The recurrence we found for the number of comparisons performed by mergesort was T(1) = 0, and for all ? > 1, T(n) = T ([n/2]) + ([n/2]) + n. We used the master theorem to show that T(n) = Theta(n log n). Show that whenever ? = 2^k, with k an integer, T(n) is exactly nlog2n. Calculate the exact values of T(n) for all integers ? up to 30 or so, until you detect a pattern that allows you to calculate T(n) without recursive calculations. Show how to find T(1000000) exactly with a minimum of calculation (and no programming)