-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | A multimap.
--   
--   This is a simple implementation of a multimap, based on
--   <a>Data.Map</a>.
@package multimap
@version 1.0


-- | A very simple Multimap, based on <a>Map</a> from the containers
--   package.
module Data.Multimap

-- | A Multimap with keys <tt>k</tt> and values <tt>v</tt>.
--   
--   A key can have multiple values (but not zero). The same value can be
--   added multiple times (thus no constraints are ever imposed on
--   <tt>v</tt>).
--   
--   Internally this is simply a <tt>Map k [v]</tt>. See <a>toMap</a> for
--   accessing the underlying <a>Map</a>.
data Multimap k v

-- | <i>O(1).</i> Check whether the multimap is empty or not.
null :: Multimap k a -> Bool

-- | <i>O(1).</i> The number of elements in the multimap.
size :: Multimap k a -> Int

-- | <i>O(1).</i> The number of keys in the multimap.
--   
--   As this is a multimap, the number of keys is not necessarily equal to
--   the number of values.
numKeys :: Multimap k a -> Word32

-- | <i>O(1).</i> The number of values in the multimap.
--   
--   As this is a multimap, the number of keys is not necessarily equal to
--   the number of values.
numValues :: Multimap k a -> Word32

-- | <i>O(log n).</i> Is the key a member of the multimap?
member :: Ord k => Multimap k a -> k -> Bool

-- | <i>O(log n).</i> Is the key not a member of the multimap?
notMember :: Ord k => Multimap k a -> k -> Bool

-- | <i>O(log n).</i> Lookup the value at a key in the map.
--   
--   The function will return the corrsponding values as a List, or the
--   empty list if no values are associated witht the given key.
lookup :: Ord k => k -> Multimap k a -> [a]
(!) :: Ord k => k -> Multimap k a -> [a]

-- | <i>O(1).</i> The empty multimap.
empty :: Multimap k a

-- | <i>O(log n).</i> Insert a new key and value in the map.
insert :: Ord k => k -> a -> Multimap k a -> Multimap k a

-- | <i>O(log n).</i> Delete a key and all its values from the map.
delete :: Ord k => k -> a -> Multimap k a -> Multimap k a

-- | Map a function over all values in the map.
map :: (a -> b) -> Multimap k a -> Multimap k b

-- | mapKeys f s is the multimap obtained by applying f to each key of s.
mapKeys :: Ord k2 => (k1 -> k2) -> Multimap k1 a -> Multimap k2 a

-- | Map a function over all key/value pairs in the map.
mapWithKey :: (k -> a -> b) -> Multimap k a -> Multimap k b
foldr :: (a -> b -> b) -> b -> Multimap k a -> b
foldl :: (a -> b -> a) -> a -> Multimap k b -> a
foldrWithKey :: (k -> a -> b -> b) -> b -> Multimap k a -> b
foldlWithKey :: (a -> k -> b -> a) -> a -> Multimap k b -> a

-- | <i>O(n).</i> Return all elements of the multimap in the ascending
--   order of their keys.
--   
--   A list of lists is returned since a key can have multiple values. Use
--   <a>concat</a> to flatten.
elems :: Multimap k a -> [[a]]

-- | <i>O(n).</i> Return all keys of the multimap in ascending order.
keys :: Multimap k a -> [k]

-- | <i>O(n).</i> The set of all keys of the multimap.
keysSet :: Multimap k a -> Set k

-- | <i>O(n).</i> Return all key/value pairs in the multimap in ascending
--   key order.
assocs :: Multimap k a -> [(k, [a])]

-- | <i>O(1).</i> Return the map of lists.
toMap :: Multimap k a -> Map k [a]

-- | /O(k*m*log m) where k is the number of keys and m the maximum number
--   of elements associated with a single key/
toMapOfSets :: Ord a => Multimap k a -> Map k (Set a)

-- | Return a flattened list of key/value pairs.
toList :: Multimap k a -> [(k, a)]

-- | <i>O(n*log n)</i> Create a multimap from a list of key/value pairs.
--   
--   <pre>
--   fromList xs == foldr (uncurry insert) empty
--   </pre>
fromList :: Ord k => [(k, a)] -> Multimap k a

-- | <i>O(log n)</i> Find the minimal key of the multimap.
findMin :: Multimap k a -> Maybe k

-- | <i>O(log n)</i> Find the maximal key of the multimap.
findMax :: Multimap k a -> Maybe k

-- | <i>O(log n)</i> Find the minimal key and the values associated with
--   it.
findMinWithValues :: Multimap k a -> Maybe (k, [a])

-- | <i>O(log n)</i> Find the maximal key and the values associated with
--   it.
findMaxWithValues :: Multimap k a -> Maybe (k, [a])