/* 

  Meeting under the clock (Julian Simon) 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?
  """

  Here we use overlap instead of abs(), 


  Cf
  - ppl_meeting_under_the_clock.pi 
  - my Gamble model gamble_meeting_under_the_clock2.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 : c1
  Probabilities (truncated):
  55: 0.0194000000000000
  44: 0.0191000000000000
  35: 0.0191000000000000
  57: 0.0189000000000000
  .........
  48: 0.0144000000000000
  27: 0.0144000000000000
  19: 0.0143000000000000
  45: 0.0139000000000000
  mean = 30.6126

  var : c2
  Probabilities (truncated):
  30: 0.0190000000000000
  3: 0.0189000000000000
  36: 0.0187000000000000
  18: 0.0187000000000000
  .........
  57: 0.0148000000000000
  41: 0.0146000000000000
  34: 0.0141000000000000
  12: 0.0140000000000000
  mean = 30.4232

  var : prob
  Probabilities:
  true: 0.5629000000000000
  false: 0.4371000000000000
  mean = [true = 0.5629,false = 0.4371]

*/
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.
  
overlap(A1,A2,B1,B2) = cond(max(A1,B1) <= min(A2,B2),true,false).
  
model() =>
  WaitTime = 20,
  C1 = random_integer1(60),
  C2 = random_integer1(60),  

  Prob = check( overlap(C1,C1+WaitTime,C2,C2+WaitTime) == true),
  
  add("c1",C1),
  add("c2",C2),
  add("prob",Prob).