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. 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 --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
