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3. (a) Consider the following algorithm. Input: Integers n and a such that n > 0 and a > 1. (1) If 0

3. (a) Consider the following algorithm. Input: Integers n and a such that n > 0 and a > 1. (1) If 0

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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3. (a) Consider the following algorithm. Input: Integers n and a such that n 20 and a > 1. (1) If 0 <n< a, stop. Otherwise, go to (2). (2) Replace n by n - a and go back to (1). How many times does this algorithm enter step (2)? Explain your answer. (Hint: the answer depends on both n and a, i.e. you should calculate the number of times that the algorithm enters step (2) as a function of n and a.) (b) Find an infinite set of functions fi(n), f2(n), fa(n), …. such that all of the following properties are satisfied: 1 • Each of the functions f1(n), f2(n), f3(n), .. grows faster than the function 2n
Transcribed Image Text:3. (a) Consider the following algorithm. Input: Integers n and a such that n 20 and a > 1. (1) If 0 <n< a, stop. Otherwise, go to (2). (2) Replace n by n - a and go back to (1). How many times does this algorithm enter step (2)? Explain your answer. (Hint: the answer depends on both n and a, i.e. you should calculate the number of times that the algorithm enters step (2) as a function of n and a.) (b) Find an infinite set of functions fi(n), f2(n), fa(n), …. such that all of the following properties are satisfied: 1 • Each of the functions f1(n), f2(n), f3(n), .. grows faster than the function 2n
grows faster than each of the functions fi(n), f2(n), f3(n),.... • For every integer i > 2, the function f:(n) grows faster than the function fi-1(n). The function 2n Note: you must write down formulas for your functions (in terms of n) and prove that your functions have the required properties. (If you do not remember what "grows faster" means, see Definition 4.5 in the coursebook.)
Transcribed Image Text:grows faster than each of the functions fi(n), f2(n), f3(n),.... • For every integer i > 2, the function f:(n) grows faster than the function fi-1(n). The function 2n Note: you must write down formulas for your functions (in terms of n) and prove that your functions have the required properties. (If you do not remember what "grows faster" means, see Definition 4.5 in the coursebook.)
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