为什么数据保存不到文件？但是在文件提前写好后却可以用程序读出来

问题遇到的现象和发生背景

输入数据保存后正常关闭程序，再打开文件数据却没有被保存进去。

问题相关代码，请勿粘贴截图

# include <iostream>
# include <fstream>
# include <string.h>
#include <conio.h>//用getch();
using namespace std;
class book
{
public:
    string book_id;
    string book_name;
    string author;
    string publishing;
    double price;
    book* Next;
    void Input()
    {
        cout << "请输入书籍编号："; cin >> book_id;
        cout << "请输入书籍名称："; cin >> book_name;
        cout << "请输入作者："; cin >> author;
        cout << "请输入出版社："; cin >> publishing;
        cout << "请输入定价："; cin >> price;
    }
    void ReadFile(istream& in)
    {
        in >> book_id >> book_name >> author >> publishing >> price;
    }
    void Show()
    {
        cout << "编号：" << book_id << "\t" << "名称：" << book_name << "\t" << "作者：" << author << "\t"
            << "出版社：" << publishing << "\t" << "定价：" << price << endl;
    }
};
class Manage
{
public:
    Manage();
    ~Manage();
    void ShowMenu();//展示菜单
    void Find();
    void Save();
    void AddItem()
    {
        End->Input();
        End->Next = new book;
        End = End->Next;
        cout << "添加成功!" << endl;
        cout << "输入任意字符！继续……";
        getch();
        Save();
    }
private:
    book* Head, * End;
    ifstream in;
    ofstream out;
    
    book* FindID(string id)
    {
        for (book* p = Head; p->Next != End; p = p->Next)//匹配成功则返回上一个指针，不成功就返回空
            if (p->Next->book_id==id)return p;
        return NULL;
    }
};
Manage::Manage()
{
    Head = new book;
    Head->Next = new book;
    End = Head->Next;
    in.open("book.txt");
    if (!in)
        cout << "这是一个新系统，无信息。请先输入。" << endl;
    else
    {
        while (!in.eof())
        {
            End->ReadFile(in);
            if (End->book_id.empty())break;//string字符串为空 
            End->Next = new book;
            End = End->Next;
        }
        in.close();
        cout << "\t\t读取信息成功!" << endl;
    }
}
Manage::~Manage()
{
    Save();
    for (book* temp; Head->Next != End;)
    {
        temp = Head->Next;
        Head->Next = Head->Next->Next;
        delete temp;
    }
    delete Head, End;
}
void Manage::ShowMenu()
{
    cout << " ▏－－－－－－－－－－－－－－－－－－－－－－－－ ▏" << endl;
    cout << " ▏              1.添加图书                         ▏" << endl;
    cout << " ▏              2.查找图书                         ▏" << endl;
    cout << " ▏              0.退出管理系统                     ▏" << endl;
    cout << " --------------------------------------------------- " << endl;
    cout << "请选择：";
}
void Manage::Find()
{
    string  id;
    book* p = NULL;
    cout << "请输入要查找的图书的编号："; cin >> id;
    if (p = FindID(id))
    {        
        p->Next->Show();
        cout << "输入任意字符！继续……";
        getch();
    }
    else
    {
        cout << "没有找到该书！" << '\n' << endl;
        cout << "输入任意字符！继续……";
        getch();
    }
    
}

void Manage::Save()
{
    out.open("book.txt");
    for (book* p = Head->Next; p->Next != End; p = p->Next)
        out << p->book_id << "\t" << p->book_name << "\t" << p->author << "\t"
        << p->publishing << "\t" << p->price << '\n';
    out.close();
}
int main()
{
    int x, i = 0;
    bool quit = false;
    Manage AA;
    while (!quit)
    {
        system("cls");
        AA.ShowMenu();
        cin >> x;
        switch (x)
        {
        case 0:quit = true; break;
        case 1:AA.AddItem(); break;
        case 2:AA.Find(); break;
        }
    }
    return 0;
}

运行结果及报错内容

我的解答思路和尝试过的方法

我想要达到的结果

如何才能保存到文件当中呢？

保存的文件路径或文件名不对
保存时打开文件的模式不对
保存时写入数据的格式不对
保存完没有关闭文件
……

你的open函数都没有传入操作方式，写什么文件啊
你总要告诉程序，到底是要读文件还是写文件啊
你不传参数，默认就是读