Design a brute-force algorithm for computing the value of a polynomial (in the image below) at a given point x0 and determine its worst-case efficiency class.   Algorithm BruteForcePolynomialEvaluation(P[0..n], x)  //The algorithm computes the value of polynomial P at a given point x //by the “highest-to-lowest term” brute-force algorithm  //Input: Array P[0..n] of the coefficients of a polynomial of degree n,  // stored from the lowest to the highest and a number x  //Output: The value of the polynomial at the point x  If the algorithm you designed is in O(n^2), design a linear algorithm for this problem.  Is it possible to design an algorithm with a better than linear efficiency for this problem? Why?

Database System Concepts
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ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Chapter1: Introduction
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Design a brute-force algorithm for computing the value of a polynomial (in the image below) at a given point x0 and determine its worst-case efficiency class.  

Algorithm BruteForcePolynomialEvaluation(P[0..n], x)

 //The algorithm computes the value of polynomial P at a given point x

//by the “highest-to-lowest term” brute-force algorithm 

//Input: Array P[0..n] of the coefficients of a polynomial of degree n, 

// stored from the lowest to the highest and a number x 

//Output: The value of the polynomial at the point x 

  1. If the algorithm you designed is in O(n^2), design a linear algorithm for this problem. 
  2. Is it possible to design an algorithm with a better than linear efficiency for this problem? Why?

 

p(x) = anx" +an-1x"-1
+... +a1x + ao
%3D
Transcribed Image Text:p(x) = anx" +an-1x"-1 +... +a1x + ao %3D
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