Polynomial类C++

Polynomial类是一个常见的数学类，用于存储和操作多项式。以下是一个简单的Polynomial类的C++代码示例：

#include <iostream>
#include <vector>

using namespace std;

class Polynomial {
private:
    vector<double> coefficients;

public:
    Polynomial() {}

    Polynomial(vector<double> coeffs) {
        coefficients = coeffs;
    }

    int degree() {
        return coefficients.size() - 1;
    }

    double operator[](int i) const {
        return coefficients[i];
    }

    double& operator[](int i) {
        return coefficients[i];
    }

    Polynomial operator+(const Polynomial& other) const {
        vector<double> result(max(degree(), other.degree()) + 1);

        for (int i = 0; i <= degree(); i++) {
            result[i] += coefficients[i];
        }

        for (int i = 0; i <= other.degree(); i++) {
            result[i] += other.coefficients[i];
        }

        return Polynomial(result);
    }

    Polynomial operator-(const Polynomial& other) const {
        vector<double> result(max(degree(), other.degree()) + 1);

        for (int i = 0; i <= degree(); i++) {
            result[i] += coefficients[i];
        }

        for (int i = 0; i <= other.degree(); i++) {
            result[i] -= other.coefficients[i];
        }

        return Polynomial(result);
    }

    Polynomial operator*(const Polynomial& other) const {
        vector<double> result(degree() + other.degree() + 1);

        for (int i = 0; i <= degree(); i++) {
            for (int j = 0; j <= other.degree(); j++) {
                result[i + j] += coefficients[i] * other.coefficients[j];
            }
        }

        return Polynomial(result);
    }

    friend ostream& operator<<(ostream& os, const Polynomial& p) {
        for (int i = p.degree(); i >= 0; i--) {
            if (p[i] == 0) {
                continue;
            }

            if (i == p.degree()) {
                os << p[i] << "x^" << i;
            } else if (i == 1) {
                os << " + " << p[i] << "x";
            } else {
                os << " + " << p[i] << "x^" << i;
            }
        }

        return os;
    }
};

int main() {
    vector<double> coeffs1 = {1, 2, 3};
    vector<double> coeffs2 = {4, 5, 6};

    Polynomial p1(coeffs1);
    Polynomial p2(coeffs2);

    cout << "p1 = " << p1 << endl;
    cout << "p2 = " << p2 << endl;

    Polynomial p3 = p1 + p2;
    Polynomial p4 = p1 - p2;
    Polynomial p5 = p1 * p2;

    cout << "p1 + p2 = " << p3 << endl;
    cout << "p1 - p2 = " << p4 << endl;
    cout << "p1 * p2 = " << p5 << endl;

    return 0;
}

这个Polynomial类支持多项式的加、减和乘法，并且可以输出多项式的字符串表示。