/* 

  Sum to one in Picat.

  https://brainstellar.com/puzzles/probability/213
  """
  On pressing a button, a random number is generated uniformly between 0 & 1. 
  You keep on generating these numbers until their sum exceeds 1. What is 
  the probability that you need to press the button more than n times? What 
  is the expected number of times you need to press the button?

  Answer: Probability: 1/n! ; Expected times: e
  """

  Cf https://math.stackexchange.com/questions/111314/choose-a-random-number-between-0-and-1-and-record-its-value-keep-doing-it-u/111343#111343

  Cf my Gamble model gamble_sum_to_one.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.

/*

  [expected_theoretical = 2.71828,p_more_than_3_times = 0.166667]
  var : len
  Probabilities:
  2: 0.4972000000000000
  3: 0.3351500000000000
  4: 0.1243000000000000
  5: 0.0346500000000000
  6: 0.0071500000000000
  7: 0.0013000000000000
  8: 0.0002500000000000
  mean = 2.7243

  var : more than 2 times
  Probabilities:
  1: 0.5028000000000000
  0: 0.4972000000000000
  mean = 0.5028

  var : more than 3 times
  Probabilities:
  0: 0.8323500000000000
  1: 0.1676500000000000
  mean = 0.16765

  var : more than 4 times
  Probabilities:
  0: 0.9566500000000000
  1: 0.0433500000000000
  mean = 0.04335

  var : more than 5 times
  Probabilities:
  0: 0.9913000000000000
  1: 0.0087000000000000
  mean = 0.0087


*/
go ?=>
  println([expected_theoretical=exp(1),p_more_than_3_times=(1/factorial(3))]),
  reset_store,
  run_model(20_000,$model,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  A = [],
  OK = false,
  while (OK == false)
   if A.sum > 1 then
     OK := A
   else
     A := A ++ [beta_dist(1,1)]
   end
  end,
  Len = A.len,
  add("len",Len),
  foreach(I in 2..5)
    add("more than " ++ I.to_string ++ " times",check1(Len > I))
  end.