A heap is a container supporting the insertion of elements and the extraction of the minimum element. This library models the implementation of asymptotically optimal purely functional heaps given by Brodal and Okasaki in their paper "Optimal Purely Functional Priority Queues". The Coq proof assistant has been used to prove this implementation correct. The proofs are available in the Cabal package or at http://code.google.com/p/priority-queues/.

This implementation is lazy. A strict implementation is available in this package as Data.MeldableHeap.Strict.

# Documentation

toList :: Ord a => PQ a -> [a]Source

`toList`

(O(n)) returns a list of the elements in the heap in some arbitrary order.

[] == toList empty

insert :: Ord a => a -> PQ a -> PQ aSource

`insert`

(O(1)) adds an element to a heap.

[1,2,1,0] == toList $ insert 1 $ insert 0 $ insert 2 $ insert 1 $ empty

findMin :: Ord a => PQ a -> Maybe aSource

`findMin`

(O(1)) returns the minimum element of a nonempty heap.

Just 0 == findMin $ insert 0 $ insert 2 $ insert 1 $ empty

extractMin :: Ord a => PQ a -> Maybe (a, PQ a)Source

`extractMin`

(O(lg n)) returns (if the heap is nonempty) a pair containing the minimum element and a heap that contains all of the other elements.
It does not remove copies of the minimum element if some exist in the heap.

(0,[2,1]) == let x = insert 0 $ insert 2 $ insert 1 $ empty in let Just (p,q) = extractMin x in (p,toList q)