/* 

  Meeting under the clock in Picat.

  """
  Meeting Under the Clock (This problem is posed by Julian Simon(1994))

  Two persons agree to arrive at the two clock sometime between 1 pm and 2 pm 
  and to stay for 20 minutes. What is the probability that they will be there
  at the same time?
  """

  Cf my Gamble model gamble_meeting_under_the_clock.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 : c1
  Probabilities (truncated):
  29: 0.0191000000000000
  31: 0.0188000000000000
  25: 0.0186000000000000
  19: 0.0179000000000000
  .........
  57: 0.0154500000000000
  18: 0.0154500000000000
  21: 0.0149500000000000
  51: 0.0149000000000000
  mean = 30.37115

  var : c2
  Probabilities (truncated):
  56: 0.0189500000000000
  37: 0.0184000000000000
  12: 0.0182500000000000
  27: 0.0181000000000000
  .........
  47: 0.0156000000000000
  17: 0.0154500000000000
  58: 0.0152000000000000
  39: 0.0149000000000000
  mean = 30.3688

  var : d
  Probabilities (truncated):
  3: 0.0332500000000000
  2: 0.0328000000000000
  1: 0.0316500000000000
  5: 0.0308000000000000
  .........
  56: 0.0019500000000000
  57: 0.0014000000000000
  58: 0.0012000000000000
  59: 0.0007500000000000
  mean = 20.0775

  var : prob
  Probabilities:
  true: 0.5641500000000000
  false: 0.4358500000000000
  mean = [true = 0.56415,false = 0.43585]

*/
go ?=>
  reset_store,
  run_model(20_000,$model,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,
  % fail,
  nl.
go => true.
  
  
model() =>
  WaitTime = 20,
  C1 = random_integer1(60),
  C2 = random_integer1(60),

  D = abs(C1-C2),
  Prob = check(D <= WaitTime),
  
  add("c1",C1),
  add("c2",C2),
  add("d",D),
  add("prob",Prob).