数据结构和算法C++语言实现：使用链表实现稀疏多项式

1、链表的基础知识

       关于链表的基础知识还有不熟悉的，请查看链表的实现（基于动态内存分配）

2、使用链表实现稀疏多项式，也是基于上述的链表来实现的。

       稀疏多项式可以当作一种链表结构，所以，可以直接从上述的链表派生过来。在派生之前应该考虑清楚稀疏多项式的结构，稀疏多项式的基本单元由系数和指数构成，所以构成该类的模板需要两个参数，声明为如下的形式：

    template<typename T,typename S>       class CPolynomial

        由于CPolynomial是从CList继承过来的，CList的声明如下所示：

template <typename T>class List{protected:class Node{public:Node *pNext;T m_data;Node(){memset(&m_data, 0, sizeof(m_data));pNext = NULL;}};//typedef Node * Link_List;int m_Lenth;public:List();List(const List &m_List);~List();const List&operator=(const List &m_List);    bool List_IsEmpty();int  List_Lenth();void List_Insert(T num);void List_Delete(int nPos);void List_Destroy();void List_Clear();void List_Display();Node * List_GetHead() const;bool List_FindElem(T num);void List_Modify(T num, int nPos);protected://Link_List pHead;Node *pHead;typedef Node* Position;};#endif

 在构建CPolynomial时，还需要考虑到基类的模板的参数化的问题，所以，这里需要提供一个模板类，用以实例化CList,定义如下：

template<typename T,typename S>class Item{public:T coeff;S index;Item(){coeff = 0;index = 0;}Item(const Item& item){coeff = item.coeff;index = item.index;}Item & operator = (const Item& item){coeff = item.coeff;index = item.index;return *this;}bool operator == (const Item& item){return coeff == item.coeff&& index == item.index;}};

为什么要按照上述的方法来定义呢？从如下的方面来考虑的：

1、该实例类需要和CPolynomial中的指数和系数对应

2、该实例化类的对象之间存在赋值，拷贝，判断相等的操作

到目前，构建该多项式类的基本工作已经完成了，下面需要来实际构建该类：

<pre name="code" class="cpp">template<typename T,typename S>class CPolynomial :public List<Item<T,S>>{public:CPolynomial();CPolynomial(const CPolynomial& poly);~CPolynomial();//操作符重载const CPolynomial &operator =(const CPolynomial &polyn);//friend CPolynomial operator+(const CPolynomial &polyn);    //①friend CPolynomial operator+<>(const CPolynomial<T,S>& polynLeft,const CPolynomial<T,S> &polynRight);template<typename T,typename S>friend CPolynomial<T, S> operator+(const CPolynomial<T, S>&, const CPolynomial<T, S>&);template<typename T,typename S>friend CPolynomial<T,S> operator-(const CPolynomial<T,S>& polynLeft,const CPolynomial<T,S> &polynRight){CPolynomial<T, S> polynTemp = polynLeft;polynTemp.PolynSubstract(polynRight);return polynTemp;}friend CPolynomial operator*(const CPolynomial &polyn){}void PolynInsert(const Item<T,S> & item);void PolynRemove(const Item<T,S> & item);bool PolynSearch(const Item<T,S> &item,int &nPos);bool PolynSearchIndex(const S& index,Position *pos = NULL);bool PolynModify(Position pos);bool PolynIsEmpty();void PolynClear();void PolynDestroy();void PolynPrint();void PolynAdd(const CPolynomial &polynSecond);void PolynSubstract(CPolynomial polynSecond);void PolynMultiply(CPolynomial polynFirst, CPolynomial polynSecond);public:int m_nLenth;List<Item<T,S>> m_List;};

上述的多项式类至此已经构建完成，接下来便进行相关的测试：

<pre name="code" class="cpp">#include "List.h"#include "List.cpp"#include "Polynomial.h"#include "Polynomial.cpp"void main(){List<int> myList;for(int i=0;i<12;i++){myList.List_Insert(i);}myList.List_Insert(15);cout<<"**myList:"<<myList.List_Lenth()<<endl;myList.List_Display();List<int> newList = myList;cout<<"**newList:"<<newList.List_Lenth()<<endl;newList.List_Display();myList.List_Insert(-2);List<int> newOpList;newOpList = myList;cout<<"**newOpList:"<<newOpList.List_Lenth()<<endl;newOpList.List_Display();for(int i=0;i<5;i++)newOpList.List_Delete(1);cout<<"**newOpList:"<<newOpList.List_Lenth()<<endl;newOpList.List_Display();newOpList.List_Destroy();     Item<double, int> item;CPolynomial<double, int> m_Polyn;for (int i = 1; i < 6; i++){item.coeff = i*3.14;item.index = i;m_Polyn.PolynInsert(item);}m_Polyn.PolynPrint();CPolynomial<double, int> m_PolynSecond;for (int i = 3; i < 8; i++){item.coeff = i*i;item.index = i;m_PolynSecond.PolynInsert(item);}cout << "Second:" << endl;m_PolynSecond.PolynPrint();m_Polyn.PolynAdd(m_PolynSecond);cout << "Add:" << endl;m_Polyn.PolynPrint();CPolynomial<double, int> m_PolynThird;m_PolynThird = m_Polyn + m_PolynSecond;cout << "+:" << endl;m_PolynThird.PolynPrint();CPolynomial<double, int> m_PolynForth;m_PolynForth = m_PolynThird - m_PolynSecond;cout << "Forth:" << endl;m_PolynForth.PolynPrint();system("pause");}

最终程序的输出如下所示：

至此，多项式的构建完成了。通过类模板和继承来实现了稀疏多项式，并且实现了操作符的重载。