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Retrieved from: http://en.literateprograms.org/Priority_Queue_(Haskell)?oldid=13634
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{-# LANGUAGE DatatypeContexts #-}



module Control.CP.PriorityQueue (

    PriorityQueue,

    empty,

    is_empty,

    minKey,

    minKeyValue,

    insert,

    deleteMin,

    deleteMinAndInsert

) where



 

import Prelude





-- Declare the data type constructors.



data Ord k => PriorityQueue k a = Nil | Branch k a (PriorityQueue k a) (PriorityQueue k a)

 



-- Declare the exported interface functions.



-- Return an empty priority queue.



is_empty Nil = True

is_empty _   = False



empty :: Ord k => PriorityQueue k a

empty = Nil





-- Return the highest-priority key.



minKey :: Ord k => PriorityQueue k a -> k

minKey = fst . minKeyValue





-- Return the highest-priority key plus its associated value.



minKeyValue :: Ord k => PriorityQueue k a -> (k, a)

minKeyValue Nil              = error "empty queue"

minKeyValue (Branch k a _ _) = (k, a)





-- Insert a key/value pair into a queue.



insert :: Ord k => k -> a -> PriorityQueue k a -> PriorityQueue k a

insert k a q = union (singleton k a) q



deleteMin :: Ord k => PriorityQueue k a -> ((k,a), PriorityQueue k a)

deleteMin(Branch k a l r) = ((k,a),union l r)



-- Delete the highest-priority key/value pair and insert a new key/value pair into the queue.



deleteMinAndInsert :: Ord k => k -> a -> PriorityQueue k a -> PriorityQueue k a

deleteMinAndInsert k a Nil              = singleton k a

deleteMinAndInsert k a (Branch _ _ l r) = union (insert k a l) r







-- Declare the private helper functions.



-- Join two queues in sorted order.



union :: Ord k => PriorityQueue k a -> PriorityQueue k a -> PriorityQueue k a

union l Nil = l

union Nil r = r

union l@(Branch kl _ _ _) r@(Branch kr _ _ _)

    | kl <= kr  = link l r

    | otherwise = link r l





-- Join two queues without regard to order.



-- (This is a helper to the union helper.)



link (Branch k a Nil m) r = Branch k a r m

link (Branch k a ll lr) r = Branch k a lr (union ll r)





-- Return a queue with a single item from a key/value pair.



singleton :: Ord k => k -> a -> PriorityQueue k a

singleton k a = Branch k a Nil Nil