Data.PriorityQueue.FingerTree

Min-priority queues implemented using the FingerTree type, following section 4.6 of

• Ralf Hinze and Ross Paterson, "Finger trees: a simple general-purpose data structure", Journal of Functional Programming 16:2 (2006) pp 197-217. http://staff.city.ac.uk/~ross/papers/FingerTree.html

These have the same big-O complexity as skew heap implementations, but are approximately an order of magnitude slower. On the other hand, they are stable, so they can be used for fair queueing. They are also shallower, so that fmap consumes less space.

An amortized running time is given for each operation, with n referring to the size of the priority queue. These bounds hold even in a persistent (shared) setting.

Note: Many of these operations have the same names as similar operations on lists in the Prelude. The ambiguity may be resolved using either qualification or the hiding clause.

Documentation

data PQueue k v

Priority queues.

Instances

Ord k => Functor (PQueue k)

Methods

fmap :: (a -> b) -> PQueue k a -> PQueue k b

(<$) :: a -> PQueue k b -> PQueue k a

Ord k => Foldable (PQueue k)

In ascending order of keys.

Methods

fold :: Monoid m => PQueue k m -> m

foldMap :: Monoid m => (a -> m) -> PQueue k a -> m

foldr :: (a -> b -> b) -> b -> PQueue k a -> b

foldr' :: (a -> b -> b) -> b -> PQueue k a -> b

foldl :: (b -> a -> b) -> b -> PQueue k a -> b

foldl' :: (b -> a -> b) -> b -> PQueue k a -> b

foldr1 :: (a -> a -> a) -> PQueue k a -> a

foldl1 :: (a -> a -> a) -> PQueue k a -> a

toList :: PQueue k a -> [a]

null :: PQueue k a -> Bool

length :: PQueue k a -> Int

elem :: Eq a => a -> PQueue k a -> Bool

maximum :: Ord a => PQueue k a -> a

minimum :: Ord a => PQueue k a -> a

sum :: Num a => PQueue k a -> a

product :: Num a => PQueue k a -> a

(Ord k, Eq v) => Eq (PQueue k v)

Methods

(==) :: PQueue k v -> PQueue k v -> Bool

(/=) :: PQueue k v -> PQueue k v -> Bool

(Ord k, Ord v) => Ord (PQueue k v)

Lexicographical ordering

Methods

compare :: PQueue k v -> PQueue k v -> Ordering

(<) :: PQueue k v -> PQueue k v -> Bool

(<=) :: PQueue k v -> PQueue k v -> Bool

(>) :: PQueue k v -> PQueue k v -> Bool

(>=) :: PQueue k v -> PQueue k v -> Bool

max :: PQueue k v -> PQueue k v -> PQueue k v

min :: PQueue k v -> PQueue k v -> PQueue k v

(Ord k, Show k, Show v) => Show (PQueue k v)

In ascending key order

Methods

showsPrec :: Int -> PQueue k v -> ShowS

show :: PQueue k v -> String

showList :: [PQueue k v] -> ShowS

Ord k => Semigroup (PQueue k v)

Methods

(<>) :: PQueue k v -> PQueue k v -> PQueue k v

sconcat :: NonEmpty (PQueue k v) -> PQueue k v

stimes :: Integral b => b -> PQueue k v -> PQueue k v

Ord k => Monoid (PQueue k v)

empty and union

Methods

mempty :: PQueue k v

mappend :: PQueue k v -> PQueue k v -> PQueue k v

mconcat :: [PQueue k v] -> PQueue k v

Construction

empty :: Ord k => PQueue k v

O(1). The empty priority queue.

singleton :: Ord k => k -> v -> PQueue k v

O(1). A singleton priority queue.

union :: Ord k => PQueue k v -> PQueue k v -> PQueue k v

O(log(min(n1,n2))). Concatenate two priority queues. union is associative, with identity empty.

If there are entries with the same priority in both arguments, minView of union xs ys will return those from xs before those from ys.

insert :: Ord k => k -> v -> PQueue k v -> PQueue k v

O(log n). Add a (priority, value) pair to the front of a priority queue.

• insert k v q = union (singleton k v) q

If q contains entries with the same priority k, minView of insert k v q will return them after this one.

add :: Ord k => k -> v -> PQueue k v -> PQueue k v

O(log n). Add a (priority, value) pair to the back of a priority queue.

• add k v q = union q (singleton k v)

If q contains entries with the same priority k, minView of add k v q will return them before this one.

fromList :: Ord k => [(k, v)] -> PQueue k v

O(n). Create a priority queue from a finite list of priorities and values.

Deconstruction

null :: Ord k => PQueue k v -> Bool

O(1). Is this the empty priority queue?

minView :: Ord k => PQueue k v -> Maybe (v, PQueue k v)

O(1) for the element, O(log(n)) for the reduced queue. Returns Nothing for an empty map, or the value associated with the minimal priority together with the rest of the priority queue.

• minView empty = Nothing

• minView (singleton k v) = Just (v, empty)

minViewWithKey :: Ord k => PQueue k v -> Maybe ((k, v), PQueue k v)

O(1) for the element, O(log(n)) for the reduced queue. Returns Nothing for an empty map, or the minimal (priority, value) pair together with the rest of the priority queue.

• minViewWithKey empty = Nothing

• minViewWithKey (singleton k v) = Just ((k, v), empty)

• If minViewWithKey qi = Just ((ki, vi), qi') and k1 <= k2, then minViewWithKey (union q1 q2) = Just ((k1, v1), union q1' q2)
• If minViewWithKey qi = Just ((ki, vi), qi') and k2 < k1, then minViewWithKey (union q1 q2) = Just ((k2, v2), union q1 q2')