std::ranges::sample(3)

NAME
std::ranges::sample - std::ranges::sample

Synopsis
   Defined in header <algorithm>
   Call signature
   template< std::input_iterator I, std::sentinel_for<I> S,
             std::weakly_incrementable O, class Gen >
   requires (std::forward_iterator<I> || std::random_access_iterator<O>) &&
             std::indirectly_copyable<I, O> && (1) (since
                        C++20)
   std::uniform_random_bit_generator<std::remove_reference_t<Gen>>
   O sample( I first, S last, O out, std::iter_difference_t<I> n, Gen&& gen
   );
   template< ranges::input_range R, std::weakly_incrementable O, class Gen
   >
   requires (ranges::forward_range<R> || std::random_access_iterator<O>) && (since
             std::indirectly_copyable<ranges::iterator_t<R>, O> && (2) C++20)
   std::uniform_random_bit_generator<std::remove_reference_t<Gen>>
   O sample( R&& r, O out, ranges::range_difference_t<R> n, Gen&& gen );
   1) Selects M = min(n, last - first) elements from the sequence [first, last)
   (without replacement) such that each possible sample has equal probability of
   appearance, and writes those selected elements into the range beginning at out.
   The algorithm is stable (preserves the relative order of the selected elements) only
   if I models std::forward_iterator.
   The behavior is undefined if out is in [first, last).
   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, that is:
     * Explicit template argument lists cannot be specified when calling any of them.
     * None of them are visible to argument-dependent lookup.
     * When any of them are found by normal unqualified lookup as the name to the left
       of the function-call operator, argument-dependent lookup is inhibited.
   In practice, they may be implemented as function objects, or with special compiler
   extensions.

Parameters
   first1, last1 - the range from which to make the sampling (the population)
   r - the range from which to make the sampling (the population)
   out - the output iterator where the samples are written
   n - number of samples to take
   gen - the random number generator used as the source of randomness

Return value
   An iterator equal to out + M, that is the end of the resulting sample range.

Complexity
   Linear: 𝓞(last - first).

Notes
   This function may implement selection sampling or reservoir sampling.

Possible implementation
   struct sample_fn
   {
       template<std::input_iterator I, std::sentinel_for<I> S,
                std::weakly_incrementable O, class Gen>
       requires (std::forward_iterator<I> or
                 std::random_access_iterator<O>) &&
                 std::indirectly_copyable<I, O> &&
                 std::uniform_random_bit_generator<std::remove_reference_t<Gen>>
       O operator()(I first, S last, O out, std::iter_difference_t<I> n, Gen&& gen) const
       {
           using diff_t = std::iter_difference_t<I>;
           using distrib_t = std::uniform_int_distribution<diff_t>;
           using param_t = typename distrib_t::param_type;
           distrib_t D{};
           if constexpr (std::forward_iterator<I>)
           {
               // this branch preserves "stability" of the sample elements
               auto rest{ranges::distance(first, last)};
               for (n = ranges::min(n, rest); n != 0; ++first)
                   if (D(gen, param_t(0, --rest)) < n)
                   {
                       *out++ = *first;
                       --n;
                   }
               return out;
           }
           else
           {
               // O is a random_access_iterator
               diff_t sample_size{};
               // copy [first, first + M) elements to "random access" output
               for (; first != last && sample_size != n; ++first)
                   out[sample_size++] = *first;
               // overwrite some of the copied elements with randomly selected ones
               for (auto pop_size{sample_size}; first != last; ++first, ++pop_size)
               {
                   const auto i{D(gen, param_t{0, pop_size})};
                   if (i < n)
                       out[i] = *first;
               }
               return out + sample_size;
           }
       }
       template<ranges::input_range R, std::weakly_incrementable O, class Gen>
       requires (ranges::forward_range<R> or std::random_access_iterator<O>) &&
                 std::indirectly_copyable<ranges::iterator_t<R>, O> &&
                 std::uniform_random_bit_generator<std::remove_reference_t<Gen>>
       O operator()(R&& r, O out, ranges::range_difference_t<R> n, Gen&& gen) const
       {
           return (*this)(ranges::begin(r), ranges::end(r), std::move(out), n,
                        std::forward<Gen>(gen));
       }
   };
   inline constexpr sample_fn sample {};

Example
// Run this code
 #include <algorithm>
 #include <iomanip>
 #include <iostream>
 #include <iterator>
 #include <random>
 #include <vector>
 void print(auto const& rem, auto const& v)
 {
     std::cout << rem << " = [" << std::size(v) << "] { ";
     for (auto const& e : v)
         std::cout << e << ' ';
     std::cout << "}\n";
 }
 int main()
 {
     const auto in = {1, 2, 3, 4, 5, 6};
     print("in", in);
     std::vector<int> out;
     const int max = in.size() + 2;
     auto gen = std::mt19937{std::random_device{}()};
     for (int n{}; n != max; ++n)
     {
         out.clear();
         std::ranges::sample(in, std::back_inserter(out), n, gen);
         std::cout << "n = " << n;
         print(", out", out);
     }
 }

Possible output:
 in = [6] { 1 2 3 4 5 6 }
 n = 0, out = [0] { }
 n = 1, out = [1] { 5 }
 n = 2, out = [2] { 4 5 }
 n = 3, out = [3] { 2 3 5 }
 n = 4, out = [4] { 2 4 5 6 }
 n = 5, out = [5] { 1 2 3 5 6 }
 n = 6, out = [6] { 1 2 3 4 5 6 }
 n = 7, out = [6] { 1 2 3 4 5 6 }

See also
   ranges::shuffle randomly re-orders elements in a range
   (C++20) (niebloid)
   sample selects N random elements from a sequence
   (C++17) (function template)