(10 points)
The classic way to evaluate a polynomial is Horner's Rule. Horner's rule
can be stated recursively as follows:
Let p(x) = a0 + a1*x + a2*x^2 + ... + ak*x^k be a polynomial. Note
that * means "times"and ^ means "to the power". To evaluate the polynomial
p(x) at c, first let r be the result of evaluating the polynomial
a1 + a2*x + a3*x^2 + ... + ak*x^(k-1) at c, then evaluate the final result
as a0 + c*r.
- Design recursive pseudocode function
which more precisely defines Horner's Rule.
Assume that the coefficients of the polynomial is stored in a linked
list with a0 stored at the head of the list.
Your function should have two arguments one for the number c and
the other for the polynomial. The return value should be a number.
- Design an iterative algorithm (no recursion)
and its pseudocode for Horner's Rule.
Your iterative algorithm should be a simple for loop. In this
case assume that the polynomial is stored in an array, not a linked
list. The array value A[0] = a0, A[1] = a1, and so on.