稀疏多项式C++链表的问题

 #include<iostream>

using namespace std;
#ifndef POLYNOMIAL_H
#define POLYNOMIAL_H
template<class T>class Polynomial;
template<class T>ostream& operator<<(ostream& out, Polynomial<T>&a );

template<class T>
class Polynomial{
private:
    class Term{
    public:
        T xishu;
        unsigned mi;
    };
    class Node{
    public:
        Term data;
        Node* next;
        Node(T x = 0, unsigned y = 0, Node* p = 0){
            data.xishu = x;
            data.mi = y;
            Node* next = p;
        }
    };
public:
    Polynomial();
    ~Polynomial();
    Polynomial<T> operator+(const Polynomial<T>&);
    Polynomial<T> operator*(const Polynomial<T>&);
    void initial();
    friend ostream& operator<< <T> (ostream& out, Polynomial<T>& a);

private:
    int highestdigit;
    Node* first;
    int num;//用来判断多项式有几项,即链表节点数,在乘法运算里也要用到
};
template<class T>
Polynomial<T>::Polynomial(){
    first = new Node();
    first->next = new Node();
    num = 0;
    highestdigit = 0;
}
template<class T>
Polynomial<T>::~Polynomial(){
    Node* p = first;
    while (p){
        Node* q = p->next;
        delete p;
        p = q;
    }
}

template<class T>
Polynomial<T> Polynomial<T>::operator+(const Polynomial<T>& second){
    Polynomial<T> sum;
    Node* pa = first->next, *pb = second.first->next, *pc = sum.first;
    int digit = 0, num = 0;
    while (pa&&pb){
        if (pa->data.mi == pb->data.mi)  // 指数相等时  
        {
            T x = pa->data.xishu + pb->data.xishu;
            if (x)     // 相加完的系数不为0时  
            {
                pc->next = new Node(x, pa->data.mi);
                pc = pc->next;
                ++num;
                digit = pa->data.mi;
            }
            pa = pa->next;
            pb = pb->next;
        }
        else if (pa->data.mi < pb->data.mi){
            pc->next = new Node(pa->data.xishu, pa->data.mi);
            pc = pc->next;
            pa = pa->next;
            ++num;
            digit = pa->data.mi;
        }
        else{
            pc->next = new Node(pb->data.xishu, pb->data.mi);
            pc = pc->next;
            pb = pb->next;
            ++num;
            digit = pb->data.mi;
        }
    }
    while (pa){
        pc->next = new Node(pa->data.xishu, pa->data.mi);
        pc = pc->next;
        pa = pa->next;
        ++num;
        digit = pa->data.mi;
    }
    while (pb){
        pc->next = new Node(pb->data.xishu, pb->data.mi);
        pc = pc->next;
        pb = pb->next;
        ++num;
        digit = pb->data.mi;
    }       
    sum.num = num;
    sum.highestdigit = digit;
    return sum;

}

template<class T>
Polynomial<T> Polynomial<T>::operator*(const Polynomial<T>& second){
    Polynomial<T> multi;
    Node* pa = first->next, *pb = second.first->next;
    if (num >=second.num){
        Polynomial<T>* p1 = new Polynomial<T>[second.num];  
        Node **p2 = new Node*[second.num];
        for (int i = 0; i < second.num; ++i){
            while (pa){
                if (pa->next == 0){
                    p1[i].highestdigit = pa->data.mi*pb->data.mi;
                    p1[i].num = num;
                }
                p2[i] = p1[i].first;
                p2[i]->next = new Node(pa->data.xishu*pb->data.xishu, pa->data.mi*pb->data.mi);
                p2[i] = p2[i]->next;
                pa = pa->next;
            }
            pb = pb->next;
            multi = multi + p1[i];
        }
        return multi;
    }
    else{
        Polynomial<T>* p1 = new Polynomial<T>[num];
        Node **p2 = new Node*[num];
        for (int i = 0; i < num; ++i){
            while (pb){
                if(pb->next == 0){
                    p1[i].highestdigit = pa->data.mi*pb->data.mi;
                    p1[i].num = num;
                }
                p2[i] = p1[i].first;
                p2[i]->next = new Node(pb->data.xishu*pa->data.xishu, pb->data.mi*pa->data.mi);
                p2[i] = p2[i]->next;
                pb = pb->next;
            }
            pa = pa->next;
            multi = multi + p1[i];
        }
        return multi;
    }
}

