# Program to multiply two polynomials maintained as linked lists

/* Program to multiply two polynomials maintained as linked lists.*/

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

/* structure representing a node of a linked list. The node can store a term of a polynomial */
struct polynode
{
float coeff ;
int exp ;
} ;

void poly_append ( struct polynode **, float, int ) ;
void display_poly ( struct polynode * ) ;
void poly_multiply ( struct polynode *, struct polynode *, struct polynode ** ) ;
void padd ( float, int, struct polynode ** ) ;

void main( )
{
struct polynode *first, *second, *mult ;
int i = 1 ;

first = second = mult = NULL ; /* empty linked lists */

poly_append ( &first, 3, 5 ) ;
poly_append ( &first, 2, 4 ) ;
poly_append ( &first, 1, 2 ) ;

clrscr( ) ;
display_poly ( first ) ;

poly_append ( &second, 1, 6 ) ;
poly_append ( &second, 2, 5 ) ;
poly_append ( &second, 3, 4 ) ;

printf ( "\n\n" ) ;
display_poly ( second ) ;

printf ( "\n" );
while ( i++ < 79 )
printf ( "-" ) ;

poly_multiply ( first, second, &mult ) ;

printf ( "\n\n" ) ;
display_poly ( mult ) ;
}

/* adds a term to a polynomial */
void poly_append ( struct polynode **q, float x, int y )
{
struct polynode *temp ;
temp = *q ;

/* create a new node if the list is empty */
if ( *q == NULL )
{
*q = malloc ( sizeof ( struct polynode ) ) ;
temp = *q ;
}
else
{
/* traverse the entire linked list */
while ( temp -> link != NULL )
temp = temp -> link ;

/* create new nodes at intermediate stages */
temp -> link = malloc ( sizeof ( struct polynode ) ) ;
temp = temp -> link ;
}

/* assign coefficient and exponent */
temp -> coeff = x ;
temp -> exp = y ;
temp -> link = NULL ;
}

/* displays the contents of linked list representing a polynomial */
void display_poly ( struct polynode *q )
{
/* traverse till the end of the linked list */
while ( q != NULL )
{
printf ( "%.1f x^%d : ", q -> coeff, q -> exp ) ;
q = q -> link ;
}

printf ( "\b\b\b " ) ; /* erases the last colon(:) */
}

/* multiplies the two polynomials */
void poly_multiply ( struct polynode *x, struct polynode *y,
struct polynode **m )
{
struct polynode *y1 ;
float coeff1, exp1 ;

y1 = y ; /* point to the starting of the second linked list */

if ( x == NULL && y == NULL )
return ;

/* if one of the list is empty */
if ( x == NULL )
*m = y ;
else
{
if ( y == NULL )
*m = x ;
else /* if both linked lists exist */
{
/* for each term of the first list */
while ( x != NULL )
{
/* multiply each term of the second linked list with a
term of the first linked list */
while ( y != NULL )
{
coeff1 = x -> coeff * y -> coeff ;
exp1 = x -> exp + y -> exp ;
y = y -> link ;

/* add the new term to the resultant polynomial */
padd ( coeff1, exp1, m ) ;
}

y = y1 ; /* reposition the pointer to the starting of

x = x -> link ; /* go to the next node */
}
}
}
}

/* adds a term to the polynomial in the descending order of the exponent */
void padd ( float c, int e, struct polynode **s )
{
struct polynode *r, *temp = *s ;

/* if list is empty or if the node is to be inserted before the first node */
if ( *s == NULL || e > ( *s ) -> exp )
{
*s = r = malloc ( sizeof ( struct polynode ) ) ;
( *s ) -> coeff = c ;
( *s ) -> exp = e ;
( *s ) -> link = temp ;
}
else
{
/* traverse the entire linked list to search the position to insert a new node */
while ( temp != NULL )
{
if ( temp -> exp == e )
{
temp -> coeff += c ;
return ;
}

if ( temp -> exp > e && ( temp -> link -> exp < e || temp -> link == NULL ) )
{
r = malloc ( sizeof ( struct polynode ) ) ;
r -> coeff = c;
r -> exp = e ;
temp -> link = r ;
return ;
}

temp = temp -> link ; /* go to next node */
}

r -> link = NULL ;
temp -> link = r ;
}
}

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