对如下多项式（Polynomial）编写类定义： +++…+ 其中，n为多项式的次数。完成如下功能： （1）可存储任意大的多项式（提示：可用动态数组实现）。 （2）定义构造函数、析构函数、拷贝构造函数。 （3）包含一个static成员存储定义的多项式数量。 （4）定义一个成员函数输出多项式。（可参照-x^4-6x^3+5格式输出，注意化简） （5）定义一个成员函数计算多项式的值。 （6）重载“+”运算符，实现两个多项式相加。 （7）重载“-”运算符，实现两个多项式相减。 （8）重载“*”运算符，实现两个多项式相乘。 （9）重载“=”运算符，实现两个多项式的赋值运算。 （10）在main函数中编写测试代码。 要求：采用多文件实现。考虑：哪些成员函数可以声明为const， 把其中某个运算符重载为友元函数。

下面是多项式类的定义，分为头文件 Polynomial.h 和源文件 Polynomial.cpp：

Polynomial.h：

#ifndef POLYNOMIAL_H
#define POLYNOMIAL_H

class Polynomial
{
public:
    Polynomial(int degree = 0);
    Polynomial(const Polynomial& rhs);
    ~Polynomial();
    void print() const;
    double evaluate(double x) const;
    Polynomial operator+(const Polynomial& rhs) const;
    Polynomial operator-(const Polynomial& rhs) const;
    Polynomial operator*(const Polynomial& rhs) const;
    Polynomial& operator=(const Polynomial& rhs);
    static int numPolynomials;
private:
    int degree;
    double* coefficients;
};

#endif // POLYNOMIAL_H

Polynomial.cpp：

#include <iostream>
#include "Polynomial.h"

using namespace std;

int Polynomial::numPolynomials = 0;

Polynomial::Polynomial(int degree)
{
    this->degree = degree;
    coefficients = new double[degree + 1];
    for (int i = 0; i <= degree; i++)
    {
        coefficients[i] = 0;
    }
    numPolynomials++;
}

Polynomial::Polynomial(const Polynomial& rhs)
{
    degree = rhs.degree;
    coefficients = new double[degree + 1];
    for (int i = 0; i <= degree; i++)
    {
        coefficients[i] = rhs.coefficients[i];
    }
    numPolynomials++;
}

Polynomial::~Polynomial()
{
    delete[] coefficients;
    numPolynomials--;
}

void Polynomial::print() const
{
    int i;
    for (i = degree; i > 1; i--)
    {
        if (coefficients[i] != 0)
        {
            cout << coefficients[i] << "x^" << i << " + ";
        }
    }
    if (coefficients[i] != 0)
    {
        cout << coefficients[i] << "x + ";
    }
    cout << coefficients[0] << endl;
}

double Polynomial::evaluate(double x) const
{
    double result = 0;
    for (int i = degree; i >= 0; i--)
    {
        result = result * x + coefficients[i];
    }
    return result;
}

Polynomial Polynomial::operator+(const Polynomial& rhs) const
{
    int maxDegree = max(degree, rhs.degree);
    Polynomial result(maxDegree);
    for (int i = 0; i <= maxDegree; i++)
    {
        result.coefficients[i] = coefficients[i] + rhs.coefficients[i];
    }
    return result;
}

Polynomial Polynomial::operator-(const Polynomial& rhs) const
{
    int maxDegree = max(degree, rhs.degree);
    Polynomial result(maxDegree);
    for (int i = 0; i <= maxDegree; i++)
    {
        result.coefficients[i] = coefficients[i] - rhs.coefficients[i];
    }
    return result;
}

Polynomial Polynomial::operator*(const Polynomial& rhs) const
{
    int resultDegree = degree + rhs.degree;
    Polynomial result(resultDegree);
    for (int i = 0; i <= degree; i++)
    {
        for (int j = 0; j <= rhs.degree; j++)
        {
            result.coefficients[i + j] += coefficients[i] * rhs.coefficients[j];
        }
    }
    return result;
}

Polynomial& Polynomial::operator=(const Polynomial& rhs)
{
    if (this != &rhs)
    {
        delete[] coefficients;
        degree = rhs.degree;
        coefficients = new double[degree + 1];
        for (int i = 0; i <= degree; i++)
        {
            coefficients[i] = rhs.coefficients[i];
        }
    }
    return *this;
}

在 main 函数中，我们可以测试多项式类的各种功能，例如：

#include <iostream>
#include "Polynomial.h"

using namespace std;

int main()
{
    Polynomial p1(3);
    p1 = 3.2 * p1 - 2.7 * p1 * p1 + 0.5 * p1 * p1 * p1;
    cout << "p1 = ";
    p1.print();
    cout << "p1(2) = " << p1.evaluate(2) << endl;

    Polynomial p2(4);
    p2 = 1 - 2 * p1 + p1 * p1;
    cout << "p2 = ";
    p2.print();
    cout << "p2(2) = " << p2.evaluate(2) << endl;

    Polynomial p3 = p1 + p2;
    cout << "p3 = p1 + p2 = ";
    p3.print();

    Polynomial p4 = p1 - p2;
    cout << "p4 = p1 - p2 = ";
    p4.print();

    Polynomial p5 = p1 * p2;
    cout << "p5 = p1 * p2 = ";
    p5.print();

    Polynomial p6 = p1;
    cout << "p6 = p1 = ";
    p6.print();
    cout << "p6(2) = " << p6.evaluate(2) << endl;

    return 0;
}