南邮数据结构实验1 一元多项式的相加和相乘

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
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;
}