Data.PQueue.Min

General purpose priority queue, supporting extract-minimum 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 MinQueue a

A priority queue with elements of type a. Supports extracting the minimum element.

Instances

Ord a => Eq (MinQueue a)

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

Ord a => Ord (MinQueue a)

NFData a => NFData (MinQueue a)

Basic operations

empty :: MinQueue a

O(1). The empty priority queue.

null :: MinQueue a -> Bool

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

size :: MinQueue a -> Int

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

Query operations

findMin :: MinQueue a -> a

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

getMin :: MinQueue a -> Maybe a

Returns the minimum element of the queue, if the queue is nonempty.

deleteMin :: Ord a => MinQueue a -> MinQueue a

O(log n). Deletes the minimum element. If the queue is empty, does nothing.

deleteFindMin :: Ord a => MinQueue a -> (a, MinQueue a)

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

minView :: Ord a => MinQueue a -> Maybe (a, MinQueue a)

Retrieves the minimum element of the queue, and the queue stripped of that element, or Nothing if passed an empty queue.

Construction operations

singleton :: a -> MinQueue a

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

insert :: Ord a => a -> MinQueue a -> MinQueue a

Amortized O(1), worst-case O(log n). Insert an element into the priority queue.

union :: Ord a => MinQueue a -> MinQueue a -> MinQueue a

Amortized O(log (min(n,m))), worst-case O(log (max (n,m))). Take the union of two priority queues.

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

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

Subsets

Extracting subsets

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

O(k log n). Index (subscript) operator, starting from 0. queue !! k returns the (k+1)th smallest element in the queue. Equivalent to toAscList queue !! k.

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

O(k log n). take k, applied to a queue queue, returns a list of the smallest k elements of queue, or all elements of queue itself if k >= size queue.

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

O(k log n). drop k, applied to a queue queue, returns queue with the smallest k elements deleted, or an empty queue if k >= size queue.

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

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

Predicates

takeWhile :: Ord a => (a -> Bool) -> MinQueue 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) -> MinQueue a -> MinQueue a

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

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

O(n). Returns the queue with all elements not satisfying p removed.

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

O(n). Returns a pair where the first queue contains all elements satisfying p, and the second queue contains all elements not satisfying p.

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

O(n). Map elements and collect the Just results.

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

O(n). Map elements and separate the Left and Right results.

Fold/Functor/Traversable variations

map :: Ord b => (a -> b) -> MinQueue a -> MinQueue b

O(n). Creates a new priority queue containing the images of the elements of this queue. Equivalent to fromList . map f . toList.

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

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

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

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

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

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

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

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

List operations

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

O(n). Returns the elements of the priority queue in ascending order. Equivalent to toAscList.

If the order of the elements is irrelevant, consider using toListU.

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

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

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

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

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

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

fromAscList :: [a] -> MinQueue a

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

fromDescList :: [a] -> MinQueue a

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

Unordered operations

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

Maps a function over the elements of the queue, ignoring order. This function is only safe if the function is monotonic. This function does not check the precondition.

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

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

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

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

elemsU :: MinQueue a -> [a]

Equivalent to toListU.

toListU :: MinQueue a -> [a]

Returns the elements of the queue, in no particular order.

Miscellaneous operations

keysQueue :: MinPQueue k a -> MinQueue k

Constructs a priority queue out of the keys of the specified MinPQueue.

seqSpine :: MinQueue a -> b -> b

Forces the spine of the priority queue.