C++算法与数据结构学习笔记------单链表实现多项式

//使用单链表实现了多项式的加减和乘法。

#include<iostream.h>
template<class T>
class List;
template<class T>
class Node{
friend class List<T>;
private:
T coef,exp;
Node<T> *next;
};
template<class T>
class List{
private:
Node<T> *first;
public:
List(){first=0;}
~List();
bool Empty() const{return first==0;}
int Length()const;
int Locate(const T& c,const T& x)const;
bool Retrieve(int k,T& c, T& x)const;
List<T>& Insert(int k,const T& c, const T& x);
List<T>& Delete(int k,T& c,T& x);
void PrintList();
List<T>& polyAdd(List<T>& poly2);
List<T>& polyMul(List<T>& poly2,List<T>& poly3);
List<T>& mergerPoly();
};
template<class T>
List<T>::~List()
{
Node<T> *next;
while(first){
next=first->next;
delete first;
first=next;
}
}
template<class T>
int List<T>::Length()const
{
Node<T> *current=first;
int len=0;
while(current){
len++;
current=current->next;
}
return len;
}
template<class T>
int List<T>::Locate(const T& c,const T& x)const
{
Node<T> *current=first;
int index=1;
while(current&¤t->coef!=c&¤t->exp!=x){
current=current->next;
index++;
}
if(current)return index;
return 0;
}
template<class T>
bool List<T>::Retrieve(int k,T& c,T& x)const
{
if(k<1)return false;
Node<T> *current=first;
int index=1;
while(index<k&¤t){
current=current->next;
index++;
}
if(current){
c=current->coef;
x=current->exp;
return true;
}
return false;
}
template<class T>
List<T>& List<T>::Insert(int k,const T& c,const T& x)
{
Node<T> *p=first;
for(int index=1;index<k&&p;index++)
p=p->next;

Node<T> *y=new Node<T>;
y->coef=c;
y->exp=x;
if(k){
y->next=p->next;
p->next=y;
}
else{
y->next=first;
first=y;
}
return *this;
}
template<class T>
List<T>& List<T>::Delete(int k,T& c,T& x)
{
Node<T> *p=first;
if(k==1)
first=first->next;
else{
Node<T> *q=first;
for(int index=1;index<k-1&&q;index++)
q=q->next;
if(!q||!q->next) return *this;
p=q->next;
q->next=p->next;
}
x=p->exp;
c=p->coef;
delete p;
return *this;
}
template<class T>
void List<T>::PrintList( )
{
Node<T> *current;
for(current=first;current;current=current->next)
{
if (current->coef>=0&¤t!=first)
{
if (0==current->exp)
cout<<"+"<<current->coef;
else if (1==current->exp)
cout<<"+"<<current->coef<<"x";
else
cout<<"+"<<current->coef<<"x^"<<current->exp;
}
else
{
if (0==current->exp)
cout<<current->coef;
else if (1==current->exp)
cout<<current->coef<<"x";
else
cout<<current->coef<<"x^"<<current->exp;
}
}
cout<<endl;
}
template<class T>
List<T>& List<T>::polyAdd(List<T>& poly2)
{
Node<T> *p=first,*q=poly2.first,*before=first;
while(q!=0)
{
if (p!=0)
{
if (p->exp<q->exp)
{
before=p;
p=p->next;
}
else if (p->exp>q->exp)
{
Insert(Locate(p->coef,p->exp),q->coef,q->exp);
q=q->next;
}
else if (p->exp==q->exp)
{
p->coef+=q->coef;
before=p;
p=p->next;
q=q->next;
}
}
else
{
Insert(Length(),q->coef,q->exp);
q=q->next;
}
}
return *this;
}
template <class T>
List<T>& List<T>::polyMul(List<T>& poly2,List<T>& poly3)
{
Node<T> *p=first,*q=poly2.first;
int i=0;
T c,x;
while(p!=0)
{
while(q!=0)
{
c=p->coef*q->coef;
x=p->exp+q->exp;
q=q->next;
poly3.Insert(i,c,x);
i++;
}
p=p->next;
q=poly2.first;
}
return *this;
}
template <class T>
List<T>& List<T>::mergerPoly()
{
Node<T> *p=first,*q=p->next,*beforeQ=first,*temp;
while(p!=0&&p->next!=0)
{
while(q!=0)
{
if (p->exp==q->exp)
{
p->coef+=q->coef;
temp=q->next;
delete q;
q=temp;
beforeQ->next=q;
}
else
{
beforeQ=q;
q=q->next;
}
}
p=p->next;
beforeQ=p;
if (beforeQ!=0)    q=p->next;
}
Node<T> *beforeP=0;
p=first;
while(p!=0)
{
if (0==p->coef)
{
temp=p->next;
delete p;
p=temp;
if (beforeP!=0)    beforeP->next=p;
else first=p;
}
else
{
beforeP=p;
p=p->next;
}
}
return *this;
}
int main()
{
List<int> poly1,poly2,poly3;
int c,x;
cout <<"输入第一个多项式，提示：输入0 0，结束多项式输入。"<<endl;
while(0!=c||0!=x)
{
cout <<"请输入多项式的系数:" ;
cin >>c;
cout <<"请输入多项式的指数:" ;
cin >>x;
if (c!=0||x!=0)
poly1.Insert(poly1.Length(),c,x);
}
c=1;
cout <<"输入第二个多项式，提示：输入0 0，结束多项式输入。"<<endl;
while(0!=c||0!=x)
{
cout <<"请输入多项式的系数:" ;
cin >>c;
cout <<"请输入多项式的指数:" ;
cin >>x;
if (c!=0||x!=0)
poly2.Insert(poly2.Length(),c,x);
}
cout<<"A(x)=";
poly1.PrintList();
cout<<"B(x)=";
poly2.PrintList();
cout <<"请输入要做的运算，1加法，2乘法：";
cin >>c;
if (1==c)
{
poly1.polyAdd(poly2);
poly1.mergerPoly();
cout <<"A(x)+B(x)=";
poly1.PrintList();
}
else if(2==c)
{
poly1.polyMul(poly2,poly3);
poly3.mergerPoly();
cout <<"A(x)*B(x)=";
poly3.PrintList();
}
else cout<<"输入错误";

return 0;
}