The conventional algorithm for evaluating a polynomial a„x" + an-x-1+... + a,x + ao at x = c can be expressed in pseudocode by procedure polynomial(c, a̟, a̟, .., an: real numbers) power := 1 Y := ao for i= 1 to n роwer» pouиer * c у3у +а; *роwer return y {y = ɑņc" + an-1c"-1 + .. + a,c + ao} where the final value of y is the value of the polynomial at x = c. a) Evaluate 3x² +x + 1 at x = 2 by working through each step of the algorithm showing the values assigned at each assignment step. ous exercise. It is called Horner's method. This pseudocode shows how to use this method to find the value of a,„" + an-pr"™-+ + a;x + a, atx = c. Pa; procedure Horner(c, ag. aq. ɑz .., q : real numbers) y= an for i= 1 to n y= y*c+ an-i return y {y = a,c" + Ar-1 .. + q̟c+ ag}

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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In this lab you will explore the conventional means to evaluate a polynomial and compare its efficiency
to Horner's method (see textbook, page 242).
1) Implement each method as a C++ function
2) Time each method against a set of test polynomials to collect some empirical data.
Recommend using C++'s high resolution clock, for an example see time point:
https://www.geeksforgeeks.org/chrono-in-c/
3) Submit your code as a .cpp file and your findings as a PDF file.
The conventional algorithm for evaluating a polynomial a„x" +
+ ... + a,x + a, at x = c can be expressed in pseudocode by
procedure polynomial(c, a̟, a̟ .., an: real numbers)
рошer3D 1
Y:= ao
for i:= 1 to n
power := power * c
Y := Y + a; * power
return y {y = Anc" + an-1c-1 + ... + a,c + ao}
where the final value of y is the value of the polynomial at x = c.
a) Evaluate 3x² + x + 1 at x = 2 by working through each step of the algorithm showing the values assigned at each assignment step.
ous
exercise. It is called Horner's method. This pseudocode shows how to use this method to find the value of a,„x" + an-r-1 + .. + a,x + a, atx = c.
Pa
procedure Horner(c, ag, a, ɑz .., q : real numbers)
y = an
for i=1 to n
y= y* c + an-i
return y {y = a,c" + an-1c"-1 + .. + a,c + ag}
a) Evaluate 3x² + x + 1 at x = 2 by working through each step of the algorithm showing the values assigned at each assignment step.
Transcribed Image Text:In this lab you will explore the conventional means to evaluate a polynomial and compare its efficiency to Horner's method (see textbook, page 242). 1) Implement each method as a C++ function 2) Time each method against a set of test polynomials to collect some empirical data. Recommend using C++'s high resolution clock, for an example see time point: https://www.geeksforgeeks.org/chrono-in-c/ 3) Submit your code as a .cpp file and your findings as a PDF file. The conventional algorithm for evaluating a polynomial a„x" + + ... + a,x + a, at x = c can be expressed in pseudocode by procedure polynomial(c, a̟, a̟ .., an: real numbers) рошer3D 1 Y:= ao for i:= 1 to n power := power * c Y := Y + a; * power return y {y = Anc" + an-1c-1 + ... + a,c + ao} where the final value of y is the value of the polynomial at x = c. a) Evaluate 3x² + x + 1 at x = 2 by working through each step of the algorithm showing the values assigned at each assignment step. ous exercise. It is called Horner's method. This pseudocode shows how to use this method to find the value of a,„x" + an-r-1 + .. + a,x + a, atx = c. Pa procedure Horner(c, ag, a, ɑz .., q : real numbers) y = an for i=1 to n y= y* c + an-i return y {y = a,c" + an-1c"-1 + .. + a,c + ag} a) Evaluate 3x² + x + 1 at x = 2 by working through each step of the algorithm showing the values assigned at each assignment step.
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