std::ranges::nth_element() algorithm

since C++20

Simplified

// (1)
constexpr I nth_element( I first, I nth, S last, Comp comp = {}, Proj proj = {} );

// (2)
constexpr ranges::borrowed_iterator_t<R>
    nth_element( R&& r, iterator_t<R> nth, Comp comp = {}, Proj proj = {} );

The type of arguments are generic and have following constraints:

• I - std::random_access_iterator
• S - std::sentinel_for<I>
• R - std::ranges::random_access_range
• Comp - (none)
• Proj - (none)

The Proj and Comp template arguments have, the following default types for all overloads: std::identity, ranges::less.

Additionally, each overload has the following constraints:

• (1) - std::sortable<I, Comp, Proj>
• (2) - std::sortable<ranges::iterator_t<R>, Comp, Proj>

Detailed

// (1)
template<
  std::random_access_iterator I,
  std::sentinel_for<I> S,
  class Comp = ranges::less,
  class Proj = std::identity
>
  requires std::sortable<I, Comp, Proj>
constexpr I
    nth_element( I first, I nth, S last, Comp comp = {}, Proj proj = {} );

// (2)
template<
  ranges::random_access_range R,
  class Comp = ranges::less,
  class Proj = std::identity
>
  requires std::sortable<iterator_t<R>, Comp, Proj>
constexpr ranges::borrowed_iterator_t<R>
    nth_element( R&& r, iterator_t<R> nth, Comp comp = {}, Proj proj = {} );

Reorders the elements in [first; last) such that:

• The element pointed at by nth is changed to whatever element would occur in that position if [first; last) were sorted with respect to comp and proj.

• All of the elements before this new nth element are less than or equal to the elements after the new nth element. That is, for every iterator i, j in the ranges [first; nth), [nth; last) respectively, the expression std::invoke(comp, std::invoke(proj, *j), std::invoke(proj, *i)) evaluates to false.

• If nth == last then the function has no effect.

• (1) Elements are compared using the given binary comparison function comp and projection proj.

• (2) Same as (1), but uses r as the source range, as if using ranges::begin(r) as first and ranges::end(r) as last.

The function-like entities described on this page are niebloids.

Parameters

first last	The range to sort.
r	The range to sort.
nth	The iterator defining the sort partition point.
comp	Comparison object to apply to the projected elements.
proj	Projection to apply to the elements.

Return value

• (1) An iterator equal to last.
• (2) Same as (1) if r is an lvalue or of a borrowed_range type. Otherwise returns std::ranges::dangling.

Complexity

Linear in ranges::distance(first, last) on average.

Exceptions

(none)

Notes

The algorithm used is typically Introselect although other Selection algorithm with suitable average-case complexity are allowed.

Examples

Main.cpp

#include <algorithm>
#include <array>
#include <functional>
#include <iostream>
#include <ranges>
#include <string_view>

void print(std::string_view rem, std::ranges::input_range auto const& a)
{
    for (std::cout << rem; const auto e : a)
        std::cout << e << ' ';
    std::cout << '\n';
}

int main()
{
    std::array v {5, 6, 4, 3, 2, 6, 7, 9, 3};
    print("Before nth_element: ", v);

    std::ranges::nth_element(v, v.begin() + v.size() / 2);
    print("After nth_element:  ", v);
    std::cout << "The median is: " << v[v.size() / 2] << '\n';

    std::ranges::nth_element(v, v.begin() + 1, std::greater<int>());
    print("After nth_element:  ", v);
    std::cout << "The second largest element is: " << v[1] << '\n';
    std::cout << "The largest element is: " << v[0] << "\n\n";

    using namespace std::literals;
    std::array names
    {
        "Diva"sv, "Cornelius"sv, "Munro"sv, "Rhod"sv,
        "Zorg"sv, "Korben"sv, "Bender"sv, "Leeloo"sv,
    };
    print("Before nth_element: ", names);
    auto fifth_element {std::ranges::next(names.begin(), 4)};
    std::ranges::nth_element(names, fifth_element);
    print("After nth_element:  ", names);
    std::cout << "The 5th element is: " << *fifth_element << '\n';
}

Output

Before nth_element: 5 6 4 3 2 6 7 9 3 
After nth_element:  2 3 3 4 5 6 6 7 9 
The median is: 5
After nth_element:  9 7 6 6 5 4 3 3 2 
The second largest element is: 7
The largest element is: 9
 
Before nth_element: Diva Cornelius Munro Rhod Zorg Korben Bender Leeloo 
After nth_element:  Diva Cornelius Bender Korben Leeloo Rhod Munro Zorg 
The 5th element is: Leeloo