procedure Horner(c, a_(0), a_(1), a_(2),… , a_(n): real numbers) y := a_(n) for i := 1 to n y := y ∗ c + a_(n−i) return y {y = a_(n)c^(n) + a_(n−1)c^(n−1) + ⋯ + a_(1)c + a_(0)} a) Evaluate 3x^(2) + x + 1 at x = 2 by working through each step of the algorithm showing the values assigned at each assignment step. b) Exactly how many multiplications and additions are used by this algorithm to evaluate a polynomial of degree n at x = c? (Do not count additions used to increment the loop variable.)

procedure Horner(c, a_(0), a_(1), a_(2),… , a_(n): real numbers) y := a_(n) for i := 1 to n y := y ∗ c + a_(n−i) return y {y = a_(n)c^(n) + a_(n−1)c^(n−1) + ⋯ + a_(1)c + a_(0)} a) Evaluate 3x^(2) + x + 1 at x = 2 by working through each step of the algorithm showing the values assigned at each assignment step. b) Exactly how many multiplications and additions are used by this algorithm to evaluate a polynomial of degree n at x = c? (Do not count additions used to increment the loop variable.)

C++ for Engineers and Scientists

4th Edition

ISBN:9781133187844

Author:Bronson, Gary J.

Publisher:Bronson, Gary J.

Chapter13: Structures

Section: Chapter Questions

Problem 4PP

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