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Quoted

int MyLayout::heightForWidth( int w ) const
{
if ( cache_dirty || cached_width != w ) {
// not all C++ compilers support "mutable"
MyLayout *that = (MyLayout*)this;
int h = calculateHeightForWidth( w );
that->cached_hfw = h;
return h;
}
return cached_hfw;
}

You get HeightForWidth() and you cahe it in another object instance.

Quoted

int MyLayout::heightForWidth( int w ) const
{
if ( cache_dirty || cached_width != w ) {
// not all C++ compilers support "mutable"
cached_hfw = calculateHeightForWidth( w );
}
return cached_hfw;
}

You store the result in the same object instance.

Quoted

other question: What does "mutable" mean?

You can get some comprehensive doc at C++ Tutorial

Quoted

Is the red part of First code nessary?
if yes, why? if not,What is the advantage?

See above.

what mutable means:

A method declared "const" must not modify any member variables or call non const methods of the class.
You can declare a member variable as "mutable" to allow a const method to modify it. This is typically used for cached values.

If a compiler does not support mutable, you can not modify members in const methods.
The trick with casting "this" to "that" is more a hack than a workaroud. It is to pretend that "that" is another object - but obviously it is the same as "this".

Hanspeter

Quoted

Originally posted by dr_super
In the second code, can I get the HeightForWidth()? (I mean I store and return it)

Why is the HeightForWidth() cached in another object? (I mean if I want to return it , I must do that?)

using that-> instead of direct is a hack if cached_hfw has not been declared mutable. Remember, a const method cannot change members, so, in your case:

1. compiler supports mutable. Use it.
or:
2. use that as a trick to allow changing value. that is a virtual other object, a trick to make the compiler believe you dont' change this.
3. If the method is not part of a property, remove the const declaration.