Homework Help is Here – Start Your Trial Now!
Engineering
Computer Engineering
Arrange the following functions in a list so that each function is big-O of the next function. Label the functions from A to F in order, where A is the slowest growing and F is the fastest. log(x^220) / x 220 log(x) 220^220 x + (220 log(x)) 220^x - x^220 (x-220)!

Arrange the following functions in a list so that each function is big-O of the next function. Label the functions from A to F in order, where A is the slowest growing and F is the fastest. log(x^220) / x 220 log(x) 220^220 x + (220 log(x)) 220^x - x^220 (x-220)!

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
See similar textbooks
icon
Related questions
Question

Correct and detailed answer will be Upvoted else downvoted. Thank you!

### Big-O Complexity Ordering of Functions **Task:** Arrange the following functions in a list so that each function is *big-O* of the next function. Label the functions from **A** to **F** in order, where **A** is the slowest growing and **F** is the fastest. 1. \( \frac{\log(x^{220})}{x} \) 2. \( 220 \log(x) \) 3. \( 220^{220} \) 4. \( x + (220 \log(x)) \) 5. \( 220^x - x^{220} \) 6. \( (x-220)! \) **Big-O Notation Explanation:** - **A** (Slowest growth): \( 220^{220} \) - **B**: \( 220 \log(x) \) - **C**: \( x + (220 \log(x)) \) - **D**: \( \frac{\log(x^{220})}{x} \) - **E**: \( 220^x - x^{220} \) - **F** (Fastest growth): \( (x-220)! \) **Explanation:** 1. \( 220^{220} \): A constant function. 2. \( 220 \log(x) \): A logarithmic function. 3. \( x + (220 \log(x)) \): A linear function plus a logarithmic term. 4. \( \frac{\log(x^{220})}{x} \): This simplifies to \( \frac{220 \log(x)}{x} \), which is smaller than \( x \). 5. \( 220^x - x^{220} \): An exponential function. 6. \( (x-220)! \): A factorial function, which grows faster than exponential functions.
Transcribed Image Text:### Big-O Complexity Ordering of Functions **Task:** Arrange the following functions in a list so that each function is *big-O* of the next function. Label the functions from **A** to **F** in order, where **A** is the slowest growing and **F** is the fastest. 1. \( \frac{\log(x^{220})}{x} \) 2. \( 220 \log(x) \) 3. \( 220^{220} \) 4. \( x + (220 \log(x)) \) 5. \( 220^x - x^{220} \) 6. \( (x-220)! \) **Big-O Notation Explanation:** - **A** (Slowest growth): \( 220^{220} \) - **B**: \( 220 \log(x) \) - **C**: \( x + (220 \log(x)) \) - **D**: \( \frac{\log(x^{220})}{x} \) - **E**: \( 220^x - x^{220} \) - **F** (Fastest growth): \( (x-220)! \) **Explanation:** 1. \( 220^{220} \): A constant function. 2. \( 220 \log(x) \): A logarithmic function. 3. \( x + (220 \log(x)) \): A linear function plus a logarithmic term. 4. \( \frac{\log(x^{220})}{x} \): This simplifies to \( \frac{220 \log(x)}{x} \), which is smaller than \( x \). 5. \( 220^x - x^{220} \): An exponential function. 6. \( (x-220)! \): A factorial function, which grows faster than exponential functions.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Computer Networking: A Top-Down Approach (7th Edi…
Computer Networking: A Top-Down Approach (7th Edi…
Computer Engineering
ISBN:
9780133594140
Author:
James Kurose, Keith Ross
Publisher:
PEARSON
Computer Organization and Design MIPS Edition, Fi…
Computer Organization and Design MIPS Edition, Fi…
Computer Engineering
ISBN:
9780124077263
Author:
David A. Patterson, John L. Hennessy
Publisher:
Elsevier Science
Network+ Guide to Networks (MindTap Course List)
Network+ Guide to Networks (MindTap Course List)
Computer Engineering
ISBN:
9781337569330
Author:
Jill West, Tamara Dean, Jean Andrews
Publisher:
Cengage Learning
Concepts of Database Management
Concepts of Database Management
Computer Engineering
ISBN:
9781337093422
Author:
Joy L. Starks, Philip J. Pratt, Mary Z. Last
Publisher:
Cengage Learning
Prelude to Programming
Prelude to Programming
Computer Engineering
ISBN:
9780133750423
Author:
VENIT, Stewart
Publisher:
Pearson Education
Sc Business Data Communications and Networking, T…
Sc Business Data Communications and Networking, T…
Computer Engineering
ISBN:
9781119368830
Author:
FITZGERALD
Publisher:
WILEY
SEE MORE TEXTBOOKS