编写一个程序exp2-9.cpp,用单链表存储一元多项式,并实现两个多项式的相加运算

在C++中，我们可以编写一个名为`exp2-9.cpp`的程序，使用结构体和单链表来表示一元多项式，并实现两个多项式的相加操作。首先，我们需要创建一个包含系数和指数的节点结构体：

// 定义多项式的节点结构
struct Term {
    double coefficient;  // 系数
    int exponent;        // 指数

    Term(double coeff = 0, int exp = 0) : coefficient(coeff), exponent(exp) {}
};

// 定义多项式链表节点
struct PolynomialNode {
    Term term;
    PolynomialNode* next;   // 指向下一个节点的指针
};

接下来，我们可以定义一个多项式类，包括添加新项、初始化以及相加功能：

class Polynomial {
private:
    PolynomialNode* head;

public:
    Polynomial() : head(nullptr) {}

    // 添加新的项到多项式
    void addTerm(Term new_term) {
        if (!head) {
            head = new PolynomialNode{new_term, nullptr};
        } else {
            PolynomialNode* current = head;
            while (current->next) {
                current = current->next;
            }
            current->next = new PolynomialNode{new_term, nullptr};
        }
    }

    // 相加两个多项式
    void add(Polynomial& other) {
        PolynomialNode* current1 = head;
        PolynomialNode* current2 = other.head;
        PolynomialNode* new_head = nullptr;
        
        while (current1 && current2) {
            double sum_coefficient = current1->term.coefficient + current2->term.coefficient;
            int sum_exponent = std::max(current1->term.exponent, current2->term.exponent);
            new_head = new PolynomialNode{sum_coefficient, sum_exponent, new_head};

            if (current1->next)
                current1 = current1->next;
            if (current2->next)
                current2 = current2->next;
        }

        if (current1) {
            while (current1) {
                new_head = new PolynomialNode{current1->term.coefficient, current1->term.exponent, new_head};
                current1 = current1->next;
            }
        } else if (current2) {
            while (current2) {
                new_head = new PolynomialNode{current2->term.coefficient, current2->term.exponent, new_head};
                current2 = current2->next;
            }
        }

        head = new_head;
    }

    // 打印多项式
    void print() {
        PolynomialNode* current = head;
        while (current) {
            std::cout << current->term.coefficient << "x^" << current->term.exponent << " ";
            current = current->next;
        }
        std::cout << "\n";
    }
};

现在，你可以用这个类来创建两个多项式实例，然后相加它们：

int main() {
    Polynomial poly1;
    poly1.addTerm({2.0, 1}); // 2x
    poly1.addTerm({1.5, 2}); // 1.5x^2
    poly1.print();

    Polynomial poly2;
    poly2.addTerm({3.0, 1}); // 3x
    poly2.addTerm({4.0, 3}); // 4x^3
    poly2.print();

    Polynomial polySum;
    polySum.add(poly1);
    polySum.add(poly2);
    polySum.print();

    return 0;
}

运行此程序会得到两个多项式的和。