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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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
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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.)
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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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