建立链式多项式类，并设计算法实现多项式的相加。(c++编写)

在C++中，我们可以创建一个链表结构表示多项式，每个节点包含系数和下一个节点的引用。以下是一个简单的链式多项式类的实现，以及用于两个多项式相加的算法：

#include <iostream>
using namespace std;

// 定义链表节点
struct Term {
    double coefficient;
    int exponent;
    Term* next;
};

// 链式多项式类
class Polynomial {
private:
    Term* head;

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

    // 添加项到多项式
    void addTerm(double c, int e) {
        Term* newNode = new Term{c, e, nullptr};
        if (head == nullptr) {
            head = newNode;
        } else {
            Term* current = head;
            while (current->next != nullptr && current->exponent < e) {
                current = current->next;
            }
            if (current->exponent == e) {
                current->coefficient += c;
            } else {
                newNode->next = current->next;
                current->next = newNode;
            }
        }
    }

    // 打印多项式
    void print() {
        Term* temp = head;
        while (temp != nullptr) {
            cout << temp->coefficient << "x^" << temp->exponent << " + ";
            temp = temp->next;
        }
        cout << "\n";
    }

    // 相加操作
    Polynomial operator+(const Polynomial& other) const {
        Polynomial result(*this);
        Term* curr = head;
        Term* otherCurr = other.head;

        while (curr != nullptr && otherCurr != nullptr) {
            if (curr->exponent > otherCurr->exponent) {
                curr = curr->next;
            } else if (curr->exponent < otherCurr->exponent) {
                otherCurr = otherCurr->next;
            } else {
                result.addTerm(curr->coefficient + otherCurr->coefficient, curr->exponent);
                curr = curr->next;
                otherCurr = otherCurr->next;
            }
        }

        // 将剩余项添加到结果
        while (curr != nullptr) {
            result.addTerm(curr->coefficient, curr->exponent);
            curr = curr->next;
        }
        while (otherCurr != nullptr) {
            result.addTerm(otherCurr->coefficient, otherCurr->exponent);
            otherCurr = otherCurr->next;
        }

        return result;
    }
};

int main() {
    Polynomial p1;
    p1.addTerm(2, 0);   // 2x^0
    p1.addTerm(3, 1);   // 3x^1

    Polynomial p2;
    p2.addTerm(4, 0);   // 4x^0
    p2.addTerm(-1, 2);  // -1x^2

    Polynomial sum = p1 + p2;
    sum.print(); // 输出: 5x^0 + 2x^1 - x^2 + 

    return 0;
}

在这个例子中，`Polynomial` 类实现了多项式的存储和打印功能，`operator+` 运算符则实现了两个多项式的相加。在 `main` 函数中，我们创建了两个多项式并求和。