/* 

  Meeting problem in Picat.

  (I'm not sure about the source. The page I got it from does not exist anymore.)
  """
  Let's say that 4 people agree to meet between 3:00 P.M. and 4:00 P.M.. 
  One man can wait for 10 minutes. Another can wait for 15 minutes. 
  Another can wait for 20 Minutes, and another still can wait for 30 
  minutes. What is the probability that all 4 will meet?
  """

  This problem was originally done using R (see http://www.hakank.org/sims/simulering.html)
  which gave the probability of meeting: 0.073.

  Cf 
  - ppl_meeting_problem2.pi
  - my Gamble model gamble_meeting_problem.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 : prob
  Probabilities:
  false: 0.9170000000000000
  true: 0.0830000000000000
  mean = [false = 0.917,true = 0.083]

  var : size
  Probabilities (truncated):
  0: 0.9170000000000000
  1: 0.0142000000000000
  2: 0.0136000000000000
  3: 0.0109000000000000
  .........
  8: 0.0045000000000000
  11: 0.0034000000000000
  9: 0.0034000000000000
  10: 0.0025000000000000
  mean = 0.3648

  var : min val
  Probabilities (truncated):
  0: 0.9170000000000000
  51: 0.0027000000000000
  55: 0.0026000000000000
  59: 0.0025000000000000
  .........
  7: 0.0003000000000000
  16: 0.0002000000000000
  10: 0.0002000000000000
  6: 0.0001000000000000
  mean = 3.2191

  var : max val
  Probabilities (truncated):
  0: 0.9170000000000000
  60: 0.0089000000000000
  55: 0.0034000000000000
  40: 0.0026000000000000
  .........
  13: 0.0004000000000000
  14: 0.0003000000000000
  12: 0.0002000000000000
  11: 0.0001000000000000
  mean = 3.5009


*/
go ?=>
  reset_store,
  run_model(20_000,$model,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,
  % fail,
  nl.
go => true.
  
  
model() =>
  W = [10,15,20,30],

  N = W.len,

  % Start times + wait times
  Ps = [ R..min(R+W[I],60)   : I in 1..N, R=random_integer(60)+1],

  % Is there a common time slot?
  Common = reduce(intersection,Ps),

  Size = Common.len,
  Prob = check(Size > 0),
  MinVal = cond(Common.len>0,Common.min,0),
  MaxVal = cond(Common.len>0,Common.max,0),

  add("prob",Prob),
  add("size",Size),
  add("min val",MinVal),
  add("max val",MaxVal).