Safe Haskell	Safe
Language	Haskell2010

Data.PSQueue

Contents

Binding Type
Priority Search Queue Type
Query
Construction
Insertion
Delete/Update
Conversion
Priority Queue
Fold

Description

A priority search queue (henceforth queue) efficiently supports the operations of both a search tree and a priority queue. A Binding is a product of a key and a priority. Bindings can be inserted, deleted, modified and queried in logarithmic time, and the binding with the least priority can be retrieved in constant time. A queue can be built from a list of bindings, sorted by keys, in linear time.

This implementation is due to Ralf Hinze.

Hinze, R., A Simple Implementation Technique for Priority Search Queues, ICFP 2001, pp. 110-121

Synopsis

data Binding k p = !k :-> !p
key :: Binding k p -> k
prio :: Binding k p -> p
data PSQ k p
size :: PSQ k p -> Int
null :: PSQ k p -> Bool
lookup :: Ord k => k -> PSQ k p -> Maybe p
empty :: PSQ k p
singleton :: k -> p -> PSQ k p
insert :: (Ord k, Ord p) => k -> p -> PSQ k p -> PSQ k p
insertWith :: (Ord k, Ord p) => (p -> p -> p) -> k -> p -> PSQ k p -> PSQ k p
delete :: (Ord k, Ord p) => k -> PSQ k p -> PSQ k p
adjust :: (Ord p, Ord k) => (p -> p) -> k -> PSQ k p -> PSQ k p
adjustWithKey :: (Ord k, Ord p) => (k -> p -> p) -> k -> PSQ k p -> PSQ k p
update :: (Ord k, Ord p) => (p -> Maybe p) -> k -> PSQ k p -> PSQ k p
updateWithKey :: (Ord k, Ord p) => (k -> p -> Maybe p) -> k -> PSQ k p -> PSQ k p
alter :: (Ord k, Ord p) => (Maybe p -> Maybe p) -> k -> PSQ k p -> PSQ k p
keys :: PSQ k p -> [k]
toList :: PSQ k p -> [Binding k p]
toAscList :: PSQ k p -> [Binding k p]
toDescList :: PSQ k p -> [Binding k p]
fromList :: (Ord k, Ord p) => [Binding k p] -> PSQ k p
fromAscList :: (Eq k, Ord p) => [Binding k p] -> PSQ k p
fromDistinctAscList :: Ord p => [Binding k p] -> PSQ k p
findMin :: PSQ k p -> Maybe (Binding k p)
deleteMin :: Ord p => PSQ k p -> PSQ k p
minView :: Ord p => PSQ k p -> Maybe (Binding k p, PSQ k p)
atMost :: Ord p => p -> PSQ k p -> [Binding k p]
atMostRange :: (Ord k, Ord p) => p -> (k, k) -> PSQ k p -> [Binding k p]
foldr :: (Binding k p -> b -> b) -> b -> PSQ k p -> b
foldl :: (b -> Binding k p -> b) -> b -> PSQ k p -> b

Binding Type

data Binding k p Source #

k :-> p binds the key k with the priority p.

Constructors

!k :-> !p infix 0

Instances

Instances details

(Read k, Read p) => Read (Binding k p) Source #
Instance details Defined in Data.PSQueue.Internal Methods readsPrec :: Int -> ReadS (Binding k p) # readList :: ReadS [Binding k p] # readPrec :: ReadPrec (Binding k p) # readListPrec :: ReadPrec [Binding k p] #
(Show k, Show p) => Show (Binding k p) Source #
Instance details Defined in Data.PSQueue.Internal Methods showsPrec :: Int -> Binding k p -> ShowS # show :: Binding k p -> String # showList :: [Binding k p] -> ShowS #
(Eq k, Eq p) => Eq (Binding k p) Source #
Instance details Defined in Data.PSQueue.Internal Methods (==) :: Binding k p -> Binding k p -> Bool # (/=) :: Binding k p -> Binding k p -> Bool #
(Ord k, Ord p) => Ord (Binding k p) Source #
Instance details Defined in Data.PSQueue.Internal Methods compare :: Binding k p -> Binding k p -> Ordering # (<) :: Binding k p -> Binding k p -> Bool # (<=) :: Binding k p -> Binding k p -> Bool # (>) :: Binding k p -> Binding k p -> Bool # (>=) :: Binding k p -> Binding k p -> Bool # max :: Binding k p -> Binding k p -> Binding k p # min :: Binding k p -> Binding k p -> Binding k p #

key :: Binding k p -> k Source #

The key of a binding

prio :: Binding k p -> p Source #

The priority of a binding

Priority Search Queue Type

data PSQ k p Source #

A mapping from keys k to priorites p.

