PSQueue-1.2.2: Priority Search Queue

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

(<) :: Binding k p -> Binding k p -> Bool Source #

(<=) :: Binding k p -> Binding k p -> Bool Source #

(>) :: Binding k p -> Binding k p -> Bool Source #

(>=) :: Binding k p -> Binding k p -> Bool Source #

max :: Binding k p -> Binding k p -> Binding k p Source #

min :: Binding k p -> Binding k p -> Binding k p Source #

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

# 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.