#! /usr/bin/env python
#
def slices ( dim_num, slice_num ):

#*****************************************************************************80
#
## SLICES: maximum number of pieces created by a given number of slices.
#
#  Discussion:
#
#    If we imagine slicing a pizza, each slice produce more pieces.  
#    The position of the slice affects the number of pieces created, but there
#    is a maximum.  
#
#    This function determines the maximum number of pieces created by a given
#    number of slices, applied to a space of a given dimension.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    26 February 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Robert Banks,
#    Slicing Pizzas, Racing Turtles, and Further Adventures in 
#    Applied Mathematics,
#    Princeton, 1999,
#    ISBN13: 9780691059471,
#    LC: QA93.B358.
#
#  Parameters:
#
#    Input, integer DIM_NUM, the spatial dimension.
#
#    Input, integer SLICE_NUM, the number of slices.
#
#    Input, integer VALUE, the maximum number of pieces that can
#    be created by the given number of slices applied in the given dimension.
#
  from i4_choose import i4_choose

  value = 0
  j_hi = min ( dim_num, slice_num ) + 1
  for j in range ( 0, j_hi ):
    value = value + i4_choose ( slice_num, j )

  return value

def slices_test ( ):

#*****************************************************************************80
#
## SLICES_TEST tests SLICES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    26 February 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  dim_max = 5
  slice_max = 8

  print ( '' )
  print ( 'SLICES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  SLICES determines the maximum number of pieces created' )
  print ( '  by SLICE_NUM slices in a DIM_NUM space.' )
  print ( '' )
  print ( '  SLICES' ),
  for slice_num in range ( 1, slice_max + 1 ):
    print ( '  %4d' % ( slice_num ) ),
  print ( '' )

  print ( '  DIM' )

  for dim_num in range ( 1, dim_max + 1 ):
    print ( '  %2d  : ' % ( dim_num ) ),
    for slice_num in range ( 1, slice_max + 1 ):
      value = slices ( dim_num, slice_num )
      print ( '  %4d' % ( value ) ),
    print ( '' )
#
#  Terminate.
#
  print ( '' )
  print ( 'SLICES_TEST:' )
  print ( '  Normal end of execution.' )
  return

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