南邮数据结构实验1 一元多项式的相加和相乘

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内容和提示:

1.设计带表头结点的单链表表示的多项式类，在该类上定义和实现教材2.4节中程序2.7的多项式类上的各个运算。

2.在该类上增加成员函数void PolyMul(Polynominal & r)，并重载*运算符。

3.实现菜单驱动的main函数，测试多项式类上各个运算：输入多项式，显示多项式，多项式加法和乘法运算。

4.提示：注意本实习采用带表头的非循环链表存储多项式。除乘法运算外，请通过修改教材2.4节的程序实现各运算。多项式相乘的算法为：将乘数多项式的每一项与被乘数多项式的所有项分别相乘（即系数相乘，指数相加），得到中间多项式；调用函数PolyAdd将这些中间多项式依次加到结果多项式中。值得注意的是，在相成的过程中不能改变两个原始多项式的值

#include<iostream>using namespace std;class Term{public:    Term(int c, int e);    Term(int c, int e, Term* nxt);    Term* InsertAfter(int c, int e);private:    int coef;    int exp;    Term* link;    friend ostream& operator<<(ostream &, const Term &);    friend class Polynominal;};Term::Term(int c, int e) :coef(c), exp(e){    link = 0;}Term::Term(int c, int e, Term *nxt) : coef(c), exp(e){    link = nxt;}Term* Term::InsertAfter(int c, int e){    link = new Term(c, e, link);    return link;}ostream& operator<<(ostream& out, const Term& val){    if (0 == val.coef)         return out;    if (1 != val.coef)        out << val.coef;    switch (val.exp)    {    case 0:break;    case 1:out << "X"; break;    default:out << "X^" << val.exp; break;    }    return out;}class Polynominal{public:    Polynominal();    ~Polynominal();    void AddTerms(istream& in);    void Output(ostream& out)const;    void PolyAdd(Polynominal& r);    void PolyMul(Polynominal& r);private:    Term* theList;    friend ostream& operator<<(ostream &, const Polynominal &);    friend istream& operator>>(istream&, Polynominal &);    friend Polynominal& operator+(Polynominal &, Polynominal &);    friend Polynominal& operator*(Polynominal &, Polynominal &);};Polynominal::Polynominal(){    theList = new Term(0, -1);  //头结点    theList->link = NULL;      //单链表尾结点指针域为空}Polynominal::~Polynominal(){    Term* p = theList->link;    while (p != NULL)    {        theList->link = p->link;        delete p;        p = theList->link;    }    delete theList;}void Polynominal::AddTerms(istream & in){    Term* q = theList;    int c, e;    for (;;)    {        cout << "Input a term(coef,exp):\n" << endl;        cin >> c >> e;        q = q->InsertAfter(c, e);        if (0 > e) break;    }}void Polynominal::Output(ostream& out)const{    int first = 1;    Term *p = theList->link;    for (; p != NULL && p->exp >= 0; p = p->link)    {        if (!first && (p->coef>0)) out << "+";        first = 0;        out << *p;    }    cout << endl;}void Polynominal::PolyAdd(Polynominal& r){    Term *q, *q1 = theList, *p;     //q1指向表头结点    p = r.theList->link;            //p指向第一个要处理的结点    q = q1->link;                   //q1是q的前驱，p和q就指向两个当前进行比较的项    while (p != NULL && p->exp >= 0)//对r的单循环链表遍历，知道全部结点都处理完    {        while (p->exp < q->exp)     //跳过q->exp大的项        {            q1 = q;            q = q->link;        }        if (p->exp == q->exp)       //当指数相等时，系数相加        {            q->coef = q->coef + p->coef;            if (q->coef == 0)       //若相加后系数为0，则删除q            {                q1->link = q->link;                delete(q);                q = q1->link;       //重置q指针            }            else            {                q1 = q;             //若相加后系数不为0，则移动q1和q                q = q->link;            }        }        else                        //p>exp>q->exp的情况            q1 = q1->InsertAfter(p->coef, p->exp); //以p的系数和指数生成新结点，插入q1后        p = p->link;    }}void Polynominal::PolyMul(Polynominal& r){    Polynominal result;             //定义相乘后的数据    Term *n = result.theList;       //n指向result的头结点    n = n->InsertAfter(0, 0);       //在result的头结点后插入新结点，系数指数均为0    Term *p = r.theList->link;      //p指向第一个要处理的结点    while(p->exp >= 0)              //对r的单循环链表遍历    {        Polynominal tmp;            //存储某段相乘后的数据        Term *m = tmp.theList;      //m指向tmp的头结点        Term *q = theList->link;    //q指向表头结点的后继结点        while(q->exp >= 0)          //对当前对象的单循环环链表遍历        {            m = m->InsertAfter((p->coef)*(q->coef), (p->exp) + (q->exp)); //生成新结点插入n后            q = q->link;                  }        result.PolyAdd(tmp);        //将temp加到result上        p = p->link;     }    Term *q = theList->link;        //q指向表头结点的后继结点    while(q != NULL)                //删除原对象的所有数据    {        theList->link = q->link;        delete q;        q = theList->link;    }    q = theList;    q = q->InsertAfter(0, 0);    PolyAdd(result);                //将result加到当前对象上}ostream &operator<<(ostream& out, const Polynominal& x){    x.Output(out);    return out;}istream &operator>>(istream& in, Polynominal &x){    x.AddTerms(in);    return in;}Polynominal & operator + (Polynominal &a, Polynominal &b){    a.PolyAdd(b);    return a;}Polynominal & operator * (Polynominal &a, Polynominal &b){    a.PolyMul(b);    return a;}int main(){    int choose;    cout << "choose calculate type   1.add   2.mul" << endl;    cin >> choose;    Polynominal p, q;    switch (choose)    {        case 1:            cin >> p; cout << p;            cin >> q; cout << q;            q = q + p;            break;        case 2:            cin >> p; cout << p;            cin >> q; cout << q;            q = q * p;            break;    }    cout << q;    return 0;}

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