C ++：如何在此抽象类的方法中返回抽象类

Question

I have an abstract class and it has two derived classes. I'm trying to overload operator+ in the base class so I could do derivedClass=derivedClass+differentDerivedClass like this:

class iMatrix{
iMatrix operator+(const iMatrix& obj)
}

class UsualMatrix : public iMatrix

class SparseMatrix : public iMatrix 

Inside of main, I want to do

SparseMatrix a, b;
UsualMatrix c=a+b;

I have copy constructors and everything that may be helpful. Now if I create the function like

iMatrix operator+(const iMatrix& obj)

Compiler (LLVM in Xcode) says "Return type 'iMatrix' is an abstract class", but theoretically everything else should work properly. I've read manuals and other StackOverflow threads, so I've tried this:

iMatrix& operator+(const iMatrix& obj)

Whereas function on its own does "add obj to this" and returns *this. The problem is when I do c=a+b, a becomes equal to c, but it should not be changed.

a=
1 1 
1 1 
b=
1 1 
1 1 
a+b=c; 
c=
2 2 
2 2 
b=
1 1 
1 1 
a=
2 2 
2 2 

What should I do? Addition and multiplying must be implemented inside of base class, and I have no idea how to fix this error. Any advice would be appreciated, thanks.

Answer 1

The problem with your intend design is the abstract return type. Abstract classes can't be returned by value. Only concrete classes can be returned by value. So, to return abstract class you'd need a pointer or a reference.

Unfortunately, this will not work with the semantics of operator+() :

• either you'd return by reference the current object, and change it with the operation; but this is not compliant with the expected semantics, and furthermore might lead to wrong answerds (eg when doing c = a+b+a+b; )
• or you'd return the reference to a temporary object. but this would be UB, because the temporaray object will decease when the function returns, making the reference irrelevant.
• finally operator+ would not have a way to decide on its own of the concrete type to use for the return. For example: SparseMatrix a; UsualMatrix b; a+b; SparseMatrix a; UsualMatrix b; a+b; what should be the type to be used for the matrix a+b ?

You can use polymorphic and abstract types within operators, but not as a return type. To implement this kind of things, you'd need to opt for your own set of operators, and letting the caller manage the temporary results manually:

UsualMatrix c,tmp; 
SparseMatrix a,b,x; 
...
a.add(b, tmp);
tmp.add(x, c);   // c = a+b+x; 

with virtual void add(const iMatrix& x, iMatrix z) = 0;

Answer 2

One solution could be a non-member function like this:

template <
  typename T,
  typename = typename std::enable_if<std::is_base_of<iMatrix, T>::value>::type
>
T operator+(T const & a, T const & b) {
   T res; 
   // calculate res
   return res;
}

Because iMatrix is an abstract class, you can not return an instance of it. In the example above we are overloading operator+ for all derived classes T of iMatrix and we can return T instances.