algorithms

Given the following recursive function: f(1)=1 f(2)=2 f(n) = f (13+5 (1:) for all multiples of 2 greater than 2 Answer 1-4 1. Write a recursive algorithm compute f(n). 2. Give a non-recursive optimal algorithm (i.e. Dynamic programming algorithm) for computing the function f(n). What is the run time for your algorithm in terms of O-notation? 3. Which is faster the recursive algorithm or the dynamic programming algorithm? Justify your I 4. Does dynamic programming always yield to an optimal solution