Given the following function that evaluates a polynomial whose coefficients are

Question

Given the following function that evaluates a polynomial whose coefficients are stored in an array:

double evaluate(double[] coefficients, double x) {

double result = coefficients[0];

double power = 1; for (int i = 1; i < coefficients.length; i++)

{ power = power * x; result = result + coefficients[i] * power; }

return result; }

Let n be the length of the array. Determine the number of additions and multiplications that are performed in the worst case as a function of n. Many thanks for the help and for clear responses as I have so much to learn!

Explanation / Answer

To determine number of addition in your polnomial equation.

double evaluate(double[] coefficients, double x) {

double result = coefficients[0];

double power = 1; for (int i = 1; i < coefficients.length; i++)

{ power = power * x; result = result + coefficients[i] * power; }

return result; }

addition will takes place exaclty to the n times (n be the length of the array)

Multiplication 2n times executed

proof:

result = result + coefficients[i] * power; \this condition accepts if the coefficient[i] = 0;so the flow starts from 0+1......n

then

result = result +0*power;

result = result

then the flow will be

=[2n+2n+................+(k-times)+2n] / k

= 2n*k/k

= 2n

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.