用c++设计时间类Time和日期类Date，Birthtime类由Time类和Date类派生，并且增加一个数据成员Childname用于表示小孩的姓名，编写程序输出小孩的姓名和出生时间。

下面是时间类Time的实现：

class Time {
public:
    Time(int hour = 0, int minute = 0, int second = 0);
    std::string to_string() const;

private:
    int hour;
    int minute;
    int second;
};

Time::Time(int hour, int minute, int second) : hour(hour), minute(minute), second(second) {}

std::string Time::to_string() const {
    return std::to_string(hour) + ":" + std::to_string(minute) + ":" + std::to_string(second);
}

下面是日期类Date的实现：

class Date {
public:
    Date(int year = 0, int month = 0, int day = 0);
    std::string to_string() const;

private:
    int year;
    int month;
    int day;
};

Date::Date(int year, int month, int day) : year(year), month(month), day(day) {}

std::string Date::to_string() const {
    return std::to_string(year) + "-" + std::to_string(month) + "-" + std::to_string(day);
}

下面是Birthtime类的实现：

class Birthtime : public Time, public Date {
public:
    Birthtime(const std::string& child_name, int year, int month, int day, int hour = 0, int minute = 0, int second = 0);
    std::string to_string() const;

private:
    std::string child_name;
};

Birthtime::Birthtime(const std::string& child_name, int year, int month, int day, int hour, int minute, int second)
    : Time(hour, minute, second), Date(year, month, day), child_name(child_name) {}

std::string Birthtime::to_string() const {
    return child_name + " was born on " + Date::to_string() + " at " + Time::to_string();
}

现在可以测试一下Birthtime类的功能：

Birthtime birth_time("Alice", 2021, 8, 1, 10, 30, 0);
std::cout << birth_time.to_string() << std::endl;

输出结果为：

Alice was born on 2021-8-1 at 10:30:0

这个例子展示了如何使用继承来创建新的类，并且如何在子类中调用父类的构造函数。注意，在输出字符串时需要使用 Date::to_string() 和 Time::to_string() 来调用父类的成员函数。