A heap alongside an element where that element would be the smallest if it were in the heap

Example

iex> l = [42, 16, 8, 4, 15, 23]
iex> h = Berg.heapify l
iex> {t, e} = Berg.extract h
iex> Berg.listify t
[8, 15, 16, 23, 42]
iex> e
4

A heap with the same elements as the list in question

A heap whose smallest element is the minimum of the element in question and the smallest element of the heap in question

Example

iex> l = [16, 8, 15, 23]
iex> h = Berg.heapify l
iex> i = h |> Berg.insert(4) |> Berg.insert(42)
iex> Berg.root(i)
4

A list in ascending order (w/ all the same elements as the heap)

The smallest element of the heap

Example

iex> l = [42, 16, 8, 4, 15, 23]
iex> h = Berg.heapify l
iex> Berg.root h
4

The heap in question w/o the smallest element

Example

iex> l = [42, 16, 8, 4, 15, 23]
iex> h = Berg.heapify l
iex> t = Berg.trunk h
iex> Berg.listify(t)
[8, 15, 16, 23, 42]

A Heap w/ just one element

Example

iex> Berg.zero? Berg.unary(4)
false

A zero heap

Predicate: is this the zero heap?

Example

iex> Berg.zero? Berg.zero()
true