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Section: 25.7.7.4 [sort.heap] Status: WP Submitter: François Dumont Opened: 2014-10-07 Last modified: 2017-07-30
Priority: 3
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Discussion:
While creating complexity tests for the GNU libstdc++ implementation I stumbled across a surprising requirement for the std::sort_heap algorithm.
In 25.7.7.4 [sort.heap] p3 the Standard states:
Complexity: At most N log(N) comparisons (where N == last - first).
As stated on the libstdc++ mailing list by Marc Glisse sort_heap can be implemented by N calls to pop_heap. As max number of comparisons of pop_heap is 2 * log(N) then sort_heap max limit should be 2 * log(1) + 2 * log(2) + .... + 2 * log(N) that is to say 2 * log(N!). In terms of log(N) we can also consider that this limit is also cap by 2 * N * log(N) which is surely what the Standard wanted to set as a limit.
This is why I would like to propose to replace paragraph 3 by:
Complexity: At most 2N log(N) comparisons (where N == last - first).
[2015-02 Cologne]
Marshall will research the maths and report back in Lenexa.
[2015-05-06 Lenexa]
STL: I dislike exact complexity requirements, they prevent one or two extra checks in debug mode. Would it be better to say O(N log(N)) not at most?
[2017-03-04, Kona]
Move to Tentatively Ready. STL may write a paper (with Thomas & Robert) offering guidance about Big-O notation vs. exact requirements.
Proposed resolution:
This wording is relative to N3936.
In 25.7.7.4 [sort.heap] p3 the Standard states:
template<class RandomAccessIterator> void sort_heap(RandomAccessIterator first, RandomAccessIterator last); template<class RandomAccessIterator, class Compare> void sort_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp);[…]
-3- Complexity: At most 2N log(N) comparisons (where N == last - first).