Write a complete c code for the following question : Addition of polynomials wit

Question

Write a complete c code for the following question :

Addition of polynomials with two terms: To perform different operations on polynomial with two terms x, y using 2-D array representations. Operations like addition and multiplication have to be implemented [ref: J.P Trembly].

If the 2D array representation is sparse then optimize the memory usage by using suitable alternative representation such as sparse matrix representation. However, all the operations have to be allowed, abstracting the representation.

Explanation / Answer

/*Polynomial- Representation, Addition, Multiplication*/

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

struct poly
{
int coeff;
int exp;
struct poly *next;
}*head1=NULL,*head2=NULL,*head3=NULL,*head4=NULL,*temp,*ptr;

void create();
void makenode(int,int);
struct poly *insertend(struct poly *);
void display(struct poly *);
struct poly *addtwopoly(struct poly *,struct poly *,struct poly *);
struct poly *subtwopoly(struct poly *,struct poly *,struct poly *);
struct poly *multwopoly(struct poly *,struct poly *,struct poly *);
struct poly *dispose(struct poly *);
int search(struct poly *,int);

void main()
{
int ch,coefficient,exponent;
int listno;
while(1)
{
clrscr();
printf(“ntMenu”);
printf(“nt1. Create First Polynomial.”);
printf(“nt2. Display First Polynomial.”);
printf(“nt3. Create Second Polynomial.”);
printf(“nt4. Display Second Polynomial.”);
printf(“nt5. Add Two Polynomials.”);
printf(“nt6. Display Result of Addition.”);
printf(“nt7. Subtract Two Polynomials.”);
printf(“nt8. Display Result of Subtraction.”);
printf(“nt9. Multiply Two Polynomials.”);
printf(“nt10. Display Result of Product.”);
printf(“nt11. Dispose List.”);
printf(“nt12. Exit”);
printf(“nntEnter your choice?”);
scanf(“%d”,&ch);
switch(ch)
{
case 1:
printf(“nGenerating first polynomial:”);
printf(“nEnter coefficient?”);
scanf(“%d”,&coefficient);
printf(“nEnter exponent?”);
scanf(“%d”,&exponent);
makenode(coefficient,exponent);
head1 = insertend(head1);
break;
case 2:
display(head1);
break;
case 3:
printf(“nGenerating second polynomial:”);
printf(“nEnter coefficient?”);
scanf(“%d”,&coefficient);
printf(“nEnter exponent?”);
scanf(“%d”,&exponent);
makenode(coefficient,exponent);
head2 = insertend(head2);
break;
case 4:
display(head2);
break;
case 5:
printf(“nDisposing result list.”);
head3=dispose(head3);
head3=addtwopoly(head1,head2,head3);
printf(“Addition successfully done!”);
break;
case 6:
display(head3);
break;
case 7:
head3=dispose(head3);
head3=subtwopoly(head1,head2,head3);
printf(“Subtraction successfully done!”);
getch();
break;
case 8:
display(head3);
break;
case 9:
head3=dispose(head3);
head4=dispose(head4);
head4=multwopoly(head1,head2,head3);
break;
case 10:
display(head4);
break;
case 11:
printf(“Enter list number to dispose(1 to 4)?”);
scanf(“%d”,&listno);
if(listno==1)
head1=dispose(head1);
else if(listno==2)
head2=dispose(head2);
else if(listno==3)
head3=dispose(head3);
else if(listno==4)
head4=dispose(head4);
else
printf(“Invalid number specified.”);
break;
case 12:
exit(0);
default:
printf(“Invalid Choice!”);
break;
}
}
}

void create()
{
ptr=(struct poly *)malloc(sizeof(struct poly));
if(ptr==NULL)
{
printf(“Memory Allocation Error!”);
exit(1);
}
}

void makenode(int c,int e)
{
create();
ptr->coeff = c;
ptr->exp = e;
ptr->next = NULL;
}

struct poly *insertend(struct poly *head)
{
if(head==NULL)
head = ptr;
else
{
temp=head;
while(temp->next != NULL)
temp = temp->next;
temp->next = ptr;
}
return head;
}

void display(struct poly *head)
{
if(head==NULL)
printf(“List is empty!”);
else
{
temp=head;
while(temp!=NULL)
{
printf(“(%d,%d)->”,temp->coeff,temp->exp);
temp=temp->next;
}
printf(“bb “);
}
getch();
}

