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谁能帮我看下下面这段代码，多项式乘法和+=操作运行不了，求助啊，到底错在哪了？

#include<iostream>
#include<cmath>
using namespace std;
class Polynomial
{
    double *p_coefs;
    int *p_exps, num;
public:
    Polynomial();
    Polynomial(double coefs[], int exps[], int size);//系数数组、指数数组和项数
    Polynomial(const Polynomial&x);
    ~Polynomial();
    //赋值操作符
    Polynomial &operator=(const Polynomial&x)
    {
        if (&x == this) return *this;
        num = x.num;
        delete[]p_coefs;
        delete[]p_exps;
        p_coefs = new double[x.num];
        p_exps = new int[x.num];
        for (int i = 0; i <x. num; i++) { p_coefs[i] = x.p_coefs[i]; }
        for (int j = 0; j <x.num; j++) { p_exps[j] = x.p_exps[j]; }
        return *this;
    }
    //最高幂指数
    int degree()const
    {
        return p_exps[num - 1];
    }
    //计算多项式的值
    double evaluate(double x) const
    {
        double value = 0, temp = x;
        for (int i = 0; i < num; i++)
        {
            for (int j = 0; j < p_exps[i]; j++) x *= temp;
            x *= p_coefs[i];
            value += x;
            x = temp;
        }
        return value;
    }
    //判断两多项式是否相等
    bool operator==(const Polynomial&x)const
    {
        if (num != x.num)return false;
        for (int i = 0; i < num; i++)
            if (p_exps[i] != x.p_exps[i] || p_coefs[i] != x.p_coefs[i])return false;
        return true;
    }
    //判断两多项式是否不相等
    bool operator!=(const Polynomial&x)const
    {
        if (num != x.num) return true;
        for (int i = 0; i < num; i++)
            if (p_exps[i] != x.p_exps[i] || p_coefs[i] != x.p_coefs[i])return true;
        return false;

    }
    //多项式的加法
    Polynomial operator+(const Polynomial&x)const
    {
        Polynomial new_poly;
        new_poly.num = num + x.num;
        new_poly.p_coefs = new double[num +x.num];
        new_poly.p_exps = new int[num + x.num];
        for (int i = 0; i < num; i++) { new_poly.p_coefs[i] = p_coefs[i]; }
        for (int j = 0; j < num; j++) { new_poly.p_exps[j] = p_exps[j]; }
        for (int i = num; i <new_poly.num; i++) { new_poly.p_coefs[i] = x.p_coefs[i - num]; }
        for (int j = num; j <new_poly.num; j++) { new_poly.p_exps[j] = x.p_exps[j - num]; }
        for (int i = 0; i < new_poly.num; i++)
            for (int j = i + 1; j < new_poly.num; j++)
            {
                if (new_poly.p_exps[i] == new_poly.p_exps[j])
                {
                    new_poly.p_coefs[i] = new_poly.p_coefs[i] + new_poly.p_coefs[j];
                    new_poly.p_coefs[j] = 0;
                }
            }
        return new_poly;
    }
    //多项式的减法
    Polynomial operator-(const Polynomial&x)const
    {
        Polynomial poly,poly1;
        poly.num = num ;
        poly.p_coefs = new double[num];
        poly.p_exps = new int[num];
        for (int i = 0; i < x.num; i++) { poly.p_coefs[i] =p_coefs[i]; }
        for (int j = 0; j < x.num; j++) { poly.p_exps[j] = p_exps[j]; }
        poly1.num = x.num;
        poly1.p_coefs = new double[x.num];
        poly1.p_exps = new int[x.num];
        for (int i = 0; i < x.num; i++) { poly1.p_coefs[i] = -x.p_coefs[i]; }
        for (int j = 0; j < x.num; j++) { poly1.p_exps[j] = x.p_exps[j]; }
        return poly+poly1;
    }
    //多项式的乘法
    Polynomial operator*(const Polynomial&x)const
    {
        Polynomial *p,sum;
        p = new Polynomial[num];
         for (int i = 0; i < num;i++)
        { 
            for (int j = 0; j < x.num; j++)
            {
                p[i].p_coefs[j] = p_coefs[i] * x.p_coefs[j];
                p[i].p_exps[j] = p_exps[i] + x.p_exps[j];
            
            }
            
         }
         for (int i = 0; i < num; i++) {
             sum =sum+p[i];
         }
        return sum;

