Re: sort_heap complexity guarantee

[Daniel Krügler <daniel dot kruegler at gmail dot com>]

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

?

Thanks,

- Daniel