Question: Problem 4. (20 points) Use the substitution method to obtain a tight big O upper bound on T(n) defined in each of the following recurrences:

Problem 4. (20 points) Use the substitution method to obtain a tight big O upper bound on T(n) defined in each of the following recurrences: a. T(1)=T(2)=d,T(n)=3T(3n)+d if n>2, where d is a positive constant. b. T(1)=d,T(n)=3T(2n)+dn if n>1, where d is a positive constant. Note that the substitution method consists of two steps: guess/derive the solution and use mathematical induction to show that the solution is correct (see Section 4.3 of the textbook)

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