/* 

  Birthday in Picat.

  From PSI test/birthday3.psi

  For d=7,p=3 (method:enumerate)
  duplicate
  Marginal:
    false : 0.6122448979591837
    true : 0.3877551020408163


  Cf my Gamble model gamble_birthday2.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 : birthdays
  Probabilities (truncated):
  [0,1,0,0,0,1,1]: 0.0210000000000000
  [0,0,1,1,0,1,0]: 0.0200000000000000
  [1,0,1,0,0,0,1]: 0.0193000000000000
  [1,1,0,0,0,0,1]: 0.0189000000000000
  .........
  [0,0,0,0,0,3,0]: 0.0027000000000000
  [0,0,3,0,0,0,0]: 0.0025000000000000
  [0,0,0,0,0,0,3]: 0.0024000000000000
  [3,0,0,0,0,0,0]: 0.0023000000000000

  var : prob
  Probabilities:
  3: 0.6089000000000000
  2: 0.3729000000000000
  1: 0.0182000000000000
  mean = 2.5907


*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  D = 7, % Days
  P = 3, % People

  Birthday = random_integer1_n(D,P),

  Birthdays = [ [ cond(I == Birthday[J],1,0) : J in 1..P].sum  :  I in 1..D ],
  println(birthdays=Birthdays),
  Prob = [ cond(B > 0,1,0) : B in Birthdays].sum,
  
  add("birthdays",Birthdays),
  add("prob",Prob).