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Showing content from https://cplusplus.github.io/LWG/issue4162 below:

Worst time complexity of non-parallel versions of nth_element is underspecified

template<class RandomAccessIterator>
  constexpr void nth_element(RandomAccessIterator first, RandomAccessIterator nth,
                             RandomAccessIterator last);
template<class ExecutionPolicy, class RandomAccessIterator>
  void nth_element(ExecutionPolicy&& exec,
                   RandomAccessIterator first, RandomAccessIterator nth,
                   RandomAccessIterator last);
template<class RandomAccessIterator, class Compare>
  constexpr void nth_element(RandomAccessIterator first, RandomAccessIterator nth,
                             RandomAccessIterator last, Compare comp);
template<class ExecutionPolicy, class RandomAccessIterator, class Compare>
  void nth_element(ExecutionPolicy&& exec,
                   RandomAccessIterator first, RandomAccessIterator nth,
                   RandomAccessIterator last, Compare comp);
template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
         class Proj = identity>
  requires sortable<I, Comp, Proj>
  constexpr I
    ranges::nth_element(I first, I nth, S last, Comp comp = {}, Proj proj = {});

[…]

-5- Complexity: For the overloads with no ExecutionPolicy, linear on average. For the overloads with an ExecutionPolicy,𝒪(N) applications of the predicate , and 𝒪(N log N) swaps, where N = last - first. For the overloads with no ExecutionPolicy, 𝒪(N) on average.

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