Determining if all items in a collection meet established critera - algorithm

Question

This seems to be a problem that comes up a lot. I've been coming up with the same solution nearly every time but was curious if people have a better method of accomplishing this.
I have one class that is a list of instances of another class. The state of the parent class is dependent upon state of ALL the children
As an example. Say I have the following classes
class Box
{
int _objectId= <insert_unique_id>;
int _itemCount = 0;
public void AddItem()
{
_itemCount = Max(_itemCount + 1, 5);
}
public int GetId()
{
return _objectId;
}
public bool IsFull()
{
return _itemCount == 5
}
}
class BiggerBox
{
Map<int, Box> _boxes;
public void AddToBox(int id)
{
_boxes[id].AddItem();
}
public bool IsFull()
{
foreach(var box in _boxes.Values)
if(!box.IsFull())
return false;
return true;
}
}
All additions to a "Box" are done via the BiggerBox.AddToBox call. What I would like to do is be able to determine box.IsFull() without iterating over every single item every time we add an element.
Typically i accomplish this by keeping a SET or a separate collection of what items are full.
Curious, has anyone come up to an ingenious solution to this or is the simple answer that there is no other way?

Answer 1

There are two things you need to do in order to accomplish what you want:
Be able to control every entrypoint to your collection
React to changes to the objects in the collection
For instance, if the objects in the collection are mutable (meaning, they can change after being added to your collection) you need your main object to react to that change.
As you say, you could create a separate set of the objects that are full, but if the objects can change afterwards, when they change you either need to take them out of that set, or add them to it.
This means that in order for you to optimize this, you need some way to observe the changes to the underlying objects, for instance if they implement INotifyPropertyChanged or similar.
If the objects cannot change after being added to your main object, or you don't really care if they do, you just need to control every entrypoint, meaning that you basically need to add the necessary checks to your AddItem method.
For your particular types I would implement an event on the Box class so that when it is full, it fires the event. Your BiggerBox class would then hook into this event in order to observe when an underlying box becomes full.

Answer 2

You can upkeep the number of complete (or non-complete) boxes in BiggerBox class, and update it in all the functions.
E.g., in AddToBox it could be:
bool wasFull = _boxes[id].IsFull;
_boxes[id].AddItem();
if (!wasFull && _boxes[id].IsFull) // After this update box has become full.
completeBoxes += 1;
It is also possible to implement this upkeep procedure in other hypothetical functions (like RemoveFromBox, AddBox, RemoveBox, etc.)