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To perform polynomial multiplication in C, we can represent each polynomial as a linked list of nodes, each with a coefficient and an exponent. The exponent represents the degree. The polynomial multiplication using a linked list in c has two polynomials that are stored in two linked lists, and we must perform operations to obtain the result as a polynomial multiplication. g a linked list in c has two polynomials which are stored in two linked lists, we have to perform operations to give the result as a polynomial multiplication. One of the most crucial data structures to learn while preparing for interviews is the linked list. We start with two polynomials in the form of linked lists, and we need to make a new list that contains the multiplicative product of the given polynomials.<\/p>\n
We assume two polynomials in the form of linked lists, and we need to create a new list containing the multiplicative product of the given polynomials.<\/p>\n
Let\u2019s try to understand the problem with the help of examples by referring to the websites to learn to program.<\/p>\n
Suppose the given linked lists are: Output<\/strong><\/p>\n Some other examples:<\/strong> Output 1<\/strong><\/p>\n Input 2<\/strong><\/p>\n Output 2<\/strong><\/p>\n Now I think from the above examples the problem statement is clear. So, let\u2019s see How can we do polynomial multiplication using linked list?<\/p>\n Here is the algorithm for polynomial multiplication using linked lists in C:<\/p>\n Let\u2019s dry run the polynomial multiplication using linked list with an example:<\/p>\n Poly1:<\/strong> 3x^3 + 6x^1 \u2013 9 To multiply the above polynomials Poly1<\/strong> and Poly2<\/strong> we will have to perform the following operations:<\/p>\n We have to multiply all the terms of Poly1<\/strong> one by one with every term of Poly2<\/strong>, so first, we will multiply 3×3 with every other term in Poly2<\/strong>.(result: 27×6 \u2013 24×5 + 21×4 + 6×3)<\/p>\n Now we take 6×1 and multiply it with every other term in Poly2<\/strong>.(result: 27×6 \u2013 24×5 + 21×4 + 6×3 + 54×4 \u2013 48×3 + 42×2 + 12×1)<\/p>\n Now we take -9 and multiply it with every other term in Poly2<\/strong>.(result: 27×6 \u2013 24×5 + 21×4 + 6×3 + 54×4 \u2013 48×3 + 42×2 + 12×1 \u2013 81×3 + 72×2 \u2013 63×1 \u2013 18)<\/p>\n We will remove all the duplicates, i.e., add the value of nodes with the same powers.<\/p>\n So the final result: 27×6 \u2013 24×5 + 75×4 \u2013 123×3 + 114×2 \u2013 51×1 \u2013 18<\/p>\n You can take examples by yourself to get a better understanding of the problem.<\/p>\n
\nPoly1:<\/strong> 3×3 + 6×1 \u2013 9
\nPoly2:<\/strong> 9×3 \u2013 8×2 + 7×1 + 2<\/p>\n\n
Resultant Polynomial: 27x6 \u2013 24x5 + 75x4 \u2013 123x3 + 114x2 \u2013 51x1 \u2013 18<\/code><\/pre>\n
\nInput 1<\/strong><\/p>\nPoly1: 6x1 \u2013 9\nPoly2: 7x1 + 2<\/code><\/pre>\nResultant Polynomial: 42x2 \u2013 51x1 \u2013 18<\/code><\/pre>\nPoly1: 8x1 + 7\nPoly2: 4x2 + 5<\/code><\/pre>\nResultant Polynomial: 32x3 + 28x2 + 40x1 + 35<\/code><\/pre>\nApproach and Algorithm of Polynomial Multiplication using Linked List in C<\/h3>\n
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Dry Run of Polynomial Multiplication using Linked List in C<\/h3>\n
\nPoly2:<\/strong> 9x^3 \u2013 8x^2 + 7x^1 + 2<\/p>\nCode Implementation of Polynomial Multiplication using Linked List in C<\/h3>\n\t\t\t\t\t\t