(i) Show that the recurrence T(n) = 4T(n/2) +O(n) has a solution T(n) = ?(n 2 ). (ii) The improved..

(i) Show that the recurrence T(n) = 4T(n/2) +O(n) has a solution T(n) = _(n 2 ). (ii) The improved recurrence for multiplying two n-bit numbers is given by TB(n) _ 3 ·TB(n/2) +O(n) With an appropriate terminating condition, show that the solution for the bit complexity TB(n) is O(n log2 3 ). (iii) Extend the idea of doing a two-way divide-and-conquer algorithm to multiply two n-bit numbers, to a four-way division by saving the number of lower order multiplications. Is there any advantage in extending this further ?