polynomial representation using array program

The coefficients of the respective exponent are placed at an appropriate index in the array.

The array representation for the below polynomial expression is given below: P(x) x 2 4 x 7.

Polynomial Representation Using Linked List An important application of linked list is to represent polynomial and their manipulations.

Main advantage of linked list for polynomial representation is that it can accommodate a number of polynomials of growing sizes so that combined size does not exceed the total memory available.

The structure of a node in order to represent a term is as shown below: struct polynomial int coefficient; int exponent; struct polynomial next.

Addition of two polynomials using linked list requires comparing the exponents, and wherever the exponents are found to be same, the coefficients are added up.

For terms with different exponents, the complete term is simply added to the result thereby making it a part of addition result.

The coeff element stores the coefficient of a term in the polynomial,while the exp element stores the exponent.

After each term of first polynomial is operated upon with each term of the second polynomial, then the result has to be added up by comparing the exponents and adding the coefficients for similar exponents and including terms as such with dissimilar exponents in the result.

Consider below program to understand multiplication of two polynomial.

These could be stored in the array termArray as shown-in Figure 2.1. Note that A.Start and B.Start give the location of the first term of A and B respectively, whereas A.Finish and B.Finish give the location of the last term of A and B.

For instance. let us consider one of the simplest and most common data structures: the ordered.

We can find many examples of this data structure.

The other lists all contain items that are written in the form.

In the study of data structures we are interested-in ways of representing ordered lists so that these operations can be carried out efficiently.

We will refer to this as sequential mapping because, using the conventional array representation, we are storing a, and ai 1 into consecutive locations i and i 1 of the array.

This gives the ability to retrieve or modify the values of random elements in the list in a constant amount of time, essentially because a computer has random access to any word in its memory.

We can access the list element values in either direction by changing the subscript values in a controlled way.

It is precisely this overhead that leads us to consider non sequential mappings of ordered lists in Chapter 4.

This problem has become the classical example for motivating the US of Est-processing techniques.

Therefore, it makes sense to look at the problem and see why arrays offer only a partially adequate solution.

The problem calls for building an ADT for the representation and manipulation of symbolic polynomials.

By symbolic, we mean the list of coefficients and exponents that accompany a polynomial; e.g.

The term with exponent equal to zero does not show the variable.

There are standard mathematical definitions for the sum and product of polynomials.

The particular operations in part are a reflection of what will be needed in our subsequent programs to manipulate polynomials.

A very reasonable first decision would be to arrange unique exponents in decreasing order.

We discuss three representations that are based on this principle.

This representation leads to very simple algorithms for many of the-operations on polynomials (addition.

To see this, let us consider polynomials that to..e many zero terms.

Such polynomials are called sparse.

Fur instance. the polynomial x 1000 1 has two nonzero terms and 999 zero terms.

Consequently, 999 of the entries in coe will be zero if Representation 2 is used.

Each element in termarray is of type term, which we define below.

Since the single array termArray is to be shared by all Polynomial objects, we declare it as a static class data member of Polynomial.

The required definitions of the static class members outside the class definition are.

Note that A.Start and B.Start give the location of the first term of A and B respectively, whereas A.Finish and B.Finish give the location of the last term of A and B.

Polynomial Representation Using Array Program