#! /usr/bin/env python
#
def polyomino_enumerate_free ( n_data ):

#*****************************************************************************80
#
## POLYOMINO_ENUMERATE_FREE counts free polyominoes (allowing holes).
#
#  Discussion:
#
#    Polyominoes are connected planar shapes formed by adjoining unit squares.
#
#    The number of unit squares in a polyomino is its order.
#
#    If we ignore reflections and rotations when comparing polyominoes,
#    then we are considering the class of "free" polyominoes.  In that case,
#    for instance, there are just 12 free polyominoes of order 5, the
#    so called "pentominoes".
#
#    As the order increases, the number of polyominoes grows very rapidly.
#    The list offered here goes no further than order 28, but the later
#    numbers in the list are too large to represent as 32 byte integers. 
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    10 April 2018
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Solomon Golomb,
#    Polyominoes: Puzzles, Patterns, Problems, and Packings,
#    Princeton University Press, 1996,
#    ISBN: 9780691024448
#
#  Parameters:
#
#    Input/output, integer N_DATA.  The user sets N_DATA to 0 before the
#    first call.  On each call, the routine increments N_DATA by 1, and
#    returns the corresponding data; when there is no more data, the
#    output value of N_DATA will be 0 again.
#
#    Output, integer ORDER, the order of a polyomino.
#
#    Output, integer NUMBER, the number of free polyominos of this order.
#
  import numpy as np

  n_max = 29

  order_vec = np.array ( [ \
    0, \
    1,  2,  3,  4,  5, \
    6,  7,  8,  9, 10, \
   11, 12, 13, 14, 15, \
   16, 17, 18, 19, 20, \
   21, 22, 23, 24, 25, \
   26, 27, 28 ] )

  number_vec = np.array ( [ \
    1, \
    1,  1,  2,  5,  12, \
    35,  108,  369,  1285,  4655, \
    17073,  63600,  238591,  901971,  3426576, \
    13079255,  50107909,  192622052,  742624232,  2870671950, \
    11123060678,  43191857688,  168047007728,  654999700403,  2557227044764, \
    9999088822075,  39153010938487,  153511100594603 ] )

  if ( n_data < 0 ):
    n_data = 0

  if ( n_max <= n_data ):
    n_data = 0
    order = 0
    number = 0
  else:
    order = order_vec[n_data]
    number = number_vec[n_data]
    n_data = n_data + 1

  return n_data, order, number

def polyomino_enumerate_free_test ( ):

#*****************************************************************************80
#
## POLYOMINO_ENUMERATE_FREE_TEST tests POLYOMINO_ENUMERATE_FREE.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    10 April 2018
#
#  Author:
#
#    John Burkardt
#
  print ( '' )
  print ( 'POLYOMINO_ENUMERATE_FREE_TEST:' )
  print ( '  POLYOMINO_ENUMERATE_FREE returns counts of' )
  print ( '  the number of free polyominoes.' )
  print ( '' )
  print ( '     Order     Number' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, order, number = polyomino_enumerate_free ( n_data )

    if ( n_data == 0 ):
      break

    print ( '  %d  %d' % (  order, number ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'POLYOMINO_ENUMERATE_FREE_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  polyomino_enumerate_free_test ( )
  timestamp ( )