多项式的乘法和除法

02-线性结构2 一元多项式的乘法与加法运算   (20分)

设计函数分别求两个一元多项式的乘积与和。

乘法主要思想：

1.将乘法运算转换为加法运算 将P1当前项(ci,ei)乘P2多项式，再加到结果多项式里 

t1 = P1; t2 = P2;

 P = (Polynomial)malloc(sizeof(struct PolyNode)); 

P->link = NULL; 

Rear = P; while (t2) {Attach(t1->coef*t2->coef, t1->expon+t2->expon, &Rear);t2 = t2->link; }

2.逐项插入 将P1当前项(c1i,e1i)乘P2当前项（c2i,e2i),并插入到结果多项式中。关键是要找到插入位置 初始结果多项式可由P1第一项乘P2获得（如上）

输入格式:

输入分2行，每行分别先给出多项式非零项的个数，再以指数递降方式输入一个多项式非零项系数和指数（绝对值均为不超过1000的整数）。数字间以空格分隔。

输出格式:

输出分2行，分别以指数递降方式输出乘积多项式以及和多项式非零项的系数和指数。数字间以空格分隔，但结尾不能有多余空格。零多项式应输出0 0。

输入样例:

4 3 4 -5 2  6 1  -2 0
3 5 20  -7 4  3 1

输出样例:

15 24 -25 22 30 21 -10 20 -21 8 35 6 -33 5 14 4 -15 3 18 2 -6 1		

#include 
#include 


typedef int ElementType ;
typedef struct Node * PNode;

struct Node
{

    ElementType exponent;
    ElementType factor;
    PNode next;
};
typedef PNode List;

List read();

void Print(List a);

List add(List a,List b);

List mult(List a,List b);
void Attach(ElementType a,ElementType b,PNode *c);
int main()
{
    List a;
    List b;
    List result;
   // freopen("11.txt","r",stdin);
    a = read();
    b = read();
    result = mult(a,b);
    Print(result);

    result = add(a,b);
    Print(result);


    return 0;
}

List read(List a)
{
    PNode Ahead;
    PNode Rear;
    PNode f;
    Ahead = (PNode)malloc(sizeof(struct Node));
    Ahead ->next = NULL;
    Rear = Ahead;
    int n;
    int exp,fac;
    scanf("%d",&n);
    while(n--)
    {
        scanf("%d %d",&fac,&exp);
        Attach(fac,exp,&Rear);
        Rear->next = NULL;
    }
    f = Ahead;
    Ahead = Ahead->next;
    free(f);
    return Ahead;
}

void Print(List a)
{
    PNode PrintNode;

    PrintNode = a;
    if(PrintNode == NULL)
    {
        printf("0 0\n");
        return;
    }
    int tag = 0;

    while(PrintNode)
    {
        if(!tag)
            tag=1;
            else
                printf(" ");

        printf("%d %d",PrintNode->factor,PrintNode->exponent);

        PrintNode = PrintNode->next;

    }
    printf("\n");
}
void Attach(int a,int b,PNode *p)
{
    PNode c;

    c = (PNode)malloc(sizeof(struct Node));
    c->factor = a;
    c->exponent = b;
    c->next = NULL;
    (*p)->next = c;
    *p = c;

}
List add(List a,List b)
{
    PNode front,rear,f;
    PNode t1,t2;
    t1=a;
    t2=b;
    rear = (PNode)malloc(sizeof(struct Node));
    rear->next=NULL;
    front = rear;
    int sum;
    while(t1&&t2)
    {
        if(t1->exponent==t2->exponent)
        {
            sum = t1->factor+t2->factor;
            if(sum)
                Attach(sum,t1->exponent,&rear);
            t1 = t1->next;
            t2 = t2->next;

        }
        else if(t1->exponent > t2->exponent)
        {
            Attach(t1->factor,t1->exponent,&rear);
            t1=t1->next;
        }
        else if(t1->exponent < t2->exponent)
        {
            Attach(t2->factor,t2->exponent,&rear);
            t2=t2->next;
        }

    }

    for(; t1; t1=t1->next)
    {
        Attach(t1->factor,t1->exponent,&rear);
    }

    for(; t2; t2=t2->next)
    {
        Attach(t2->factor,t2->exponent,&rear);
    }

    rear->next = NULL;
    f = front;
    front = front->next;
    free(f);

    return front;

}

List mult(List a,List b)
{
    PNode t1,t2,rear,front,t;
    int fac,exp;
    if(!a||!b)
    {
        return NULL;
    }
    t1 = a;
    t2 = b;

    front = (PNode)malloc(sizeof(struct Node));
    front ->next=NULL;
    rear = front;

    while(t2)
    {
        Attach(t1->factor*t2->factor,t1->exponent+t2->exponent,&rear);
        t2 = t2->next;
    }
    t1=t1->next;

    while(t1)
    {
        t2 = b;
        rear = front;
        while(t2)
        {
            fac = t1->factor*t2->factor;
            exp = t1->exponent+t2->exponent;
            while(rear->next&&rear->next->exponent > exp)
                rear=rear->next;
            if(rear->next&&rear->next->exponent == exp)
            {
                if(rear->next->factor+fac)
                    rear->next->factor+=fac;
                else
                {
                    t = rear->next;
                    rear->next = t->next;
                    free(t);
                }
            }
            else
            {
                t = (PNode)malloc(sizeof(struct Node));
                t->exponent = exp;
                t->factor = fac;
                t->next = rear->next;
                rear->next = t;
                rear=rear->next;

            }
            t2=t2->next;
        }

        t1=t1->next;

    }

    t2 = front;
    front = front->next;
    free(t2);
   return front;
}