This example shows how to multiply two polynomials using C program. For multiplication of two polynomials we will use here Structure, which is a composite data type, in which we can define all data types under the same name or object. Size of the Structure is determined by computing the size of all data types, plus any internal padding. The key word struct is used to declare the Structure. A Polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

For example, the addition result of two polynomials -5+4x and -6+3x+2x^2 would be 30x^0-39x^1+2x^2+8x^3

The complete example would be as given below

/* 
 * File:   polynomialMul.c
 * Author: https://www.roytuts.com
 *
 */

#include <stdio.h>
#include <stdlib.h>

typedef struct termType {
    int coefficient, exponent;
} termType;

typedef struct poly {
    termType terms[100];
    int noOfTerms;
} poly;

poly * addPoly(poly *p1, poly *p2) {
    int i, j, k, l;
    poly *p3 = malloc(sizeof (poly));

    for (i = 0, j = 0, k = 0; ((i < p1->noOfTerms)&&(j < p2->noOfTerms)); k++) {
        if (p1->terms[i].exponent == p2->terms[j].exponent) {
            p3->terms[k].coefficient = p1->terms[i].coefficient + p2->terms[j].coefficient;
            p3->terms[k].exponent = p1->terms[i].exponent;
            i++;
            j++;
        } else if (p1->terms[i].exponent < p2->terms[j].exponent) {
            p3->terms[k].coefficient = p1->terms[i].coefficient;
            p3->terms[k].exponent = p1->terms[i].exponent;
            i++;
        } else {
            p3->terms[k].coefficient = p2->terms[j].coefficient;
            p3->terms[k].exponent = p2->terms[j].exponent;
            j++;
        }
    }

    if (i < p1->noOfTerms) {
        for (l = i; l < p1->noOfTerms; l++, k++) {
            p3->terms[k].coefficient = p1->terms[l].coefficient;
            p3->terms[k].exponent = p1->terms[l].exponent;
        }
    } else {
        for (l = j; l < p2->noOfTerms; l++, k++) {
            p3->terms[k].coefficient = p2->terms[l].coefficient;
            p3->terms[k].exponent = p2->terms[l].exponent;
        }
    }
    p3->noOfTerms = k;

    return p3;
}

poly * mulPoly(poly *p1, poly *p2) {
    int i, j, k;
    poly *p3 = malloc(sizeof (poly));
    poly *p4 = malloc(sizeof (poly));
    poly *p5 = malloc(sizeof (poly));

    p3->noOfTerms = 0;
    p4->noOfTerms = 0;
    p5->noOfTerms = 0;

    for (i = 0; i < p1->noOfTerms; i++) {
        for (j = 0, k = 0; j < p2->noOfTerms; j++, k++) {
            p3->terms[k].coefficient = p1->terms[i].coefficient * p2->terms[j].coefficient;
            p3->terms[k].exponent = p1->terms[i].exponent + p2->terms[j].exponent;
        }
        p3->noOfTerms = k;
        p5 = addPoly(p3, p4);
        p4 = p5;
    }
    return p4;
}

void print(poly *p) {
    int i, c;
    c = 0;
    for (i = 0; i < p->noOfTerms; i++) {
        if (c != 0 && c < p->noOfTerms && p->terms[i].coefficient > 0) {
            printf("+");
        }
        printf("%dx^%d", p->terms[i].coefficient, p->terms[i].exponent);
        c++;
    }
}

int main() {
    termType t1, t2, t3, t4, t5, t6;
    poly *p1, *p2, *p3;

    p1 = malloc(sizeof (poly));
    p2 = malloc(sizeof (poly));

    t1.coefficient = -5;
    t1.exponent = 0;
    t2.coefficient = 4;
    t2.exponent = 1;
    //t3.coefficient = 1;
    //t3.exponent = 4;

    t4.coefficient = -6;
    t4.exponent = 0;
    t5.coefficient = 3;
    t5.exponent = 1;
    t6.coefficient = 2;
    t6.exponent = 2;

    p1->terms[0] = t1;
    p1->terms[1] = t2;
    //p1->terms[2] = t3;
    p1->noOfTerms = 2;

    p2->terms[0] = t4;
    p2->terms[1] = t5;
    p2->terms[2] = t6;
    p2->noOfTerms = 3;

    p3 = mulPoly(p1, p2);

    print(p3);
}

Thanks for reading.

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