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Showing content from https://en.cppreference.com/w/cpp/language/../keyword/../algorithm/ranges/sort.html below:

std::ranges::sort - cppreference.com

Call signature

(1) (since C++20) (2) (since C++20)

Sorts the elements in the range [firstlast) in non-descending order. The order of equivalent elements is not guaranteed to be preserved.

A sequence is sorted with respect to a comparator comp if for any iterator it pointing to the sequence and any non-negative integer n such that it + n is a valid iterator pointing to an element of the sequence, std::invoke(comp, std::invoke(proj, *(it + n)), std::invoke(proj, *it)) evaluates to false.

1) Elements are compared using the given binary comparison function comp.

The function-like entities described on this page are algorithm function objects (informally known as niebloids), that is:

[edit] Parameters first, last - the iterator-sentinel pair defining the range of elements to sort r - the range to sort comp - comparison to apply to the projected elements proj - projection to apply to the elements [edit] Return value

An iterator equal to last.

[edit] Complexity

\(\scriptsize \mathcal{O}(N\cdot\log{(N)})\)𝓞(N·log(N)) comparisons and projections, where N = ranges::distance(first, last).

[edit] Possible implementation

Note that typical implementations use Introsort. See also the implementation in MSVC STL and libstdc++.

struct sort_fn
{
    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
        operator()(I first, S last, Comp comp = {}, Proj proj = {}) const
    {
        if (first == last)
            return first;
 
        I last_iter = ranges::next(first, last);
        ranges::make_heap(first, last_iter, std::ref(comp), std::ref(proj));
        ranges::sort_heap(first, last_iter, std::ref(comp), std::ref(proj));
 
        return last_iter;
    }
 
    template<ranges::random_access_range R, class Comp = ranges::less,
             class Proj = std::identity>
    requires std::sortable<ranges::iterator_t<R>, Comp, Proj>
    constexpr ranges::borrowed_iterator_t<R>
        operator()(R&& r, Comp comp = {}, Proj proj = {}) const
    {
        return (*this)(ranges::begin(r), ranges::end(r), std::move(comp), std::move(proj));
    }
};
 
inline constexpr sort_fn sort {};
[edit] Notes

std::sort uses std::iter_swap to swap elements, whereas ranges::sort instead uses ranges::iter_swap (which performs ADL for iter_swap, unlike std::iter_swap)

[edit] Example
#include <algorithm>
#include <array>
#include <functional>
#include <iomanip>
#include <iostream>
 
void print(auto comment, auto const& seq, char term = ' ')
{
    for (std::cout << comment << '\n'; auto const& elem : seq)
        std::cout << elem << term;
    std::cout << '\n';
}
 
struct Particle
{
    std::string name; double mass; // MeV
    template<class Os> friend
    Os& operator<<(Os& os, Particle const& p)
    {
        return os << std::left << std::setw(8) << p.name << " : " << p.mass << ' ';
    }
};
 
int main()
{
    std::array s {5, 7, 4, 2, 8, 6, 1, 9, 0, 3};
 
    namespace ranges = std::ranges;
 
    ranges::sort(s);
    print("Sort using the default operator<", s);
 
    ranges::sort(s, ranges::greater());
    print("Sort using a standard library compare function object", s);
 
    struct
    {
        bool operator()(int a, int b) const { return a < b; }
    } customLess;
    ranges::sort(s.begin(), s.end(), customLess);
    print("Sort using a custom function object", s);
 
    ranges::sort(s, [](int a, int b) { return a > b; });
    print("Sort using a lambda expression", s);
 
    Particle particles[]
    {
        {"Electron", 0.511}, {"Muon", 105.66}, {"Tau", 1776.86},
        {"Positron", 0.511}, {"Proton", 938.27}, {"Neutron", 939.57}
    };
    ranges::sort(particles, {}, &Particle::name);
    print("\nSort by name using a projection", particles, '\n');
    ranges::sort(particles, {}, &Particle::mass);
    print("Sort by mass using a projection", particles, '\n');
}

Output:

Sort using the default operator<
0 1 2 3 4 5 6 7 8 9
Sort using a standard library compare function object
9 8 7 6 5 4 3 2 1 0
Sort using a custom function object
0 1 2 3 4 5 6 7 8 9
Sort using a lambda expression
9 8 7 6 5 4 3 2 1 0
 
Sort by name using a projection
Electron : 0.511
Muon     : 105.66
Neutron  : 939.57
Positron : 0.511
Proton   : 938.27
Tau      : 1776.86
 
Sort by mass using a projection
Electron : 0.511
Positron : 0.511
Muon     : 105.66
Proton   : 938.27
Neutron  : 939.57
Tau      : 1776.86
[edit] See also

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