Let p(x) be a polynomial of degree n, that is,
a. Describe a simple O(n2)-time algorithm for computing p(x).
b. Describe an O(nlogn)-time algorithm for computing p(x), based upon a more efficient calculation of xi.
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c. Now consider a rewriting of p(x) as
Which is known as Horner’s method. Using the big-Oh notation, characterize the number of arithmetic operations this method executes.