For each of the following recurrences, give an expression for the runtime T (n) if the recurrence can be solved with the Master Theorem. Otherwise, indicate that the Master Theorem does not apply. (i) T (n) = T (n/2) + T(n/2) + T(n/2) + n2 (ii) T (n) = 0.5T (n/2)+ 1/n (iii) T (n) = 3T (n/3) + n (iv) T (n) = 4T (n/2) + nlogn

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Recurrence relation

A recurrence relation or recursive relation is an equation that represents a function in terms of the values of its smaller inputs. Every recurrence relation T(n) is a recursive function of integer n and consists of a base case and a recursive case.