-- -- Copyright (c) 2009 - 2010 Brendan Hickey - http://bhickey.net -- New BSD License (see http://www.opensource.org/licenses/bsd-license.php) -- module Data.Heap.Binomial (BinomialHeap, head, tail, merge, singleton, empty, null, fromList, toList, insert) where import Prelude hiding (head, tail, null) import Data.List (delete) data (Ord a, Ord b, Eq a, Eq b) => HeapNode a b = HeapNode a {-# UNPACK #-} !Int [b] data (Ord a, Eq a) => BinomialHeap a = EmptyHeap | Heap {-# UNPACK #-} ![HeapNode a (BinomialHeap a)] deriving (Eq, Ord) instance (Ord a, Ord b, Eq a, Eq b) => Ord (HeapNode a b) where compare (HeapNode e1 _ _) (HeapNode e2 _ _) = compare e1 e2 instance (Ord a, Ord b, Eq a, Eq b) => Eq (HeapNode a b) where (HeapNode e1 _ _) == (HeapNode e2 _ _) = e1 == e2 rank :: (Ord a, Ord b, Eq a, Eq b) => HeapNode a b -> Int rank (HeapNode _ n _) = n hRank :: (Ord a, Ord b, Eq a, Eq b) => [HeapNode a b] -> Int hRank [] = 0 hRank (hd:_) = rank hd extract :: (Ord a, Ord b, Eq a, Eq b) => HeapNode a b -> a extract (HeapNode n _ _) = n empty :: (Ord a) => BinomialHeap a empty = EmptyHeap null :: (Ord a) => BinomialHeap a -> Bool null EmptyHeap = True null _ = False -- | /O(1)/. singleton :: (Ord a) => a -> BinomialHeap a singleton n = Heap [HeapNode n 1 []] -- | /O(lg n)/ insert :: (Ord a) => a -> BinomialHeap a -> BinomialHeap a insert a = merge (singleton a) -- | /O(lg n)/. merge :: (Ord a) => BinomialHeap a -> BinomialHeap a -> BinomialHeap a merge EmptyHeap n = n merge n EmptyHeap = n merge (Heap h1) (Heap h2) = Heap \$! mergeNodes h1 h2 mergeNodes :: (Ord a, Eq a) => [HeapNode a (BinomialHeap a)] -> [HeapNode a (BinomialHeap a)] -> [HeapNode a (BinomialHeap a)] mergeNodes [] h = h mergeNodes h [] = h mergeNodes f@(h1 : t1) s@(h2 : t2) | rank h1 == rank h2 = let merged = combine h1 h2 r = rank merged in if r /= hRank t1 then if r /= hRank t2 then merged : mergeNodes t1 t2 else mergeNodes (merged : t1) t2 else if r /= hRank t2 then mergeNodes t1 (merged : t2) else merged : mergeNodes t1 t2 | rank h1 < rank h2 = h1 : mergeNodes t1 s | otherwise = h2 : mergeNodes t2 f combine :: (Ord a, Eq a) => HeapNode a (BinomialHeap a) -> HeapNode a (BinomialHeap a) -> HeapNode a (BinomialHeap a) combine h1@(HeapNode e1 n1 l1) h2 = if h1 <= h2 then HeapNode e1 (n1 + 1) (l1 ++ [Heap [h2]]) else combine h2 h1 -- | /O(lg n)/ head :: (Ord a) => BinomialHeap a -> a head EmptyHeap = error "Data.Heap: empty list" head (Heap hn) = extract \$! minimum hn -- | /O(lg n)/ tail :: (Ord a) => BinomialHeap a -> BinomialHeap a tail EmptyHeap = error "Data.Heap: empty list" tail (Heap hn) = let n@(HeapNode _ _ hd) = (minimum hn) in foldl merge (Heap (delete n hn)) hd -- | /O(n)/ fromList :: (Ord a, Eq a) => [a] -> BinomialHeap a fromList = foldl merge EmptyHeap . map singleton -- | /O(n lg n)/ toList :: (Ord a) => BinomialHeap a -> [a] toList EmptyHeap = [] toList (Heap []) = [] toList h@(Heap _) = head h : (toList \$ if null h then h else tail h)