# include <cstdlib>
# include <iostream>
void perm_next ( int n, int p[], int &rank );

using namespace std;

int main ( )
//
//  TRIP_COUNTING seeks the shortest round trip by checking every permutation.
//
{
  double dist[5][5] = { {0, 3, 4, 2, 7},
                        {3, 0, 4, 6, 3},
                        {4, 4, 0, 5, 8},
                        {2, 6, 5, 0, 6},
                        {7, 3, 8, 6, 0} }; 
  double d, dmin;
  int i, n = 5, next, old, p[5], pmin[5], rank;

  dmin = 10000000;
  rank = -1;

  while ( true )
  {
//
//  Generate the next permutation.
//
    perm_next ( n, p, rank );

    if ( rank == -1 ) 
    {
      break;
    }
//
//  Compute the distance for this trip.
//
    old = p[n-1];
    d = 0.0;
    for ( i = 0; i < n; i++ )
    {
      next = p[i];
      d = d + dist[old][next];
      old = next;
    }
//
//  Is this distance shorter?
//
    if ( d < dmin )
    {
      dmin = d;
      for ( i = 0; i < n; i++ )
      {
        pmin[i] = p[i];
      }
    }
  }

  cout << "Shortest round trip has length " << dmin << "\n";
  for ( i = 0; i < n; i++ )
  {
    cout << "  " << pmin[i];
  }
  cout << "\n";

  return 0;
}