链表中的Bigint算术运算

Question

我有两个带有未知长度的数字节点的双向链表。 我需要添加和乘以两个列表。什么是解决问题的好方法 ？我尝试使用运算符重载+，*但不清楚算法

主要在这里

//get line input from file
while (getline(ifs, line)){

    string operation=" ";
    string num1=" ";
    string num2=" ";
    int operationIndex=0;
    //get string from stringstream
    //delimiter here + - * / to split string to two part
    for (int i=0; i<line.length(); i++) {
        if (ispunct(line[i])) {
            operationIndex = i;
        }
    }
    num1 = line.substr(0,operationIndex);
    num2 = line.substr(operationIndex+1);
    operation = line[operationIndex];

    //Dynamic lists
    DoublyLinkedList* l1 = new DoublyLinkedList(num1,digitsPerNode);
    DoublyLinkedList* l2 = new DoublyLinkedList(num2,digitsPerNode);
    DoublyLinkedList* result = new DoublyLinkedList;

    //Do math here
    if (operation == "+") {
        //*result = *l1 + *l2;

    }
    else if(operation == "*"){
        //*result = *l1 + *l2;
    }

    //print answer here
    cout << num1 << operation << num2 << "=";

    result->printList();
    //l1->printList();
    //l2->printList();

    //free lists memory
    delete l1;
    delete l2;
    delete result;
}

在这里重载

//addition
DoublyLinkedList DoublyLinkedList::operator+(const DoublyLinkedList &l2) const
{
    DoublyLinkedList result;


    return result;
}
//multiplication
DoublyLinkedList DoublyLinkedList::operator*(const DoublyLinkedList &l2) const
{
    DoublyLinkedList result;


    return result;
}