A polynomial p(x) is the expression in variable x which is in the form (axn + bxn-1 + …. + jx+ k), where a, b, c …., k fall in the category of real numbers and 'n' is non negative integer, which is called the degree of polynomial.
An essential characteristic of the polynomial is that each term in the polynomial expression consists of two parts:
•one is the coefficient
•other is the exponent
Example:
10x2 + 26x,
here 10 and 26 are coefficients and 2, 1 is its exponential value.
Polynomial can be represented in the various ways. These are:
By the use of arrays
By the use of Linked List
Representation of polynomial using arrays:
There may arise some situation where you need to evaluate many polynomial expressions and perform basic arithmetic operations like addition and subtraction with those numbers. For this, you will have to get a way to represent those polynomials. The simple way is to represent a polynomial with degree 'n' and store the coefficient of n+1 terms of the polynomial in the array. So every array element will consist of two values:
•Coefficient
•Exponent
Representation of polynomial using Linked list:
A polynomial can be thought of as an ordered list of non zero terms. Each non zero term is a two-tuple which holds two pieces of information:
•The exponent part
•The coefficient part
• Program for addition of polynomial
#include<stdio.h>
#include<conio.h>
#include<stdlib.h>
#include<math.h>
struct node
{
int coef, xexp, yexp ,zexp;
struct node *link;
};
typedef struct node *NODE;
void display(NODE head)
{
NODE temp;
temp=head->link;
while(temp!= head)
{
if(temp->coef<0)
printf("%dx^%d y^%d z^%d ",temp->coef, temp->xexp, temp->yexp,temp->zexp);
else
printf("+%dx^%d y^%d z^%d ",temp->coef, temp->xexp,temp->yexp,temp- >zexp);temp=temp->link;
}
printf("\n");
}
NODE attach (int coef, int xexpon, int yexpon, int zexpon, NODE head)
{
NODE temp,cur;
temp=(NODE)malloc(sizeof(struct node));
temp->coef =coef;
temp->xexp=xexpon;
temp->yexp=yexpon;
temp->zexp=zexpon;
cur=head->link;
while(cur->link!=head)
cur=cur->link;
cur->link=temp;
temp->link=head;
return head;
}
NODE readpoly(NODE head)
{
int i=1,coef, xexpon, yexpon, zexpon;
printf("enter the coefficient as -99 to end the polynomial\n");
while(1)
{
printf("enter the %d term of the polynomial\n",i++);
printf("enter the coefficient:\n");
scanf("%d",&coef);
if(coef==-99)
break;
printf("enter the xexponent:\n");
scanf("%d",&xexpon);
printf("enter the yexponent:\n");
scanf("%d",&yexpon);
printf("enter the zexponent:\n");
scanf("%d",&zexpon);
head=attach(coef,xexpon,yexpon,zexpon,head);
}
display(head);
return head;
}
int evaluate(NODE head)
{
NODE temp;
int x,y,z,value=0;
temp=head->link;
printf("Enter the value of x,y and z\n");
scanf("%d%d%d",&x,&y,&z);
while(temp!=head)
{
value=value+temp->coef*(pow(x,temp->xexp)*pow(y,temp->yexp)*pow(z,temp- >zexp));
temp=temp->link;
}
return value;
}
NODE addpoly(NODE head1, NODE head2, NODE head3)
{
NODE a,b;
int sum;
a=head1->link;
b=head2->link;
while(a!=head1 && b!=head2)
{
if(a->xexp==b->xexp)
{
if(a->yexp==b->yexp)
{
if(a->zexp==b->zexp)
{
sum=a->coef+b->coef;
attach(sum, a->xexp,a->yexp,a->zexp, head3);
a=a->link;
b=b->link;
}
else if(a->zexp>b->zexp)
{
attach(a->coef, a->xexp, a->yexp, a->zexp, head3);
a=a->link;
}
else
{
attach(b->coef, b->xexp, b->yexp, b->zexp, head3);
b=b->link;
}
}
else if(a->yexp>b->yexp)
{
attach(a->coef, a->xexp, a->yexp ,a->zexp,head3);
a=a->link;
}
else
{
attach(b->coef, b->xexp, b->yexp,b->zexp,head3);
b=b->link;
}
}
else if(a->xexp > b->xexp)
{
attach(a->coef,a->xexp,a->yexp,a->zexp,head3);
a=a->link;
}
else
{
attach(b->coef,b->xexp,b->yexp,b->zexp,head3);
b=b->link;
}
}
while(a!=head1)
{
head3=attach(a->coef,a->xexp,a->yexp,a->zexp,head3);
a=a->link;
}
while(b!=head2)
{
head3=attach(b->coef,b->xexp,b->yexp,b->zexp,head3);
b=b->link;
}
return head3;
}
void main()
{
int ch;
NODE head,head1,head2,head3;
head1=(NODE)malloc(sizeof(struct node));
head2=(NODE)malloc(sizeof(struct node));
head3=(NODE)malloc(sizeof(struct node));
while(1)
{
printf("\n1.Polynomial Evaluation \n2.Polynomial Addition \n3.Exit\n");
printf("\nEnter the choice\n");
scanf("%d",&ch);
switch(ch)
{
case 1: head->link=head;
printf("Enter the polynomial\n");
readpoly(head);
printf("The result of polynomial is:%d",evaluate(head));
break;
case 2: head1->link=head1;
head2->link=head2;
head3->link=head3;
printf("Enter the first polynomial\n"); readpoly(head1);
printf("\nEnter the second polynomial\n"); readpoly(head2);
printf("\nthe first polynomial is:");
display(head1);
printf("\nthe second polynomial is:");
display(head2);
addpoly(head1,head2,head3);
printf("\nthe result of adding two polynomials is:");
display(head3);
break;
case 3 :exit(0);
}
}
}
