Rotation and permutation

Remember our code from Swapping, reversing, and partitioning to reverse the order of words in a sentence? When the "sentence" contains only two words, there is another way to look at the reversal: you could consider it a cyclic rotation of the elements in the underlying range. std::rotate(a,mid,b) rotates the elements of the range [a,b) so that the element formerly addressed by mid is now at a (and returns an iterator pointing to the element whose value was formerly at a):

    template<class FwdIt>
    FwdIt rotate(FwdIt a, FwdIt mid, FwdIt b)
    {
      auto result = a + (b - mid);

      // First, reverse the whole range.
      std::reverse(a, b);

      // Next, un-reverse each individual segment.
      std::reverse(a, result);
      std::reverse(result, b);

      return result;
    }

    void test()
    {
      std::vector<int> v = {1, 2, 3, 4, 5, 6};
      auto five = std::find(v.begin(), v.end(), 5);
      auto one = std::rotate(v.begin(), five...