Data.PSQueue.Internal

Binding Type

data Binding k p

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

Constructors

!k :-> !p infix 0

Instances

(Read k, Read p) => Read (Binding k p)

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)

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)

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)

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

The key of a binding

prio :: Binding k p -> p

The priority of a binding

Priority Search Queue Type

data PSQ k p

A mapping from keys k to priorites p.

Constructors

Void

Winner !k !p !(LTree k p) !k

Instances

(Show k, Show p) => Show (PSQ k p)

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)

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

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

null :: PSQ k p -> Bool

O(1) True if the queue is empty.

lookup :: 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

empty :: PSQ k p

singleton :: k -> p -> PSQ k p

O(1) Build a queue with one binding.

Insertion

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

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

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

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

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

Delete/Update

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

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

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

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

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

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

update :: (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.

updateWithKey :: (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.

alter :: (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

keys :: PSQ k p -> [k]

O(n) The keys of a priority queue

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

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

fromAscList :: (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.

fromDistinctAscList :: 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.

foldm :: (a -> a -> a) -> a -> [a] -> a

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

O(n) Convert a queue to a list.

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

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

toAscLists :: PSQ k p -> Sequ (Binding k p)

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

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

toDescLists :: PSQ k p -> Sequ (Binding k p)

Priority Queue

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

O(1) The binding with the lowest priority.

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

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

minView :: 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.

secondBest :: Ord p => LTree k p -> k -> PSQ k p

atMost :: 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

atMosts :: Ord p => p -> PSQ k p -> Sequ (Binding k p)

atMostRange :: (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'

atMostRanges :: (Ord k, Ord p) => p -> (k, k) -> PSQ k p -> Sequ (Binding k p)

inrange :: Ord a => a -> (a, a) -> Bool

Fold

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

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

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

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

Internals

type Size = Int

data LTree k p

Constructors

Start

LLoser !Size !k !p !(LTree k p) !k !(LTree k p)

RLoser !Size !k !p !(LTree k p) !k !(LTree k p)

size' :: LTree k p -> Size

left :: LTree a b -> LTree a b

right :: LTree a b -> LTree a b

maxKey :: PSQ k p -> k

lloser :: k -> p -> LTree k p -> k -> LTree k p -> LTree k p

rloser :: k -> p -> LTree k p -> k -> LTree k p -> LTree k p

omega :: Int

lbalance :: Ord p => k -> p -> LTree k p -> k -> LTree k p -> LTree k p

rbalance :: Ord p => k -> p -> LTree k p -> k -> LTree k p -> LTree k p

lbalanceLeft :: Ord p => k -> p -> LTree k p -> k -> LTree k p -> LTree k p

lbalanceRight :: Ord p => k -> p -> LTree k p -> k -> LTree k p -> LTree k p

rbalanceLeft :: Ord p => k -> p -> LTree k p -> k -> LTree k p -> LTree k p

rbalanceRight :: Ord p => k -> p -> LTree k p -> k -> LTree k p -> LTree k p

lsingleLeft :: Ord p => k -> p -> LTree k p -> k -> LTree k p -> LTree k p

rsingleLeft :: k -> p -> LTree k p -> k -> LTree k p -> LTree k p

lsingleRight :: k -> p -> LTree k p -> k -> LTree k p -> LTree k p

rsingleRight :: Ord p => k -> p -> LTree k p -> k -> LTree k p -> LTree k p

ldoubleLeft :: Ord p => k -> p -> LTree k p -> k -> LTree k p -> LTree k p

ldoubleRight :: Ord p => k -> p -> LTree k p -> k -> LTree k p -> LTree k p

rdoubleLeft :: Ord p => k -> p -> LTree k p -> k -> LTree k p -> LTree k p

rdoubleRight :: Ord p => k -> p -> LTree k p -> k -> LTree k p -> LTree k p

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

data TourView k p

Constructors

Null

Single !k !p

!(PSQ k p) `Play` !(PSQ k p)

tourView :: PSQ k p -> TourView k p