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Exercise 3: Consider the algorithm below: 1. in; 2. while (iz 1){ 3. x=x+1 4. i=i/2} Trace the algorithm, and fill the table that indicates the number of times x-x+1 for the following values of n C00m n 8 16 79 32 i (range) (8,4,2,1) #times x=x+1 executed 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". Note that if n=2", then k-log2(n).

Exercise 3: Consider the algorithm below: 1. in; 2. while (iz 1){ 3. x=x+1 4. i=i/2} Trace the algorithm, and fill the table that indicates the number of times x-x+1 for the following values of n C00m n 8 16 79 32 i (range) (8,4,2,1) #times x=x+1 executed 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". Note that if n=2", then k-log2(n).

Database System Concepts
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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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 \( k = \log_2(n) \).
Transcribed Image Text:**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 \( k = \log_2(n) \).
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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