C++ FAQ Celebrating Twenty-One Years of the C++ FAQ!!!
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Section 17:
[17.8] How can I handle a constructor that fails?

Throw an exception.

Constructors don't have a return type, so it's not possible to use return codes. The best way to signal constructor failure is therefore to throw an exception. If you don't have the option of using exceptions, the "least bad" work-around is to put the object into a "zombie" state by setting an internal status bit so the object acts sort of like it's dead even though it is technically still alive.

The idea of a "zombie" object has a lot of down-side. You need to add a query ("inspector") member function to check this "zombie" bit so users of your class can find out if their object is truly alive, or if it's a zombie (i.e., a "living dead" object), and just about every place you construct one of your objects (including within a larger object or an array of objects) you need to check that status flag via an if statement. You'll also want to add an if to your other member functions: if the object is a zombie, do a no-op or perhaps something more obnoxious.

In practice the "zombie" thing gets pretty ugly. Certainly you should prefer exceptions over zombie objects, but if you do not have the option of using exceptions, zombie objects might be the "least bad" alternative.

Note: if a constructor finishes by throwing an exception, the memory associated with the object itself is cleaned up — there is no memory leak. For example:

void f()
  X x;              if X::X() throws, the memory for x itself will not leak
  Y* p = new Y();   if Y::Y() throws, the memory for *p itself will not leak
There is some fine print on this topic, so you need to keep reading. Specifically you need to know how to prevent memory leaks if the constructor itself allocates memory, and you also need to be aware of what happens if you use "placement" new rather than the ordinary new used in the sample code above.