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A Sparse Implementation of ADT Polynomial

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Purpose

This programming assignment exercises dynamic memory allocation, pointer operations, and copy constructor design through designing a doubly-linked circular list with a dummy header. Using such a list, you will implement an ADT polynomial. ADT Polynomial

The specification of our ADT polynomial has the following public functions:

• degree( )

Returns the degree of a polynomial. For example, when p1 = 4x5 + 7x3 - x2 + 9, p1.degree( ) is 5.

• coefficient( power )

Returns the coefficient of the xpower term. For example, when p1 = 4x5 + 7x3 - x2 + 9, p1.coefficient(3) is 7

• changeCoefficient( newCoefficient, power )

Replaces the coefficient of the xpower term with newCoeffcient. For instance, p1.changeCoefficient(-3, 7) produces the polynomial p1 = -3x7 + 4x5 + 7x3 - x2 + 9

arithmetic operations + and -

Add two polynomials or subtract the 2nd polynomial from the 1st one. For instance, assuming p1 = 4x5 + 7x3 - x2 + 9 and p2 = 6x4 + 3x2 + 2x, then the answer of p1 + p2 must be 4x5 + 6x4 + 7x3 + 2x2 + 2x + 9. Note that you do not have to implement operations * and /.

boolean comparison operators == and !=

Returns true in == when corresponding terms of two given polynomial matches each other, otherwise false. Needless to say about !=. Note that >, >=, <, and <= are meaningless.

assignment operators =, +=, -=

Note that you need to take care of self-assignment when implementing =.

output operator <<

The output must have the form of cnx^n + cn-1x^(n-1) + ... + c1x + c0 For example, p1 = -3x7 + 4x5 + 7x3 - x2 + 9 should be printed out in the form of -3x^7 + 4x^5 + 7x^3 - x^2 + 9. Note that you don't have to implement operator>>.