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: PEARSON
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### 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.
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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.
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