一元多项式的乘法与加法运算——链表实现

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

15 24 -25 22 30 21 -10 20 -21 8 35 6 -33 5 14 4 -15 3 18 2 -6 1
5 20 -4 4 -5 2 9 1 -2 0

#include<iostream>
using namespace std;

/* 带附加头结点的单链表的类定义 */

typedef struct PolyNode * Polynomial;　　//指向结点的指针
struct PolyNode          //链表结点类的定义
{
    int coef;            //系数
    int expon;           //指数
    Polynomial link;     //链指针域
};

/*  函数声明部分  */
Polynomial ReadPoly();
void Attach(int c,int e,Polynomial *pRear);
Polynomial Add(Polynomial P1,Polynomial P2);
Polynomial Mult(Polynomial P1,Polynomial P2);
void PrintPoly(Polynomial P);

int main()
{
    Polynomial P1,P2,PP,PS;

    P1 = ReadPoly();    
    P2 = ReadPoly();
    PP = Mult(P1,P2);
    PrintPoly(PP);
    PS = Add(P1,P2);
    PrintPoly(PS);

    return 0;

}

Polynomial ReadPoly()    //读入多项式构成链表，并返回链表的头指针
{
    Polynomial first,rear,t;
    int N,c,e;    
    scanf("%d",&N);

    first = new PolyNode;//链表附加头结点,这样可以免除首节点的判断，保持了操作的一致性
    first->link = NULL;
    rear = first;
    while (N--)
    {
        scanf("%d %d",&c,&e);
        Attach(c,e,&rear);    //将当前项插入多项式链表尾部
    }
    t = first; first = first->link; delete t;//最后删除附加头结点
    return first;
}

void Attach(int c,int e,Polynomial *pRear)//将当前项插入多项式链表尾部
{
    Polynomial P;
    P = new PolyNode;        //创建新节点
    P->coef = c;
    P->expon = e;
    P->link = NULL;
    (*pRear)->link = P;      //连接新结点
    *pRear = P;              //尾指针指向新节点
}

Polynomial Add(Polynomial P1,Polynomial P2)//多项式加法
{
    Polynomial first,rear,t;
    int sum;
    first = new PolyNode;    //链表附加头结点
    first->link = NULL;
    rear = first;
    while(P1&&P2)
    {
        if (P1->expon == P2->expon)//两数据项指数相等
        {
            sum = P1->coef + P2->coef;
            if(sum)    Attach(sum,P1->expon,&rear);//注意判断系数和是否为0
            P1 = P1->link;
            P2 = P2->link;
        }
        else if (P1->expon > P2->expon)      //P1中的数据项指数较大
        {
            Attach(P1->coef,P1->expon,&rear);//把此P1项结点插入到结果多项式链表中
            P1 = P1->link;
        }
        else
        {
            Attach(P2->coef,P2->expon,&rear);
            P2 = P2->link;
        }

    }
    /*  将未处理完的另一个多项式的所有节点依次复制到结果多项式中去  */
    for(;P1;P1=P1->link)    Attach(P1->coef,P1->expon,&rear);
    for(;P2;P2=P2->link)    Attach(P2->coef,P2->expon,&rear);

    t = first; first = first->link; delete t;//删除附加头结点
    return first;
}

Polynomial Mult(Polynomial P1,Polynomial P2)
{
    Polynomial first,rear,temp,sP2;
    int c,e;
    if(!P1||!P2)    return NULL;

    first = new PolyNode;//链表附加头结点
    first->link = NULL;
    rear = first;
    
    sP2 = P2;    //保存一下P2初始位置

    while(P2)    //先用P1的第一项乘以P2,得到一个结果多项式链表
    {
        Attach(P1->coef*P2->coef,P1->expon+P2->expon,&rear);
        P2 = P2->link;
    }
    P1 = P1->link;
    while (P1)    //再用P1的其它项乘以P2，将结果添加到前面的多项式链表中
    {
        P2 = sP2;        //恢复P2初始位置
        rear = first;    //从表头开始扫描结果多项式链表
        while (P2)
        {
            c = P1->coef*P2->coef;
            e = P1->expon+P2->expon;
            while (rear->link && rear->link->expon > e)     //结果多项式链表中的数据项指数较大
            {
                rear = rear->link;
            }
            if(rear->link && rear->link->expon == e)    //两数据项指数相等
            {
                if(rear->link->coef + c)    //系数和非0
                    rear->link->coef += c;
                else                        //系数和为0，需要在结果多项式链表中删除次表项
                {
                    temp = rear->link;
                    rear->link = temp->link;
                    delete temp;
                }
            }
            else                                        //结果多项式链表中的数据项指数较小
            {
                temp = new PolyNode;
                temp->coef = c;
                temp->expon = e;
                temp->link = rear->link;        //把新表项插入到结果多项式链表中
                rear->link = temp;
                rear = rear->link;
                
            }
            P2 = P2->link;
        }
        P1 = P1->link;
    }
    temp = first; first = first->link; delete temp;//删除附加头结点
    return first;
}

void PrintPoly(Polynomial P)    //输出多项式
{
    int flag=0;        //输出序号，用来辅助调整输出格式
    if(!P){ printf("0 0\n"); return;}  //当多项式链表为空

    while(P)
    {
        if(!flag)    flag=1;  //第一次输出,没有前置空格
        else   printf(" ");   //输出前置空格
        printf("%d %d",P->coef,P->expon);
        P = P->link;
    }
    printf("\n");
     
}