Re: [boost] proposal for tree container

Subject: Re: [boost] proposal for tree container
From: Ross Levine (ross.levine_at_[hidden])
Date: 2009-07-16 02:18:28

On Thu, Jul 16, 2009 at 12:26 AM, Gottlob Frege <gottlobfrege_at_[hidden]>wrote:

> What are the requirements of 'tree-ness'?  Containers like
> std::map/list/deque/vector/... all have well defined requirements.

This is one of those questions that seems trivial but is very important to
actually lay out.

Here's what I can come up with:

1. A tree is a node-based container. If nonempty, every node has exactly one
parent, except for one node. This node is called the _root node_.
2. Every node has a finite, non-negative number of children. A node's
children is the same as the set of nodes which have that node as a parent.
Corollary: There is exactly one simple path between any two different nodes
(a simple path is a path that has no repeated vertices).
Corollary: A node's parent lies on the path between it and the root node.

Definitions:
1. If any node in tree T have at most K children, then T is a _K-ary tree_.
2. A K-ary tree is _full_ if every node has either 0 or K children.
3. The _distance_ between two nodes, A and B, is the number of edges in the
path that connects A and B.
4. The _height_ of tree T is equal to the maximum distance from the root
node to any other node.
5. The _degree_ of a node is the number of children, plus the number of
parents. Since every node (except the root) has exactly one parent, the
degree of a non-root node is the number of children plus 1.
6. A node is a _leaf_ node if it has no children.
7. An _ordered tree_ is a tree in which the position of the nodes, and the
order of a node's children, is significant.

That's all I can think of right now. Someone check my work.