std::ranges::sample() 算法

自 C++20 起

简化

// (1)
O sample( I first, S last, O out, std::iter_difference_t<I> n, Gen&& gen );

// (2)
O sample( R&& r, O out, ranges::range_difference_t<R> n, Gen&& gen );

参数类型是泛型的，并具有以下约束

• I - std::input_iterator
• S - std::sentinel_for<I>
• O - std::weakly_incrementable
• R - std::ranges::input_range
• Gen - (无)

此外，每个重载都有以下约束

• (1):

  (forward_iterator<I> || random_access_iterator<O>)
  && indirectly_copyable<I, O>
  && uniform_random_bit_generator<remove_reference_t<Gen>>
• (2):

  (ranges::forward_range<R> || random_access_iterator<O>)
  && indirectly_copyable<ranges::iterator_t<R>, O>
  && uniform_random_bit_generator<remove_reference_t<Gen>>

(为便于阅读，省略了 std:: 命名空间)

详细

// (1)
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> &&
            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 );

// (2)
template<
  ranges::input_range R,
  std::weakly_incrementable O,
  class Gen
>
  requires (ranges::forward_range<R> || std::random_access_iterator<O>) &&
            std::indirectly_copyable<ranges::iterator_t<R>, O> &&
            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) 从序列 [first; last) 中选择 M = min(n, last - first) 个元素（不替换），使得每个可能的样本出现概率相等，并将这些选定的元素写入从 out 开始的范围。

  仅当 I 建模 std::forward_iterator 时，算法才稳定（保留选定元素的相对顺序）。

  未定义行为

  行为未定义

  如果 out 在 [first; last) 中。

• (2) 与 (1) 相同，但使用 r 作为范围，如同使用 ranges::begin(r) 作为 first 和 ranges::end(r) 作为 last。

本页描述的函数类实体是niebloids。

参数

first last	从中进行抽样的元素范围（总体）。
r	从中进行抽样的元素范围（总体）。
out	写入样本的输出迭代器。
n	要获取的样本数量。
gen	用作随机性来源的随机数生成器。

返回值

其中 M 定义为 min(n, last - first)。

一个等于 out + M 的迭代器，即结果样本范围的末尾。

复杂度

(last - first) 的线性时间复杂度。

异常

(无)

可能的实现

sample(1) 和 sample(2)

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 {};

示例

Main.cpp

#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);
    }
}

可能的输出

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 }