template<class T>
void Polynomial<T>::initial(){
    T a;
    Node* p = first;
    unsigned b, high=0;
    while (cin >> a&&a!=0&&cin>>b){   //输入a=0时结束输入
        if (b >= high)high= b;
        ++num;
        p->next = new Node(a, b);
        p = p->next;
    }
    highestdigit = high;
}
template<class T>
ostream& operator<<(ostream& out, Polynomial<T>& a){
        Polynomial<T>::Node *p = a.first->next;
        if (p->data.xishu == 0)cout << 0 << endl;
        else{
            if (p->data.xishu != 1)
                out << p->data.xishu << "x^" << p->data.mi;
            else    out << "x^" << p->data.mi;          
        }
        p = p->next;
        while (p){
            out << '+';
            if (p->data.xishu != 1)
                out << p->data.xishu << "x^" << p->data.mi;
            else    out << "x^" << p->data.mi;
            p = p->next;
        }
        return out;
    }
    template<class T>
Polynomial<T> Polynomial<T>::operator*(const Polynomial<T>& second){
    Polynomial<T> multi;
    Node* pa = first->next, *pb = second.first->next;
    if (num >=second.num){
        Polynomial<T>* p1 = new Polynomial<T>[second.num];  
        Node **p2 = new Node*[second.num];
        for (int i = 0; i < second.num; ++i){
            while (pa){
                if (pa->next == 0){
                    p1[i].highestdigit = pa->data.mi*pb->data.mi;
                    p1[i].num = num;
                }
                p2[i] = p1[i].first;
                p2[i]->next = new Node(pa->data.xishu*pb->data.xishu, pa->data.mi*pb->data.mi);
                p2[i] = p2[i]->next;
                pa = pa->next;
            }
            pb = pb->next;
            multi = multi + p1[i];
        }
        return multi;
    }
    else{
        Polynomial<T>* p1 = new Polynomial<T>[num];
        Node **p2 = new Node*[num];
        for (int i = 0; i < num; ++i){
            while (pb){
                if(pb->next == 0){
                    p1[i].highestdigit = pa->data.mi*pb->data.mi;
                    p1[i].num = num;
                }
                p2[i] = p1[i].first;
                p2[i]->next = new Node(pb->data.xishu*pa->data.xishu, pb->data.mi*pa->data.mi);
                p2[i] = p2[i]->next;
                pb = pb->next;
            }
            pa = pa->next;
            multi = multi + p1[i];
        }
        return multi;
    }
}
#endif

测试代码如下：
#include "Polynomial.h"
#include<iostream>
using namespace std;
int main(){
    Polynomial<int> a, b, c;
    a.initial();    
    cout << a <<endl;
    b.initial();
    cout << b << endl;
    cout << a + b << endl;
    return 0;
}
看了好久好久了啊，每次输出a+b都是0

删除了你的类析构函数，链表节点的释放改为成员函数myfree()来实现。
这样在+重载函数返回时不会自动释放链表。

 #include<iostream>
using namespace std;

//约定稀疏多项式输入降幂排列
template<class T>class Polynomial;
template<class T>ostream& operator<<(ostream& out, Polynomial<T>&a );

template<class T>
class Polynomial
{
private:
    class Term
    {
    public:
        T xishu;
        unsigned mi;
    };
    class Node
    {
    public:
        Term data;
        Node* next;
        Node(T x = 0, unsigned y = 0, Node* p = 0)
        {
            data.xishu = x;
            data.mi = y;
            next = p;//修改
        }
    };
public:
    Polynomial();
    void myfree();//释放链表各节点
    Polynomial<T>& operator=(const Polynomial<T>& second);
    Polynomial<T> operator+(const Polynomial<T>&);
    void initial();
    friend ostream& operator<< <T> (ostream& out, Polynomial<T>& a);

private:
    int highestdigit;
    Node* first;
    int num;//用来判断多项式有几项,即链表节点数,在乘法运算里也要用到
};
template<class T>
Polynomial<T>::Polynomial()
{
    first = new Node;
    num = 0;
    highestdigit = 0;
}

template<class T>
void Polynomial<T>::myfree()    //释放链表各节点
{
    Node* p = first,* q;
    while (p)
    {
        q = p->next;
        delete p;
        p = q;
    }
}

template<class T>
Polynomial<T>& Polynomial<T>::operator=(const Polynomial<T>& second)
{
    highestdigit = second.highestdigit;
    num=second.num;
    Node* p1=first,*p2=second.first;

    while (p2->next)
    {
        p1->next = new Node();
        p1 = p1->next;
        p2 = p2->next;
        *p1=*p2;
    }       
    return *this;
}

template<class T>
Polynomial<T> Polynomial<T>::operator+(const Polynomial<T>& second)
{
    Polynomial<T> sum;
    Node* pa = first->next, *pb = second.first->next, *pc = sum.first;
    while (pa&&pb)
    {
        if (pa->data.mi == pb->data.mi)  // 指数相等时  
        {
            T x = pa->data.xishu + pb->data.xishu;
            if (x)     // 相加完的系数不为0时  
            {
                pc->next = new Node(x, pa->data.mi);
                pc = pc->next;
                ++sum.num;
                sum.highestdigit = pa->data.mi;
            }
            pa = pa->next;
            pb = pb->next;
        }
        else if (pa->data.mi > pb->data.mi){ 
            pc->next = new Node(pa->data.xishu, pa->data.mi);
            pc = pc->next;
            pa = pa->next;
            ++sum.num;
            sum.highestdigit = pa->data.mi;
        }
        else{
            pc->next = new Node(pb->data.xishu, pb->data.mi);
            pc = pc->next;
            pb = pb->next;
            ++sum.num;
            sum.highestdigit = pb->data.mi;
        }
    }
    while (pa){
        pc->next = new Node(pa->data.xishu, pa->data.mi);
        pc = pc->next;
        pa = pa->next;
        ++sum.num;
        sum.highestdigit = pa->data.mi;
    }
    while (pb){
        pc->next = new Node(pb->data.xishu, pb->data.mi);
        pc = pc->next;
        pb = pb->next;
        ++sum.num;
        sum.highestdigit = pb->data.mi;
    }       
    return sum;
}

template<class T>
void Polynomial<T>::initial()
{
    //释放链表，保留头节点
    Node* p = first->next,* q;
    while (p)
    {
        q = p->next;
        delete p;
        p = q;
    }
    p = first;

