Issue 2444: Inconsistent complexity for std::sort_heap (original) (raw)

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2444. Inconsistent complexity for std::sort_heap

Section: 26.8.8.5 [sort.heap] Status: C++20 Submitter: François Dumont Opened: 2014-10-07 Last modified: 2021-02-25

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 26.8.8.5 [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_heapmax 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 2_N_ 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.

  1. In 26.8.8.5 [sort.heap] p3 the Standard states:

    template
    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 2_N_ log(_N_) comparisons (where _N_ == last - first).