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b. The reason that the recursive algorithm is so slow is because the algorithm used to simulate recursion. To compute FN, there is one call to FN-1 and FN-2. However, since FN-1 recursively makes a call to FN-2and FN-3, there are actually two separate calls to compute FN-2. If one traces out the entire algorithm, then we can see that FN-3 is computed three times, FN-4 is computed five times, FN-5 is computed eight times, and so on. As shown Figure Q2b, the growth of redundant calculations is expensive.

b. The reason that the recursive algorithm is so slow is because the algorithm used to simulate recursion. To compute FN, there is one call to FN-1 and FN-2. However, since FN-1 recursively makes a call to FN-2and FN-3, there are actually two separate calls to compute FN-2. If one traces out the entire algorithm, then we can see that FN-3 is computed three times, FN-4 is computed five times, FN-5 is computed eight times, and so on. As shown Figure Q2b, the growth of redundant calculations is expensive.

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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b. The reason that the recursive algorithm is so slow is because the algorithm used to simulate recursion. To compute FN, there is one call to FN-1 and FN-2. However, since FN-1 recursively makes a call to FN-2and FN-3, there are actually two separate calls to compute FN-2. If one traces out the entire algorithm, then we can see that FN-3 is computed three times, FN-4 is computed five times, FN-5 is computed eight times, and so on. As shown Figure Q2b, the growth of redundant calculations is expensive. F6. „F5 F4 F3 F3 'F2 F3 F2 FI FI FO FI FO `F2 F2 FI FI FI FO FI FO FI FO Figure Q2b Write a pseudo code that will reduce the time complexity from o (2n ) to O (n) class of efficiency.
Transcribed Image Text:b. The reason that the recursive algorithm is so slow is because the algorithm used to simulate recursion. To compute FN, there is one call to FN-1 and FN-2. However, since FN-1 recursively makes a call to FN-2and FN-3, there are actually two separate calls to compute FN-2. If one traces out the entire algorithm, then we can see that FN-3 is computed three times, FN-4 is computed five times, FN-5 is computed eight times, and so on. As shown Figure Q2b, the growth of redundant calculations is expensive. F6. „F5 F4 F3 F3 'F2 F3 F2 FI FI FO FI FO `F2 F2 FI FI FI FO FI FO FI FO Figure Q2b Write a pseudo code that will reduce the time complexity from o (2n ) to O (n) class of efficiency.
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