9. Develop a Program in C for the following operations on Singly Circular Linked List (SCLL) with header nodes.
a) Represent and Evaluate a Polynomial P(x,y,z) = 6x2y2z-4yz5+3x3yz+2xy5z-2xyz3 .
b) Find the sum of two polynomials POLY1(x,y,z) and POLY2(x,y,z) and store the result in POLYSUM(x,y,z).
PROGRAM:
#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#define COMPARE(x, y)((x == y) ? 0 : (x > y) ? 1 : -1)
struct node
{
int coef;
int xexp, yexp, zexp;
struct node * link;
};
typedef struct node * NODE;
NODE getnode()
{
NODE x;
x = (NODE) malloc(sizeof(struct node));
if (x == NULL)
{
printf("Running out of memory \n");
return NULL;
}
return x;
}
NODE attach(int coef, int xexp, int yexp, int zexp, NODE head)
{
NODE temp, cur;
temp = getnode();
temp -> coef = coef;
temp -> xexp = xexp;
temp -> yexp = yexp;
temp -> zexp = zexp;
cur = head -> link;
while (cur -> link != head)
{
cur = cur -> link;
}
cur -> link = temp;
temp -> link = head;
return head;
}
NODE read_poly(NODE head)
{
int i, j, coef, xexp, yexp, zexp, n;
printf("\nEnter the no of terms in the polynomial: ");
scanf("%d", & n);
for (i = 1; i <= n; i++)
{
printf("\n\tEnter the %d term: ", i);
printf("\n\t\tCoef = ");
scanf("%d", & coef);
printf("\n\t\tEnter Pow(x) Pow(y) and Pow(z): ");
scanf("%d", & xexp);
scanf("%d", & yexp);
scanf("%d", & zexp);
head = attach(coef, xexp, yexp, zexp, head);
}
return head;
}
void display(NODE head)
{
NODE temp;
if (head -> link == head)
{
printf("\nPolynomial does not exist.");
return;
}
temp = head -> link;
while (temp != head)
{
printf("%dx^%dy^%dz^%d", temp -> coef, temp -> xexp, temp -> yexp, temp -> zexp);
temp = temp -> link;
if (temp != head)
printf(" + ");
}
}
int poly_evaluate(NODE head)
{
int x, y, z, sum = 0;
NODE poly;
printf("\nEnter the value of x,y and z: ");
scanf("%d %d %d", & x, & y, & z);
poly = head -> link;
while (poly != head)
{
sum += poly -> coef * pow(x, poly -> xexp) * pow(y, poly -> yexp) * pow(z, poly -> zexp);
poly = poly -> link;
}
return sum;
}
NODE poly_sum(NODE head1, NODE head2, NODE head3)
{
NODE a, b;
int coef;
a = head1 -> link;
b = head2 -> link;
while (a != head1 && b != head2)
{
while (1)
{
if (a -> xexp == b -> xexp && a -> yexp == b -> yexp && a -> zexp == b -> zexp)
{
coef = a -> coef + b -> coef;
head3 = attach(coef, a -> xexp, a -> yexp, a -> zexp, head3);
a = a -> link;
b = b -> link;
break;
}
if (a -> xexp != 0 || b -> xexp != 0)
{
switch (COMPARE(a -> xexp, b -> xexp))
{
case -1:
head3 = attach(b -> coef, b -> xexp, b -> yexp, b -> zexp, head3);
b = b -> link;
break;
case 0:
if (a -> yexp > b -> yexp)
{
head3 = attach(a -> coef, a -> xexp, a -> yexp, a -> zexp, head3);
a = a -> link;
break;
}
else if (a -> yexp < b -> yexp)
{
head3 = attach(b -> coef, b -> xexp, b -> yexp, b -> zexp, head3);
b = b -> link;
break;
}
else if (a -> zexp > b -> zexp)
{
head3 = attach(a -> coef, a -> xexp, a -> yexp, a -> zexp, head3);
a = a -> link;
break;
}
else if (a -> zexp < b -> zexp)
{
head3 = attach(b -> coef, b -> xexp, b -> yexp, b -> zexp, head3);
b = b -> link;
break;
}
case 1:
head3 = attach(a -> coef, a -> xexp, a -> yexp, a -> zexp, head3);
a = a -> link;
break;
}
break;
}
if (a -> yexp != 0 || b -> yexp != 0)
{
switch (COMPARE(a -> yexp, b -> yexp))
{
case -1:
head3 = attach(b -> coef, b -> xexp, b -> yexp, b -> zexp, head3);
b = b -> link;
break;
case 0:
if (a -> zexp > b -> zexp)
{
head3 = attach(a -> coef, a -> xexp, a -> yexp, a -> zexp, head3);
a = a -> link;
break;
}
else if (a -> zexp < b -> zexp)
{
head3 = attach(b -> coef, b -> xexp, b -> yexp, b -> zexp, head3);
b = b -> link;
break;
}
case 1:
head3 = attach(a -> coef, a -> xexp, a -> yexp, a -> zexp, head3);
a = a -> link;
break;
}
break;
}
if (a -> zexp != 0 || b -> zexp != 0)
{
switch (COMPARE(a -> zexp, b -> zexp))
{
case -1:
head3 = attach(b -> coef, b -> xexp, b -> yexp, b -> zexp, head3);
b = b -> link;
break;
case 1:
head3 = attach(a -> coef, a -> xexp, a -> yexp, a -> zexp, head3);
a = a -> link;
break;
}
break;
}
}
}
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()
{
NODE head, head1, head2, head3;
int res, ch;
head = getnode();
head1 = getnode();
head2 = getnode();
head3 = getnode();
head -> link = head;
head1 -> link = head1;
head2 -> link = head2;
head3 -> link = head3;
while (1)
{
printf("\n--------Menu--------");
printf("\n1.Represent and Evaluate a Polynomial P(x,y,z)");
printf("\n2.Find the sum of two polynomials POLY1(x,y,z)");
printf("\nEnter your choice:");
scanf("%d", & ch);
switch (ch)
{
case 1:
printf("\n----Polynomial evaluation P(x,y,z)----\n");
head = read_poly(head);
printf("\nRepresentation of Polynomial for evaluation: \n");
display(head);
res = poly_evaluate(head);
printf("\nResult of polynomial evaluation is : %d \n", res);
break;
case 2:
printf("\nEnter the POLY1(x,y,z): \n");
head1 = read_poly(head1);
printf("\nPolynomial 1 is: \n");
display(head1);
printf("\nEnter the POLY2(x,y,z): \n");
head2 = read_poly(head2);
printf("\nPolynomial 2 is: \n");
display(head2);
printf("\nPolynomial addition result: \n");
head3 = poly_sum(head1, head2, head3);
display(head3);
break;
case 3:
exit(0);
}
}
}OUTPUT:
--------Menu--------
1.Represent and Evaluate a Polynomial P(x,y,z)
2.Find the sum of two polynomials POLY1(x,y,z) and POLY2(x,y,z)
Enter your choice: 1
----Polynomial evaluation P(x,y,z)----
Enter the no of terms in the polynomial: 5
Enter the 1 term:
Coef = 6
Enter Pow(x) Pow(y) and Pow(z): 2 2 1
Enter the 2 term:
Coef = -4
Enter Pow(x) Pow(y) and Pow(z): 0 1 5
Enter the 3 term:
Coef = 3
Enter Pow(x) Pow(y) and Pow(z): 3 1 1
Enter the 4 term:
Coef = 2
Enter Pow(x) Pow(y) and Pow(z): 1 5 1
Enter the 5 term:
Coef = -2
Enter Pow(x) Pow(y) and Pow(z): 1 1 3
Representation of Polynomial for evaluation:
6x^2y^2z^1 + -4x^0y^1z^5 + 3x^3y^1z^1 + 2x^1y^5z^1 + -2x^1y^1z^3
Enter the value of x,y and z: 1 1 1
Result of polynomial evaluation is : 5
--------Menu--------
1.Represent and Evaluate a Polynomial P(x,y,z)
2.Find the sum of two polynomials POLY1(x,y,z) and POLY2(x,y,z)
Enter your choice: 2
Enter the POLY1(x,y,z):
Enter the no of terms in the polynomial: 5
Enter the 1 term:
Coef = 6
Enter Pow(x) Pow(y) and Pow(z): 4 4 4
Enter the 2 term:
Coef = 3
Enter Pow(x) Pow(y) and Pow(z): 4 3 1
Enter the 3 term:
Coef = 5
Enter Pow(x) Pow(y) and Pow(z): 0 1 1
Enter the 4 term:
Coef = 10
Enter Pow(x) Pow(y) and Pow(z): 0 1 0
Enter the 5 term:
Coef = 5
Enter Pow(x) Pow(y) and Pow(z): 0 0 0
Polynomial 1 is:
6x^4y^4z^4 + 3x^4y^3z^1 + 5x^0y^1z^1 + 10x^0y^1z^0 + 5x^0y^0z^0
Enter the POLY2(x,y,z):
Enter the no of terms in the polynomial: 5
Enter the 1 term:
Coef = 8
Enter Pow(x) Pow(y) and Pow(z): 4 4 4
Enter the 2 term:
Coef = 4
Enter Pow(x) Pow(y) and Pow(z): 4 2 1
Enter the 3 term:
Coef = 30
Enter Pow(x) Pow(y) and Pow(z): 0 1 0
Enter the 4 term:
Coef = 20
Enter Pow(x) Pow(y) and Pow(z): 0 0 1
Enter the 5 term:
Coef = 3
Enter Pow(x) Pow(y) and Pow(z): 0 0 0
Polynomial 2 is:
8x^4y^4z^4 + 4x^4y^2z^1 + 30x^0y^1z^0 + 20x^0y^0z^1 + 3x^0y^0z^0
Polynomial addition result:
14x^4y^4z^4 + 3x^4y^3z^1 + 4x^4y^2z^1 + 5x^0y^1z^1 + 40x^0y^1z^0 + 20x^0y^0z^1 + 8x^0y^0z^0
--------Menu--------
1.Represent and Evaluate a Polynomial P(x,y,z)
2.Find the sum of two polynomials POLY1(x,y,z) and POLY2(x,y,z)
Enter your choice:3