Chapter 2, Problem 3P

(a)

Program Plan Intro

To find the running time of the Horner’s rule in $\Theta$ -notation.

(b)

Program Plan Intro

To write the pseudo code of the naïve polynomial evaluation to compute each term of the polynomial from scratch and also find the running time of the algorithm and compare it with Horner’s rule.

(c)

Program Plan Intro

To interpret a summation with no terms as equaling 0 and also show that at termination $y={\displaystyle \sum _{k=0}^n{a}_k{x}^k}$ .

(d)

Program Plan Intro

To conclude that the given code fragment correctly evaluates a polynomial characterized by the coefficients $a_0,a_1,\mathrm{...},a_n$ .