从右侧到奇数位置，从左侧到就位

这只是算法本身。有关详细信息，解释和替代方法，请参见反问题的答案。

1. 初始化指向右侧元素的指针到N/2。
2. 获得最大的子阵列，其尺寸为3 ^k 1
3. join（3 ^k 1）/2个元素，来自数组的开头，（3 ^k 1）/2元素元素的元素交换适当的子阵列。更新泳池指针。
4. 从位置1、3、9，... 3 ^k-1 ：将元素移至其在子阵列中的适当位置（从右侧到位置的左侧的元素，从右侧到奇数位置），替换的元素也应移至其适当位置等。直到此过程返回起始位置为止。
5. 使用步骤2 ..4。
，递归处理阵列的其余部分

这个问题比OP中提到的反面问题要简单，因为在这里我们必须从较大的阵列开始，以与执行周期领导者算法相同的顺序（反问题必须单独这样做，并且以相反的顺序从较小的开始到获得O（n）复杂性）。

我终于找到了直接和反向问题的解决方案：

#include <iterator>
#include <algorithm>
#include <type_traits>
#include <limits>
#include <deque>
#include <utility>
#include <cassert>
template< typename Iterator >
struct perfect_shuffle_permutation
{
    static_assert(std::is_same< typename std::iterator_traits< Iterator >::iterator_category, std::random_access_iterator_tag >::value,
                  "!");
    using difference_type = typename std::iterator_traits< Iterator >::difference_type;
    using value_type = typename std::iterator_traits< Iterator >::value_type;
    perfect_shuffle_permutation()
    {
        for (difference_type power3_ = 1; power3_ < std::numeric_limits< difference_type >::max() / 3; power3_ *= 3) {
            powers3_.emplace_back(power3_ + 1);
        }
        powers3_.emplace_back(std::numeric_limits< difference_type >::max());
    }
    void
    forward(Iterator _begin, Iterator _end) const
    {
        return forward(_begin, std::distance(_begin, _end));
    }
    void
    backward(Iterator _begin, Iterator _end) const
    {
        return backward(_begin, std::distance(_begin, _end));
    }
    void
    forward(Iterator _begin, difference_type const _size) const
    {
        assert(0 < _size);
        assert(_size % 2 == 0);
        difference_type const left_size_ = *(std::upper_bound(powers3_.cbegin(), powers3_.cend(), _size) - 1);
        cycle_leader_forward(_begin, left_size_);
        difference_type const rest_ = _size - left_size_;
        if (rest_ != 0) {
            Iterator middle_ = _begin + left_size_;
            forward(middle_, rest_);
            std::rotate(_begin + left_size_ / 2, middle_, middle_ + rest_ / 2);
        }
    }
    void
    backward(Iterator _begin, difference_type const _size) const
    {
        assert(0 < _size);
        assert(_size % 2 == 0);
        difference_type const left_size_ = *(std::upper_bound(powers3_.cbegin(), powers3_.cend(), _size) - 1);
        std::rotate(_begin + left_size_ / 2, _begin + _size / 2, _begin + (_size + left_size_) / 2);
        cycle_leader_backward(_begin, left_size_);
        difference_type const rest_ = _size - left_size_;
        if (rest_ != 0) {
            Iterator middle_ = _begin + left_size_;
            backward(middle_, rest_);
        }
    }
private :
    void
    cycle_leader_forward(Iterator _begin, difference_type const _size) const
    {
        for (difference_type leader_ = 1; leader_ != _size - 1; leader_ *= 3) {
            permutation_forward permutation_(leader_, _size);
            Iterator current_ = _begin + leader_;
            value_type first_ = std::move(*current_);
            while (++permutation_) {
                assert(permutation_ < _size);
                Iterator next_ = _begin + permutation_;
                *current_ = std::move(*next_);
                current_ = next_;
            }
            *current_ = std::move(first_);
        }
    }
    void
    cycle_leader_backward(Iterator _begin, difference_type const _size) const
    {
        for (difference_type leader_ = 1; leader_ != _size - 1; leader_ *= 3) {
            permutation_backward permutation_(leader_, _size);
            Iterator current_ = _begin + leader_;
            value_type first_ = std::move(*current_);
            while (++permutation_) {
                assert(permutation_ < _size);
                Iterator next_ = _begin + permutation_;
                *current_ = std::move(*next_);
                current_ = next_;
            }
            *current_ = std::move(first_);
        }
    }
    struct permutation_forward
    {
        permutation_forward(difference_type const _leader, difference_type const _size)
            : leader_(_leader)
            , current_(_leader)
            , half_size_(_size / 2)
        { ; }
        bool
        operator ++ ()
        {
            if (current_ < half_size_) {
                current_ += current_;
            } else {
                current_ = 1 + (current_ - half_size_) * 2;
            }
            return (current_ != leader_);
        }
        operator difference_type () const
        {
            return current_;
        }
    private :
        difference_type const leader_;
        difference_type current_;
        difference_type const half_size_;
    };
    struct permutation_backward
    {
        permutation_backward(difference_type const _leader, difference_type const _size)
            : leader_(_leader)
            , current_(_leader)
            , half_size_(_size / 2)
        { ; }
        bool
        operator ++ ()
        {
            if ((current_ % 2) == 0) {
                current_ /= 2;
            } else {
                current_ = (current_ - 1) / 2 + half_size_;
            }
            return (current_ != leader_);
        }
        operator difference_type () const
        {
            return current_;
        }
    private :
        difference_type const leader_;
        difference_type current_;
        difference_type const half_size_;
    };
    std::deque< difference_type > powers3_;
};