How many elements in the heap of 200 elements do not have any child?

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
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How many elements in the heap of 200 elements do not have any child?

Expert Solution
Step 1

Heap is a complete binary tree.

Leaf elements are those elements that do not have any child.

The height of a complete binary tree with n elements=floor(log2n)

In the given problem, 

                                n=200

So, the height of the complete binary tree with 200 elements=floor(log2200)

                                                                                             =7

A complete binary tree with height h contains a maximum 2h+1-1number of elements

So, a complete binary tree with height 7 contains a maximum 27+1-1=255 number of elements

In the problem, the heap tree contains 200 elements. So, the last level is not completely filled.

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