#! /usr/bin/env python3
#
def best_of_the_bunch_simulation ( n, k ):

#*****************************************************************************80
#
## best_of_the_bunch_simulation() tries to select the best of N options.
#
#  Discussion:
#
#    The options are presented in some permuted sequence.
#    The user can take the option and quit.
#    Otherwise, that option is rejected and the next is presented.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    07 July 2022
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    integer n: the number of options.
#
#    integer k: the number of options to examine and reject.
#    k = 0: accept very first option.
#    k = n-1: accept the very last option.
#
#  Output:
#
#    integer winnings: the value of the option chosen.
#
#    integer max_seen: the maximum value seen.
#
#    integer max_value: the maximum option value.
#
  from numpy.random import default_rng
  import numpy as np

  rng = default_rng ( )
  value = np.arange ( 1, n + 1 )
  value = rng.permutation ( value )
  max_value = np.max ( value )

  if ( k == 0 ):
    max_seen = - np.Inf
  else:
    max_seen = np.max ( value[0:k] )

  for i in range ( k, n ):
    if ( ( max_seen < value[i] ) or ( i == n - 1 ) ):
      winnings = value[i]
      break

  return winnings, max_seen, max_value, value

def best_of_the_bunch_simulation_test ( ):

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

  print ( '' )
  print ( 'best_of_the_bunch_simulation_test()' )
  print ( '  There are N objects, of varying value.' )
  print ( '  You can examine each object, in order, once.' )
  print ( '  If you accept the object, you are done.' )
  print ( '  Otherwise, you can view the next object.' )
  print ( '  Your goal is to maximize your winnings.' )

  n = 10
  k = 0
  tries = 10
  print ( '' )
  print ( '  Try k =', k )
  print ( '' )
  total = 0
  for i in range ( 0, tries ):
    winnings, max_seen, max_value, value = best_of_the_bunch_simulation ( n, k )
    print ( '[', value, '], choice = ', winnings ) 
    total = total + winnings
  print ( '  Average winnings = ', total / tries )

  n = 10
  k = n - 1
  tries = 10
  print ( '' )
  print ( '  Try k =', k )
  print ( '' )
  total = 0
  for i in range ( 0, tries ):
    winnings, max_seen, max_value, value = best_of_the_bunch_simulation ( n, k )
    print ( '[', value, '], choice = ', winnings ) 
    total = total + winnings
  print ( '  Average winnings = ', total / tries )

  n = 10
  k = 3
  tries = 10
  print ( '' )
  print ( '  Try k =', k )
  print ( '' )
  total = 0
  for i in range ( 0, tries ):
    winnings, max_seen, max_value, value = best_of_the_bunch_simulation ( n, k )
    print ( '[', value, '], choice = ', winnings ) 
    total = total + winnings
  print ( '  Average winnings = ', total / tries )


  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 ( )
  best_of_the_bunch_simulation_test ( )
  timestamp ( )