Something about virtual function and pure virtual function

Firstly, let's demonstrate a fact that virtual function must be implemented.

class A {public:A() { a = 0; }    virtual void a1();    int a2();private:    int a;};int main() {A a;return 0;}

A strange error about construction occurs. Now, let's see the correct version.

class A {public:A() { a = 0; }    virtual void a1() { a = 1;}    int a2();private:    int a;};int main() {A a;return 0;}

It is right. By the way, you can see the common member function could avoid implementation.

In contrast, the pure virtual function mustn't be implemented.

class A {public:A() { a = 0; }    virtual void a3() =0 { a = 1;}private:    int a;};int main() {return 0;}

Another example:

class A {public:A() { a = 0; }    virtual void a3() =0;private:    int a;};class B: public A {public:B(): A() { }};class C: public B {public:C(): B() {}void a3() {}};int main() {B b;C c;return 0;}

However, the correct should be

class A {public:A() { a = 0; }    virtual void a3() =0;private:    int a;};class B: public A {public:B(): A() { }};class C: public B {public:C(): B() {}void a3() {}};int main() {//B b;C c;return 0;}

From this experiment, we can see that pure virtual function doesn't necessarily be implemented in its subclass and hence its subclass is still a virtual class.