    T a;
    int b;
    num=0; highestdigit=0;//修改
    while (cin >> a&&a!=0&&cin>>b){   //输入a=0时结束输入
        if (b >= highestdigit) highestdigit= b;
        ++num;
        p->next = new Node(a, b);
        p =p->next;
    }
    fflush(stdin);//修改
}

template<class T>
ostream& operator<<(ostream& out, Polynomial<T>& a)
{
    Polynomial<T>::Node *p = a.first->next;

    if( p==NULL ) return out;//修改

    if (p->data.xishu == 0)cout << endl;//修改
    else{
        if (p->data.xishu != 1)
            out << p->data.xishu << "x^" << p->data.mi;
        else    out << "x^" << p->data.mi;          
    }
    p = p->next;
    while (p)
    {
        out << '+';
        if (p->data.xishu != 1)
            out << p->data.xishu << "x^" << p->data.mi;
        else    out << "x^" << p->data.mi;
        p = p->next;
    }
    return out;
}


int main(){
    Polynomial<int> a,b, c;

    a.initial();    
    cout <<"a= "<< a <<endl;

    b.initial();
    cout <<"b="<< b << endl;

    c=a+b;
    cout << "c="<< c << endl;

    a.myfree();
    b.myfree();
    c.myfree();

    return 0;
}

运行结果：

是不是拷贝不全？编译就没通过。
T xishu;
T是哪来的？

#include
using namespace std;
#ifndef POLYNOMIAL_H
#define POLYNOMIAL_H
templateclass Polynomial;
templateostream& operator<<(ostream& out, Polynomial&a );

template
class Polynomial{
private:
class Term{
public:
T xishu;
unsigned mi;
};
class Node{
public:
Term data;
Node* next;
Node(T x = 0, unsigned y = 0, Node* p = 0){
data.xishu = x;
data.mi = y;
Node* next = p;
}
};
public:
Polynomial();
~Polynomial();
Polynomial operator+(const Polynomial&);
Polynomial operator*(const Polynomial&);
void initial();
friend ostream& operator<< (ostream& out, Polynomial& a);

private:
int highestdigit;
Node* first;
int num;//用来判断多项式有几项,即链表节点数,在乘法运算里也要用到
};
template
Polynomial::Polynomial(){
first = new Node();
first->next = new Node();
num = 0;
highestdigit = 0;
}
template
Polynomial::~Polynomial(){
Node* p = first;
while (p){
Node* q = p->next;
delete p;
p = q;
}
}

template
Polynomial Polynomial::operator+(const Polynomial& second){
Polynomial sum;
Node* pa = first->next, *pb = second.first->next, *pc = sum.first;
int digit = 0, num = 0;
while (pa&&pb){
if (pa->data.mi == pb->data.mi) // 指数相等时

{
T x = pa->data.xishu + pb->data.xishu;
if (x) // 相加完的系数不为0时

{
pc->next = new Node(x, pa->data.mi);
pc = pc->next;
++num;
digit = pa->data.mi;
}
pa = pa->next;
pb = pb->next;
}
else if (pa->data.mi < pb->data.mi){
pc->next = new Node(pa->data.xishu, pa->data.mi);
pc = pc->next;
pa = pa->next;
++num;
digit = pa->data.mi;
}
else{
pc->next = new Node(pb->data.xishu, pb->data.mi);
pc = pc->next;
pb = pb->next;
++num;
digit = pb->data.mi;
}
}
while (pa){
pc->next = new Node(pa->data.xishu, pa->data.mi);
pc = pc->next;
pa = pa->next;
++num;
digit = pa->data.mi;
}
while (pb){
pc->next = new Node(pb->data.xishu, pb->data.mi);
pc = pc->next;
pb = pb->next;
++num;
digit = pb->data.mi;
}

sum.num = num;
sum.highestdigit = digit;
return sum;

}

template
Polynomial Polynomial::operator*(const Polynomial& second){
Polynomial multi;
Node* pa = first->next, pb = second.first->next;
if (num >=second.num){
Polynomial p1 = new Polynomial[second.num];

