Consider the following algorithm segment. For each positive integer n, let b be the number of iterations of the following while loop. while (n > 0) n := n div(3) end while Find a recurrence relation for b
Consider the following algorithm segment. For each positive integer n, let b be the number of iterations of the following while loop. while (n > 0) n := n div(3) end while Find a recurrence relation for b
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
Related questions
Question
![Consider the following algorithm segment.
For each positive integer n, let bn be the number of iterations of the following while loop.
while (n > 0)
n := n div(3)
end while
Find a recurrence relation for b
Ⓒ
To answer this question, observe that for each integer k ≥ 3, n div(3) = Lk/3]
Thus, when the algorithm segment is run for a particular k and the while loop has iterated one time, the input to the next iteration is [k/3]
It follows that the number of iterations of the loop for k is 1✔✔ more than the number of iterations for [k/3]
In other words, for every integer k ≥ 1
, we have which of the following?
bk = 1 + bkl
o b₁ = 1 + b
k/3
Lk/3]
bk = 1 + b[k/31
bk = 3 + bk/3
b₁ = 3 + blk/31
bk = 3 + b
DIK/31
In addition, the initial values for the sequence b₁,b₂, bz₁
are b₁ = 1
and b₂ = 1
©](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6079d35-87cd-40f3-9f1d-c5b52e1d4d86%2Fcb174e20-952a-4426-8bbe-399ff69b884f%2Fvthjua_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following algorithm segment.
For each positive integer n, let bn be the number of iterations of the following while loop.
while (n > 0)
n := n div(3)
end while
Find a recurrence relation for b
Ⓒ
To answer this question, observe that for each integer k ≥ 3, n div(3) = Lk/3]
Thus, when the algorithm segment is run for a particular k and the while loop has iterated one time, the input to the next iteration is [k/3]
It follows that the number of iterations of the loop for k is 1✔✔ more than the number of iterations for [k/3]
In other words, for every integer k ≥ 1
, we have which of the following?
bk = 1 + bkl
o b₁ = 1 + b
k/3
Lk/3]
bk = 1 + b[k/31
bk = 3 + bk/3
b₁ = 3 + blk/31
bk = 3 + b
DIK/31
In addition, the initial values for the sequence b₁,b₂, bz₁
are b₁ = 1
and b₂ = 1
©
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Database System Concepts](https://www.bartleby.com/isbn_cover_images/9780078022159/9780078022159_smallCoverImage.jpg)
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
![Starting Out with Python (4th Edition)](https://www.bartleby.com/isbn_cover_images/9780134444321/9780134444321_smallCoverImage.gif)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
![Digital Fundamentals (11th Edition)](https://www.bartleby.com/isbn_cover_images/9780132737968/9780132737968_smallCoverImage.gif)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
![Database System Concepts](https://www.bartleby.com/isbn_cover_images/9780078022159/9780078022159_smallCoverImage.jpg)
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
![Starting Out with Python (4th Edition)](https://www.bartleby.com/isbn_cover_images/9780134444321/9780134444321_smallCoverImage.gif)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
![Digital Fundamentals (11th Edition)](https://www.bartleby.com/isbn_cover_images/9780132737968/9780132737968_smallCoverImage.gif)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
![C How to Program (8th Edition)](https://www.bartleby.com/isbn_cover_images/9780133976892/9780133976892_smallCoverImage.gif)
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
![Database Systems: Design, Implementation, & Manag…](https://www.bartleby.com/isbn_cover_images/9781337627900/9781337627900_smallCoverImage.gif)
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
![Programmable Logic Controllers](https://www.bartleby.com/isbn_cover_images/9780073373843/9780073373843_smallCoverImage.gif)
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education