#! /usr/bin/env python
#
def collatz_count ( n ):

#*****************************************************************************80
#
## COLLATZ_COUNT counts the number of terms in a Collatz sequence.
#
#  Discussion:
#
#    The rules for generation of the Collatz sequence are recursive.
#    If T is the current entry of the sequence, (T is
#    assumed to be a positive integer), then the next
#    entry, U is determined as follows:
#
#      if T is 1 (or less)
#        terminate the sequence;
#      else if T is even
#        U = T/2.
#      else (if T is odd and not 1)
#        U = 3*T+1;
#
#     N  Sequence                                                Length
#
#     1                                                               1
#     2   1                                                           2
#     3  10,  5, 16,  8,  4,  2,  1                                   8
#     4   2   1                                                       3
#     5  16,  8,  4,  2,  1                                           6
#     6   3, 10,  5, 16,  8,  4,  2,  1                               9
#     7  22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1   17
#     8   4,  2,  1                                                   4
#     9  28, 14,  7, ...                                             20
#    10   5, 16,  8,  4,  2,  1                                       7
#    11  34, 17, 52, 26, 13, 40, 20, 10,  5, 16, 8, 4, 2, 1          15
#    12   6,  3, 10,  5, 16,  8,  4,  2,  1                          10
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    24 January 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Eric Weisstein,
#    "The Collatz Problem",
#    CRC Concise Encyclopedia of Mathematics,
#    CRC 1998.
#
#  Parameters:
#
#    Input, integer N, the first element of the sequence.
#
#    Output, integer COUNT, the number of elements in
#    the Collatz sequence that begins with N.
#
  value = 1

  while ( True ):

    if ( n <= 1 ):
      break
    elif ( ( n % 2 ) == 0 ):
      n = n // 2
    else:
      n = 3 * n + 1

    value = value + 1

  return value

def collatz_count_test ( ):

#*****************************************************************************80
#
## COLLATZ_COUNT_TEST tests COLLATZ_COUNT.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    24 January 2015
#
#  Author:
#
#    John Burkardt
#
  import platform
  from collatz_count_values import collatz_count_values

  print ( '' )
  print ( 'COLLATZ_COUNT_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  COLLATZ_COUNT(N) counts the length of the' )
  print ( '  Collatz sequence beginning with N.' )
  print ( '' )
  print ( '       N       COUNT(N)     COUNT(N)' )
  print ( '              (computed)    (table)' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, n, value1 = collatz_count_values ( n_data )

    if ( n_data == 0 ):
      break

    value2 = collatz_count ( n )

    print ( '  %4d  %6d  %6d' % ( n, value1, value2 ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'COLLATZ_COUNT_TEST' )
  print ( '  Normal end of execution.' )
  return

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