As I remember and checked, the usual way for traversing a tree or crawling the web breadth first (BFS) is by using a queue. Is there actually a way to implement it not using a queue?
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You really should be using a queue, as its easier to implement. Also, a queue allows for multiple machines to work together (one queues site while another pops sites off of the queue to traverse).
The only other way I see to do this is by using recursion (much more difficult, and uses only marginally either more or less memory).