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A question¹ that has been around for some time was recently closed as duplicate² by moderator overrule.

I don't agree with this closure for three reasons:

  1. It's not a duplicate of the question provided²: it asks for the analysis of a nested loop, not about particularities of Landau notation. The OP does end up making the "sum of Landau terms"-mistake -- but incidentally.

  2. Leaving duplicate aside, this is not a dump question since the OP does provide an attempt. The reasoning is succinct enough so that the question "Is my reasoning correct?" is a focussed enough question.

  3. Given the elaborate and well-written answers, this is a question I'd like to use as target for duplicate closures of other "nested loop runtime" questions.

Since we did not find consens among the moderators (the majority being biased by having provided answers to the question¹) and multiple users have voted to "Leave Closed", I'm posing this question here.

  • Should the question remain closed? Why?
  • If so, should we change the linked duplicate?

  1. What is the asymptotic runtime of this nested loop?
    Full disclosure: After the question was closed, I edited it in order to emphasise the points that make it distinct from the question chosen (which is how I understood it originally).
  2. What goes wrong with sums of Landau terms?
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  • $\begingroup$ -1, apparently the main reason this is being raised here is (1) mods have answers they dont want to lose & (2) mods cant find a way to agree on something not worth much attn/effort (question considered only has 3 votes) ... what goes around comes around ... $\endgroup$ – vzn Mar 31 '14 at 20:24
  • $\begingroup$ Should we perhaps write a new question that can be used as a dup target for other "nested loop runtime" questions? What is the common theme there? Is the common theme that people don't even know how to start? (If so, maybe we should write a question that asks "how do I begin to analyze the running time of nested loops?") Or is there a common misconception/point of confusion that could help us make that dup-target question more focused and more helpful? $\endgroup$ – D.W. Apr 6 '14 at 6:52
  • $\begingroup$ @D.W.: I'm on it. (See chat.) $\endgroup$ – Raphael Apr 6 '14 at 17:07
  • $\begingroup$ Just saw this discussion, sorry for being late to the party. I closed this question after reading it since the real question seems to be "why doesn't using Landau notation on this random example work?" Sometimes, people don't really know what question they mean to ask, and closing things as Duplicate can help users find what they're really looking for. Duplicate content isn't removed, AFAIK, so we're not losing the answers... at most, it would be nice to let dupe targets refer back to closed questions, but that's a broader criticism of the SE system (unless it already exists :)) $\endgroup$ – Patrick87 Apr 21 '14 at 18:14
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As I see it, there are several possible views of the question:

  1. The actual question asked is "Is my analysis correct?" (This is even more obvious in the original version of the question.) As I understand the previous discussions, these questions are considered close-worthy most of the time.

  2. It happens to be the case that the answer to 1. is "No", making an actual SE-worthy question of "What is wrong?" resp. "Why is this wrong?" This question is what Gilles answered. It also is a duplicate of the linked question.

  3. If we ignore the failed attempt of the OP, we arrive at the question that you and Subhayan answered. However, without that attempt, the question is merely a problem dump.

Conclusion: As the question stands, it is not clear if 2. or 3. is the actual question. So the question should be closed as "unclear what you're asking". If it is changed to be clearly 2. (or 3.), it should be closed as a duplicate (resp. a problem dump).

Option:

Remove the answer attempt by the OP (or turn it into an answer), ignore the fact that it is a problem dump and either adapt Gilles' answer to fit question 3. or move it to the duplicate (this will probably require some adapting as well).

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