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

Extracted 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="">