/* 

  No birthdays in Picat.

  From John Allen Paulos
  https://twitter.com/JohnAllenPaulos/status/1584278111579181056
  """
  Randomly select 365 people and mark their birthdays on a calendar. 
  Days on which none of the 365 people have a birthday will remain 
  unmarked. Let U be the number of such unmarked days. Then 365/U is 
  approximately the transcendentally ubiquitous number e, 2.718 … Eerie! 
  """

  Cf my Gamble model gamble_no_birthdays.rkt

  This program was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import ppl_distributions, ppl_utils.
import util.
% import ordset.

main => go.

/*
  var : p
  Probabilities (truncated):
  2.744360902255639: 0.0661000000000000
  2.723880597014925: 0.0653000000000000
  2.703703703703704: 0.0643500000000000
  2.765151515151515: 0.0628500000000000
  .........
  2.32484076433121: 0.0001500000000000
  3.201754385964912: 0.0001000000000000
  3.258928571428572: 0.0000500000000000
  2.29559748427673: 0.0000500000000000
  mean = 2.72667

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean % ,
                           % show_percentiles,
                           % show_hpd_intervals,hpd_intervals=[0.94],
                           % show_histogram,
                           % min_accepted_samples=1000,show_accepted_samples=true
                          ]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  N = 365,
  P = N / (N - random_integer1_n(N,N).remove_dups.len),
  
  add("p",P).