#! /usr/bin/env python3
#
def full_deck_expected ( card_num ):

#*****************************************************************************80
#
## full_deck_expected(): expected value of the general full deck problem.
#
#  Discussion:
#
#    The expected value, given a deck of N distinct cards, is n*Hn, where
#    Hn is the n-th harmonic number.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    06 July 2022
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Herbert Wilf,
#    Some New Aspects of the Coupon Collector's Problem,
#    SIAM Review,
#    Volume 48, Number 3, September 2006, pages 549-565.
#
#  Input:
#
#    integer card_num: the number of cards in the deck.
#
#  Output:
#
#    real ev: the expected number of cards that must be collected in order
#    to acquire at least one of every kind.
#
  ev = 0.0
  for i in range ( 1, card_num + 1 ):
    ev = ev + card_num / i

  return ev

def full_deck_expected_test ( ):

#*****************************************************************************80
#
## full_deck_expected_test() tests full_deck_expected().
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    06 July 2022
#
#  Author:
#
#    John Burkardt
#
  print ( '' )
  print ( 'full_deck_expected_test():' )
  print ( '  full_deck_expected() reports the expected value for' )
  print ( '  the number of cards drawn before seeing every card,' )
  print ( '  for the general full deck process, using M cards.' )
  print ( '' )
  print ( '  card_num  Expected' )
  print ( '' )
  for card_num in [ 10, 52, 100, 365, 500 ]:
    ev = full_deck_expected ( card_num )
    print ( '  %3d    %10.2f' % ( card_num, ev ) )

  return

def full_deck_histogram ( n, card_num ):

#*****************************************************************************80
#
## full_deck_histogram() histograms full_deck statistics.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    11 July 2022
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    integer N, the number of trials to make.
#
  import matplotlib.pyplot as plt
  import numpy as np

  print ( '' )
  print ( 'full_deck_histogram():' )
  print ( '  Create a histogram of the full deck process.' )

  m = np.zeros ( n )
  for i in range ( 0, n ):
    deck = full_deck_try ( card_num )
    m[i] = np.sum ( deck )

  plt.hist ( m, bins = 20, rwidth = 0.95, density = True )
  plt.grid ( True )
  plt.xlabel ( '<-- Number of draws -->' )
  plt.ylabel ( '<-- Probability -->' )
  plt.title ( 'PDF for draws needed to see full deck' )
  filename = 'full_deck_pdf.png'
  plt.savefig ( filename )
  print ( '  Graphics saved as "%s"' % ( filename ) )
  plt.show ( block = False )
  plt.close ( )
 
  return

def full_deck_simulation_test ( ):

#*****************************************************************************80
#
## full_deck_simulation_test() tests full_deck_simulation().
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    06 July 2022
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'full_deck_simulation_test():' )
  print ( '  Python version: ' + platform.python_version ( ) )
  print ( '  full_deck_simulation() simulates a process in which' )
  print ( '  a card is drawn from a deck of 52 cards, then returned.' )
  print ( '  The process is continued until all cards have been seen' )
  print ( '  at least once.' )

  full_deck_try_test ( )
  full_deck_stats_test ( )
  full_deck_expected_test ( )
  n = 2000
  card_num = 52
  full_deck_histogram ( n, card_num )
  full_deck_variance_test ( )
#
#  Terminate.
#
  print ( '' )
  print ( 'full_deck_simulation_test():' )
  print ( '  Normal end of execution.' )

  return

def full_deck_stats ( n, card_num ):

#*****************************************************************************80
#
## full_deck_stats() returns statistics for N tries of the full deck problem.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    06 July 2022
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    integer n: the number of times the process will be carried out.
#
#  Output:
#
#    integer tries_min, real tries_mean, integer tries_max, real tries_std: 
#    the minimum, average, maximum and std for the number of cards drawn 
#    over all the processes.
#
  import numpy as np

  m = np.zeros ( n )
  for i in range ( 0, n ):
    deck = full_deck_try ( card_num )
    m[i] = np.sum ( deck )

  tries_min = np.min ( m )
  tries_max = np.max ( m )
  tries_mean = np.mean ( m )
  tries_std = np.std ( m )

  return tries_min, tries_mean, tries_max, tries_std

def full_deck_stats_test ( ):

