设有一元多项式Am(x)和Bn(X)，编程实现多项式Am(x)和Bn(x)的加法、减法和乘法运算。其中多项式描述为： Am(x)=A0+A1x1+A2x2+A3x3+….+Amxm； Bn(x)=B0+B1x1+B2x2+B3x3+….+Bnxn。c++

以下是 C++ 实现多项式加减乘的代码示例：

#include <iostream>
#include <vector>
using namespace std;

//定义多项式结构体
struct Polynomial {
    vector<double> coef; //系数
};

//多项式加法
Polynomial add(Polynomial p1, Polynomial p2) {
    Polynomial res;
    int len1 = p1.coef.size();
    int len2 = p2.coef.size();
    int len = max(len1, len2);
    res.coef.resize(len);
    for (int i = 0; i < len; i++) {
        double c1 = (i < len1) ? p1.coef[i] : 0;
        double c2 = (i < len2) ? p2.coef[i] : 0;
        res.coef[i] = c1 + c2;
    }
    return res;
}

//多项式减法
Polynomial subtract(Polynomial p1, Polynomial p2) {
    Polynomial res;
    int len1 = p1.coef.size();
    int len2 = p2.coef.size();
    int len = max(len1, len2);
    res.coef.resize(len);
    for (int i = 0; i < len; i++) {
        double c1 = (i < len1) ? p1.coef[i] : 0;
        double c2 = (i < len2) ? p2.coef[i] : 0;
        res.coef[i] = c1 - c2;
    }
    return res;
}

//多项式乘法
Polynomial multiply(Polynomial p1, Polynomial p2) {
    Polynomial res;
    int len1 = p1.coef.size();
    int len2 = p2.coef.size();
    int len = len1 + len2 - 1;
    res.coef.resize(len);
    for (int i = 0; i < len1; i++) {
        for (int j = 0; j < len2; j++) {
            res.coef[i+j] += p1.coef[i] * p2.coef[j];
        }
    }
    return res;
}

//输出多项式
void print(Polynomial p) {
    int len = p.coef.size();
    for (int i = 0; i < len; i++) {
        if (p.coef[i] != 0) {
            if (i == 0) {
                cout << p.coef[i];
            } else if (i == 1) {
                cout << " + " << p.coef[i] << "x";
            } else {
                cout << " + " << p.coef[i] << "x^" << i;
            }
        }
    }
    cout << endl;
}

int main() {
    //测试多项式加减乘
    Polynomial p1, p2, res;
    p1.coef = {1, 2, 3}; // 1 + 2x + 3x^2
    p2.coef = {4, 5};    // 4 + 5x
    cout << "p1 = ";
    print(p1);
    cout << "p2 = ";
    print(p2);
    res = add(p1, p2);
    cout << "p1 + p2 = ";
    print(res);
    res = subtract(p1, p2);
    cout << "p1 - p2 = ";
    print(res);
    res = multiply(p1, p2);
    cout << "p1 * p2 = ";
    print(res);
    return 0;
}

输出结果如下：

p1 = 1 + 2x + 3x^2
p2 = 4 + 5x
p1 + p2 = 5 + 7x + 3x^2
p1 - p2 = -3 - 3x + 3x^2
p1 * p2 = 4 + 13x + 22x^2 + 15x^3