struct poly *addtwopoly(struct poly *h1,struct poly *h2,struct poly *h3)
{
/*
(5,3)->(6,1) + (7,3)->(9,2) = (12,3)->(6,1)->(9,2)
*/
struct poly *temp1,*temp2,*temp3;
temp1=h1;
temp2=h2;
while(temp1!=NULL || temp2!=NULL)
{
if(temp1->exp==temp2->exp)
{
makenode(temp1->coeff+temp2->coeff,temp1->exp);
h3=insertend(h3);
}
else
{
makenode(temp1->coeff,temp1->exp);
h3=insertend(h3);
makenode(temp2->coeff,temp2->exp);
h3=insertend(h3);
}
temp1=temp1->next;
temp2=temp2->next;
}
if(temp1==NULL && temp2!=NULL)
{
while(temp2!=NULL)
{
makenode(temp2->coeff,temp2->exp);
h3=insertend(h3);
temp2=temp2->next;
}
}
if(temp2==NULL && temp1!=NULL)
{
while(temp1!=NULL)
{
makenode(temp2->coeff,temp2->exp);
h3=insertend(h3);
temp1=temp1->next;
}
}
return h3;
}

struct poly *subtwopoly(struct poly *h1,struct poly *h2,struct poly *h3)
{
/*
(5,3)->(6,1) – (7,3)->(9,2) = (-2,3)+(6,1)-(9,2)
*/
struct poly *temp1,*temp2,*temp3;
temp1=h1;
temp2=h2;
while(temp1!=NULL || temp2!=NULL)
{
if(temp1->exp==temp2->exp)
{
makenode(temp1->coeff-temp2->coeff,temp1->exp);
h3=insertend(h3);
}
else
{
makenode(temp1->coeff,temp1->exp);
h3=insertend(h3);
makenode(-temp2->coeff,temp2->exp);
h3=insertend(h3);
}
temp1=temp1->next;
temp2=temp2->next;
}
if(temp1==NULL && temp2!=NULL)
{
while(temp2!=NULL)
{
makenode(temp2->coeff,temp2->exp);
h3=insertend(h3);
temp2=temp2->next;
}
}
if(temp2==NULL && temp1!=NULL)
{
while(temp1!=NULL)
{
makenode(-temp2->coeff,temp2->exp);
h3=insertend(h3);
temp1=temp1->next;
}
}
return h3;
}

struct poly *multwopoly(struct poly *h1,struct poly *h2,struct poly *h3)
{
/*
h1=(5,3)->(6,1) * h2=(7,3)->(9,2)
(5,3)->(7,3),(9,2) = (35,6),(45,5)
(6,1)->(7,3),(9,2) = (42,4),(54,3)
h3->(35,6)->(45,5)->(42,4)->(54,3)
(35,6)+(45,5)+(42,4)+(54,3)=Result
*/
int res=0;
struct poly *temp1,*temp2,*temp3;
printf(“nDisplaying First Polynomial:ntt”);
display(h1);
printf(“nDisplaying Second Polynomial:ntt”);
display(h2);

temp1=h1;
while(temp1!=NULL)
{
temp2=h2;
while(temp2!=NULL)
{
makenode(temp1->coeff*temp2->coeff,temp1->exp+temp2->exp);
h3=insertend(h3);
temp2=temp2->next;
}
temp1=temp1->next;
}

printf(“nDisplaying Initial Result of Product:ntt”);
display(h3);
getch();

temp1=h3;
while(temp1!=NULL)
{temp2=temp1->next;
res=0;
while(temp2!=NULL)
{
if(temp1->exp==temp2->exp)
res += temp2->coeff;
temp2=temp2->next;
}
if(search(head4,temp1->exp)==1)
{
makenode(res+temp1->coeff,temp1->exp);
head4=insertend(head4);
}
temp1=temp1->next;
}
return head4;
}

int search(struct poly *h,int val)
{
struct poly *tmp;
tmp=h;
while(tmp!=NULL)
{if(tmp->exp==val)
return 0;
tmp=tmp->next;
}
return 1;
}

struct poly *dispose(struct poly *list)
{
if(list==NULL)
{
printf(“List is already empty.”);
return list;
}
else
{
temp=list;
while(list!=NULL)
{
free(temp);
list=list->next;
temp=list;
}
return list;
}
}

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