#*****************************************************************************80
#
## full_deck_stats_test() tests full_deck_stats().
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    06 July 2022
#
#  Author:
#
#    John Burkardt
#
  print ( '' )
  print ( 'full_deck_stats_test():' )
  print ( '  full_deck_stats() reports statistics for N instances' )
  print ( '  of the 52-card full deck process.' )
  print ( '' )
  print ( '       N  Min    Mean  Max    Std' )
  print ( '' )

  card_num = 52
  for n in [ 10, 20, 50, 100, 1000, 10000 ]:
    tmin, tmean, tmax, tstd = full_deck_stats ( n, card_num )
    print ( '   %5d  %3d  %6.2f  %2d  %6.2f' % ( n, tmin, tmean, tmax, tstd ) )

  print ( '' )
  print ( '       N  Min    Mean  Max    Std' )
  print ( '' )
  card_num = 300
  for n in [ 10, 20, 50, 100, 1000, 10000 ]:
    tmin, tmean, tmax, tstd = full_deck_stats ( n, card_num )
    print ( '   %5d  %3d  %6.2f  %2d  %6.2f' % ( n, tmin, tmean, tmax, tstd ) )

  return

def full_deck_try ( card_num ):

#*****************************************************************************80
#
## full_deck_try() returns all the cards drawn for a full deck problem.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    06 July 2022
#
#  Author:
#
#    John Burkardt
#
#  Output:
#
#    integer deck(52): the number of times each card was drawn.
#
  from numpy.random import default_rng
  import numpy as np

  rng = default_rng()

  deck = np.zeros ( card_num )
  while ( True ):
    card = rng.integers ( low = 0, high = card_num )
    deck[card] = deck[card] + 1
    if ( np.all ( 0 < deck ) ):
      break

  return deck

def full_deck_try_test ( ):

#*****************************************************************************80
#
## full_deck_try_test() tests full_deck_try().
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    06 July 2022
#
#  Author:
#
#    John Burkardt
#
  import numpy as np

  print ( '' )
  print ( 'full_deck_try_test():' )
  print ( '  full_deck_try() repeatedly draws a random card' )
  print ( '  from a 52-card deck until all cards have been seen' )
  print ( '  at least once.' )
  print ( '' )
  print ( '  Try  Min    Mean Max  Total' )
  print ( '' )

  card_num = 52
  for i in range ( 0, 10 ):
    cards = full_deck_try ( card_num )
    print ( '   %2d  %3d  %6.2f  %2d   %4d' % \
      ( i, np.min ( cards ), np.mean ( cards ), np.max ( cards ), np.sum ( cards ) ) )

  return

def full_deck_variance ( card_num ):

#*****************************************************************************80
#
## full_deck_variance() returns the variance of the full deck problem.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    06 July 2022
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Herbert Wilf,
#    Some New Aspects of the Coupon Collector's Problem,
#    SIAM Review,
#    Volume 48, Number 3, September 2006, pages 549-565.
#
#  Input:
#
#    integer card_num: the number of cards in the deck.
#
#  Output:
#
#    real variance: the variance in the number of cards that must be 
#    collected in order to acquire at least one of every kind.
#
  variance = 0.0
  for i in range ( 2, card_num + 1 ):
    variance = variance + ( i - 1 ) / ( card_num - i + 1 )**2

  variance = card_num * variance

  return variance

def full_deck_variance_test ( ):

#*****************************************************************************80
#
## full_deck_variance_test() tests full_deck_variance().
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    06 July 2022
#
#  Author:
#
#    John Burkardt
#
  print ( '' )
  print ( 'full_deck_variance_test():' )
  print ( '  full_deck_variance() reports the variance for' )
  print ( '  the number of cards drawn in the full deck process.' )
  print ( '' )
  print ( '    N     Variance' )
  print ( '' )
  for card_num in [ 10, 52, 100, 365, 500 ]:
    variance = full_deck_variance ( card_num )
    print ( '  %3d  %10.2f' % ( card_num, variance ) )

  return

def timestamp ( ):

#*****************************************************************************80
#
## timestamp() prints the date as a timestamp.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    21 August 2019
#
#  Author:
#
#    John Burkardt
#
  import time

  t = time.time ( )
  print ( time.ctime ( t ) )

  return

if ( __name__ == '__main__' ):
  timestamp ( )
  full_deck_simulation_test ( )
  timestamp ( )