#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 ;
    struct polynode *link ;
} ;

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
                         the second linked list */


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

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

        }

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