On 19/05/07, Andrew Coppin <andrewcoppin@btinternet.com> wrote:

Greetings.

I have just implemented a heap. But... um... I can't acutally figure out
*which kind* of heap it is! LOL. Any ideas?

(Seems to work really well, whatever it is. Oh, and I discovered that
you can sort data just by shoving it all into a heap, and then taking it
all out again. Apparently this is a standard algorithm, and it's known
as a "heap sort", unsurprisingly. You learn something every day...)

module Heap where

import Data.List (intersperse, unfoldr)

data Heap t = Node !t !(Heap t) !(Heap t) | Null

instance (Show t) => Show (Heap t) where
  show = work "" where
    work p (Null) = p ++ "-"
    work p (Node v t0 t1) = concat $ intersperse "\n" $ [work (' ':p)
t0, p ++ show v, work (' ':p) t1]

empty = Null

is_empty Null = True
is_empty _    = False

insert v (Null) = Node v Null Null
insert v (Node v0 t0 t1) =
  let lo = min v v0
      hi = max v v0
  in  Node hi (insert lo t1) t0

get_max (Null) = error "heap is empty"
get_max (Node v _ _) = v

delete_max (Null) = error "heap is empty"
delete_max (Node _ Null Null) = Null
delete_max (Node _ Null t1)   = t1
delete_max (Node _ t0   Null) = t0
delete_max (Node _ t0   t1)
  | get_max t0 > get_max t1 = Node (get_max t0) (delete_max t0)      t1
  | otherwise               = Node (get_max t1)             t0
(delete_max t1)

size (Null) = 0
size (Node _ t0 t1) = 1 + (size t0) + (size t1)

from_list :: (Ord t) => [t] -> Heap t
from_list = foldr insert empty

to_list   :: (Ord t) => Heap t -> [t]
to_list   = unfoldr (\h -> if is_empty h then Nothing else Just (get_max
h, delete_max h))

heap_sort :: (Ord t) => [t] -> [t]
heap_sort = to_list . from_list

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