Basis: A single vertex with no edges is a full binary tree. The root is the only vertex in the tree. Recursive rule: If T1 and T2 are full binary trees, then a new tree T' can be constructed by first placing T1 to the left of T2, adding a new vertex v at the top and then adding an edge between v and the root of T1 and an edge between v and the root of T2. The new vertex v is the root of T'. Which of the following is a fully binary tree, and which is not? Explain your response. a. b. C. d.

Basis: A single vertex with no edges is a full binary tree. The root is the only vertex in the tree. Recursive rule: If T1 and T2 are full binary trees, then a new tree T' can be constructed by first placing T1 to the left of T2, adding a new vertex v at the top and then adding an edge between v and the root of T1 and an edge between v and the root of T2. The new vertex v is the root of T'. Which of the following is a fully binary tree, and which is not? Explain your response. a. b. C. d.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Concept explainers

Binomial Heap

A binomial heap is a group of binomial trees. This data structure acts as a priority queue and implements the merge operation faster.

Question

Recall that the set of full binary trees is defined as follows:

Basis: A single vertex with no edges is a full binary tree. The root is the only vertex in the tree.
Recursive rule: If T1 and T2 are full binary trees, then a new tree T' can be constructed by first
placing T1 to the left of T2, adding a new vertex v at the top and then adding an edge between v and
the root of T1 and an edge between v and the root of T2. The new vertex v is the root of T'. Which
of the following is a fully binary tree, and which is not? Explain your response.
a.
b.
C.
d.

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