首先list.h

#ifndef LIST_H
#define LIST_H

#include <string>
#include <iostream>
#include <cassert>

using namespace std;
typedef 	struct NODE		node;
typedef 	struct NODE*	nodeptr;
typedef 	string::size_type	size_type;

struct NODE
{
	nodeptr link;
	int value;
};

class List
{
private :
	nodeptr head;
	nodeptr tail;
	int charToInt(char ch)
	{
		return ((int)ch - 48);
	}

public :
	List();
	void create(string& str); 		
	void insertBack(int value);
	void reverse();
	List& operator+(List& list);
	void show();
};
#endif

//建構函式，預設構造一個只有頭結點的連結串列
List :: List()
{
	head = (nodeptr)operator new(sizeof(node));
	assert(head != NULL);
	head -> link = NULL;
	head -> value = 0;
	tail = NULL;
}

//根據傳入的大數字符串建立一個相對應的連結串列
void List :: create(string& str)
{
	for(size_type i = 0; i < str.size(); ++ i)	
	{
		insertBack(charToInt(str[i]));
	}
}

//每次都在連結串列的後面插入
void List :: insertBack(int value)
{
	if(tail == NULL)
	{
		head -> value = value;
		tail = head;
		return;
	}
	nodeptr newNode = (nodeptr)operator new(sizeof(node));	
	assert(tail != NULL);
	assert(newNode != NULL);
	newNode -> link = tail -> link;
	tail -> link = newNode;
	newNode -> value = value;
	tail = newNode;
}

//用三個指標實現單鏈表的逆序，這是面試真題
void List :: reverse()
{
	nodeptr curr = head;
	nodeptr pre = NULL;
	nodeptr next;
	
	while(curr != NULL)
	{
		next = curr -> link;
		curr -> link = pre;
		pre = curr;
		curr = next;
	}
	head = pre;
}

//過載+運算子
//單鏈表實現大數運算最主要的函式
List& List :: operator+(List& list)
{
	List *list3 = new List();
	int bitAdd = 0;
	int jinWei = 0;
	this -> reverse();
	list.reverse();
	nodeptr pList1 = this -> head;
	nodeptr pList2 = list.head;

	while(pList1 != NULL || pList2 != NULL)	
	{
		if(pList1 != NULL && pList2 != NULL)	
		{
			bitAdd = pList1 -> value + pList2 -> value + jinWei;	
			jinWei = bitAdd / 10;
			bitAdd = bitAdd % 10;
			pList1 = pList1 -> link;
			pList2 = pList2 -> link;
		}
		else if(pList1 == NULL)
		{
			bitAdd = pList2 -> value;
			jinWei = 0;
			pList2 = pList2 -> link;
		}
		else
		{
			bitAdd = pList1 -> value;
			jinWei = 0;
			pList1 = pList1 -> link;
		}
		list3 -> insertBack(bitAdd);
	}
	if(jinWei != 0)
		list3 -> insertBack(jinWei);
	list3 -> reverse();
	return *list3;
}

//螢幕上打印出連結串列
void List :: show()
{
	nodeptr it = head;
	while(it != NULL)
	{
		cout << it -> value;
		it = it -> link;
	}
	cout << endl;
}
 

#include "list.h"
#include <iostream>

using namespace std;

int main()
{
	string str1;
	string str2;

	cout << "please input the number1: ";
	cin >> str1;
	cout << "please input the number2: ";
	cin >> str2;

	List bigNum1;
	List bigNum2;
	List result;

	bigNum1.create(str1);
	bigNum2.create(str2);
	result = bigNum1 + bigNum2;
	cout << "result : " << endl;
	result.show();
	return 0;
}