Purely functional top-down splay heaps.

- D.D. Sleator and R.E. Rarjan, "Self-Adjusting Binary Search Tree", Journal of the Association for Computing Machinery, Vol 32, No 3, July 1985, pp 652-686. http://www.cs.cmu.edu/~sleator/papers/self-adjusting.pdf

- data Heap a
- data Splay a
- empty :: Heap a
- singleton :: a -> Heap a
- insert :: Ord a => a -> Heap a -> Heap a
- fromList :: Ord a => [a] -> Heap a
- toList :: Heap a -> [a]
- deleteMin :: Heap a -> Heap a
- null :: Heap a -> Bool
- partition :: Ord a => a -> Splay a -> (Splay a, Splay a)
- merge :: Ord a => Heap a -> Heap a -> Heap a
- minimum :: Heap a -> Maybe a
- valid :: Ord a => Heap a -> Bool
- heapSort :: Ord a => Heap a -> [a]
- showHeap :: Show a => Splay a -> String
- printHeap :: Show a => Splay a -> IO ()

# Data structures

# Creating heaps

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

Insertion.

`>>>`

True`insert 7 (fromList [5,3]) == fromList [3,5,7]`

`>>>`

True`insert 5 empty == singleton 5`

fromList :: Ord a => [a] -> Heap aSource

Creating a heap from a list.

`>>>`

True`empty == fromList []`

`>>>`

True`singleton 'a' == fromList ['a']`

`>>>`

True`fromList [5,3] == fromList [5,3]`

# Converting to a list

Creating a list from a heap. O(N)

`>>>`

`let xs = [5,3,5]`

`>>>`

True`length (toList (fromList xs)) == length xs`

`>>>`

[]`toList empty`

# Deleting

deleteMin :: Heap a -> Heap aSource

Deleting the minimum element.

`>>>`

True`deleteMin (fromList [5,3,7]) == fromList [5,7]`

`>>>`

True`deleteMin empty == empty`

# Checking heaps

See if the heap is empty.

`>>>`

True`Data.Heap.Splay.null empty`

`>>>`

False`Data.Heap.Splay.null (singleton 1)`

# Helper functions

partition :: Ord a => a -> Splay a -> (Splay a, Splay a)Source

Splitting smaller and bigger with splay. Since this is a heap implementation, members is not necessarily unique.

merge :: Ord a => Heap a -> Heap a -> Heap aSource

Merging two heaps

`>>>`

True`merge (fromList [5,3]) (fromList [5,7]) == fromList [3,5,5,7]`