# Boost :

Subject: Re: [boost] proposal for tree container
From: Arash Partow (arash_at_[hidden])
Date: 2009-07-16 03:12:56

Let me shorten that for you:

"A tree should be an acyclic simple graph."

Quoting Ross Levine <ross.levine_at_[hidden]>:
> 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.
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