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That doesn't make much sense. I guess it should be while NOT empty Q. Note that in many programming languages, the "not" is expressed with the exclamation mark. Perhaps you overlooked it... or it disappeared from the question. In that case (not empty), the meaning would be something like: while there is something in the queue (i.e., while not empty queue), process the elements in the queue (do something with the element). The statement is incomplete; instead of just "q1" it should say something like "process q1" or "q1.process()".

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