/* 

  Color switches in Picat.

  https://brainstellar.com/puzzles/probability/1020
  """
  You are given an urn with 100 balls (50 black and 50 white). You pick 
  balls from urn one by one without replacements until all the balls are 
  out. A black followed by a white or a white followed by a black is 
  "a colour change". Calculate the expected number of colour-changes if 
  the balls are being picked randomly from the urn.

  Answer: 50
  """

  With N black and N white balls, the estimated number of colour-changes is N.

  Cf my Gamble model gamble_colored_switches.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.

/*

  n = 5
  var : num color switches
  Probabilities:
  5: 0.2925000000000000
  4: 0.1895000000000000
  6: 0.1868000000000000
  7: 0.1274000000000000
  3: 0.1240000000000000
  8: 0.0327000000000000
  2: 0.0307000000000000
  1: 0.0084000000000000
  9: 0.0080000000000000
  mean = 5.0085


  n = 10
  var : num color switches
  Probabilities (truncated):
  10: 0.1690000000000000
  11: 0.1686000000000000
  9: 0.1644000000000000
  8: 0.1172000000000000
  .........
  3: 0.0008000000000000
  2: 0.0003000000000000
  19: 0.0001000000000000
  18: 0.0001000000000000
  mean = 10.0229


  n = 50
  var : num color switches
  Probabilities (truncated):
  51: 0.0812000000000000
  50: 0.0803000000000000
  52: 0.0772000000000000
  49: 0.0747000000000000
  .........
  34: 0.0004000000000000
  68: 0.0003000000000000
  33: 0.0002000000000000
  32: 0.0001000000000000
  mean = 50.0048


  n = 100
  var : num color switches
  Probabilities (truncated):
  100: 0.0573000000000000
  101: 0.0570000000000000
  99: 0.0559000000000000
  103: 0.0547000000000000
  .........
  128: 0.0001000000000000
  125: 0.0001000000000000
  75: 0.0001000000000000
  73: 0.0001000000000000
  mean = 100.013

*/
go ?=>
  member(N,[5,10,50,100]),
  println(n=N),
  reset_store,
  run_model(10_000,$model(N),[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  fail,
  nl.
go => true.
  
  
model(N) =>
  Balls = ones(N,black) ++ ones(N,white),
  BallsShuffled = draw_without_replacement(Balls),

  NumColorSwitches = [cond(BallsShuffled[I-1] != BallsShuffled[I],1,0)  : I in 2..Balls.len].sum,

  add("num color switches",NumColorSwitches).