Data.Queue.Binomial

Simple binomial heaps, with a statically-enforced shape.

Documentation

data Binomial rk a

A binomial heap, where the sizes of the nodes are enforced in the types.

The implementation is based on:

• Hinze, Ralf. “Functional Pearls: Explaining Binomial Heaps.” Journal of Functional Programming 9, no. 1 (January 1999): 93–104. doi:10.1017/S0956796899003317.
• Wasserman, Louis. “Playing with Priority Queues.” The Monad.Reader, May 12, 2010.

It is a list of binomial trees, equivalent to a binary number (stored least-significant-bit first).

Constructors

Nil

The empty heap

Skip (Binomial (S rk) a)

Skip a child tree (equivalent to a zero in the binary representation of the data structure).

(:-) !(Tree rk a) (Binomial (S rk) a) infixr 5

A child tree. Equivalent to a one in the binary representation.

Instances

Functor (Binomial rk)

Methods

fmap :: (a -> b) -> Binomial rk a -> Binomial rk b

(<$) :: a -> Binomial rk b -> Binomial rk a

Foldable (Binomial rk)

Methods

fold :: Monoid m => Binomial rk m -> m

foldMap :: Monoid m => (a -> m) -> Binomial rk a -> m

foldr :: (a -> b -> b) -> b -> Binomial rk a -> b

foldr' :: (a -> b -> b) -> b -> Binomial rk a -> b

foldl :: (b -> a -> b) -> b -> Binomial rk a -> b

foldl' :: (b -> a -> b) -> b -> Binomial rk a -> b

foldr1 :: (a -> a -> a) -> Binomial rk a -> a

foldl1 :: (a -> a -> a) -> Binomial rk a -> a

toList :: Binomial rk a -> [a]

null :: Binomial rk a -> Bool

length :: Binomial rk a -> Int

elem :: Eq a => a -> Binomial rk a -> Bool

maximum :: Ord a => Binomial rk a -> a

minimum :: Ord a => Binomial rk a -> a

sum :: Num a => Binomial rk a -> a

product :: Num a => Binomial rk a -> a

Traversable (Binomial rk)

Methods

traverse :: Applicative f => (a -> f b) -> Binomial rk a -> f (Binomial rk b)

sequenceA :: Applicative f => Binomial rk (f a) -> f (Binomial rk a)

mapM :: Monad m => (a -> m b) -> Binomial rk a -> m (Binomial rk b)

sequence :: Monad m => Binomial rk (m a) -> m (Binomial rk a)

Generic1 (Binomial n)

Associated Types

type Rep1 (Binomial n :: * -> *) :: * -> *

Methods

from1 :: Binomial n a -> Rep1 (Binomial n) a

to1 :: Rep1 (Binomial n) a -> Binomial n a

Ord a => MeldableQueue (Binomial Z) a

Methods

merge :: Binomial Z a -> Binomial Z a -> Binomial Z a

fromFoldable :: Foldable f => f a -> Binomial Z a

Ord a => Queue (Binomial Z) a

Methods

minView :: Binomial Z a -> Maybe (a, Binomial Z a)

insert :: a -> Binomial Z a -> Binomial Z a

empty :: Binomial Z a

singleton :: a -> Binomial Z a

toList :: Binomial Z a -> [a]

fromList :: [a] -> Binomial Z a

heapSort :: p (Binomial Z) -> [a] -> [a]

Ord a => Eq (Binomial Z a)

Methods

(==) :: Binomial Z a -> Binomial Z a -> Bool

(/=) :: Binomial Z a -> Binomial Z a -> Bool

Ord a => Ord (Binomial Z a)

Methods

compare :: Binomial Z a -> Binomial Z a -> Ordering

(<) :: Binomial Z a -> Binomial Z a -> Bool

(<=) :: Binomial Z a -> Binomial Z a -> Bool

(>) :: Binomial Z a -> Binomial Z a -> Bool

(>=) :: Binomial Z a -> Binomial Z a -> Bool

max :: Binomial Z a -> Binomial Z a -> Binomial Z a

min :: Binomial Z a -> Binomial Z a -> Binomial Z a

(Read a, Ord a) => Read (Binomial Z a)

Methods

readsPrec :: Int -> ReadS (Binomial Z a)

readList :: ReadS [Binomial Z a]

readPrec :: ReadPrec (Binomial Z a)

readListPrec :: ReadPrec [Binomial Z a]

(Show a, Ord a) => Show (Binomial Z a)

Methods

showsPrec :: Int -> Binomial Z a -> ShowS

show :: Binomial Z a -> String

showList :: [Binomial Z a] -> ShowS

Generic (Binomial n a)

Associated Types

type Rep (Binomial n a) :: * -> *

Methods

from :: Binomial n a -> Rep (Binomial n a) x

to :: Rep (Binomial n a) x -> Binomial n a

Ord a => Monoid (Binomial rk a)

Methods

mempty :: Binomial rk a

mappend :: Binomial rk a -> Binomial rk a -> Binomial rk a

mconcat :: [Binomial rk a] -> Binomial rk a

NFData a => NFData (Binomial rk a)