Node **p2 = new Node*[second.num];
for (int i = 0; i < second.num; ++i){
while (pa){
if (pa->next == 0){
p1[i].highestdigit = pa->data.mi*pb->data.mi;
p1[i].num = num;
}
p2[i] = p1[i].first;
p2[i]->next = new Node(pa->data.xishu*pb->data.xishu, pa->data.mi*pb->data.mi);
p2[i] = p2[i]->next;
pa = pa->next;
}
pb = pb->next;
multi = multi + p1[i];
}
return multi;
}
else{
Polynomial* p1 = new Polynomial[num];
Node **p2 = new Node*[num];
for (int i = 0; i < num; ++i){
while (pb){
if(pb->next == 0){
p1[i].highestdigit = pa->data.mi*pb->data.mi;
p1[i].num = num;
}
p2[i] = p1[i].first;
p2[i]->next = new Node(pb->data.xishu*pa->data.xishu, pb->data.mi*pa->data.mi);
p2[i] = p2[i]->next;
pb = pb->next;
}
pa = pa->next;
multi = multi + p1[i];
}
return multi;
}
}

template
void Polynomial::initial(){
T a;
Node* p = first;
unsigned b, high=0;
while (cin >> a&&a!=0&&cin>>b){ //输入a=0时结束输入
if (b >= high)high= b;
++num;
p->next = new Node(a, b);
p = p->next;
}
highestdigit = high;
}
template
ostream& operator<<(ostream& out, Polynomial& a){
Polynomial::Node p = a.first->next;
if (p->data.xishu == 0)cout << 0 << endl;
else{
if (p->data.xishu != 1)
out << p->data.xishu << "x^" << p->data.mi;
else out << "x^" << p->data.mi;

}
p = p->next;
while (p){
out << '+';
if (p->data.xishu != 1)
out << p->data.xishu << "x^" << p->data.mi;
else out << "x^" << p->data.mi;
p = p->next;
}
return out;
}
template
Polynomial Polynomial::operator=(const Polynomial&second){
Node p = first->next;
while (p){
Node* q = p->next;
delete p;
p = q;
}
Node* p2 = second.first->next;
p = first;
while (p2){
p->next = new Node(p2->data.xishu, p2->data.mi);
p = p->next;
p2 = p2->next;
}
return *this;
}

#endif

#include
using namespace std;
#ifndef POLYNOMIAL_H
#define POLYNOMIAL_H
templateclass Polynomial;
templateostream& operator<<(ostream& out, Polynomial&a );

template
class Polynomial{
private:
class Term{
public:
T xishu;
unsigned mi;
};
class Node{
public:
Term data;
Node* next;
Node(T x = 0, unsigned y = 0, Node* p = 0){
data.xishu = x;
data.mi = y;
Node* next = p;
}
};
public:
Polynomial();
~Polynomial();
Polynomial operator+(const Polynomial&);
Polynomial operator*(const Polynomial&);
void initial();
friend ostream& operator<< (ostream& out, Polynomial& a);

private:
int highestdigit;
Node* first;
int num;//用来判断多项式有几项,即链表节点数,在乘法运算里也要用到
};
template
Polynomial::Polynomial(){
first = new Node();
first->next = new Node();
num = 0;
highestdigit = 0;
}
template
Polynomial::~Polynomial(){
Node* p = first;
while (p){
Node* q = p->next;
delete p;
p = q;
}
}

template
Polynomial Polynomial::operator+(const Polynomial& second){
Polynomial sum;
Node* pa = first->next, *pb = second.first->next, *pc = sum.first;
int digit = 0, num = 0;
while (pa&&pb){
if (pa->data.mi == pb->data.mi) // 指数相等时

{
T x = pa->data.xishu + pb->data.xishu;
if (x) // 相加完的系数不为0时

{
pc->next = new Node(x, pa->data.mi);
pc = pc->next;
++num;
digit = pa->data.mi;
}
pa = pa->next;
pb = pb->next;
}
else if (pa->data.mi < pb->data.mi){
pc->next = new Node(pa->data.xishu, pa->data.mi);
pc = pc->next;
pa = pa->next;
++num;
digit = pa->data.mi;
}
else{
pc->next = new Node(pb->data.xishu, pb->data.mi);
pc = pc->next;
pb = pb->next;
++num;
digit = pb->data.mi;
}
}
while (pa){
pc->next = new Node(pa->data.xishu, pa->data.mi);
pc = pc->next;
pa = pa->next;
++num;
digit = pa->data.mi;
}
while (pb){
pc->next = new Node(pb->data.xishu, pb->data.mi);
pc = pc->next;
pb = pb->next;
++num;
digit = pb->data.mi;
}

sum.num = num;
sum.highestdigit = digit;
return sum;

}

template
Polynomial Polynomial::operator*(const Polynomial& second){
Polynomial multi;
Node* pa = first->next, pb = second.first->next;
if (num >=second.num){
Polynomial p1 = new Polynomial[second.num];

