient hedge-union algorithm.

unionWithKey :: Ord k => (k -> a -> a -> a) -> Map k a -> Map k a -> Map k a

O(n+m). Union with a combining function. The implementation uses the efficient hedge-union algorithm.

unions :: Ord k => [Map k a] -> Map k a

The union of a list of maps: (unions == foldl union empty).

Difference

difference :: Ord k => Map k a -> Map k a -> Map k a

O(n+m). Difference of two maps. The implementation uses an efficient hedge algorithm comparable with hedge-union.

differenceWith :: Ord k => (a -> a -> Maybe a) -> Map k a -> Map k a -> Map k a

O(n+m). Difference with a combining function. The implementation uses an efficient hedge algorithm comparable with hedge-union.

differenceWithKey :: Ord k => (k -> a -> a -> Maybe a) -> Map k a -> Map k a -> Map k 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 (Just y), the element is updated with a new value y. The implementation uses an efficient hedge algorithm comparable with hedge-union.

Intersection

intersection :: Ord k => Map k a -> Map k a -> Map k a

O(n+m). Intersection of two maps. The values in the first map are returned, i.e. (intersection m1 m2 == intersectionWith const m1 m2).

intersectionWith :: Ord k => (a -> a -> a) -> Map k a -> Map k a -> Map k a

O(n+m). Intersection with a combining function.

intersectionWithKey :: Ord k => (k -> a -> a -> a) -> Map k a -> Map k a -> Map k a

O(n+m). Intersection with a combining function.

Traversal

Map

map :: (a -> b) -> Map k a -> Map k b

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

mapWithKey :: (k -> a -> b) -> Map k a -> Map k b

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

mapAccum :: (a -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)

O(n). The function mapAccum threads an accumulating argument through the map in an unspecified order.

mapAccumWithKey :: (a -> k -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)

O(n). The function mapAccumWithKey threads an accumulating argument through the map in unspecified order. (= ascending pre-order)

Fold

fold :: (a -> b -> b) -> b -> Map k a -> b

O(n). Fold the map in an unspecified order. (= descending post-order).

foldWithKey :: (k -> a -> b -> b) -> b -> Map k a -> b

O(n). Fold the map in an unspecified order. (= descending post-order).

Conversion

elems :: Map k a -> [a]

O(n). Return all elements of the map.

keys :: Map k a -> [k]

O(n). Return all keys of the map.

assocs :: Map k a -> [(k, a)]

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

Lists

toList :: Map k a -> [(k, a)]

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

fromList :: Ord k => [(k, a)] -> Map k a

O(n*log n). Build a map from a list of key/value pairs. See also fromAscList.

fromListWith :: Ord k => (a -> a -> a) -> [(k, a)] -> Map k a

O(n*log n). Build a map from a list of key/value pairs with a combining function. See also fromAscListWith.

fromListWithKey :: Ord k => (k -> a -> a -> a) -> [(k, a)] -> Map k a

O(n*log n). Build a map from a list of key/value pairs with a combining function. See also fromAscListWithKey.

Ordered lists

toAscList :: Map k a -> [(k, a)]

O(n). Convert to an ascending list.

fromAscList :: Eq k => [(k, a)] -> Map k a

O(n). Build a map from an ascending list in linear time.

fromAscListWith :: Eq k => (a -> a -> a) -> [(k, a)] -> Map k a

O(n). Build a map from an ascending list in linear time with a combining function for equal keys.

fromAscListWithKey :: Eq k => (k -> a -> a -> a) -> [(k, a)] -> Map k a

O(n). Build a map from an ascending list in linear time with a combining function for equal keys

fromDistinctAscList :: [(k, a)] -> Map k a

O(n). Build a map from an ascending list of distinct elements in linear time.

Filter

filter :: Ord k => (a -> Bool) -> Map k a -> Map k a

O(n). Filter all values that satisfy the predicate.

filterWithKey :: Ord k => (k -> a -> Bool) -> Map k a -> Map k a

O(n). Filter all keysvalues that satisfy the predicate.

partition :: Ord k => (a -> Bool) -> Map k a -> (Map k a, Map k a)

O(n). partition the map according to a predicate. The first map contains all elements that satisfy the predicate, the second all elements that fail the predicate. See also split.

partitionWithKey :: Ord k => (k -> a -> Bool) -> Map k a -> (Map k a, Map k a)

O(n). partition the map according to a predicate. The first map contains all elements that satisfy the predicate, the second all elements that fail the predicate. See also split.

split :: Ord k => k -> Map k a -> (Map k a, Map k a)

O(log n). The expression (split k map) is a pair (map1,map2) where the keys in map1 are smaller than k and the keys in map2 larger than k.

splitLookup :: Ord k => k -> Map k a -> (Maybe a, Map k a, Map k a)

O(log n). The expression (splitLookup k map) splits a map just like split but also returns lookup k map.

