HK (20 points) (a) Let f(n) be an increasing function that satisfies the recurrence relation, f(n) = af()+cn", whenever n = b , where k and a are positive integers; c and d are nonnegative real numbers. Then for f(n), state the big o expressions when (i) a 0. (b) T(n) is an increasing function that satisfies the recurrence relation, T(n) = 4T (11/3) + log2 (n) and n = 3. Use 5(a) to give a tight asymptotic bound on T(n). Hint: Let m = log2 n. HK (20 points) (a) Let f(n) be an increasing function that satisfies the recurrence relation, f(n) = af()+cn", whenever n = b , where k and a are positive integers; c and d are nonnegative real numbers. Then for f(n), state the big o expressions when (i) a 0. (b) T(n) is an increasing function that satisfies the recurrence relation, T(n) = 4T (11/3) + log2 (n) and n = 3. Use 5(a) to give a tight asymptotic bound on T(n). Hint: Let m = log2 n