Node **p2 = new Node*[second.num];
for (int i = 0; i < second.num; ++i){
while (pa){
if (pa->next == 0){
p1[i].highestdigit = pa->data.mi*pb->data.mi;
p1[i].num = num;
}
p2[i] = p1[i].first;
p2[i]->next = new Node(pa->data.xishu*pb->data.xishu, pa->data.mi*pb->data.mi);
p2[i] = p2[i]->next;
pa = pa->next;
}
pb = pb->next;
multi = multi + p1[i];
}
return multi;
}
else{
Polynomial* p1 = new Polynomial[num];
Node **p2 = new Node*[num];
for (int i = 0; i < num; ++i){
while (pb){
if(pb->next == 0){
p1[i].highestdigit = pa->data.mi*pb->data.mi;
p1[i].num = num;
}
p2[i] = p1[i].first;
p2[i]->next = new Node(pb->data.xishu*pa->data.xishu, pb->data.mi*pa->data.mi);
p2[i] = p2[i]->next;
pb = pb->next;
}
pa = pa->next;
multi = multi + p1[i];
}
return multi;
}
}

template
void Polynomial::initial(){
T a;
Node* p = first;
unsigned b, high=0;
while (cin >> a&&a!=0&&cin>>b){ //输入a=0时结束输入
if (b >= high)high= b;
++num;
p->next = new Node(a, b);
p = p->next;
}
highestdigit = high;
}
template
ostream& operator<<(ostream& out, Polynomial& a){
Polynomial::Node p = a.first->next;
if (p->data.xishu == 0)cout << 0 << endl;
else{
if (p->data.xishu != 1)
out << p->data.xishu << "x^" << p->data.mi;
else out << "x^" << p->data.mi;

}
p = p->next;
while (p){
out << '+';
if (p->data.xishu != 1)
out << p->data.xishu << "x^" << p->data.mi;
else out << "x^" << p->data.mi;
p = p->next;
}
return out;
}
template
Polynomial Polynomial::operator=(const Polynomial&second){
Node p = first->next;
while (p){
Node* q = p->next;
delete p;
p = q;
}
Node* p2 = second.first->next;
p = first;
while (p2){
p->next = new Node(p2->data.xishu, p2->data.mi);
p = p->next;
p2 = p2->next;
}
return *this;
}

#endif

我这个事模板类，但是复制粘贴代码的时候template粘贴不出来

把代码放到代码片里。工具栏里有插入代码片。
就像下面这样：

 void Polynomial::initial(){
T a;
Node* p = first;
unsigned b, high=0;
while (cin >> a&&a!=0&&cin>>b){ //输入a=0时结束输入
if (b >= high)high= b;
++num;
p->next = new Node(a, b);
p = p->next;
}
highestdigit = high;
}

#include
using namespace std;
#ifndef POLYNOMIAL_H
#define POLYNOMIAL_H
templateclass Polynomial;
templateostream& operator<<(ostream& out, Polynomial&a );

template
class Polynomial{
private:
class Term{
public:
T xishu;
unsigned mi;
};
class Node{
public:
Term data;
Node* next;
Node(T x = 0, unsigned y = 0, Node* p = 0){
data.xishu = x;
data.mi = y;
Node* next = p;
}
};
public:
Polynomial();
~Polynomial();
Polynomial operator+(const Polynomial&);
Polynomial operator*(const Polynomial&);
void initial();
friend ostream& operator<< (ostream& out, Polynomial& a);

private:
int highestdigit;
Node* first;
int num;//用来判断多项式有几项,即链表节点数,在乘法运算里也要用到
};
template
Polynomial::Polynomial(){
first = new Node();
first->next = new Node();
num = 0;
highestdigit = 0;
}
template
Polynomial::~Polynomial(){
Node* p = first;
while (p){
Node* q = p->next;
delete p;
p = q;
}
}

template
Polynomial Polynomial::operator+(const Polynomial& second){
Polynomial sum;
Node* pa = first->next, *pb = second.first->next, *pc = sum.first;
int digit = 0, num = 0;
while (pa&&pb){
if (pa->data.mi == pb->data.mi) // 指数相等时

{
T x = pa->data.xishu + pb->data.xishu;
if (x) // 相加完的系数不为0时

{
pc->next = new Node(x, pa->data.mi);
pc = pc->next;
++num;
digit = pa->data.mi;
}
pa = pa->next;
pb = pb->next;
}
else if (pa->data.mi < pb->data.mi){
pc->next = new Node(pa->data.xishu, pa->data.mi);
pc = pc->next;
pa = pa->next;
++num;
digit = pa->data.mi;
}
else{
pc->next = new Node(pb->data.xishu, pb->data.mi);
pc = pc->next;
pb = pb->next;
++num;
digit = pb->data.mi;
}
}
while (pa){
pc->next = new Node(pa->data.xishu, pa->data.mi);
pc = pc->next;
pa = pa->next;
++num;
digit = pa->data.mi;
}
while (pb){
pc->next = new Node(pb->data.xishu, pb->data.mi);
pc = pc->next;
pb = pb->next;
++num;
digit = pb->data.mi;
}

sum.num = num;
sum.highestdigit = digit;
return sum;

}

template
Polynomial Polynomial::operator*(const Polynomial& second){
Polynomial multi;
Node* pa = first->next, pb = second.first->next;
if (num >=second.num){
Polynomial p1 = new Polynomial[second.num];

