In this assignment you are going to create a Java class representing single-variable polynomials. A single-variable polynomial has the general form of

a₀ + a₁x + a₂x² + ... + a_n-1x^n-1 + a_nxⁿ

Usually there are two ways to represent a polynomial in computer programs: using an array or using a linked list. For example, the polynomial 1 + 5x² + x⁵ can be represented with an array of [1, 0, 5, 0, 0, 1], or a linked list of (1,0) -> (5,2) -> (1,5). Clearly, the linked list representation is better in general because the array representation wastes lots of space to store the zero coefficients.

1. (50pt) Write a Java class Polynomial which represents a polynomial using a linked list of Terms, where each term consists of a coefficient and an exponent. Note that

• The terms in the linked list must be sorted at all time in the ascending order of the exponents.
• There cannot be two terms in the list that have the same exponent.

For example, the polynomial 1 + x + 3x⁴ should be represented as (1,0) -> (1,1) -> (3,4), but not (3,4) -> (1,0) -> (1,1) or (1,0) -> (1,1) -> (1,4) -> (2,4).

• public Polynomial() - constructs a zero polynomial (a polynomial with a single term 0).
• public void insertTerm( int coefficient, int exponent ) - inserts a new term into the polynomial.
  
• public Polynomial add( Polynomial other ) - returns a new polynomial which is the sum of the two polynomials.
• public Polynomial multiply( Polynomial other ) - returns a new polynomial which is the product of the two polynomials.
• public void print() - outputs the polynomials.
• public static void main( String args[] ) - creates a few Polynomial objects and test each method properly.