/* 

  Empty boxes in Picat.

  From https://medium.com/@moligninip/this-key-concept-will-simplify-all-your-probability-calculations-6e8d4b563b76
  """
  A total of k differently colored balls are randomly placed into n differently colored boxes. 
  What is the expected number of empty boxes?
  """


  Cf my Gamble model gamble_empty_boxes.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.

/*

  [num_balls = 3,num_boxes = 4]
  var : num empty boxes
  Probabilities:
  2: 0.5629000000000000
  1: 0.3783000000000000
  3: 0.0588000000000000
  mean = 1.6805

  [num_balls = 5,num_boxes = 3]
  var : num empty boxes
  Probabilities:
  0: 0.6198000000000000
  1: 0.3685000000000000
  2: 0.0117000000000000
  mean = 0.3919


*/
go ?=>
  member([NumBalls,NumBoxes],[[3,4],[5,3]]),
  println([num_balls=NumBalls,num_boxes=NumBoxes]),
  reset_store,
  run_model(10_000,$model(NumBalls,NumBoxes),[show_probs_trunc,mean % ,
                           % show_simple_stats,
                           % show_percentiles,
                           % show_hpd_intervals,hpd_intervals=[0.84,0.9,0.94,0.99,0.99999]
                           % show_histogram,
                           % min_accepted_samples=1000,show_accepted_samples=true
                          ]),
  nl,
  % show_store_lengths,nl,
  fail,
  nl.
go => true.
  
  
model(NumBalls,NumBoxes) =>


  % Place the NumBalls balls into one of the NumBoxes boxes
  X = random_integer1_n(NumBoxes,NumBalls),

  Boxes = count_occurrences_list(1..NumBoxes,X),

  NumEmptyBoxes = count_occurrences(0,Boxes),
  add("num empty boxes",NumEmptyBoxes).