polynomial representation using array program

If the new coefficient is equal to 0, then the term is dropped, and if it is not zero, it is inserted at the end of the new linked list containing the resulting polynomial. If the two exponents are equal, the coefficients are added to create a new coefficient. We take corresponding terms of the list P and Q and compare their exponents. To add two polynomials, we traverse the list P and Q. Such representation of polynomial using linked lists makes the operations like subtraction, addition, multiplication, etc., on polynomial very easy. Moreover, the terms are stored to decrease exponents in the linked list.

Observe that the number of nodes equals the number of terms in the polynomial. On representing this polynomial using a linked list, we have Here 7, 15, -2, and 9 are the coefficients, and 4,3,2,0 are the exponents of the terms in the polynomial. The structure of a node of a linked list that represents a polynomial is shown below:Ĭonsider a polynomial P(x) = 7x 2 + 15x 3 - 2 x 2 + 9.

The third part, LINK points to the next term (next node).

The second part contains the value of the exponent.

The first part contains the value of the coefficient of the term.

The coefficient takes a value of 1.Įach node of a linked list representing polynomial constitute three parts:

Also, no two terms have the same exponent, and no term has a zero coefficient and without coefficients. To get better efficiency in processing, we assume that the term of every polynomial is stored within the linked list in the order of decreasing exponents. While representing a polynomial using a linked list, each polynomial term represents a node in the linked list. This representation makes polynomial manipulation efficient.

It can be represented using a linked list. A polynomial is a collection of different terms, each comprising coefficients, and exponents. Polynomials are an important part of mathematics not inherently supported as a data type by most languages. Polynomial manipulations are one of the most important applications of linked lists. Linked list is used in a wide variety of applications such as What do you mean by Linked list?Ī linked list is a linear data structure consisting of elements called nodes where each node is composed of two parts: an information part and a link part, also called the next pointer part. In this article, we will understand the linked list applications in detail.

Polynomial representation using array program