Purchase Solution

Internal Path Length (IPL) of a tree

Not what you're looking for?

Ask Custom Question

The Internal Path Length (IPL) of a tree is the sum of the length of the paths from the root to all nodes in the tree.

Use structural induction (induction over the height of the tree, h) to show that:

IPL( T ) = IPL( left( T )) + IPL( right( T )) + num_nodes( T ) - 1

Purchase this Solution

Solution Summary

This response considers an empty tree (that is, a tree without any nodes) of height 0, and a tree with just one node as of height 1.

Solution Preview

This response is intended as a mere guidance. Please express it in your own words in case you want to use it for any assignment/exam submission.

In this response, I am considering an empty tree (that is, a tree without any nodes) of height 0 and a tree with just one node as of height 1. Height of tree is indicated by "h" in following explanation.

Base case (h=0):

When there are no nodes in a tree, there are no paths and thus the sum of the length of the paths from the root to all nodes in the tree = 0.
That is to say,
h=0 => IPL(T) = 0

Base case (h=1):

When there is just one node in the tree, there will be just one path from the root to all nodes in the tree. Since this node is root ...

Purchase this Solution


Free BrainMass Quizzes
Inserting and deleting in a linked list

This quiz tests your understanding of how to insert and delete elements in a linked list. Understanding of the use of linked lists, and the related performance aspects, is an important fundamental skill of computer science data structures.

Basic Computer Terms

We use many basic terms like bit, pixel in our usual conversations about computers. Are we aware of what these mean? This little quiz is an attempt towards discovering that.

Excel Introductory Quiz

This quiz tests your knowledge of basics of MS-Excel.

C# variables and classes

This quiz contains questions about C# classes and variables.

Basic Networking Questions

This quiz consists of some basic networking questions.