Problem 1: The Mysterious Function We have come through an old interesting function whose pseudo-code was defined as follows: Algorithm 1 MYSTERIOUS-FUNCTION(n) Require: n E Z ^n< 350 if n > 350 then return n- 47 else return MYSTERIOUS-FUNCTION(MYSTERIOUS-FUNCTION(n + 48)) end if a) Implement the algorithm in Python b) Try various inputs, within the valid rangen< 350, what have you noticed of the output? c) Prove your thoughts, hypothesis, in part (b) [Hint: use your implementation to prove a property of the output at a particular input along with inductive scheme] d) Empirically, show the performance curve of the algorithm using time measurements
Problem 1: The Mysterious Function We have come through an old interesting function whose pseudo-code was defined as follows: Algorithm 1 MYSTERIOUS-FUNCTION(n) Require: n E Z ^n< 350 if n > 350 then return n- 47 else return MYSTERIOUS-FUNCTION(MYSTERIOUS-FUNCTION(n + 48)) end if a) Implement the algorithm in Python b) Try various inputs, within the valid rangen< 350, what have you noticed of the output? c) Prove your thoughts, hypothesis, in part (b) [Hint: use your implementation to prove a property of the output at a particular input along with inductive scheme] d) Empirically, show the performance curve of the algorithm using time measurements
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
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![Problem 1: The Mysterious Function
We have come through an old interesting function whose pseudo-code was defined as
follows:
Algorithm 1 MYSTERIOUS-FUNCTION(n)
Require: n E ZAn< 350
if n > 350 then
return n- 47
else
return MYSTERIOUS-FUNCTION(MYSTERIOUS-FUNCTION(n + 48))
end if
a) Implement the algorithm in Python
b) Try various inputs, within the valid rangen< 350, what have you noticed of the
output?
c) Prove your thoughts, hypothesis, in part (b)
[Hint: use your implementation to prove a property of the output at a particular
input along with inductive scheme]
d) Empirically, show the performance curve of the algorithm using time measurements](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7bf0b604-61e9-4d3f-84d7-18cace0a0de8%2F2a49a768-c5d1-45a9-8b0b-15045a6c541f%2F0pqkf18_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 1: The Mysterious Function
We have come through an old interesting function whose pseudo-code was defined as
follows:
Algorithm 1 MYSTERIOUS-FUNCTION(n)
Require: n E ZAn< 350
if n > 350 then
return n- 47
else
return MYSTERIOUS-FUNCTION(MYSTERIOUS-FUNCTION(n + 48))
end if
a) Implement the algorithm in Python
b) Try various inputs, within the valid rangen< 350, what have you noticed of the
output?
c) Prove your thoughts, hypothesis, in part (b)
[Hint: use your implementation to prove a property of the output at a particular
input along with inductive scheme]
d) Empirically, show the performance curve of the algorithm using time measurements
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