methods of visiting the nodes on a level of a tree

[nuzzle]

Yes you are right this is a good improvement. It doesn't prevent all the nodes from being visited.

No it doesn't, but you don't have to visit any nodes below desiredlevel and that can be a substantial saving considering that the bulk of the nodes tend to be at the deepest levels.

I see.And this would also be done when the tree is constructed? Right?

That's a possibility but in principle it can be done at any time. And of course if the tree is changed structurally the "level lists" must be updated to reflect that.

This solution is the fastest because you visit only exactly the nodes at desiredlevel. The drawback is that it requires an additional data structure which needs to be updated each time the tree changes. To what extent this is a problem depends on how often the tree is changed of course. If it never changes the only cost is the extra data structure.