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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 Z An < 222 if n 2 222 then return n – 14 else return MYSTERIOUS-FUNCTION(MYSTERIOUS-FUNCTION(n + 15)) end if

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

Database System Concepts
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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solve this problem, please. Thanks in advance

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
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 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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