Hello, can you please help me omplete the table of this exercise. Thank you (: **Exercise 3:**Consider the algorithm below:1. \( i = n; \)2. while \( i \geq 1 \) {3. \( x = x + 1 \)4. \( i = i / 2 \)5. }Trace the algorithm, and fill the table that indicates the number of times \( x = x + 1 \) is executed for the following values of \( n \):| n | i (range) | #times x=x+1 executed ||----|--------------|------------------------|| 8 | (8, 4, 2, 1) | 4 || 16 | | || 32 | | |Find a theta notation in terms of \( n \) for the number of times the statement \( x = x + 1 \) is executed based on generalizing the results above for \( n = 2^k \). Note that if \( n = 2^k \), then \( k = \log_2(n) \).

Answered: Exercise 3: Consider the algorithm…

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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Hello, can you please help me omplete the table of this exercise. Thank you (:

**Exercise 3:**

Consider the algorithm below:

1. \( i = n; \)
2. while \( i \geq 1 \) {
3. &emsp;\( x = x + 1 \)
4. &emsp;\( i = i / 2 \)
5. }

Trace the algorithm, and fill the table that indicates the number of times \( x = x + 1 \) is executed for the following values of \( n \):

| n | i (range) | #times x=x+1 executed |
|----|--------------|------------------------|
| 8 | (8, 4, 2, 1) | 4 |
| 16 | | |
| 32 | | |

Find a theta notation in terms of \( n \) for the number of times the statement \( x = x + 1 \) is executed based on generalizing the results above for \( n = 2^k \). Note that if \( n = 2^k \), then \( k = \log_2(n) \).

Expert Solution

Step 1: Concept of Loop Analysis and Time Complexity

The concept of time complexity in computer science quantifies the duration a code or algorithm takes to run based on the input's size. It establishes an upper limit on the execution time of an algorithm. In this exercise, we aim to analyze how many times a specific statement (x=y+1) is executed relative to different input values and subsequently determine its time complexity concerning 'n.'

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