/* 

  Collecting lucky coupons in Picat.

  https://brainstellar.com/puzzles/probability/206
  """
  A soda company is holding a contest where everyone who collects 
  one each of N different coupons wins some prize. You get a coupon 
  with each purchase of a soda, and each coupon is equally likely. 
  What’s the expected number of soda bottles you have to buy in order 
  to collect all the coupons?
  """

  Cf
  - ppl_coupon_collectors_problem.pi
  - ppl_coupon_collectors3.pi
  - my Gamble model gamble_collecting_lucky_coupons.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.

main => go.

/*

var : len
Probabilities (truncated):
22: 0.0487000000000000
21: 0.0448000000000000
25: 0.0445000000000000
23: 0.0439000000000000
.........
90: 0.0001000000000000
89: 0.0001000000000000
85: 0.0001000000000000
77: 0.0001000000000000
mean = 29.151
Histogram (total 10000)
 10.000:    31 #                                                            (0.003 / 0.003)
 12.300:   121 ######                                                       (0.012 / 0.015)
 14.600:   312 ###############                                              (0.031 / 0.046)
 16.900:   958 ##############################################               (0.096 / 0.142)
 19.200:   803 ######################################                       (0.080 / 0.222)
 21.500:   935 #############################################                (0.093 / 0.316)
 23.800:   875 ##########################################                   (0.087 / 0.403)
 26.100:  1257 ############################################################ (0.126 / 0.529)
 28.400:   745 ####################################                         (0.074 / 0.604)
 30.700:   643 ###############################                              (0.064 / 0.668)
 33.000:   776 #####################################                        (0.078 / 0.746)
 35.300:   444 #####################                                        (0.044 / 0.790)
 37.600:   402 ###################                                          (0.040 / 0.830)
 39.900:   421 ####################                                         (0.042 / 0.872)
 42.200:   229 ###########                                                  (0.023 / 0.895)
 44.500:   192 #########                                                    (0.019 / 0.914)
 46.800:   144 #######                                                      (0.014 / 0.929)
 49.100:   181 #########                                                    (0.018 / 0.947)
 51.400:    93 ####                                                         (0.009 / 0.956)
 53.700:    83 ####                                                         (0.008 / 0.965)
 56.000:    82 ####                                                         (0.008 / 0.973)
 58.300:    65 ###                                                          (0.006 / 0.979)
 60.600:    38 ##                                                           (0.004 / 0.983)
 62.900:    51 ##                                                           (0.005 / 0.988)
 65.200:    20 #                                                            (0.002 / 0.990)
 67.500:    19 #                                                            (0.002 / 0.992)
 69.800:    18 #                                                            (0.002 / 0.994)
 72.100:    13 #                                                            (0.001 / 0.995)
 74.400:    13 #                                                            (0.001 / 0.996)
 76.700:     5                                                              (0.001 / 0.997)
 79.000:     6                                                              (0.001 / 0.997)
 81.300:     7                                                              (0.001 / 0.998)
 83.600:     7                                                              (0.001 / 0.999)
 85.900:     1                                                              (0.000 / 0.999)
 88.200:     3                                                              (0.000 / 0.999)
 90.500:     3                                                              (0.000 / 1.000)
 92.800:     1                                                              (0.000 / 1.000)
 95.100:     0                                                              (0.000 / 1.000)
 97.400:     1                                                              (0.000 / 1.000)
 99.700:     2                                                              (0.000 / 1.000)

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean,show_histogram]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  

collecting_coupons(A,N) = Res =>
  if N == A.remove_dups.len then
    Res = A
  else
    Res = collecting_coupons(A ++ [random_integer1(N)],N)
  end.
model() =>
  N = 10,
  
  A = collecting_coupons([],N),
  add("len",A.len).