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59 lines
1.5 KiB
Haskell
59 lines
1.5 KiB
Haskell
module Heap where
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data Heap a = Nil | Node Int a (Heap a) (Heap a) deriving Show
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emptyHeap :: Heap a
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emptyHeap = Nil
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isEmpty :: Heap a -> Bool
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isEmpty Nil = True
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isEmpty _ = False
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size Nil = 0
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size (Node s _ _ _) = s
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root (Node _ x _ _) = x
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isHeap (Node s x hl hr) = s == 1 + sl + sr && sl >= sr &&
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(isEmpty hl || x >= root hl) &&
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(isEmpty hr || x >= root hr) &&
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isHeap hl && isHeap hr
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where (sl, sr) = (size hl, size hr)
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realign :: Heap a -> Heap a
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realign Nil = Nil
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realign h@(Node s x hl hr)
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| size hl >= size hr = h
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| otherwise = Node s x hr hl
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union :: Ord a => Heap a -> Heap a -> Heap a
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union h Nil = h
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union Nil h = h
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union h1@(Node s1 x h1l h1r) h2@(Node s2 y h2l h2r)
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| x >= y = realign
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(Node (s1+s2) x h1l (union h1r h2))
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| otherwise = realign
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(Node (s1+s2) y h2l (union h1 h2r))
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insert :: Ord a => a -> Heap a -> Heap a
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insert x h = union (Node 1 x Nil Nil) h
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findMax :: Heap a -> Maybe a
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findMax h = if isEmpty h then Nothing
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else Just (root h)
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deleteMax :: Ord a => Heap a -> (Maybe a, Heap a)
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deleteMax Nil = (Nothing, Nil)
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deleteMax (Node _ x hl hr) = (Just x, union hl hr)
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instance Functor Heap where
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fmap f Nil = Nil
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fmap f (Node n x left right) = Node n (f x) left' right' where
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left' = fmap f left
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right' = fmap f right
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instance Foldable Heap where
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foldr _ acc Nil = acc
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foldr f base (Node _ x left right) = f x $ foldr f acc right where
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acc = foldr f base left
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