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For each pair (f, g) of functions below, state whether either, neither, or both of the ollowing are true: f(n) = 0(g(n)), g(n) = O(f(n)). Briefly justify your answers. . f(n) = ln(n), g(n) = lg(n). Note that In denotes log to the base e and lg denotes log to the base 2. o. f(n) = 3", g(n) = n² = n100 c. f(n) = 3", g(n) = 2" d. f(n) 1000n? + 2000n + 4000, g(n) = 3n³ + 1 ||

For each pair (f, g) of functions below, state whether either, neither, or both of the ollowing are true: f(n) = 0(g(n)), g(n) = O(f(n)). Briefly justify your answers. . f(n) = ln(n), g(n) = lg(n). Note that In denotes log to the base e and lg denotes log to the base 2. o. f(n) = 3", g(n) = n² = n100 c. f(n) = 3", g(n) = 2" d. f(n) 1000n? + 2000n + 4000, g(n) = 3n³ + 1 ||

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...
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Consider the following code fragment. Compute the worst-case time complexity in terms of n. for (i=0; i<=n-1; i++){ for (j=i+1; j<=n-1; j++){ body of loop } } For each pair (f, g) of functions below, state whether either, neither, or both of the following are true: f(n) = 0(g(n)), g(n) O(f(n)). Briefly justify your answers. a. f(n) = In(n), g(n) = lg(n). Note that In denotes log to the base e and lg denotes log to the base 2. b. f(n) = 3", g(n) = n100 c. f(n) = 3", g(n) = 2" d. f(n) = 1000n² + 2000n + 4000, g(n) = 3n3 + 1
Transcribed Image Text:Consider the following code fragment. Compute the worst-case time complexity in terms of n. for (i=0; i<=n-1; i++){ for (j=i+1; j<=n-1; j++){ body of loop } } For each pair (f, g) of functions below, state whether either, neither, or both of the following are true: f(n) = 0(g(n)), g(n) O(f(n)). Briefly justify your answers. a. f(n) = In(n), g(n) = lg(n). Note that In denotes log to the base e and lg denotes log to the base 2. b. f(n) = 3", g(n) = n100 c. f(n) = 3", g(n) = 2" d. f(n) = 1000n² + 2000n + 4000, g(n) = 3n3 + 1
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