Data Structures (in Java) - Ch. 2 Programming Assignment 2-3

We can represent a polynomial as a list of terms, where the terms are in decreasing order by the exponent.

• You should define a class Term that contains data fields coef and exponent. For example, 5x⁴ has a coef value of 5 and an exponent value of 4.
• To add two polynomials, you traverse both lists and examine the two terms at the current iterator position.
• If the exponent of one is smaller than the exponent of the other, then insert the larger one into the result and advance that lists iterator.
• If the exponents are equal, then create a new term with that exponent and the sum of the two coefficients, and advance both iterators. For example: 3x⁴ + 2x² + 3x + 7 added to 2x³ + -5x + 5 is 3x⁴ + 2x³ + 2x² + -2x +12.

Write a polynomial class with an inner class Term.

• The polynomial class should have a data field terms that is of type LinkedList .
• Provide an addpoly method and a readpoly method.
• Method readypoly reads a string representing a polynomial such as 2x³ + -4x² and returns a polynomial list with two terms.
• You also need a toString method for class Term and Polynomial that would display this stored polynomial 2x^3 + 4x^2.

Provide a multiple method for your polynomial class.

• To multiply, you iterate through polynomial A and then multiply all terms of polynomial B by the current term of polynomial A.
• You then add each term you get by multiplying two terms to the polynomial result.
• Hint: to multiply two terms, multiply their coefficients and add their exponents. For example, 2x³ x 4x² is 8x⁵.