/* 

  Ratio between 1 and 2 in Picat.

  From Pascal Bercker: 1 < Ratio of A to B < 2 …? Reply to BL
  https://medium.com/@pbercker/1-ratio-of-a-to-b-2-reply-to-bl-bde967735a9f
  """
  A and B are two points chosen at random between 0 & 1.
  What is the probability that the ratio A/B lies between 1 & 2?
  """

  BL's post: "An Interesting Geometry Puzzle In Disguised - 
  How would you unscramble this probability challenge?":
  https://medium.com/math-games/an-interesting-geometry-puzzle-in-disguised-6e391617557e

  This is the same problem as ppl_random_ratio.pi (from BrainStellar), which see.

  Pascal added this:
  """
  What are the most probable values for A and B if the ratio is indeed 
  in the specified range? What will be the updated probability that A > B, given 
  that the ratio is in that range?
  """

  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, ppl_common_utils.
import util.
% import ordset.

main => go.

/*


*/
go ?=>
  reset_store,
  run_model(30_000,$model,[show_probs_trunc,mean,
                           show_hpd_intervals,hpd_intervals=[0.84,0.9,0.94,0.99,0.99999],
                           show_histogram
                          ]),
  Store = get_store(),
  A = Store.get("a"),
  B = Store.get("b"),
  [A,B].transpose.show_scatter_plot,
  
  nl,
  show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  A = uniform(0,1),
  B = uniform(0,1),  

  Ratio = A/B,
  
  observe( (Ratio>= 1, Ratio<=2)),
  
  if observed_ok then
    add("a",A),
    add("b",B),
    add("ratio",Ratio),
  end.