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138 lines
3.0 KiB
Elm
138 lines
3.0 KiB
Elm
module PairingHeap exposing
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( PairingHeap, empty
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, insert, merge, findMin, deleteMin
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, fromList, toSortedList
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)
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{-| This is a simple pairing heap implementation written in Elm usable as a priority queue. This code is
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based heavily on the pseudocode available at [the Wikipedia page](https://en.wikipedia.org/wiki/Pairing_heap).
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# Type and Constructor
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@docs PairingHeap, empty
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# Operations
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@docs insert, merge, findMin, deleteMin
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# Convenience functions
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@docs fromList, toSortedList
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-}
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{-| A `PairingHeap` has comparable keys and values of an arbitrary type.
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-}
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type PairingHeap comparable a
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= Empty
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| Heap comparable a (List (PairingHeap comparable a))
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{-| Create an empty PairingHeap.
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-}
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empty : PairingHeap comparable a
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empty =
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Empty
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{-| Find the minimum value in a heap returning Nothing if the heap is empty.
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Complexity: O(1)
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findMin (fromList [ ( 10, () ), ( 3, () ), ( 8, () ) ]) == Just 3
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-}
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findMin : PairingHeap comparable a -> Maybe ( comparable, a )
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findMin x =
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case x of
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Empty ->
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Nothing
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Heap k v _ ->
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Just ( k, v )
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{-| Merges two `PairingHeap`s together into one new heap containing all of the key-value pairs from both inputs.
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Complexity: O(1)
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-}
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merge : PairingHeap comparable a -> PairingHeap comparable a -> PairingHeap comparable a
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merge heap1 heap2 =
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case ( heap1, heap2 ) of
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( Empty, _ ) ->
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heap2
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( _, Empty ) ->
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heap1
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( Heap k1 v1 hs1, Heap k2 v2 hs2 ) ->
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if k1 < k2 then
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Heap k1 v1 (heap2 :: hs1)
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else
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Heap k2 v2 (heap1 :: hs2)
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{-| Inserts a new element into a `PairingHeap`.
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Complexity: O(1)
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-}
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insert : comparable -> a -> PairingHeap comparable a -> PairingHeap comparable a
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insert k v heap =
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merge (Heap k v []) heap
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{-| Removes the minimum element from a `PairingHeap` returning a new heap without that element.
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This will return an empty heap if given an empty heap as input.
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Complexity: O(log n)
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-}
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deleteMin : PairingHeap comparable a -> PairingHeap comparable a
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deleteMin heap =
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case heap of
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Empty ->
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Empty
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Heap k v heaps ->
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mergePairs heaps
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{-| This is an internal function used by deleteMin.
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-}
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mergePairs : List (PairingHeap comparable a) -> PairingHeap comparable a
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mergePairs heaps =
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case heaps of
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[] ->
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Empty
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x :: [] ->
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x
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x :: (y :: xs) ->
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merge (merge x y) (mergePairs xs)
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-- Extra convenience functions
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{-| This function turns a list of key-value pairs into a `PairingHeap`.
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Complexity: O(n)
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-}
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fromList : List ( comparable, a ) -> PairingHeap comparable a
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fromList =
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List.foldl (\( k, v ) -> insert k v) empty
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{-| This function turns a `PairingHeap` into a sorted list of key-value pairs.
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Complexity: O(n log n)
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-}
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toSortedList : PairingHeap comparable a -> List ( comparable, a )
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toSortedList heap =
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case heap of
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Empty ->
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[]
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Heap k v _ ->
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( k, v ) :: toSortedList (deleteMin heap)
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