Data.PQueue.Max

General purpose priority queue, supporting view-maximum operations.

An amortized running time is given for each operation, with n referring to the length of the sequence and k being the integral index used by some operations. These bounds hold even in a persistent (shared) setting.

This implementation is based on a binomial heap augmented with a global root. The spine of the heap is maintained lazily. To force the spine of the heap, use seqSpine.

This implementation does not guarantee stable behavior.

This implementation offers a number of methods of the form xxxU, where U stands for unordered. No guarantees whatsoever are made on the execution or traversal order of these functions.

Documentation

data MaxQueue a

A priority queue with elements of type a. Supports extracting the maximum element. Implemented as a wrapper around MinQueue.

Instances

Typeable1 MaxQueue

Ord a => Eq (MaxQueue a)

(Data a, Ord a) => Data (MaxQueue a)

Ord a => Ord (MaxQueue a)

Read a => Read (MaxQueue a)

(Ord a, Show a) => Show (MaxQueue a)

Ord a => Monoid (MaxQueue a)

NFData a => NFData (MaxQueue a)

Basic operations

empty :: MaxQueue a

O(1). The empty priority queue.

null :: MaxQueue a -> Bool

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

size :: MaxQueue a -> Int

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

Query operations

findMax :: MaxQueue a -> a

O(1). Returns the maximum element of the queue. Throws an error on an empty queue.

getMax :: MaxQueue a -> Maybe a

O(1). The top (maximum) element of the queue, if there is one.

deleteMax :: Ord a => MaxQueue a -> MaxQueue a

O(log n). Deletes the maximum element of the queue. Does nothing on an empty queue.

deleteFindMax :: Ord a => MaxQueue a -> (a, MaxQueue a)

O(log n). Extracts the maximum element of the queue. Throws an error on an empty queue.

maxView :: Ord a => MaxQueue a -> Maybe (a, MaxQueue a)

O(log n). Extract the top (maximum) element of the sequence, if there is one.

Construction operations

singleton :: a -> MaxQueue a

O(1). Construct a priority queue with a single element.

insert :: Ord a => a -> MaxQueue a -> MaxQueue a

O(1). Insert an element into the priority queue.

union :: Ord a => MaxQueue a -> MaxQueue a -> MaxQueue a

O(log (min(n1,n2))). Take the union of two priority queues.

unions :: Ord a => [MaxQueue a] -> MaxQueue a

Takes the union of a list of priority queues. Equivalent to foldl union empty.

Subsets

Extracting subsets

(!!) :: Ord a => MaxQueue a -> Int -> a

O(k log n). Returns the (k+1)th largest element of the queue.

take :: Ord a => Int -> MaxQueue a -> [a]

O(k log n). Returns the list of the k largest elements of the queue, in descending order, or all elements of the queue, if k >= n.

drop :: Ord a => Int -> MaxQueue a -> MaxQueue a

O(k log n). Returns the queue with the k largest elements deleted, or the empty queue if k >= n.

splitAt :: Ord a => Int -> MaxQueue a -> ([a], MaxQueue a)

O(k log n). Equivalent to (take k queue, drop k queue).

Predicates

takeWhile :: Ord a => (a -> Bool) -> MaxQueue a -> [a]

takeWhile, applied to a predicate p and a queue queue, returns the longest prefix (possibly empty) of queue of elements that satisfy p.

dropWhile :: Ord a => (a -> Bool) -> MaxQueue a -> MaxQueue a

dropWhile p queue returns the queue remaining after takeWhile p queue.

span :: Ord a => (a -> Bool) -> MaxQueue a -> ([a], MaxQueue a)

span, applied to a predicate p and a queue queue, returns a tuple where first element is longest prefix (possibly empty) of queue of elements that satisfy p and second element is the remainder of the queue.

break :: Ord a => (a -> Bool) -> MaxQueue a -> ([a], MaxQueue a)

break, applied to a predicate p and a queue queue, returns a tuple where first element is longest prefix (possibly empty) of queue of elements that do not satisfy p and second element is the remainder of the queue.

Filter/Map

filter :: Ord a => (a -> Bool) -> MaxQueue a -> MaxQueue a

O(n). Returns a queue of those elements which satisfy the predicate.

partition :: Ord a => (a -> Bool) -> MaxQueue a -> (MaxQueue a, MaxQueue a)

O(n). Returns a pair of queues, where the left queue contains those elements that satisfy the predicate, and the right queue contains those that do not.

mapMaybe :: Ord b => (a -> Maybe b) -> MaxQueue a -> MaxQueue b

O(n). Maps a function over the elements of the queue, and collects the Just values.

mapEither :: (Ord b, Ord c) => (a -> Either b c) -> MaxQueue a -> (MaxQueue b, MaxQueue c)

O(n). Maps a function over the elements of the queue, and separates the Left and Right values.

Fold/Functor/Traversable variations

map :: (a -> b) -> [a] -> [b]

map f xs is the list obtained by applying f to each element of xs, i.e.,

 map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn]
 map f [x1, x2, ...] == [f x1, f x2, ...]

foldrAsc :: Ord a => (a -> b -> b) -> b -> MaxQueue a -> b

O(n log n). Performs a right-fold on the elements of a priority queue in ascending order. foldrAsc f z q == foldlDesc (flip f) z q.

foldlAsc :: Ord a => (b -> a -> b) -> b -> MaxQueue a -> b

O(n log n). Performs a left-fold on the elements of a priority queue in descending order. foldlAsc f z q == foldrDesc (flip f) z q.

foldrDesc :: Ord a => (a -> b -> b) -> b -> MaxQueue a -> b

O(n log n). Performs a right-fold on the elements of a priority queue in descending order.

foldlDesc :: Ord a => (b -> a -> b) -> b -> MaxQueue a -> b

O(n log n). Performs a left-fold on the elements of a priority queue in descending order.

List operations

toList :: Ord a => MaxQueue a -> [a]

O(n). Returns the elements of the priority queue in no particular order.

toAscList :: Ord a => MaxQueue a -> [a]

O(n log n). Extracts the elements of the priority queue in ascending order.

toDescList :: Ord a => MaxQueue a -> [a]

O(n log n). Extracts the elements of the priority queue in descending order.

fromList :: Ord a => [a] -> MaxQueue a

O(n log n). Constructs a priority queue from an unordered list.

fromAscList :: [a] -> MaxQueue a

O(n). Constructs a priority queue from an ascending list. Warning: Does not check the precondition.

fromDescList :: [a] -> MaxQueue a

O(n). Constructs a priority queue from a descending list. Warning: Does not check the precondition.

Unordered operations

mapU :: (a -> b) -> MaxQueue a -> MaxQueue b

O(n). Assumes that the function it is given is monotonic, and applies this function to every element of the priority queue. Does not check the precondition.

foldrU :: (a -> b -> b) -> b -> MaxQueue a -> b

O(n). Unordered right fold on a priority queue.

foldlU :: (b -> a -> b) -> b -> MaxQueue a -> b

O(n). Unordered left fold on a priority queue.

elemsU :: MaxQueue a -> [a]

Equivalent to toListU.

toListU :: MaxQueue a -> [a]

O(n). Returns a list of the elements of the priority queue, in no particular order.

Miscellaneous operations

keysQueue :: MaxPQueue k a -> MaxQueue k

O(n). Constructs a priority queue from the keys of a MaxPQueue.

seqSpine :: MaxQueue a -> b -> b

O(log n). Forces the spine of the heap.