On constructing 2-3 trees

We consider the task of constructing 2-3 trees. Given a sequence of elements we seek to build a 2-3 tree–in linear time–that contains the elements in symmetric order. We discuss three approaches: top-down, bottom-up, and incremental. The incremental approach is more flexible than the other two in that it allows us to interleave the construction work with other operations, for example, queries.