Generate the polynomial coefficients and the point to be evaluated

)

Each coefficient should be an integer between 1 and 100. You use an integer array

to store all the coefficients generated, and the size of the array is determined by the

degree of the polynomial. Based on my experiments, a good choice of the degree

number should be between 100

,

000 and 200

,

000.

The value of the variable

x

should be a

double

between

0.0

and

1.0

, exclusive.

The reason to choose the value in this range is simple: We can easily avoid the

overflow

problem. If the value is

0.0

or

1.0

, the evaluation time is very fast, and

it does not reflect the general case. When you detect if this case happens, call the

1

random function another time.

3. (

User's interface

)

In order to provide the users a convenient way to test your program, you should

create a simple

user's interface

. When a user runs your program, you display a

simple menu by printing out appropriate messages on the screen. Your program

asks the user to choose one of the three methods to evaluate the polynomial using

1, 2,

or

3

to represent the selected method. Put your testing part in a

while

loop,

so that the user can test all the methods in one execution, and use

0

for the exit code.

4. (

Monomial evaluation

)

In the first two methods, we use the

straightforward

method to evaluate the polyno-

mials, in which we need to evaluate the monomials

x

k

. Our first algorithm just uses

direct multiplications in a for-loop. Our second algorithm uses a power function,

such as

Math.pow(x, k)

, to calculate the monomials.

5. (

Horner's Rule

)

Our third algorithm uses the

Horner's Rule

to evaluate the whole polynomial with-

out calculating the monomials. The main objective of this project is to see how

much faster this algorithm is comparing with the first two simple algorithms.

6. (

Output

)

Before you display the menu on the screen, you print out the degree number of the

polynomial first, because this number only needs to be displayed once. Then for

each algorithm, you need to display the result first, and then the execution time

in milliseconds. We expect that all three algorithms produce the same evaluation

result. After the user enters

0

code to terminate the program, display a (

Bye!

)

message to tell the user that the whole program completes the execution.