Problem 1: The Mysterious Function We have come through an old interesting function whose pseudo-code was defined as follows: Algorithm 1 MYSTERIOUS-FUNCTION(1n) Require: n E Z An< 222 if n > 222 then return n- 14 else return MYSTERIOUS-FUNCTION(MYSTERIOUS-FUNCTION(n + 15)) end if a) Implement the algorithm in Python b) Try various inputs, within the valid range n< 222, 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(1n) Require: n E Z An< 222 if n > 222 then return n- 14 else return MYSTERIOUS-FUNCTION(MYSTERIOUS-FUNCTION(n + 15)) end if a) Implement the algorithm in Python b) Try various inputs, within the valid range n< 222, 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

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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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 e Z An< 222
if n 2 222 then
return n – 14
else
return MYSTERIOUS-FUNCTION(MYSTERIOUS-FUNCTION(n + 15))
end if
a) Implement the algorithm in Python
b) Try various inputs, within the valid range n < 222, 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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