C+++中用顺序表计算两个多项式的和与乘积

在C++中，我们可以使用顺序表（如`std::vector`）来存储多项式的系数及其对应的幂次。首先，你需要创建两个有序的顺序表来表示两个多项式，每个元素包含系数和指数。

计算两个多项式的和（addition）:

// 定义多项式结构体或类
struct Polynomial {
    double coefficient;
    int exponent;
};

// 添加函数
Polynomial addPolynomials(std::vector<Polynomial>& poly1, std::vector<Polynomial>& poly2) {
    std::vector<Polynomial> result(poly1.size() + poly2.size());
    int i = 0, j = 0, k = 0;

    while (i < poly1.size() && j < poly2.size()) {
        if (poly1[i].exponent > poly2[j].exponent) {
            result[k++] = poly1[i];
            i++;
        } else if (poly1[i].exponent < poly2[j].exponent) {
            result[k++] = poly2[j];
            j++;
        } else { // 同等级别的项相加
            result[k].coefficient += poly1[i].coefficient + poly2[j].coefficient;
            result[k++].exponent = poly1[i].exponent; // 取较小的指数
            i++, j++;
        }
    }

    // 处理剩下的项（如果有的话）
    while (i < poly1.size()) {
        result[k++] = poly1[i];
        i++;
    }
    while (j < poly2.size()) {
        result[k++] = poly2[j];
        j++;
    }

    return result;
}

计算两个多项式的乘积（multiplication）:

// 乘法函数，假设我们有一个乘法运算符重载
Polynomial multiplyPolynomials(const Polynomial& poly1, const Polynomial& poly2) {
    Polynomial result(0, poly1.exponent + poly2.exponent);
    for (int i = 0; i <= poly1.exponent; ++i) {
        for (int j = 0; j <= poly2.exponent - i; ++j) {
            result.coefficient += poly1.coefficient * poly2.coefficient * pow(10, i + j); // 根据指数调整系数
        }
    }
    return result;
}

// 使用示例
std::vector<Polynomial> polynomial1 = { {2, 2}, {1, 1} }; // 2x^2 + x
std::vector<Polynomial> polynomial2 = { {3, 1}, {4, 0} }; // 3x + 4

std::vector<Polynomial> sum = addPolynomials(polynomial1, polynomial2);
Polynomial product = multiplyPolynomials(polynomial1, polynomial2);