What is the default constructor for C++ pointer?

The expression data_type() value-initializes an object. For a class type with a default constructor, it is invoked; if it doesn’t exist (or is defaulted), such as pointers, the object is zero-initialized.

So yes, you can rely on your map creating a NULL pointer.

UPDATE: I completed my program and that very line I was asking about is causing it to crash sometimes, but at a later stage. The problem is that I'm creating a new object without changing the pointer stored in std::map. What is really needed is either reference or pointer to that pointer.

MapIndex *mi = mapM[s];  // <- question about this line
if (!mi)
    mi = new MapIndex();
mi->add(values);

should be changed to:

MapIndex* &mi = mapM[s];  // <- question about this line
if (!mi)
    mi = new MapIndex();
mi->add(values);

I'm surprised nobody noticed this.

Yes it should be a zero (NULL) pointer as stl containers will default initialise objects when they aren't explicitly stored (ie accessing a non-existant key in a map as you are doing or resizing a vector to a larger size).

C++ Standard, 8.5 paragraph 5 states:

To default-initialize an object of type T means:

• If T is a non-POD class type (clause class), the default constructor for T is called (and the initialization is ill-formed if T has no accessible default constructor)
• If T is an array type, each element is default-initialized
• Otherwise, the storage for the object iszero-initialized.

You should also note that default initialisation is different to simply ommiting the constructor. When you omit the constructor and simply declare a simple type you will get an indeterminate value.

int a; // not default constructed, will have random data 
int b = int(); // will be initialised to zero

It'll create a NULL (0) pointer, which is an invalid pointer anyway :)