In C++ check if two instances of a base class are infact of the same subclass

The below code explains the problem. Fill in same_sub_class to detect if the two pointers to virtual base class A are in fact the same concrete class.

struct A {
    ...
}:

struct B : public A {
    ...
}:

struct C : public A {
    ...
}


bool same_sub_class(A * a1, A * a2){
    // Fill this in to return true if a1 and a2 are
    // of the same concrete class
}

EDIT:

As I look at my application I need something slightly different from the above. I need to be able to group instances by their type_id.

FYI. I have a mini symbolic algerbra system so to do manipulations it is important to know the class type sometimes for sorting, and rearranging expressions.

So given a vector of pointers to instance how to group them by their type_id. I'd either need to be able to hash the type_id or generate a unique integer for every class.