Node **p2 = new Node*[second.num];
for (int i = 0; i < second.num; ++i){
while (pa){
if (pa->next == 0){
p1[i].highestdigit = pa->data.mi*pb->data.mi;
p1[i].num = num;
}
p2[i] = p1[i].first;
p2[i]->next = new Node(pa->data.xishu*pb->data.xishu, pa->data.mi*pb->data.mi);
p2[i] = p2[i]->next;
pa = pa->next;
}
pb = pb->next;
multi = multi + p1[i];
}
return multi;
}
else{
Polynomial* p1 = new Polynomial[num];
Node **p2 = new Node*[num];
for (int i = 0; i < num; ++i){
while (pb){
if(pb->next == 0){
p1[i].highestdigit = pa->data.mi*pb->data.mi;
p1[i].num = num;
}
p2[i] = p1[i].first;
p2[i]->next = new Node(pb->data.xishu*pa->data.xishu, pb->data.mi*pa->data.mi);
p2[i] = p2[i]->next;
pb = pb->next;
}
pa = pa->next;
multi = multi + p1[i];
}
return multi;
}
}

template
void Polynomial::initial(){
T a;
Node* p = first;
unsigned b, high=0;
while (cin >> a&&a!=0&&cin>>b){ //输入a=0时结束输入
if (b >= high)high= b;
++num;
p->next = new Node(a, b);
p = p->next;
}
highestdigit = high;
}
template
ostream& operator<<(ostream& out, Polynomial& a){
Polynomial::Node p = a.first->next;
if (p->data.xishu == 0)cout << 0 << endl;
else{
if (p->data.xishu != 1)
out << p->data.xishu << "x^" << p->data.mi;
else out << "x^" << p->data.mi;

}
p = p->next;
while (p){
out << '+';
if (p->data.xishu != 1)
out << p->data.xishu << "x^" << p->data.mi;
else out << "x^" << p->data.mi;
p = p->next;
}
return out;
}
template
Polynomial Polynomial::operator=(const Polynomial&second){
Node p = first->next;
while (p){
Node* q = p->next;
delete p;
p = q;
}
Node* p2 = second.first->next;
p = first;
while (p2){
p->next = new Node(p2->data.xishu, p2->data.mi);
p = p->next;
p2 = p2->next;
}
return *this;
}

#endif

 #include "Polynomial.h"
#include<iostream>
using namespace std;
int main(){
    Polynomial<int> a, b, c;
    a.initial();    
    cout << a <<endl;
    b.initial();
    cout << b << endl;
    cout << a + b << endl;
    return 0;
}

1、实现了a.initial()、<<重载、=重载
2、由于Polynomial模板类含有链表，则对象a、b的大小不同，a+b函数重载在返回sum时，sum被释放，无法得到和的返回值。
即含链表的类无法实现加法重载。因为和无法返回。
采用成员函数方法来实现的。

 #include<iostream>
using namespace std;
#ifndef POLYNOMIAL_H
#define POLYNOMIAL_H
//约定多项式输入降幂排列
template<class T>class Polynomial;
template<class T>ostream& operator<<(ostream& out, Polynomial<T>&a );

template<class T>
class Polynomial{
private:
    class Term{
    public:
        T xishu;
        unsigned mi;
    };
    class Node{
    public:
        Term data;
        Node* next;
        Node(T x = 0, unsigned y = 0, Node* p = 0){
            data.xishu = x;
            data.mi = y;
            next = p;//修改
        }
    };
public:
    Polynomial();
    ~Polynomial();
    void add(const Polynomial<T>& c1,const Polynomial<T>& c2);
    Polynomial<T>& operator=(const Polynomial<T>& second);
    Polynomial<T> operator*(const Polynomial<T>&);
    void initial();
    friend ostream& operator<< <T> (ostream& out, Polynomial<T>& a);

private:
    int highestdigit;
    Node* first;
    int num;//用来判断多项式有几项,即链表节点数,在乘法运算里也要用到
};
template<class T>
Polynomial<T>::Polynomial(){
    first = new Node();
    //first->next = new Node();
    num = 0;
    highestdigit = 0;
}
template<class T>
Polynomial<T>::~Polynomial(){
    Node* p = first,* q;
    while (p){
        q = p->next;
        delete p;
        p = q;
    }
}

template<class T>
Polynomial<T>& Polynomial<T>::operator=(const Polynomial<T>& second)
{
    highestdigit = second.highestdigit;
    num=second.num;
    Node* p1=first,*p2=second.first;

    while (p2->next)
    {
        p1->next = new Node();
        p1 = p1->next;
        p2 = p2->next;
        *p1=*p2;
    }       
    return *this;
}

//sum=c1+c2
template<class T>
void Polynomial<T>::add(const Polynomial<T>& c1,const Polynomial<T>& c2)
{
    Node* pa = c1.first->next, *pb = c2.first->next, *pc = first;
    highestdigit = 0, num = 0;
    while (pa&&pb){
        if (pa->data.mi == pb->data.mi)  // 指数相等时  
        {
            T x = pa->data.xishu + pb->data.xishu;
            if (x)     // 相加完的系数不为0时  
            {
                pc->next = new Node(x, pa->data.mi);
                pc = pc->next;
                ++num;
                highestdigit = pa->data.mi;
            }
            pa = pa->next;
            pb = pb->next;
        }
        else if (pa->data.mi > pb->data.mi){ //
            pc->next = new Node(pa->data.xishu, pa->data.mi);
            pc = pc->next;
            pa = pa->next;
            ++num;
            highestdigit = pa->data.mi;
        }
        else{
            pc->next = new Node(pb->data.xishu, pb->data.mi);
            pc = pc->next;
            pb = pb->next;
            ++num;
            highestdigit = pb->data.mi;
        }
    }
    while (pa){
        pc->next = new Node(pa->data.xishu, pa->data.mi);
        pc = pc->next;
        pa = pa->next;
        ++num;
        highestdigit = pa->data.mi;
    }
    while (pb){
        pc->next = new Node(pb->data.xishu, pb->data.mi);
        pc = pc->next;
        pb = pb->next;
        ++num;
        highestdigit = pb->data.mi;
    }       
}

