Chapter 4, Problem 16C

a.

Explanation of Solution

Expression evaluation:

• The given polynomial expression is,

$\text{p(x)=}{{\displaystyle {\sum }_{\text{i=0}}^{\text{n}}{\text{a}}_{\text{i}}\text{x}}}^{\text{i}}$

• Given that the given polynomial can be evaluated in “${\text{O(n}}^{\text{2}}\text{)}$” using the following algorithm,

set sum <- 0

loop for from “0” to “n”

    set sum <- a[i]*( pow(x,i))

endfor

• For each iteration, the number of multiplications in the above algorithm is increased by “1”

b.

Explanation of Solution

Characterization of number of arithmetic operations using Big-Oh notation:

• In evaluating a polynomial, exactly one multiplication and one addition operation is performed in Horner’s method...