Wow...Got it. My refined understanding,
1) An empty tree is haveing zero nodes. Fine. Case (a) ====== I have only 1 node in a binary tree. That means it is a binary tree with 2 empty subtrees. Case (b) ====== I have only 2 nodes in a binary tree. That means it is a binary tree with 1 left subtree and 0 right subtree. Fine. Got a question here. Why one always makes the left node first and then the right node? 2) In literature they talk about Nodes. Nodes can have anything stored on them. Thanks Dave for explaining with a nice example. On Jun 3, 8:58 pm, Dave <[EMAIL PROTECTED]> wrote: > Does that aspect of his question matter as to whether the tree is a > binary tree or a general tree? The point is that the node and the > value associated with the node are entirely different things. > > For that matter, my uncle's family tree is not a tree at all, since he > has two paths up the tree to the same ancestor. This happened because > someone in one subtree of that person married someone in anther > subtree many generations later. > > Dave > > On Jun 3, 10:48 am, "Ajinkya Kale" <[EMAIL PROTECTED]> wrote: > > > > > On Tue, Jun 3, 2008 at 1:35 PM, Dave <[EMAIL PROTECTED]> wrote: > > > > The definition is recursive. The empty binary tree is the base case > > > for the recursion. If a binary tree couldn't be empty, then all binary > > > trees would have to be infinite. One way to think of this is that the > > > left and right subtrees of the leaf nodes of the tree are empty trees. > > > > Don't confuse the nodes with any values associated with the nodes. The > > > nodes are divided into three disjoint subsets, but duplicate values do > > > not have to be divided correspondingly. Think of a tree describing > > > family relationships. I have a second cousin whose name is the same as > > > mine. There would be two nodes distinct nodes in the tree with value > > > "David S Dodson." These nodes would have different parents and > > > grandparents, but the same great-grandparents. > > > Nice example. Nevertheless family tree are suitable examples for general > > trees rather than binary trees , isnt it ? > > > > Dave > > > > On Jun 3, 5:55 am, Vinodh <[EMAIL PROTECTED]> wrote: > > > > Started reading about Binary Trees and got the following questions in > > > > mind. Please help. > > > > > Definition of a Binary Tree from "Data Structures using C and C++ by > > > > Tanenbaum" goes like this, > > > > "A binary tree is a finite set of elements that is either empty or is > > > > partitioned into three disjoint subsets. The first subset contains a > > > > single element called the 'Root' of the tree. The other two subsets > > > > are themselves binary trees, called the 'Left' and 'Right' subtrees of > > > > the original tree." > > > > > My Questions: > > > > 1) Why they talk about a binary tree that is totally empty? I mean a > > > > binary tree with Zero elements? > > > > > 2) A binary tree is partioned into three disjoint subsets. That means > > > > all the elements in a binary tree should be unique? Duplicate elements > > > > are allowed within a subtree? Any significance of this? > > > > > Thanks, > > > > Vinodh > > > -- > > Ciao, > > Ajinkya- Hide quoted text - > > > - Show quoted text -- Hide quoted text - > > - Show quoted text - --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/algogeeks -~----------~----~----~----~------~----~------~--~---
