用C++写程序1.实现带头结点的单链表的建立、求长度,取元素、修改元素、插入、删除等单链表的基本操作。 2.多项式的乘法,已知2个多项式,设计一个算法完成2个多项式的乘法。

在C++中，我们可以使用结构体（struct）来定义单链表节点，并实现一些基本操作：

// 定义链表节点
struct ListNode {
    int val;      // 节点值
    ListNode* next; // 指向下一个节点的指针
};

// 创建空链表
ListNode* createList() {
    return nullptr;
}

// 链表长度
int length(ListNode* head) {
    int count = 0;
    while (head != nullptr) {
        ++count;
        head = head->next;
    }
    return count;
}

// 取元素
int get(int index, ListNode* head) {
    if (index < 0 || index >= length(head)) {
        throw std::out_of_range("Index out of range");
    }
    ListNode* current = head;
    for (int i = 0; i < index; ++i) {
        current = current->next;
    }
    return current->val;
}

// 修改元素
void set(int index, int newValue, ListNode*& head) {
    if (index < 0 || index >= length(head)) {
        throw std::out_of_range("Index out of range");
    }
    ListNode* current = head;
    for (int i = 0; i < index; ++i) {
        current = current->next;
    }
    current->val = newValue;
}

// 插入元素
void insert(int index, int value, ListNode*& head) {
    if (index <= 0) {
        new ListNode{value, head};
        head = head->next;
    } else {
        ListNode* newNode = new ListNode{value};
        ListNode* prevNode = head;
        for (int i = 0; i < index - 1 && prevNode != nullptr; ++i) {
            prevNode = prevNode->next;
        }
        if (prevNode == nullptr) {
            throw std::out_of_range("Invalid insertion position");
        }
        newNode->next = prevNode->next;
        prevNode->next = newNode;
    }
}

// 删除元素
void deleteElement(int index, ListNode*& head) {
    if (index < 0 || index >= length(head)) {
        throw std::out_of_range("Index out of range");
    }
    if (index == 0) {
        head = head->next;
    } else {
        ListNode* curr = head;
        for (int i = 0; i < index - 1; ++i) {
            curr = curr->next;
        }
        curr->next = curr->next->next;
    }
}

// 多项式乘法示例（简化版）
class Polynomial {
private:
    struct Term {
        int coef;
        int exp;
    };
    vector<Term> terms;

public:
    void multiply(Polynomial& other) {
        for (const auto& term : terms) {
            for (const auto& otherTerm : other.terms) {
                if (term.exp + otherTerm.exp > MAX_EXPONENT) {
                    break; // 如果指数过大，避免整数溢出
                }
                terms.push_back({term.coef * otherTerm.coef, term.exp + otherTerm.exp});
            }
        }
    }

    friend std::ostream& operator<<(std::ostream& os, const Polynomial& poly);
};

std::ostream& operator<<(std::ostream& os, const Polynomial& poly) {
    os << "Polynomial [";
    for (size_t i = 0; i < poly.terms.size(); ++i) {
        if (i > 0) {
            os << "+ ";
        }
        os << poly.terms[i].coef << "x^" << poly.terms[i].exp;
    }
    os << "]";
    return os;
}