Methods

rnf :: Binomial rk a -> ()

type Rep1 (Binomial n)

type Rep1 (Binomial n) = D1 (MetaData "Binomial" "Data.Queue.Binomial" "type-indexed-queues-0.1.0.1-GPaLldpmb1Q20PpM0x8M72" False) ((:+:) (C1 (MetaCons "Nil" PrefixI False) U1) ((:+:) (C1 (MetaCons "Skip" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 (Binomial (S n))))) (C1 (MetaCons ":-" PrefixI False) ((:*:) (S1 (MetaSel (Nothing Symbol) SourceUnpack SourceStrict DecidedUnpack) (Rec1 (Tree n))) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 (Binomial (S n))))))))

type Rep (Binomial n a)

type Rep (Binomial n a) = D1 (MetaData "Binomial" "Data.Queue.Binomial" "type-indexed-queues-0.1.0.1-GPaLldpmb1Q20PpM0x8M72" False) ((:+:) (C1 (MetaCons "Nil" PrefixI False) U1) ((:+:) (C1 (MetaCons "Skip" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Binomial (S n) a)))) (C1 (MetaCons ":-" PrefixI False) ((:*:) (S1 (MetaSel (Nothing Symbol) SourceUnpack SourceStrict DecidedUnpack) (Rec0 (Tree n a))) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Binomial (S n) a)))))))

data Node n a where

A list of binomial trees, indexed by their sizes in ascending order.

Constructors

NilN :: Node Z a

(:<) :: !(Tree n a) -> Node n a -> Node (S n) a

Instances

Functor (Node rk)

Methods

fmap :: (a -> b) -> Node rk a -> Node rk b

(<$) :: a -> Node rk b -> Node rk a

Foldable (Node rk)

Methods

fold :: Monoid m => Node rk m -> m

foldMap :: Monoid m => (a -> m) -> Node rk a -> m

foldr :: (a -> b -> b) -> b -> Node rk a -> b

foldr' :: (a -> b -> b) -> b -> Node rk a -> b

foldl :: (b -> a -> b) -> b -> Node rk a -> b

foldl' :: (b -> a -> b) -> b -> Node rk a -> b

foldr1 :: (a -> a -> a) -> Node rk a -> a

foldl1 :: (a -> a -> a) -> Node rk a -> a

toList :: Node rk a -> [a]

null :: Node rk a -> Bool

length :: Node rk a -> Int

elem :: Eq a => a -> Node rk a -> Bool

maximum :: Ord a => Node rk a -> a

minimum :: Ord a => Node rk a -> a

sum :: Num a => Node rk a -> a

product :: Num a => Node rk a -> a

Traversable (Node rk)

Methods

traverse :: Applicative f => (a -> f b) -> Node rk a -> f (Node rk b)

sequenceA :: Applicative f => Node rk (f a) -> f (Node rk a)

mapM :: Monad m => (a -> m b) -> Node rk a -> m (Node rk b)

sequence :: Monad m => Node rk (m a) -> m (Node rk a)

NFData a => NFData (Node rk a)

Methods

rnf :: Node rk a -> ()

data Tree rk a

A rose tree, where the children are indexed.

Constructors

Root a (Node rk a)

Instances

Functor (Tree rk)

Methods

fmap :: (a -> b) -> Tree rk a -> Tree rk b

(<$) :: a -> Tree rk b -> Tree rk a

Foldable (Tree rk)

Methods

fold :: Monoid m => Tree rk m -> m

foldMap :: Monoid m => (a -> m) -> Tree rk a -> m

foldr :: (a -> b -> b) -> b -> Tree rk a -> b

foldr' :: (a -> b -> b) -> b -> Tree rk a -> b

foldl :: (b -> a -> b) -> b -> Tree rk a -> b

foldl' :: (b -> a -> b) -> b -> Tree rk a -> b

foldr1 :: (a -> a -> a) -> Tree rk a -> a

foldl1 :: (a -> a -> a) -> Tree rk a -> a

toList :: Tree rk a -> [a]

null :: Tree rk a -> Bool

length :: Tree rk a -> Int

elem :: Eq a => a -> Tree rk a -> Bool

maximum :: Ord a => Tree rk a -> a

minimum :: Ord a => Tree rk a -> a

sum :: Num a => Tree rk a -> a

product :: Num a => Tree rk a -> a

Traversable (Tree rk)

Methods

traverse :: Applicative f => (a -> f b) -> Tree rk a -> f (Tree rk b)

sequenceA :: Applicative f => Tree rk (f a) -> f (Tree rk a)

mapM :: Monad m => (a -> m b) -> Tree rk a -> m (Tree rk b)

sequence :: Monad m => Tree rk (m a) -> m (Tree rk a)

Generic1 (Tree n)

Associated Types

type Rep1 (Tree n :: * -> *) :: * -> *

Methods

from1 :: Tree n a -> Rep1 (Tree n) a

to1 :: Rep1 (Tree n) a -> Tree n a

Generic (Tree n a)

Associated Types

type Rep (Tree n a) :: * -> *

Methods

from :: Tree n a -> Rep (Tree n a) x

to :: Rep (Tree n a) x -> Tree n a

NFData a => NFData (Tree rk a)

Methods

rnf :: Tree rk a -> ()

type Rep1 (Tree n)

type Rep1 (Tree n) = D1 (MetaData "Tree" "Data.Queue.Binomial" "type-indexed-queues-0.1.0.1-GPaLldpmb1Q20PpM0x8M72" False) (C1 (MetaCons "Root" PrefixI False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 (Node n)))))

type Rep (Tree n a)

type Rep (Tree n a) = D1 (MetaData "Tree" "Data.Queue.Binomial" "type-indexed-queues-0.1.0.1-GPaLldpmb1Q20PpM0x8M72" False) (C1 (MetaCons "Root" PrefixI False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Node n a)))))