Subset

subset :: (Ord k, Eq a) => Map k a -> Map k a -> Bool

O(n+m). This function is defined as (subset = subsetBy (==)).

subsetBy :: Ord k => (a -> a -> Bool) -> Map k a -> Map k a -> Bool

O(n+m). The expression (subsetBy f t1 t2) returns True if all keys in t1 are in tree t2, and when f returns True when applied to their respective values. For example, the following expressions are all True.

 subsetBy (==) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
 subsetBy (<=) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
 subsetBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1),('b',2)])

But the following are all False:

 subsetBy (==) (fromList [('a',2)]) (fromList [('a',1),('b',2)])
 subsetBy (<)  (fromList [('a',1)]) (fromList [('a',1),('b',2)])
 subsetBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1)])

properSubset :: (Ord k, Eq a) => Map k a -> Map k a -> Bool

O(n+m). Is this a proper subset? (ie. a subset but not equal). Defined as (properSubset = properSubsetBy (==)).

properSubsetBy :: (Ord k, Eq a) => (a -> a -> Bool) -> Map k a -> Map k a -> Bool

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

 properSubsetBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
 properSubsetBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])

But the following are all False:

 properSubsetBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])
 properSubsetBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
 properSubsetBy (<)  (fromList [(1,1)])       (fromList [(1,1),(2,2)])

Indexed

lookupIndex :: Ord k => k -> Map k a -> Maybe Int

O(log n). Lookup the index of a key. The index is a number from 0 up to, but not including, the size of the map.

findIndex :: Ord k => k -> Map k a -> Int

O(log n). Return the index of a key. The index is a number from 0 up to, but not including, the size of the map. Calls error when the key is not a member of the map.

elemAt :: Int -> Map k a -> (k, a)

O(log n). Retrieve an element by index. Calls error when an invalid index is used.

updateAt :: (k -> a -> Maybe a) -> Int -> Map k a -> Map k a

O(log n). Update the element at index. Calls error when an invalid index is used.

deleteAt :: Int -> Map k a -> Map k a

O(log n). Delete the element at index. Defined as (deleteAt i map = updateAt (k x -> Nothing) i map).

Min/Max

findMin :: Map k a -> (k, a)

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

findMax :: Map k a -> (k, a)

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

deleteMin :: Map k a -> Map k a

O(log n). Delete the minimal key

deleteMax :: Map k a -> Map k a

O(log n). Delete the maximal key

deleteFindMin :: Map k a -> ((k, a), Map k a)

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

deleteFindMax :: Map k a -> ((k, a), Map k a)

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

updateMin :: (a -> Maybe a) -> Map k a -> Map k a

O(log n). Update the minimal key

updateMax :: (a -> Maybe a) -> Map k a -> Map k a

O(log n). Update the maximal key

updateMinWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a

O(log n). Update the minimal key

updateMaxWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a

O(log n). Update the maximal key

Debugging

showTree :: (Show k, Show a) => Map k a -> String

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

showTreeWith :: (k -> a -> String) -> Bool -> Bool -> Map k a -> String

O(n). The expression (showTreeWith showelem hang wide map) shows the tree that implements the map. Elements are shown using the showElem function. 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.

  Map> putStrLn $ showTreeWith (\k x -> show (k,x)) True False $ fromDistinctAscList [(x,()) | x <- [1..5]]
  (4,())
  +--(2,())
  |  +--(1,())
  |  +--(3,())
  +--(5,())

  Map> putStrLn $ showTreeWith (\k x -> show (k,x)) True True $ fromDistinctAscList [(x,()) | x <- [1..5]]
  (4,())
  |
  +--(2,())
  |  |
  |  +--(1,())
  |  |
  |  +--(3,())
  |
  +--(5,())

  Map> putStrLn $ showTreeWith (\k x -> show (k,x)) False True $ fromDistinctAscList [(x,()) | x <- [1..5]]
  +--(5,())
  |
  (4,())
  |
  |  +--(3,())
  |  |
  +--(2,())
     |
     +--(1,())

valid :: Ord k => Map k a -> Bool

O(n). Test if the internal map structure is valid.