public List<Integer> findCheapestPath(int begin,int end,float[][] matrix){
  init(matrix);
  floyd(matrix);
  result.add(begin);
  findPath(begin,end);
  result.add(end);
  return result;
}

public List < Integer > findCheapestPath ( int begin , int end , float [ ] [ ] matrix ) { init ( matrix ) ; floyd ( matrix ) ; result . add ( begin ) ; findPath ( begin , end ) ; result . add ( end ) ; return result ; }
the shortest between begin to end
