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Bottom up parsers in worst case take O($n^3$) time, and i believe that LR parser being a bottom up parser should also take O($n^3$) time, but i read on wiki that they are able to solve problems in linear time. How can this be possible?

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  • $\begingroup$ Which "wiki" did you read that? Could you provide a reference or quoted text? $\endgroup$ – dkaeae Jul 15 '19 at 7:06
  • $\begingroup$ @dkaeae en.m.wikipedia.org/wiki/LR_parser , Moreover see the ans below provided by rici, so he is also suggesting O(n)! $\endgroup$ – Turing101 Jul 15 '19 at 9:07
  • $\begingroup$ @downvoter please explain the proper reason of downvote rather than downvoting without any justification..PEACE $\endgroup$ – Turing101 Jul 15 '19 at 17:19
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It's because they can only recognise a subset of context-free languages. In fact, it is the subset which can be parsed in linear time: languages with a deterministic grammar.

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  • $\begingroup$ so worst case case of LR parser is O(n)? $\endgroup$ – Turing101 Jul 15 '19 at 9:08
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    $\begingroup$ @hirak: yes, the LR parser always takes O(n) time. It can only take less time if the input can be rejected early. $\endgroup$ – rici Jul 15 '19 at 14:01

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