/* 

  Ball entering Q in Picat.

  Cf my Gamble model gamble_ball_entering_q.rkt

  https://medium.com/intuition/a-probability-challenge-93d9936b9ef0
  (Note: This page is not available)
  """
  How likely is the ball to enter Q?


                o              0
              |   |  
              / . \          1   2
             / . . \       3   4   5
            / . . . \     6  7   8   9
           / . . . . \  10 11 12  13  14  
           |P|Q|R|S|T|   P  Q  R   S   T 

  """


  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.

/*

  var : p
  Probabilities:
  0: 0.9389000000000000
  1: 0.0611000000000000
  mean = 0.0611

  var : q
  Probabilities:
  0: 0.7419000000000000
  1: 0.2581000000000000
  mean = 0.2581

  var : r
  Probabilities:
  0: 0.6214000000000000
  1: 0.3786000000000000
  mean = 0.3786

  var : s
  Probabilities:
  0: 0.7569000000000000
  1: 0.2431000000000000
  mean = 0.2431

  var : t
  Probabilities:
  0: 0.9409000000000000
  1: 0.0591000000000000
  mean = 0.0591

  var : v
  Probabilities:
  r: 0.3786000000000000
  q: 0.2581000000000000
  s: 0.2431000000000000
  p: 0.0611000000000000
  t: 0.0591000000000000
  mean = [r = 0.3786,q = 0.2581,s = 0.2431,p = 0.0611,t = 0.0591]


  The exact probabilities:
      P     Q    R     S    T
   0.0625 0.25 0.375 0.25 0.0625

  I.e. a normal distribution.

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

next(A,Paths) = Res =>
  I = A.last, % What's last/current pin?
  if membchk(I,[p,q,r,s,t]) then
    Res = A
  else
    T = Paths[I+1], % Adjust for 0-based
    % Get the next
    Res = next(A ++ [condt(flip(0.5), T.first, T.second)] , Paths)
  end.
  
model() =>
  Paths = [[1, 2], % This is 0 based (from the Gamble model
           [3, 4],
           [4, 5],
           [6, 7],
           [7, 8],
           [8, 9], 
           [p, q],
           [q, r],
           [r, s],
           [s, t]
           ],

  % How likely is the ball to enter Q? (and P,R,S,T)

  A = next([0],Paths),
  V = A.last,
  
  PP = check1(V == p),
  PQ = check1(V == q),
  PR = check1(V == r),
  PS = check1(V == s),
  PT = check1(V == t),
  % add("a",A),
  add("v",V),  
  add("p",PP),
  add("q",PQ),
  add("r",PR),
  add("s",PS),
  add("t",PT).