#! /usr/bin/env python3
#
def sudden_death ( trial_num, card_num ):

#*****************************************************************************80
#
## sudden_death() simulates a "sudden death" if card 0 is observed in a deck.
#
#  Licensing:
#
#    This code is distributed under the MIT license. 
#
#  Modified:
#
#    10 February 2023
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    integer trial_num: the number of trials.
#
#    integer card_num: the number of cards in the deck.
#
#  Output:
#
#    integer days[n]: the number of times a card was chosen (and replaced)
#    before the 0 card was encountered.
#
  import numpy as np

  days = np.zeros ( trial_num )

  for i in range ( 0, trial_num ):

    deck = np.arange ( 0, card_num )
    days[i] = 0
    while ( True ):
      days[i] = days[i] + 1
      np.random.shuffle ( deck )
      if ( deck[0] == 0 ):
        break

  return days

def sudden_death_test ( ):

#*****************************************************************************80
#
## sudden_death_test() tests sudden_death().
#
#  Licensing:
#
#    This code is distributed under the MIT license. 
#
#  Modified:
#
#    10 February 2023
#
#  Author:
#
#    John Burkardt
#
  import matplotlib.pyplot as plt
  import numpy as np

  print ( '' )
  print ( 'sudden_death_test():' )
  print ( '  Count the number of times a card was picked from a deck' )
  print ( '  and then replaced, until card 0 was picked.' )

  card_num = 10

  print ( '' )
  print ( '  Number of cards in deck is ', card_num )  
  print ( '       n  min      mean     max         std' )
  print ( '' )

  for trial_num in [ 10, 100, 1000, 10000, 100000 ]:
    days = sudden_death ( trial_num, card_num )
    print ( '  %6d   %2d  %8.2f  %6d    %8.2f' \
      % ( trial_num, np.min ( days ), np.mean ( days ), np.max ( days ), np.std ( days ) ) )
#
#  Make a histogram.
#
  trial_num = 10000
  card_num = 10
  days = sudden_death ( trial_num, card_num )
  plt.clf ( )
  plt.hist ( days, bins = 100, density = True )
  plt.grid ( True )
  plt.xlabel ( '<-- Number of times a card was picked -->' )
  plt.ylabel ( '<-- Frequency -->' )
  filename = 'sudden_death_' + str ( card_num ) + '_pdf.png'
  plt.savefig ( filename )
  print ( '  Graphics saved as "' + filename + '"' )
  plt.close ( )

  card_num = 52

  print ( '' )
  print ( '  Number of cards in deck is ', card_num )  
  print ( '       n  min      mean     max         std' )
  print ( '' )

  for trial_num in [ 10, 100, 1000, 10000, 100000 ]:
    days = sudden_death ( trial_num, card_num )
    print ( '  %6d   %2d  %8.2f  %6d    %8.2f' \
      % ( trial_num, np.min ( days ), np.mean ( days ), np.max ( days ), np.std ( days ) ) )

#
#  Make a histogram.
#
  trial_num = 10000
  card_num = 52
  days = sudden_death ( trial_num, card_num )
  plt.clf ( )
  plt.hist ( days, bins = 100, density = True )
  plt.grid ( True )
  plt.xlabel ( '<-- Number of times a card was picked -->' )
  plt.ylabel ( '<-- Frequency -->' )
  filename = 'sudden_death_' + str ( card_num ) + '_pdf.png'
  plt.savefig ( filename )
  print ( '  Graphics saved as "' + filename + '"' )
  plt.close ( )

  return

if ( __name__ == "__main__" ):
  sudden_death_test ( )