polynomial multiplcation

use simple linked list ADT:

about the running time of polynode multiply2(const polynode p1,const polynode p2), assume size of p1 is M,size of p2 is N, the result should be:

M*N+2N+3N+4N+5N+…+(M-1)N=M*N+(M+1)*(M-1)*N/2=O(M²*N)

#include <stdio.h>
#include <stdlib.h>
struct node;
typedef struct node *ptr_to_node;
typedef ptr_to_node polynode;
struct node
{
    int coefficient;
    int exponent;
    polynode next;
};
void duplicate_and_combine(polynode p1,const polynode p2);

void print_poly(polynode p)
{
    polynode c=p->next;
    if(c==NULL)
    {
        printf("empty polynomial\n");
        return;
    }

    while(c->next!=NULL)
    {
        printf("%d*X(%d)+",c->coefficient,c->exponent);
        c=c->next;
    }
    printf("%d*X(%d)\n",c->coefficient,c->exponent);
}

void emptypoly(polynode p)
{
    p->next=NULL;
    p->coefficient=p->exponent=0;
}

polynode create_newpoly()
{
    polynode p=malloc(sizeof(struct node));
    emptypoly(p);
    return p;
}

/*
link the second polynomial after the tail of first polynomial
no sorting, O(M+N)
*/
polynode add_polynomial1(const polynode p1,const polynode p2)
{
    polynode sum=create_newpoly();
    duplicate_and_combine(sum,p1);
    duplicate_and_combine(sum,p2);
    return sum;
}

/*
link the two polynomial step by step with power sort with asdending
assume the original two polynomial are already sorted and combined
O(M+N)
*/
polynode add_polynomial2(const polynode p1, polynode p2)
{
    polynode sum=create_newpoly();
    polynode c1=p1->next;
    polynode c2=p2->next;
    polynode c3=sum;

    while(c1!=NULL && c2!=NULL)
    {
        c3->next=create_newpoly();
        if(c1->exponent>c2->exponent)
        {
            c3->next->exponent=c1->exponent;
            c3->next->coefficient=c1->coefficient;
            c1=c1->next;
        }
        else if(c1->exponent==c2->exponent)
        {
            c3->next->exponent=c1->exponent;
            c3->next->coefficient=c1->coefficient+c2->coefficient;
            c1=c1->next;
            c2=c2->next;
        }
        else
        {
            c3->next->exponent=c2->exponent;
            c3->next->coefficient=c2->coefficient;
            c2=c2->next;
        }
        c3=c3->next;
    }

    polynode c4=NULL;
    if(c1!=NULL)
    {
        c4=c1;
    }
    else if(c2!=NULL)
    {
        c4=c2;
    }

    while(c4!=NULL)
    {
        c3->next=create_newpoly();
        c3->next->exponent=c4->exponent;
        c3->next->coefficient=c4->coefficient;
        c4=c4->next;
        c3=c3->next;
    }

    return sum;
}

/*
multiply two polynomials, no sorting
O(M*N)
*/
polynode multiply1(const polynode p1,const polynode p2)
{
    polynode res=create_newpoly();
    polynode c1=p1->next;
    polynode c3=res;

    while(c1!=NULL)
    {
        polynode c2=p2->next;
        while(c2!=NULL)
        {
            c3->next=create_newpoly();
            c3->next->coefficient=c1->coefficient*c2->coefficient;
            c3->next->exponent=c1->exponent+c2->exponent;
            c3=c3->next;
            c2=c2->next;
        }
        c1=c1->next;
    }
    return res;
}

/*
multiply two polynomials with exponent sorted output
assume the original two polynomials are in sorted order
O(M*M*N)
*/
polynode multiply2(const polynode p1,const polynode p2)
{
    polynode res=create_newpoly();
    polynode c1=p1->next;


    while(c1!=NULL)
    {
        polynode temp=create_newpoly();
        polynode c2=p2->next;
        polynode c3=temp;
        while(c2!=NULL)
        {
            c3->next=create_newpoly();
            c3->next->coefficient=c1->coefficient*c2->coefficient;
            c3->next->exponent=c1->exponent+c2->exponent;
            c3=c3->next;
            c2=c2->next;
        }

        res=add_polynomial2(res,temp);
        c1=c1->next;
    }

    return res;
}

/*
combine the second to the first
*/
void duplicate_and_combine(polynode p1,const polynode p2)
{
    polynode c1=p1;
    polynode c2=p2->next;
    while(c1->next!=NULL)
    {
        c1=c1->next;
    }

    while(c2!=NULL)
    {
        c1->next=create_newpoly();
        c1->next->coefficient=c2->coefficient;
        c1->next->exponent=c2->exponent;
        c2=c2->next;
        c1=c1->next;
    }
}

int main()
{
    polynode p1=create_newpoly();
    p1->next=create_newpoly();
    p1->next->next=create_newpoly();
    p1->next->coefficient=5;
    p1->next->exponent=5;
    p1->next->next->coefficient=4;
    p1->next->next->exponent=4;
    polynode p2=create_newpoly();
    p2->next=create_newpoly();
    p2->next->next=create_newpoly();
    p2->next->coefficient=4;
    p2->next->exponent=4;
    p2->next->next->coefficient=3;
    p2->next->next->exponent=3;
    print_poly(p1);
    print_poly(p2);

    polynode sum=add_polynomial1(p1,p2);
    print_poly(sum);
    sum=add_polynomial1(sum,p2);
    print_poly(sum);
    print_poly(p1);
    print_poly(p2);

    sum=add_polynomial2(p1,p2);
    print_poly(sum);
    print_poly(p1);
    print_poly(p2);

    polynode res=multiply1(p1,p2);
    print_poly(res);
    print_poly(p1);
    print_poly(p2);

    polynode res2=multiply2(p1,p2);
    print_poly(res2);
    print_poly(p1);
    print_poly(p2);
    printf("Hello world!\n");
    return 0;
}

在第80行需要handle系数之和为0的情况, 修改add_polynomial2函数fix此问题：

polynode add_polynomial2(const polynode p1, polynode p2)
{
    polynode sum=create_newpoly();
    polynode c1=p1->next;
    polynode c2=p2->next;
    polynode c3=sum;

    while(c1!=NULL && c2!=NULL)
    {
        if(c1->coefficient+c2->coefficient==0)
        {
            continue;
        }
        else
        {
            c3->next=create_newpoly();
        }


        if(c1->exponent>c2->exponent)
        {
            c3->next->exponent=c1->exponent;
            c3->next->coefficient=c1->coefficient;
            c1=c1->next;
        }
        else if(c1->exponent==c2->exponent)
        {
            c3->next->exponent=c1->exponent;
            c3->next->coefficient=c1->coefficient+c2->coefficient;
            c1=c1->next;
            c2=c2->next;

        }
        else
        {
            c3->next->exponent=c2->exponent;
            c3->next->coefficient=c2->coefficient;
            c2=c2->next;
        }
        c3=c3->next;
    }

    polynode c4=NULL;
    if(c1!=NULL)
    {
        c4=c1;
    }
    else if(c2!=NULL)
    {
        c4=c2;
    }

    while(c4!=NULL)
    {
        c3->next=create_newpoly();
        c3->next->exponent=c4->exponent;
        c3->next->coefficient=c4->coefficient;
        c4=c4->next;
        c3=c3->next;
    }

    return sum;
}