Instances

Instances details

(Show k, Show p) => Show (PSQ k p) Source #
Instance details Defined in Data.PSQueue.Internal Methods showsPrec :: Int -> PSQ k p -> ShowS # show :: PSQ k p -> String # showList :: [PSQ k p] -> ShowS #
(Eq k, Eq p) => Eq (PSQ k p) Source #
Instance details Defined in Data.PSQueue.Internal Methods (==) :: PSQ k p -> PSQ k p -> Bool # (/=) :: PSQ k p -> PSQ k p -> Bool #

Query

size :: PSQ k p -> Int Source #

O(1) The number of bindings in a queue.

null :: PSQ k p -> Bool Source #

O(1) True if the queue is empty.

lookup :: Ord k => k -> PSQ k p -> Maybe p Source #

O(log n) The priority of a given key, or Nothing if the key is not bound.

Construction

empty :: PSQ k p Source #

singleton :: k -> p -> PSQ k p Source #

O(1) Build a queue with one binding.

Insertion

insert :: (Ord k, Ord p) => k -> p -> PSQ k p -> PSQ k p Source #

O(log n) Insert a binding into the queue.

insertWith :: (Ord k, Ord p) => (p -> p -> p) -> k -> p -> PSQ k p -> PSQ k p Source #

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

Delete/Update

delete :: (Ord k, Ord p) => k -> PSQ k p -> PSQ k p Source #

O(log n) Remove a binding from the queue.

adjust :: (Ord p, Ord k) => (p -> p) -> k -> PSQ k p -> PSQ k p Source #

O(log n) Adjust the priority of a key.

adjustWithKey :: (Ord k, Ord p) => (k -> p -> p) -> k -> PSQ k p -> PSQ k p Source #

O(log n) Adjust the priority of a key.

update :: (Ord k, Ord p) => (p -> Maybe p) -> k -> PSQ k p -> PSQ k p Source #

O(log n) The expression (update f k q) updates the priority p bound k (if it is in the queue). If (f p) is Nothing, the binding is deleted. If it is (Just z), the key k is bound to the new priority z.

updateWithKey :: (Ord k, Ord p) => (k -> p -> Maybe p) -> k -> PSQ k p -> PSQ k p Source #

O(log n). The expression (updateWithKey f k q) updates the priority p bound k (if it is in the queue). If (f k p) is Nothing, the binding is deleted. If it is (Just z), the key k is bound to the new priority z.

alter :: (Ord k, Ord p) => (Maybe p -> Maybe p) -> k -> PSQ k p -> PSQ k p Source #

O(log n). The expression (alter f k q) alters the priority p bound to k, or absence thereof. alter can be used to insert, delete, or update a priority in a queue.

Conversion

keys :: PSQ k p -> [k] Source #

O(n) The keys of a priority queue

toList :: PSQ k p -> [Binding k p] Source #

O(n) Convert a queue to a list.

toAscList :: PSQ k p -> [Binding k p] Source #

O(n) Convert a queue to a list in ascending order of keys.

toDescList :: PSQ k p -> [Binding k p] Source #

O(n) Convert a queue to a list in descending order of keys.

fromList :: (Ord k, Ord p) => [Binding k p] -> PSQ k p Source #

O(n log n) Build a queue from a list of bindings.

fromAscList :: (Eq k, Ord p) => [Binding k p] -> PSQ k p Source #

O(n) Build a queue from a list of bindings in order of ascending keys. The precondition that the keys are ascending is not checked.

fromDistinctAscList :: Ord p => [Binding k p] -> PSQ k p Source #

O(n) Build a queue from a list of distinct bindings in order of ascending keys. The precondition that keys are distinct and ascending is not checked.

Priority Queue

findMin :: PSQ k p -> Maybe (Binding k p) Source #

O(1) The binding with the lowest priority.

deleteMin :: Ord p => PSQ k p -> PSQ k p Source #

O(log n) Remove the binding with the lowest priority.

minView :: Ord p => PSQ k p -> Maybe (Binding k p, PSQ k p) Source #

O(log n) Retrieve the binding with the least priority, and the rest of the queue stripped of that binding.

atMost :: Ord p => p -> PSQ k p -> [Binding k p] Source #

O(r(log n - log r) atMost p q is a list of all the bindings in q with priority less than p, in order of ascending keys. Effectively,

  atMost p' q = filter (\(k:->p) -> p<=p') . toList

atMostRange :: (Ord k, Ord p) => p -> (k, k) -> PSQ k p -> [Binding k p] Source #

O(r(log n - log r)) atMostRange p (l,u) q is a list of all the bindings in q with a priority less than p and a key in the range (l,u) inclusive. Effectively,

   atMostRange p' (l,u) q = filter (\(k:->p) -> l<=k && k<=u ) . atMost p'

Fold

foldr :: (Binding k p -> b -> b) -> b -> PSQ k p -> b Source #

Right fold over the bindings in the queue, in key order.

foldl :: (b -> Binding k p -> b) -> b -> PSQ k p -> b Source #

Left fold over the bindings in the queue, in key order.