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< 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 range n < 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 An< 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 range n < 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
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter18: Deterministic Dynamic Programming
Section: Chapter Questions
Problem 10RP
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Answer (b) and the other subparts please.
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