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Erm... Well the constructor shouldn't consume any part of the iterator. And hasNext() also shouldn't consume, so I assume there's an issue somewhere in there.
I find it quite likely that you're overcomplicating it or trying to consume the whole iterator into a stack or something like that, when the iterator should largely be completely passive and only make method calls to the double ended iterator as and ...
It's a reversed double ended iterator. If you're calling next, it should be consuming from the end of the double ended iterator passed in the constructor, if you're calling reverseNext, it should be consuming from the start of the double ended iterat...
While this has been asked indirectly previously, is the constructor for the Empty class strictly necessary, as it's redundant due to the implicit constructor already allocating required memory and no variables needing to be initialised with specific ...