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Stacks are not only the preferred data structure for bottom up parsing, they are the only data structure suitable for bottom up parsing.

Bottom-up parsing is usually referred to as depth-first search. Top-down parsing is referred to as breadth-first search. The two are exactly the same in terms of implementation, the difference is only in the structure used to store information collated from the previous iterations. With top-down parsing you use a queue, pushing to the back and popping from the front. With bottom-up parsing you use a stack, pushing to and popping from the back.

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