CS102- Algorithms and Programming II Lab 01 Solved

CS102- Algorithms and Programming II 
Lab 01

Lab Objectives: Arrays​ 

Notes:

●      For all labs in CS 102, your solutions must conform to these CS101/102 styl​          e guidelines.​  

●      Create a Java Project named Lab01. Put all of your classes in this project.

●      Remember to include javadoc​            ​ comments​     for each class and method.​   

●      Upload your solution as a single .zip file​       to the Lab01 assignment for your section​      by the end of your section’s lab session on the week of February 8. You must use the following naming convention: Lab01_Surname_FirstName.zip where Surname is your family name and FirstName is your first name. You may upload multiple times; the last upload will be considered.  

Question In​ this lab, you are going to implement2 an Polynomial​ class that​ represents polynomials of the form P(x) = c​0 + c​1x + c​2x​ ​ + ... + c​nx​

                                                     ​           ​              ​                          ​

The class should do the following:

1.     Polynomial class should contain its coefficients in an array. Use double type for​  coefficients.

2.     Include a constructor that takes an integer, d​ , and a double, ​          c​ , to construct​             polynomials of the form P(x) = cx​ ​d​.

Include a default constructor that takes no argument and constructs a zero polynomial (P(x) = 0​ ).​

3.     Include another constructor that takes an array of coefficients and produces a polynomial with these coefficients.

4.     Add a getter method for a coefficient which takes degree and returns the coefficient of the term with that degree.

5.     Include getDegree()​            method that returns the degree of the polynomial. Degree of a​        polynomial is the degree of highest non-zero term in a polynomial. For example, the degree of polynomial P(x) = 4 - 5x​         ​2​ + 12x​3​ is 3. You can assume that the degree of zero polynomial is 0.

6.     Add toString()​        ​ method that returns ​ String​            representation of the polynomial.​       Zero terms in the polynomial should not be included in the string.

For instance, for the polynomial P(x)​ = 4 – 5x​2 + 2x​3​, toString()​ method should return “4.0 - 5.0x^2 + 2.0x^3”​     .​

7.     Add eval( double x )​       method that evaluates the polynomial at ​     x ​        and returns​      the result.

1.     Use Math.pow( double a, double b )​           method to evaluate each term​ individually and the polynomial as a sum of the terms.

2.     Implement another method, eval2( double x )​  that evaluates the​       polynomial using Horner’s method. Horner’s method is an efficient way of evaluating polynomials at a given point. A polynomial P(x) = c​         ​0 + c​   ​1x +​       c​2x​ 2​ ​ + ... + c​nx​ n​ ​ can be evaluated at x​ ​0 by rearranging computation as​             

P(x​0)​ = (( ... ( (c​n)​ x​0 + c​ n-1​​) x​0 ... + c​ 4​ ) x​ ​0​ + c ​3)​ x​0 + c​ ​1)​ x​0 + c​ ​0 and​ computing the result from the innermost parentheses to outwards. 

8.     Implement a class called PolynomialTester​         to test your ​    Polynomial​   class.​