链表实现多项式求和求积

#include <iostream>
#include <cstdio>
#include<cstdlib>
using namespace std;

struct Node {
    double coef;
    int expn;
    Node *next;
};

void CreatPolynomial(Node *&head, int n)        //    生成带表头结点的单链表，除头结点外另生成n个结点
{
    head = (Node *)malloc(sizeof(Node));
    head->coef = 0;
    head->expn = 0;
    head->next = NULL;                            //    初始化头结点
    cout << "请输入各项系数及指数：" << endl;
    Node *p = head;
    for(int i = 0; i < n; i++) {
        p->next = (Node *)malloc(sizeof(Node));    //    生成新结点，尾插入生成链表
        p = p->next;
        cin >> p->coef >> p->expn;
        p->next = NULL;
    }
}

void PrintPolynomial(Node *&head)
{
    if(head->next == NULL)                            //    结果是0时直接输出0
        putchar(‘0‘);
    else {
        for(Node *p = head->next; p != NULL; p = p->next) {
            if(p != head->next && p->coef >0)        //    当p非首项且指向的系数为正时才输出‘+‘
                putchar(‘+‘);                        //    之前只判定了p->coef >0
            
            if(p->coef == 1) {                        //    系数为1或-1时特殊处理
                if(p->expn == 0)
                    putchar(‘1‘);                    //    判断条件不能写在一起：
            }                                        //    if(p->coef == 1 && p->expn == 0) putchar(‘1‘);
            else if(p->coef == -1)
                putchar(‘-‘);
            else
                cout << p->coef;
            
            switch(p->expn) {                        //  指数为0或1时特殊处理
                
            case 0:
                break;
                
            case 1:
                putchar(‘x‘);
                break;
                
            default:
                p->expn < 0 ? printf("x^(%d)", p->expn) : printf("x^%d", p->expn);    //    指数小于0时打括号
                break;
            }
        }
    }
    cout << endl;
}
//    上面的函数中若系数为int型，那么也可以改为switch结构，这是C语言的缺陷？

void Free(Node *&head)
{
    Node *q = NULL;
    for(Node *p = head; p != NULL; p = q) {
        q = p->next;
        free(p);
    }
}

char cmp(int a, int b)
{
    if(a > b)
        return ‘>‘;
    if(a < b)
        return ‘<‘;
    return ‘=‘;
}
//求乘积
Node * mul(Node *&pA,Node *&pB)
{
    cout<<"mul :"<<endl;
    Node *ha=pA->next;
    Node *hb=pB->next;
    Node *pC=(Node*)malloc(sizeof(Node));
    Node *p=pC;
    while(ha)
    {
        hb=pB->next;
        while(hb)
        {
            p=pC;
            int expn=ha->expn+hb->expn;
            double coef=ha->coef*hb->coef;
            cout<<expn<<" mul "<<coef<<endl;
            while(p->next&&p->next->expn!=expn)
            {
                p=p->next;
            }
            if(!p->next)
            {
                Node* new1=(Node*)malloc(sizeof(Node));
                new1->expn=expn;
                new1->coef=coef;
                p->next=new1;
                new1->next=NULL;
            }
            else if(p->next->expn==expn)
            {
                p->next->expn=expn;
                p->next->coef+=coef;
            }
            hb=hb->next;
        }
        ha=ha->next; 
    }
    return pC;
}

void AddPolynomial(Node *&pA, Node *&pB)        //    传进两个链表的头指针
{
    Node *ha = pA;
    Node *hb = pB;
    Node *qa = ha->next;                        //    ha, hb分别跟在qa, qb的后一位置
    Node *qb = hb->next;                        //    qa, qb分别指向Pa, Pb中当前比较元素
    while(qa && qb) 
    {
        double sum = 0;
        int a = qa->expn;
        int b = qb->expn;
        switch( cmp(a, b) ) {
            
        case ‘<‘:
            ha = qa;
            qa = qa->next;                        //    非ha = ha->next;
            break;
            
        case ‘=‘:            
            sum = qa->coef + qb->coef;
            if(sum != 0.0) {
                qa->coef = sum;
                ha = qa;                
            }
            else {
                if(ha->next != qa)
                    cout << "Error: ha->next != qa" << endl;
                ha->next = ha->next->next;        //  删除和为0的结点，ha不变，还在qa后一位置
                free(qa);
            }
            if(hb->next != qb)
                cout << "Error: hb->next != qb" << endl;
            hb->next = hb->next->next;
            free(qb);
            qb = hb->next;
            qa = ha->next;
            break;
            
        case ‘>‘:
            hb->next = hb->next->next;            //    删除qb指向的结点
            qb->next = ha->next;                //    将qb插入ha后qa前
            ha->next = qb;
            
            qb = hb->next;                        //    not qb = ha->next
            ha = ha->next;
            break;
            
        default:
            cout << "Error!" << endl;
            break;
        }
    }
    if(qb)
        ha->next = qb;
    free(hb);
}

int main(void)
{
//    freopen("cin.txt", "r", stdin);
    Node *A = NULL;
    Node *B = NULL; 
    int lenA;
    int lenB;
    while(cout << "请输入A的项数：" << endl, cin >> lenA) {
        CreatPolynomial(A, lenA);                    //    生成A链表        
        cout << "请输入B的项数：" << endl;            //    生成B链表
        cin >> lenB;
        CreatPolynomial(B, lenB);
        
        cout << " A = ";                            //    输出A链表
        PrintPolynomial(A);
        cout << " B = ";                            //    输出B链表
        PrintPolynomial(B);
        
        cout<<"A*B= ";
        Node *C=mul(A,B);
        PrintPolynomial(C);
        AddPolynomial(A, B);                        //    A = A + B
        cout << "A+B= ";
        PrintPolynomial(A);  //    输出和
        cout << endl;
        
        Free(A);                                    //    务必释放结点
    }
    return 0;
}