Consider the function: f(1) = 1 n)=2-1 to n-1 n >1 a. Give a recursive algorithm which, given n, calculates f(n). b. Give and solve a recurrence, as a function of n, for the number of scalar multiplications required by your algorithm from part (a) c. Give a dynamic programming algorithm which, given n, calculates f(n) d. Find, as a function of n, the number of scalar multiplication operations required by your algorithm from part (c). e. Give an algorithm which, given n, calculates f(n) using only a linear number of scalar multiplications (this includes multiplications and divisions). Hint: First find a closed form for the value of f(n)