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Re: sort_heap complexity guarantee


On 06/10/2014 23:05, Daniel Krügler wrote:
2014-10-06 23:00 GMT+02:00 François Dumont <frs.dumont@gmail.com>:
On 05/10/2014 22:54, Marc Glisse wrote:
On Sun, 5 Oct 2014, François Dumont wrote:

    I took a look at PR 61217 regarding pop_heap complexity guarantee.
Looks like we have no test to check complexity of our algos so I start
writing some starting with the heap operations. I found no issue with
make_heap, push_heap and pop_heap despite what the bug report is saying
however the attached testcase for sort_heap is failing.

    Standard is saying std::sort_heap shall use less than N * log(N)
comparisons but with my test using 1000 random values the test is showing:

8687 comparisons on 6907.76 max allowed

    Is this a known issue of sort_heap ? Do you confirm that the test is
valid ?
I would first look for confirmation that the standard didn't just forget a
big-O or something. I would expect an implementation as n calls to pop_heap
to be legal, and if pop_heap makes 2*log(n) comparisons, that naively sums
to too much. And I don't expect the standard to contain an advanced
amortized analysis or anything like that...

Good point, with n calls to pop_heap it means that limit must be 2*log(1) +
2*log(2) +... + 2*log(n) which is 2*log(n!) and  which is also necessarily <
2*n*log(n). I guess Standard comittee has forgotten the factor 2 in the
limit so this is what I am using as limit in the final test, unless someone
prefer the stricter 2*log(n!) ?
François, could you please submit a corresponding LWG issue by sending
an email using the recipe described here:

http://www.open-std.org/jtc1/sc22/wg21/docs/lwg-active.html#submit_issue

?

I just did requesting to use 2N log(N).

And is it ok to commit those ?

François


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