Creating a new kind of set

Creating a whole new collection requires some preliminary work. We need to have new algorithms or new internal data structures that offer significant improvements over the built-in collections. It's important to do thorough "Big-O" complexity calculations before designing a new collection. It's also important to use timeit after an implementation to be sure that the new collection really is an improvement on the built-in class.

We might, for example, want to create a binary search tree structure that will keep the elements in a proper order. As we want this to be a mutable structure, we'll have to perform the following kinds of design activities:

• Design the essential binary tree structure

• Decide which structure is the basis: MutableSequence, MutableMapping, or MutableSet

• Look at the special methods for the collection in the collections.abc section of the Python Standard Library documentation, section 8.4.1.

A binary search tree has nodes with two branches: a "less...