Suppose you want to have a program that evaluates polynomials. Here's (presumably) the simplest possible program. Input: polynomial p(x) = a_0 + a_1x + a_2x^2 + + a_n x^n n, the degree alpha, a real number Output: p(alpha) (the value of p at x = alpha) Return (a_0 + middot alpha + a_2 middot alpha^2 + + a_n middot alpha^n) How many additions and multiplications occur when this code is run? What is the asymptotic time complexity? (Important: exponentiation does not count as an "atomic operation"; you need to count the number of multiplication needed.) The above is pretty wasteful; why should the computer calculate alpha^12 and later alpha^13 from scratch? Write pseudo code that saves computation time by looping through the terms of the polynomial, calculating successive powers of alpha more efficiently. What is its asymptotic time complexity