# Polynomial Addition Using Structure [with C program]

Learn: How to add two polynomials using structures in C? This article explains how to implement structure of polynomial, algorithm and C program for polynomial addition.
Submitted by Abhishek Jain, on June 20, 2017

## What is Polynomial?

A polynomial is an expression that contains more than two terms. A term is made up of coefficient and exponent.
Example: P(x) = 4x3+6x2+7x+9

A polynomial may be represented using array or structure. A structure may be defined such that it contains two parts – one is the coefficient and second is the corresponding exponent. The structure definition may be given as shown below:

```Struct polynomial{
int coefficient;
int exponent;
};```

The basic idea of polynomial addition is to add coefficient parts of the polynomials having same exponent.

Algorithm:

`AddPoly(Struct Poly p1,Struct Poly p2,int t1,int t2,Struct Poly p3)`
```1.) [Initialize segment variables]
[Initialize Counter] Set i=0,j=0,k=0

2.) Repeat step 3 while i<t1 and j<t2

3.) If p1[i].expo=p2[j].expo, then
p3[i].coeff=p1[i].coeff+p2[i].coeff
p3[k].expo=p1[i].expo
[Increase counter] Set i=i+1,j=j+1,k=k+1
else if p1[i].expo > p2[j].expo, then
p3[k].coeff=p1[i].coeff
p3[k].expo=p1[i].expo
[Increase counter] Set i=i+1,k=k+1
else
p3[k].coeff=p2[j].coeff
p3[k].expo=p2[j].expo
Set j=j+1,k=k+1
[End of If]
[End of loop]

4.) Repeat while i<t1
p3[k].coeff=p1[i].coeff
p3[k].expo=p1[i].expo
Set i=i+1,k=k+1
[End of loop]

5.) Repeat while j<t2
p3[k].coeff=p2[j].coeff
p3[k].expo=p2[j].expo
Set j=j+1,k=k+1
[End of loop]

6.) Return k
7.) Exit```

### C program for Polynomial Addition Using Structure

```/* program for addition of two polynomials
* polynomial are stored using structure
* and program uses array of structure
*/
#include<stdio.h>

/* declare structure for polynomial */
struct poly
{
int coeff;
int expo;
};
/* declare three arrays p1, p2, p3 of type structure poly.
* each polynomial can have maximum of ten terms
* addition result of p1 and p2 is stored in p3 */

struct poly p1,p2,p3;

/* function prototypes */
int addPoly(struct poly [],struct poly [],int ,int ,struct poly []);
void displayPoly( struct poly [],int terms);

int main()
{
int t1,t2,t3;

/* read and display first polynomial */
printf(" \n First polynomial : ");
displayPoly(p1,t1);
/* read and display second polynomial */
printf(" \n Second polynomial : ");
displayPoly(p2,t2);

/* add two polynomials and display resultant polynomial */
printf(" \n\n Resultant polynomial after addition : ");
displayPoly(p3,t3);
printf("\n");

return 0;
}

{
int t1,i;

printf("\n\n Enter the total number of terms in the polynomial:");
scanf("%d",&t1);

printf("\n Enter the COEFFICIENT and EXPONENT in DESCENDING ORDER\n");
for(i=0;i<t1;i++)
{
printf("   Enter the Coefficient(%d): ",i+1);
scanf("%d",&p[i].coeff);
printf("      Enter the exponent(%d): ",i+1);
scanf("%d",&p[i].expo);        /* only statement in loop */
}
return(t1);
}

int addPoly(struct poly p1,struct poly p2,int t1,int t2,struct poly p3)
{
int i,j,k;

i=0;
j=0;
k=0;

while(i<t1 && j<t2)
{
if(p1[i].expo==p2[j].expo)
{
p3[k].coeff=p1[i].coeff + p2[j].coeff;
p3[k].expo=p1[i].expo;

i++;
j++;
k++;
}
else if(p1[i].expo>p2[j].expo)
{
p3[k].coeff=p1[i].coeff;
p3[k].expo=p1[i].expo;
i++;
k++;
}
else
{
p3[k].coeff=p2[j].coeff;
p3[k].expo=p2[j].expo;
j++;
k++;
}
}

/* for rest over terms of polynomial 1 */
while(i<t1)
{
p3[k].coeff=p1[i].coeff;
p3[k].expo=p1[i].expo;
i++;
k++;
}
/* for rest over terms of polynomial 2 */
while(j<t2)
{
p3[k].coeff=p2[j].coeff;
p3[k].expo=p2[j].expo;
j++;
k++;
}

return(k); /* k is number of terms in resultant polynomial*/
}

void displayPoly(struct poly p,int term)
{
int k;

for(k=0;k<term-1;k++)
printf("%d(x^%d)+",p[k].coeff,p[k].expo);
printf("%d(x^%d)",p[term-1].coeff,p[term-1].expo);
}
```

Output

```Enter the total number of terms in the polynomial:4
Enter the COEFFICIENT and EXPONENT in DESCENDING ORDER
Enter the Coefficient(1): 3
Enter the exponent(1): 4
Enter the Coefficient(2): 7
Enter the exponent(2): 3
Enter the Coefficient(3): 5
Enter the exponent(3): 1
Enter the Coefficient(4): 8
Enter the exponent(4): 0

First polynomial : 3(x^4)+7(x^3)+5(x^1)+8(x^0)

Enter the total number of terms in the polynomial:5
Enter the COEFFICIENT and EXPONENT in DESCENDING ORDER
Enter the Coefficient(1): 7
Enter the exponent(1): 5
Enter the Coefficient(2): 6
Enter the exponent(2): 4
Enter the Coefficient(3): 8
Enter the exponent(3): 2
Enter the Coefficient(4): 9
Enter the exponent(4): 1
Enter the Coefficient(5): 2
Enter the exponent(5): 0
Second polynomial : 7(x^5)+6(x^4)+8(x^2)+9(x^1)+2(x^0)

Resultant polynomial after addition : 7(x^5)+9(x^4)+7(x^3)+8(x^2)+14(x^1)+10(x^0)
```

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