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GHC 10.0.0.20260917 · lts/ghc-10.0.x · 8fef28d · 2026-11-02

ModulePSQueue-1.2.2Haskell2010

Data.PSQueue

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

Contents

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

Synopsis

PackagePSQueue-1.2.2
Exports31
LanguageHaskell2010
LicenceBSD-3-Clause
SourcePSQueue.hs

Binding Type

datadata Binding k p

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

Constructors

k :-> pinfix 0

Instances4Eq, Ord, Read, Show

(Eq k, Eq p) => Eq (Binding k p)Defined in PSQueue-1.2.2 · Data.PSQueue.Internal
(Ord k, Ord p) => Ord (Binding k p)Defined in PSQueue-1.2.2 · Data.PSQueue.Internal
(Read k, Read p) => Read (Binding k p)Defined in PSQueue-1.2.2 · Data.PSQueue.Internal
(Show k, Show p) => Show (Binding k p)Defined in PSQueue-1.2.2 · Data.PSQueue.Internal

valuekey :: Binding k p -> k

The key of a binding

valueprio :: Binding k p -> p

The priority of a binding

Priority Search Queue Type

datadata PSQ k p

A mapping from keys k to priorites p.

Instances2Eq, Show

(Eq k, Eq p) => Eq (PSQ k p)Defined in PSQueue-1.2.2 · Data.PSQueue.Internal
(Show k, Show p) => Show (PSQ k p)Defined in PSQueue-1.2.2 · Data.PSQueue.Internal

Query

valuesize :: PSQ k p -> Int

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

valuenull :: PSQ k p -> Bool

O(1) True if the queue is empty.

valuelookup :: Ord k => k -> PSQ k p -> Maybe p

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

Construction

valueempty :: PSQ k p

valuesingleton :: k -> p -> PSQ k p

O(1) Build a queue with one binding.

Insertion

valueinsert :: (Ord k, Ord p) => k -> p -> PSQ k p -> PSQ k p

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

valueinsertWith

:: (Ord k, Ord p)
=> p -> p -> p
-> k
-> p
-> PSQ k p
-> PSQ k p

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

Delete/Update

valuedelete :: (Ord k, Ord p) => k -> PSQ k p -> PSQ k p

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

valueadjust :: (Ord p, Ord k) => (p -> p) -> k -> PSQ k p -> PSQ k p

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

valueadjustWithKey :: (Ord k, Ord p) => (k -> p -> p) -> k -> PSQ k p -> PSQ k p

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

valueupdate :: (Ord k, Ord p) => (p -> Maybe p) -> k -> PSQ k p -> PSQ k p

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.

valueupdateWithKey

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

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.

valuealter :: (Ord k, Ord p) => (Maybe p -> Maybe p) -> k -> PSQ k p -> PSQ k p

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

valuekeys :: PSQ k p -> [k]

O(n) The keys of a priority queue

valuetoList :: PSQ k p -> [Binding k p]

O(n) Convert a queue to a list.

valuetoAscList :: PSQ k p -> [Binding k p]

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

valuetoDescList :: PSQ k p -> [Binding k p]

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

valuefromList :: (Ord k, Ord p) => [Binding k p] -> PSQ k p

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

valuefromAscList :: (Eq k, Ord p) => [Binding k p] -> PSQ k p

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.

valuefromDistinctAscList :: Ord p => [Binding k p] -> PSQ k p

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

valuefindMin :: PSQ k p -> Maybe (Binding k p)

O(1) The binding with the lowest priority.

valuedeleteMin :: Ord p => PSQ k p -> PSQ k p

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

valueminView :: Ord p => PSQ k p -> Maybe (Binding k p, PSQ k p)

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

valueatMost :: Ord p => p -> PSQ k p -> [Binding k p]

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

valueatMostRange :: (Ord k, Ord p) => p -> (k, k) -> PSQ k p -> [Binding k p]

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

valuefoldr :: (Binding k p -> b -> b) -> b -> PSQ k p -> b

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

valuefoldl :: (b -> Binding k p -> b) -> b -> PSQ k p -> b

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