template<class T>
Polynomial<T> Polynomial<T>::operator*(const Polynomial<T>& second){
    Polynomial<T> multi;
    Node* pa = first->next, *pb = second.first->next;
    if (num >=second.num){
        Polynomial<T>* p1 = new Polynomial<T>[second.num];  
        Node **p2 = new Node*[second.num];
        for (int i = 0; i < second.num; ++i){
            while (pa){
                if (pa->next == 0){
                    p1[i].highestdigit = pa->data.mi*pb->data.mi;
                    p1[i].num = num;
                }
                p2[i] = p1[i].first;
                p2[i]->next = new Node(pa->data.xishu*pb->data.xishu, pa->data.mi*pb->data.mi);
                p2[i] = p2[i]->next;
                pa = pa->next;
            }
            pb = pb->next;
            multi = multi + p1[i];
        }
        return multi;
    }
    else{
        Polynomial<T>* p1 = new Polynomial<T>[num];
        Node **p2 = new Node*[num];
        for (int i = 0; i < num; ++i){
            while (pb){
                if(pb->next == 0){
                    p1[i].highestdigit = pa->data.mi*pb->data.mi;
                    p1[i].num = num;
                }
                p2[i] = p1[i].first;
                p2[i]->next = new Node(pb->data.xishu*pa->data.xishu, pb->data.mi*pa->data.mi);
                p2[i] = p2[i]->next;
                pb = pb->next;
            }
            pa = pa->next;
            multi = multi + p1[i];
        }
        return multi;
    }
}

template<class T>
void Polynomial<T>::initial()
{
    T a;
    Node* p = first;
    int b;
    num=0; highestdigit=0;//修改
    while (cin >> a&&a!=0&&cin>>b){   //输入a=0时结束输入
        if (b >= highestdigit) highestdigit= b;
        ++num;
        p->next = new Node(a, b);
        p =p->next;
    }
    fflush(stdin);//修改
}
template<class T>
ostream& operator<<(ostream& out, Polynomial<T>& a)
{
    Polynomial<T>::Node *p = a.first->next;

    if( p==NULL ) return out;//修改

    if (p->data.xishu == 0)cout << endl;//修改
    else{
        if (p->data.xishu != 1)
            out << p->data.xishu << "x^" << p->data.mi;
        else    out << "x^" << p->data.mi;          
    }
    p = p->next;
    while (p){
        out << '+';
        if (p->data.xishu != 1)
            out << p->data.xishu << "x^" << p->data.mi;
        else    out << "x^" << p->data.mi;
        p = p->next;
    }
    return out;
}

#endif

int main(){
    Polynomial<int> a,b, c;

    a.initial();    
    cout <<"a= "<< a <<endl;

    b.initial();
    cout <<"b="<< b << endl;

    c=a;
    cout << "c="<< c << endl;

    c.add(a,b);
    cout << "c="<< c << endl;
    return 0;
}

运行结果：

把代码放到代码片里。工具栏里有插入代码片。
就像下面这样：

void Polynomial::initial(){
T a;
Node* p = first;
unsigned b, high=0;
while (cin >> a&&a!=0&&cin>>b){ //输入a=0时结束输入
if (b >= high)high= b;
++num;
p->next = new Node(a, b);
p = p->next;
}
highestdigit = high;
}

你的意思我懂了，那我
c=a+b;
cout<<c<<endl;为什么还是不对呢，operator+返回的只是一个局部对象啊，c=a+b,就是再进行一次赋值构造啊，而且返回的对象里面也只有头结点，为什么会不对呢
（怎么@某人啊）

给你改过的程序c=a;运行正确。但是c=a+b是不行的。原因是这里先调用a+b,在+重载函数中，return sum时，sum被释放了，调用了析构函数把链表都释放了。返回值没有链表。
接着执行c的=重载函数，但是形参过来的对象已经没有链表了。
所以含链表的类无法实现+重载，只能用成员函数来实现。

 #include<iostream>
using namespace std;

