The third class is OrderedList, which is a utility class that contains two overloaded implementations of a

method named checkSorted, which determines whether a List object, supplied as a parameter, is in strictly

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ascending order. Both methods should be class (static) methods. The first of the overloaded methods should

accept a list that contains elements that implement Comparable. The second should instead be supplied an

additional parameter that is an object of a class that implements the Comparator interface. Refer to the

signatures of the two sort methods in the predefined Java Collections class as a model for how these two

methods should be defined. Do not duplicate code, but instead ensure that first overloaded method calls the


The fourth outer class is the class that contains the main method. The main method should allow the user to

select the input file from the default directory by using an object of the JFileChooser class. It should then

populate an ArrayList of objects of type Polynomial as it reads in the lines of the file. As the polynomials

are read in, they should also be displayed in the format provided by the toString method. Should the

InvalidPolynomialSyntax exception be thrown, it should be caught and a JOptionPane message should

be displayed containing the reason for the invalid syntax. The list of polynomials should be then checked to see

whether it is in sorted order according to two orderings. The first check is the one that uses the compareTo

method of the Polynomial class. We refer to this first ordering as the strong order. The second results from

the use of a comparator. We refer to it as the weak order. It should display whether it fails to be sorted by either

of both of the two orderings or if it is sorted according to both.

Inside the main class, a named lambda expession should be defined that implements the Comparator interface.

Its compare method should consider only the exponents and not the coefficients in comparing the polynomials,

much like how functions are categorized by Big-O.

As an example, consider the following list of polynomials:

4.0×3 + 2.5x + 8.0

5.0×4 + 5.0

4.5×4 + 5.7×2 + 8.6

This list fails to be sorted by the strong order that considers both the coefficients and exponents because the

third polynomial is less than the second because of the coefficients on the x4 terms. The coefficient on that term

in the second polynomial is 5.0, which is greater than 4.5, the coefficient on the corresponding term in the third


They are sorted by the weak order that considers only the exponents, however. The third polynomial is greater

than the second because the third has a x2 term and the second one does not.

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