On 7/31/2012 5:49 PM, Ian Kelly wrote:

> On Tue, Jul 31, 2012 at 3:28 PM, Ifthikhan Nazeem <(E-Mail Removed)> wrote:

>> as many as (about) 2*N - log2(N) parent child relationships

>>

>> I would like to know how did you come up with the above formula? Forgive my

>> ignorance.
By non-rigorous experimentation, which did not quite count everything.

> I come up with 2N - 2 myself. If there are N leaf nodes and N - 1

> non-leaf nodes, then there are 2N - 1 total nodes, each of which has

> one parent except for the root. That's 2N - 2 parent-child

> relationships.
That looks right. I was trying to think recursively, which in this case

is more rather than less complicated. That actually sharpens my original

point. N-1 new nodes and 2N-2 new relationships is 3N-3 new entities.

The internal node limit of N-1 only applies to full-proper-strict binary

trees without one-child internal nodes. Otherwise, a single leaf node

could have an indefinite number of ancestors.

from

https://en.wikipedia.org/wiki/Binary_tree
"A full binary tree (sometimes proper binary tree or 2-tree or strictly

binary tree) is a tree in which every node other than the leaves has two

children."

--

Terry Jan Reedy