/* 

  Breaking stick in Picat.

  https://brainstellar.com/puzzles/probability/119 
  """
  The stick drops and breaks at a random point distributed uniformly across 
  the length. What is the expected length of the smaller part?
  """

  Cf my Gamble model gamble_breaking_stick.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.

/*

  Using sticks with length 1:

  var : smallest
  Probabilities (truncated):
  0.499999668330164: 0.0001000000000000
  0.49999303125161: 0.0001000000000000
  0.49995817817713: 0.0001000000000000
  0.499955813619885: 0.0001000000000000
  .........
  0.000066352811305: 0.0001000000000000
  0.000062417797997: 0.0001000000000000
  0.000061309556395: 0.0001000000000000
  0.000027947769181: 0.0001000000000000
  mean = 0.249902


*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  Part1 = beta_dist(1,1),
  Part2 = 1- Part1,

  Smallest = cond(Part1 < Part2, Part1,Part2),
  
  add("smallest",Smallest).


/*
  Using integers (1..100) instead.

  Same behaviour:

  var : smallest
  Probabilities (truncated):
  34: 0.0240000000000000
  49: 0.0232000000000000
  21: 0.0220000000000000
  15: 0.0218000000000000
  .........
  29: 0.0170000000000000
  11: 0.0160000000000000
  50: 0.0103000000000000
  0: 0.0088000000000000
  mean = 25.0015


*/
go2 ?=>
  reset_store,
  run_model(10_000,$model2,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go2 => true.
  
  
model2() =>
  N = 100,
  Part1 = random_integer1(N),
  Part2 = N - Part1,

  Smallest = cond(Part1 < Part2, Part1,Part2),
  
  add("smallest",Smallest).