    }
    //多项式的加法
    Polynomial& operator+=(const Polynomial&x)
    {
        {return *this+ x; }
    }
    //多项式的减法
    Polynomial& operator-=(const Polynomial&x)
    {return *this - x;}
    Polynomial& operator*=(const Polynomial&x)
    {
        return *this * x;
    }
    void display()const;
};
//下面两个重载函数实现构造函数
Polynomial::Polynomial()
{
    p_coefs = NULL; p_exps = NULL;
    num = 0;
}
Polynomial::Polynomial(double coefs[], int exps[], int size)
{
    num = size;
    p_coefs = new double[num];
    p_exps = new int[num];
    for (int i = 0; i < num; i++) { p_coefs[i] = coefs[i]; }
    for (int j = 0; j < num; j++) { p_exps[j] = exps[j]; }
}
Polynomial::Polynomial(const Polynomial&x)
{

    num = x.num;
    p_coefs = new double[num];
    p_exps = new int[num];
    for (int i = 0; i < num; i++) { p_coefs[i] = x.p_coefs[i]; }
    for (int j = 0; j < num; j++) { p_exps[j] = x.p_exps[j]; }
}
//析构函数
Polynomial::~Polynomial()
{
    delete[]p_coefs;
    p_coefs = NULL;
    delete[]p_exps;
    p_exps = NULL;
    num = 0;
}

//显示多项式
void Polynomial::display()const
{
    double t1;
    int t2;
    //冒泡排序
    for (int j = 0; j < num - 1; j++)
        for (int i = 0; i < num - 1 - j; i++)
            if (p_exps[i]>p_exps[i + 1])
            {
                t1 = p_coefs[i]; t2 = p_exps[i];
                p_coefs[i] = p_coefs[i + 1]; p_exps[i] = p_exps[i + 1];
                p_coefs[i + 1] = t1; p_exps[i + 1] = t2;
            }
    if (p_coefs[0] != 0)
    {
        if (p_exps[0] != 0 && p_exps[0] != 1)
        {
            if (p_coefs[0] != 1 && p_coefs[0] != -1)cout << p_coefs[0] << "x^" << p_exps[0];
            else if (p_coefs[0] == 1)cout << "x^" << p_exps[0];
            else cout << "-x^" << p_exps[0];
        }
        else if (p_exps[0] == 0)
        {
            cout << p_coefs[0];
        }
        else
        {
            if (p_coefs[0] != 1 && p_coefs[0] != -1)cout << p_coefs[0] << "x";
            else if (p_coefs[0] == 1)cout << "x";
            else cout << "-x";
        }

    }
    for (int i = 1; i < num; i++)
    {
        if (p_coefs[i] != 0)
        {
            if (p_exps[i] != 0 && p_exps[i] != 1)
            {
                if (p_coefs[i] > 0 && p_coefs[i] != 1 && p_coefs[i] != -1)cout << '+' << p_coefs[i] << "x^" << p_exps[i];
                else if (p_coefs[i] == 1)cout << "+x^" << p_exps[i];
                else if (p_coefs[i] == -1)cout << "-x^" << p_exps[i];
                else cout << p_coefs[i] << "x^" << p_exps[i];
            }
            else if (p_exps[i] == 0)
            {
                cout << p_coefs[i];
            }
            else
            {
                if (p_coefs[i] != 1 && p_coefs[i] != -1)cout << p_coefs[i] << "x";
                else if (p_coefs[i] == 1)cout << "x";
                else cout << "-x";
            }

        }
    }
    cout << endl;
}
int main()
{
    double a[5] = { 1,2,3,4,5 }, i[5] = { 1,3,5,7,10 };
    int c = 5, b[5] = { 1,2,3,4,5 }, j[5] = { 1,3,5,8,7 };
    Polynomial poly1(a, b, c), poly2, poly3(i, j, c),poly4,poly5;
    cout << "多项式一:"; poly1.display();
    poly2 = poly1;
    cout << "多项式二:"; poly2.display();
    cout << "多项式三:"; poly3.display();
    cout <<"多项式一最高次幂:"<< poly1.degree() << endl;
    cout << "多项式一值为:" << poly1.evaluate(3) << endl;
    cout <<"多项式二与三是否相等:"<< boolalpha << (poly2 == poly3) << endl;
    cout << "多项式二与三是否不相等:" << boolalpha << (poly2 != poly3) << endl;
    cout << "多项式一与三的和:"; (poly1 + poly3).display();
    cout << "多项式一与三的差:"; (poly1 - poly3).display();
    cout << "多项式一与三的积:"; (poly1 * poly3).display();
    poly2 += poly3; 
    cout << "多项式二增加后:";     poly2.display();
    poly2 -= poly3;
    cout << "多项式二减少后:"; poly2.display();
    poly2 *= poly3;
    cout << "多项式二相乘后:"; poly2.display();
    system("pause");
    return 0;
}

大体看了一下，有几个问题。

  1. 几个复合赋值运算符定义有问题，比如：

    Polynomial& operator+=(const Polynomial&x) {
  return *this+ x;  // 此处返回了局部变量的引用，是未定义行为
}

    原因是*this+x调用了Polynomial::operator+，返回了一个新的Polynomial变量，这个变量是operator+=的局部变量，而operator+=的返回值是这个新变量的引用，所以是未定义行为。其他几个复合赋值运算符类似。

  2. 题主几个操作符重载的实现不是很好，比如：

    • operator!=和operator==中只有一个需要具体实现，另一个应该调用被实现的那个；

    • operator+=应该具体实现，而operator+应该调用operator+=，原因参考这里，减法、乘法类似；

  3. 构造函数初始化成员时应尽量使用成员初始化列表赋初值。

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