//约定稀疏多项式输入降幂排列
template<class T>class Polynomial;
template<class T>ostream& operator<<(ostream& out, Polynomial<T>&a);

template<class T>
class Polynomial
{
private:
    class Term
    {
    public:
        T xishu;
        unsigned mi;
    };
    class Node
    {
    public:
        Term data;
        Node* next;
        Node(T x = 0, unsigned y = 0, Node* p = 0)
        {
            data.xishu = x;
            data.mi = y;
            next = p;//修改
        }
    };
public:
    Polynomial();
    void myfree();//释放链表各节点
    Polynomial<T>& operator=(const Polynomial<T>&);
    Polynomial<T> operator+(const Polynomial<T>&);
    Polynomial<T> operator*(const Polynomial<T>&);
    void initial();
    friend ostream& operator<< <T> (ostream& out, Polynomial<T>& a);

private:
    int highestdigit;
    Node* first;
    int num;//用来判断多项式有几项,即链表节点数,在乘法运算里也要用到
};
template<class T>
Polynomial<T>::Polynomial()
{
    first = new Node;
    num = 0;
    highestdigit = 0;
}

template<class T>
void Polynomial<T>::myfree()    //释放链表各节点
{
    Node* p = first, *q;
    while (p)
    {
        q = p->next;
        delete p;
        p = q;
    }
}

template<class T>
Polynomial<T>& Polynomial<T>::operator=(const Polynomial<T>& second)
{
    highestdigit = second.highestdigit;
    num = second.num;
    Node* p1 = first, *p2 = second.first;

    while (p2->next)
    {
        p1->next = new Node();
        p1 = p1->next;
        p2 = p2->next;
        *p1 = *p2;
    }
    return *this;
}

template<class T>
Polynomial<T> Polynomial<T>::operator+(const Polynomial<T>& second)
{
    Polynomial<T> sum;
    Node* pa = first->next, *pb = second.first->next, *pc = sum.first;
    while (pa&&pb)
    {
        if (pa->data.mi == pb->data.mi)  // 指数相等时  
        {
            T x = pa->data.xishu + pb->data.xishu;
            if (x)     // 相加完的系数不为0时  
            {
                pc->next = new Node(x, pa->data.mi);
                pc = pc->next;
                ++sum.num;
                sum.highestdigit = pa->data.mi;
            }
            pa = pa->next;
            pb = pb->next;
        }
        else if (pa->data.mi > pb->data.mi){
            pc->next = new Node(pa->data.xishu, pa->data.mi);
            pc = pc->next;
            pa = pa->next;
            ++sum.num;
            sum.highestdigit = pa->data.mi;
        }
        else{
            pc->next = new Node(pb->data.xishu, pb->data.mi);
            pc = pc->next;
            pb = pb->next;
            ++sum.num;
            sum.highestdigit = pb->data.mi;
        }
    }
    while (pa){
        pc->next = new Node(pa->data.xishu, pa->data.mi);
        pc = pc->next;
        pa = pa->next;
        ++sum.num;
        sum.highestdigit = pa->data.mi;
    }
    while (pb){
        pc->next = new Node(pb->data.xishu, pb->data.mi);
        pc = pc->next;
        pb = pb->next;
        ++sum.num;
        sum.highestdigit = pb->data.mi;
    }
    return sum;
}
template<class T>
Polynomial<T> Polynomial<T>::operator*(const Polynomial<T>& second){
    Polynomial<T> multi;
    Node* pa = first->next, *pb = second.first->next;
    if (num >= second.num){ //拿项数多的那个链表乘以项数少的那个
        Polynomial<T> temp; 
        Node* pt;
        while(pb){          //pb是项数少的那个，
        pt = temp.first;
            while (pa){     //项数多的开始遍历  
                pt->next = new Node(pa->data.xishu*pb->data.xishu, pa->data.mi*pb->data.mi);
                pt = pt->next;
                pa = pa->next;
            }
            multi= temp+multi;
            temp.myfree();
            temp.first = new Node();
            pb = pb->next;
        }
        return multi;
    }
    else{
        Polynomial<T> temp;
        Node* pt;
        while(pa){
            pt = temp.first;
            while (pb){
                pt->next = new Node(pa->data.xishu*pb->data.xishu, pa->data.mi*pb->data.mi);
                pt = pt->next;
                pb = pb->next;
            }
            multi = temp+multi;
            temp.myfree();
            temp.first = new Node();
            pa = pa->next;
        }
        return multi;
    }
}
template<class T>
void Polynomial<T>::initial()
{
    //释放链表，保留头节点
    Node* p = first->next, *q;
    while (p)
    {
        q = p->next;
        delete p;
        p = q;
    }
    p = first;

    T a;
    int b;
    num = 0; highestdigit = 0;//修改
    while (cin >> a&&a != 0 && cin >> b){   //输入a=0时结束输入
        if (b >= highestdigit) highestdigit = b;
        ++num;
        p->next = new Node(a, b);
        p = p->next;
    }
    fflush(stdin);//修改
}

template<class T>
ostream& operator<<(ostream& out, Polynomial<T>& a)
{
    Polynomial<T>::Node *p = a.first->next;

    if (p == NULL) return out;//修改

    if (p->data.xishu == 0)cout << endl;//修改
    else{
        if (p->data.xishu != 1)
            out << p->data.xishu << "x^" << p->data.mi;
        else    out << "x^" << p->data.mi;
    }
    p = p->next;
    while (p)
    {
        out << '+';
        if (p->data.xishu != 1)
            out << p->data.xishu << "x^" << p->data.mi;
        else    out << "x^" << p->data.mi;
        p = p->next;
    }
    return out;
}