/* 

  Break a stick in two in Picat.

  From Julia Simon "Resample Stats", page 42:
  """
  In a book of puzzles about probability (Mosteller, 1965/1987,#42), 
  this problem appears: "If a stick is broken in two at random, what is 
  the average length of the smaller piece?"
  ...
  Yet a rephrasing of the problem reveals its tie to the concept of probability,
  to wit: What is the probability that the smaller piece will be (say) more than 
  half the length of the larger piece? Or, what is the probability distribution of the 
  sizes of the shorter piece?
  """

  Cf my Gamble model gamble_break_a_stick_in_two.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 : min U
  Probabilities (truncated):
  0.49998813006095: 0.0001000000000000
  0.499913797946607: 0.0001000000000000
  0.499899011338083: 0.0001000000000000
  0.499874599045084: 0.0001000000000000
  .........
  0.00018374715009: 0.0001000000000000
  0.000179820228452: 0.0001000000000000
  0.000074018258636: 0.0001000000000000
  0.000052016228462: 0.0001000000000000
  mean = 0.25227
  HPD intervals:
  HPD interval (0.84): 0.08265175068874..0.49908960727001

  var : p
  Probabilities:
  false: 0.6602000000000000
  true: 0.3398000000000000
  mean = [false = 0.6602,true = 0.3398]
  HPD intervals:
  show_hpd_intervals: data is not numeric

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean,
                           show_hpd_intervals,hpd_intervals=[0.84]]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  
  % Let's assume that the stick is 1 unit long
  U1 = uniform(0,1),
  U2 = 1 - U1,
  MinU  = min(U1,U2),
  MaxU  = max(U1,U2),   

  % What is the probability that the smaller piece will be (say) more than 
  % half the length of the larger piece?
  P = check(MinU > (MaxU / 2)),
  add("min U",MinU),
  add("p",P).