/* 

  Meeting collegues at office in Picat.

  https://www.reddit.com/r/Probability/comments/1fksuqo/probably_of_two_colleagues_being_in_the_office_on/
  """
  Probably of two colleagues being in the office on the same days

  If two different colleagues independently chose 3 days to go into an office
  Whats the probability that At least 1 match at least 2 match At least 3 match
  1 is 100% as no matter what you will have 1 matching day but beyond that 
  I’m slightly stumped
  """


  Cf my Gamble model gamble_meeting_collegues_at_office.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.

/*
  Some different scenarios:

  [num_people = 2,workdays = 5,num_in_office = 3]
  var : num matches
  Probabilities:
  2: 0.5985000000000000
  1: 0.3037000000000000
  3: 0.0978000000000000
  mean = 1.7941


  [num_people = 2,workdays = 10,num_in_office = 5]
  var : num matches
  Probabilities:
  3: 0.3989000000000000
  2: 0.3974000000000000
  1: 0.0987000000000000
  4: 0.0975000000000000
  5: 0.0040000000000000
  0: 0.0035000000000000
  mean = 2.5002


  [num_people = 2,workdays = 30,num_in_office = 10]
  var : num matches
  Probabilities:
  3: 0.3101000000000000
  4: 0.2697000000000000
  2: 0.1869000000000000
  5: 0.1312000000000000
  1: 0.0534000000000000
  6: 0.0368000000000000
  0: 0.0063000000000000
  7: 0.0053000000000000
  8: 0.0003000000000000
  mean = 3.3526


  [num_people = 3,workdays = 5,num_in_office = 3]
  var : num matches
  Probabilities:
  1: 0.5784000000000000
  2: 0.2345000000000000
  0: 0.1781000000000000
  3: 0.0090000000000000
  mean = 1.0744


  [num_people = 4,workdays = 5,num_in_office = 3]
  var : num matches
  Probabilities:
  1: 0.4886000000000000
  0: 0.4311000000000000
  2: 0.0791000000000000
  3: 0.0012000000000000
  mean = 0.6504


*/
go ?=>
  member([NumPeople,Workdays,NumInOffice],[[2,5,3],
                                           [2,10,5],
                                           [2,30,10],
                                           [3,5,3],
                                           [4,5,3]
                                           ]),
  println([num_people=NumPeople,workdays=Workdays,num_in_office=NumInOffice]),
  reset_store,
  run_model(10_000,$model(NumPeople,Workdays,NumInOffice),[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  fail,
  nl.
go => true.
  
  
model(NumPeople,Workdays,NumInOffice) =>
  Days = 1..Workdays,
  People = [draw_without_replacement(NumInOffice,Days).sort : _ in 1..NumPeople],
  NumMatches = reduce(intersection,People).len,
  
  add("num matches",NumMatches).