Question: Question 4 (Recurrence Relation. 30 points). Suppose that you have a function T(n) defined by T(1) = 1 and T(n) = 3T( In/2) + n

Question 4 (Recurrence Relation. 30 points). Suppose that you have a

Question 4 (Recurrence Relation. 30 points). Suppose that you have a function T(n) defined by T(1) = 1 and T(n) = 3T( In/2) + n for n > 1. (a) Show that. T(2")=6(3*) (Hint: Show that T(2") is between 3n and 3n+1 2n+1.) [15 points] (b) Consider the following "proof" that T(n)-O(n) (note that this contradicts part (a)) We proceed by strong induction on n. Clearly T(1) = 0(1), which gives us our base case. If we assume that T(m)-0(m) for all m

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