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< 251 if n > 250 then
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< 251 if n > 250 then
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Please I want the code in python and the ploting of the curve of the empirical analysis by matplotlib and done the inductive proof scheme, so please follow the same instructions written in the question.
![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 EZAN< 251
if n > 250 then
return n - 43
else
return MYSTERIOUS-FUNCTION(MYSTERIOUS-FUNCTION(n + 44))
end if
a) Implement the algorithm in Python
b) Try various inputs, within the valid range n < 251, 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 proof 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%2F216565d9-b9f9-4481-95f5-2b304f022838%2F5da991d2-9981-4b31-b8cd-bebe6e481c2c%2Fx37t29b_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 EZAN< 251
if n > 250 then
return n - 43
else
return MYSTERIOUS-FUNCTION(MYSTERIOUS-FUNCTION(n + 44))
end if
a) Implement the algorithm in Python
b) Try various inputs, within the valid range n < 251, 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 proof scheme]
d) Empirically, show the performance curve of the algorithm using time measurements
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