Evaluating Polynomials Consider a polynomial given by p(x) = ao+a₁x+a₂x² + ... + a₂x².Consider the problem of evaluating it at some point xo, i.e. computing p(xo). (a) The naive algorithm computes independently each of the terms aixo, a2x, a3x,...,anx andthen adds all of these numbers to ao to obtain p(xo). How many sums and how many multiplicationsare used by this algorithm, as a function of n? (You can give your answer in O-notation.)

We need to find how many multiplication and sums are used for polynomial p(x)=a0+a1x+a2x2+...+anxn…

(a) -The naive algorithm computes independently each of the terms aixo, a₂x, a3x,...,anx and then adds all of these numbers to ao to obtain p(xo). How many sums and how many multiplications are used by this algorithm, as a function of n? (You can give your answer in O-notation.)

(a) -The naive algorithm computes independently each of the terms aixo, a₂x, a3x,...,anx and then adds all of these numbers to ao to obtain p(xo). How many sums and how many multiplications are used by this algorithm, as a function of n? (You can give your answer in O-notation.)

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter2: Basic Linear Algebra

Section: Chapter Questions

Problem 15RP

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Concept explainers

Rod Cutting

A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exponential time complexity. So there is a need to figure out a better method than this.

Question

Evaluating Polynomials Consider a polynomial given by p(x) = ao+a₁x+a₂x² + ... + a₂x².
Consider the problem of evaluating it at some point xo, i.e. computing p(xo).

(a) The naive algorithm computes independently each of the terms aixo, a2x, a3x,...,anx and
then adds all of these numbers to ao to obtain p(xo). How many sums and how many multiplications
are used by this algorithm, as a function of n? (You can give your answer in O-notation.)

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