   Chapter 10.5, Problem 4TY ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# If k is a positive integer and T is a full binary tree with k internal vertices. then T has a total of _____ vertices and has leaves.

To determine

To fill the blanks in the statement, “If k is a positive integer and T is a full binary tree with k internal vertices, then T has a total of _____ vertices and has _____ leaves.”

Explanation

Given information:

In the full binary tree T, there are k number of internal vertices.

In a full binary tree, every vertex has a parent vertex except the root vertex. Hence, the total number of vertices are one greater than the number of all vertices that have a parent. Since every parent has exactly two children vertices, for k number of internal vertices, we can obtain 2k number of vertices that have a parent.

Then, the total number of vertices are 2k+1.

Also, the terminal vertices in a rooted tree are called as leaves. Then, from among all he vertices in a full binary tree, there are only internal vertices or terminal vertices(leaves).

Hence,

The total number of= The number of internal + The number of�

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