//Prototype an inverse permutaiion function.
//
#include <boost/utility/trace_scope.hpp>
#include <boost/array_stepper/mk_iota.hpp>
#include <boost/array_stepper/vector_print.hpp>
#include <algorithm>

using namespace boost::array_stepper;

  std::vector<unsigned>
invert_permute( std::vector<unsigned>const& permut_p)
{
    unsigned const n=permut_p.size();
    std::vector<unsigned> permut_i(n);
    for
    ( unsigned i=0
    ; i<n
    ; ++i
    )
    {
        permut_i[permut_p[i]]=i;
    }
    return permut_i;
}  

int main()
{
    boost::iostreams::indent_scoped_ostreambuf<char> indent_outbuf(std::cout,2);
    unsigned const rank=3;
    typedef std::vector<unsigned> permut_t;
    permut_t permut_o=mk_iota<unsigned>( 0, rank);
    {
        permut_t permut_p(permut_o);
        unsigned count=0;
        do
        {
            std::cout<<":count="<<count<<"\n";
            std::cout<<":permut_p="<<permut_p<<"\n";
            permut_t const permut_i(invert_permute(permut_p));
            std::cout<<":permut_i="<<permut_i<<"\n";
            for( unsigned i=0; i<rank; ++i)
            {
                unsigned pi=permut_p[permut_i[i]];
                if(permut_o[i]!=pi)
                {
                    std::cout<<":inversion failed:permut_p[permut_i["<<i<<"]]="<<pi<<"\n";
                }
            }
        }while 
          (  ++count< 130
          && std::next_permutation
             ( permut_p.begin()
             , permut_p.end()
             )
          );
    }
    return 0;
}