C++算法与数据结构学习笔记------单链表实现多项式

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//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;}

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