南邮数据结构实验1.3 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<iostream.h>
class Term        // 多项式的每一项类
{

private:      
int coef;
int exp;
Term *link; 
public:    
Term(int c, int e);       
Term(int c, int e, Term *nxt);         
Term * InsertAfter(int c, int e);      

friend ostream & operator<< (ostream &out, const Term &val);  //输出每一项运算符重载

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)        //插入一项  p调用  调用结束 p指向插进来的项                  
{
link = new Term(c, e, link);
return link;
}

ostream &  operator<< (ostream &out,const  Term &val)    //输出每一项运算符重载
{
if (val.coef == 0) return out;
out << val.coef;
switch (val.exp)
{
case 0:break;
case 1:out << "X"; break;
default:out << "X^" << val.exp; break;
}
return out;
}

//#include"term.h"
class Polynominal
{

private:
Term  * first;    
public:
Polynominal();
~Polynominal();
void AddTerms(istream& in);
void Output(ostream& out)const;
void PolyAdd(Polynominal &r);
void PolyMul(Polynominal &r);
friend ostream& operator<<(ostream&, const Polynominal &);
friend istream& operator>>(istream&, Polynominal&);
friend Polynominal& operator +(Polynominal&, Polynominal&);         //友员可以忽略
friend Polynominal& operator *(Polynominal&, Polynominal&);
};

Polynominal::Polynominal()                                          //带表头的 非循环链表
{
first=new Term(0,-1);                                           //创建一个表头 由first指向
first->link = NULL;     
}

Polynominal::~Polynominal()                                         //带表头结点单链表的析构
{
Term * p=first->link;
while (p)
{

first->link=p->link;
delete p;
p=first->link;
}
}

void Polynominal::AddTerms(istream& in) //多项式 输入各项
{
Term * q = first;//  q指向单链接表的头结点
int c, e;
for (;;)
{
cout << "Input a term(coef,exp):\n" << endl;
cin >> c >> e;
if (e < 0) break;
q = q->InsertAfter(c, e);//调用term类里的 插入项函数 直到指数为负数
}
}

void Polynominal::Output(ostream& out)const //多项式 输出各项   
{
int a = 1; Term * p = first->link;//p指向单链接表的第一个元素

cout << "the polynominal is :\n" <<endl;
do{
if (!a && (p->coef>0)) out << "+";//若a=0并且是正数 输出+
a = 0;                              
out << *p;                          
p = p->link;                 
} while (p);
cout << "\n" << endl;
}

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;
}

void Polynominal::PolyAdd(Polynominal& r)           //多项式相加
{                                               
Term* q, *q1 = first, *p;//q1指向表头节点
p = r.first->link;//P 指向第一个元素
q = q1->link;   //q指向第一个元素
                                        
while(p)                //带表头的链接表遍历  循环单链表可以最后指向头结点的 exp -1
{
while(p->exp < q->exp)   
{
if(!q->link) break;
q1 = q; q = q->link;  //q后移
}                    //经过此循环，q里次数比p里所有元素高的都在前面。
if (p->exp == q->exp)    
{
q->coef = q->coef + p->coef;   

if(q->link)
{
q1 = q; q = q->link; 
}
}
else if(p->exp >q->exp) 
{
    q1 = q1->InsertAfter(p->coef, p->exp);//q的指数比p小 插入此时q的最前面
}

else 
{
q = q->InsertAfter(p->coef, p->exp);    //插入之后，q指向新插入的结点
}
p = p->link; 
}
}
                                 
void Polynominal::PolyMul(Polynominal& r)                 //多项式乘法
{
   Term* q, *q1 = first, *p; //q1指向表头节点
p = r.first->link;   //P 指向第一个元素
q = q1->link;          //q指向第一个元素
Polynominal T;
Term *t=T.first;         //临时指针;

while(p)
{
while(q)
{
t=t->InsertAfter(q->coef*p->coef,q->exp+p->exp);
if(!q->link) break;
q1 = q; q = q->link;  //q后移

}
q1=first; q=q1->link;     //q 归位
p=p->link;

}   

Term *t1=T.first->link; //增加的代码
    Term *b_t=T.first->link; //对T的每一项进行排序，并且合并。 最终降幂排序。
t=b_t->link;
while(t1)
{
while(t)
{
if(t->exp==t1->exp) 
{ 
t1->coef+=t->coef; 
b_t->link=t->link;
t->coef=0;
t=b_t->link;
}
else
{
t=t->link;
b_t=b_t->link;
}
}
t1=t1->link;
b_t=t1;
t=t1->link;
if(!t) break;
}

while(q)
{ 
q->coef=0;
q1 = q; q = q->link;    //q后移
}
q1=first; q=first->link;     //q 归位
PolyAdd(T); 
}

void Menu()
{
    cout<<"*****Input       Polynominal p - Input 1 *****"<<endl<<endl;

cout<<"*****Input       Polynominal q - Input 2 *****"<<endl<<endl;

cout<<"*****Add     two Polynominals  - Input 3 *****"<<endl<<endl;

cout<<"*****Multiply two Polynominals - Input 4 *****"<<endl<<endl;

cout<<"*****           Exit  -Input 0           *****"<<endl<<endl;

cout<<"Input your choice:"<<endl;
}

void Choice(int &choice)
{
Polynominal A, B;

switch(choice)
{
case 1:cin>>A;cout<<"A---"<<A<<endl;Menu();break;
case 2:cin>>B;cout<<"B---"<<B<<endl;Menu();break;
case 3:cout<<"Please input  two   Polynominals: "<<endl;
  cin>>A;cin>>B;cout<<"Add:"<<A+B<<endl;Menu();break; 
case 4:cout<<"Please input  two   Polynominals: "<<endl;
  cin>>A;cin>>B;cout<<"Multiply:"<<A*B<<endl;Menu();break; 
case 0:cout<<"*****                See U !               *****"<<endl; break;
}

}

//#include"polynominal.h"
//#include"a.h"

void main()
{
Menu();
cout<<"降幂输入"<<endl;
    int choice; 
do
{   
cin>>choice;
Choice(choice);

}while(choice);
}