/* 

  Hiring your or old in Picat.

  I'm buying some stuff in two different stores and have observed that
  store A is staffed mainly by older people (for any definition of older) and
  store C is staffed only by young people (for any definition of young).

  Let's add another store, store B, that age indifferent and don't care about 
  the age.

  What can be said of the outcome hiring people in such a stores?
  For simplicity - and to be able to work a little with Markov processes :-) -
  let's assume that the last person hired is the one who hires the next.
  
  Cf my Gamble model gamble_hiring_young_or_old.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.

/*

  transitions = [[0.9,0.1,0.0],[0.333333,0.333333,0.333333],[0.2,0.2,0.6]]
  init = [1,0,0]
  Random:
  [2,1,2,2,3,1,1,2,1,1,1,1,1,1,3,3,1,1,1,1,1,1,1,2,1,1,1,1,3,1]

  PDF:
  young = 0.736514
  neutral = 0.145455
  old = 0.118031

  CDF:
  young = 0.736514
  neutral = 0.881969
  old = 1.0

  Quantile:
  0.000001 = young
  0.00001 = young
  0.001 = young
  0.01 = young
  0.025 = young
  0.05 = young
  0.1 = young
  0.25 = young
  0.5 = young
  0.75 = neutral
  0.84 = neutral
  0.9 = old
  0.975 = old
  0.99 = old
  0.999 = old
  0.99999 = old
  0.999999 = old

  Markov chains:
  young starts = [1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,1,1,1,1,1,1,1,1,1]
  neutral starts = [2,3,3,3,2,2,2,3,3,3,3,1,1,2,3,3,2,3,3,2,3,1,1,1,1,1,1,1,1,1]
  old starts = [3,3,3,3,3,3,2,3,3,3,3,2,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2]

  Stationary:
  young     : 0.73170731707317
  neutral   : 0.14634146341463
  old       : 0.12195121951220

  young     : 0.73170731707176
  neutral   : 0.14634146341489
  old       : 0.12195121951334


*/
go ?=>
  [Young,Neutral,Old] = [1,2,3],
  Map = new_map([Young=young,Neutral=neutral,Old=old]),
  %             young   neural  old
  Transitions = [[9/10,  1/10,  0/10], % young (almost always hire younger people
                 [1/3 ,  1/3 ,  1/3 ], % neutral
                 [2/10, 2/10,  6/10]], % old (mostly hire older people)
  println(transitions=Transitions),
  Init = one_hot(3,1),
  println(init=Init),
  println("Random:"),
  println(discrete_markov_process_dist_n(Transitions,Init,10,30)),
  nl,
  println("PDF:"),
  println(young=discrete_markov_process_dist_pdf(Transitions,Init,10,Young)),
  println(neutral=discrete_markov_process_dist_pdf(Transitions,Init,10,Neutral)),
  println(old=discrete_markov_process_dist_pdf(Transitions,Init,10,Old)),
  nl,
  println("CDF:"),
  println(young=discrete_markov_process_dist_cdf(Transitions,Init,10,Young)),
  println(neutral=discrete_markov_process_dist_cdf(Transitions,Init,10,Neutral)),
  println(old=discrete_markov_process_dist_cdf(Transitions,Init,10,Old)),
  nl,
  println("Quantile:"),
  foreach(Q in quantile_qs())
    println(Q=Map.get(discrete_markov_process_dist_quantile(Transitions,Init,10,Q)))
  end,
  nl,
  println("Markov chains:"),
  println("young starts"=markov_chain(Transitions,one_hot(3,Young),30)),
  println("neutral starts"=markov_chain(Transitions,one_hot(3,Neutral),30)),
  println("old starts"=markov_chain(Transitions,one_hot(3,Old),30)),  
  nl,
  println("Stationary:"),
  Stationary1 = stationary_dist1(Transitions,1.0e-16),
  foreach({I,S} in zip(Young..Old,Stationary1))
    printf("%-10w: %.14f\n",Map.get(I),S)
  end,
  nl,
  Stationary2 = stationary_dist(Transitions),
  foreach({I,S} in zip(Young..Old,Stationary2))
    printf("%-10w: %.14f\n",Map.get(I),S)
  end,
  nl.

/*
  Simulation of this using markov_chain/3.

  first_hirer = young
  var : v
  mean = 1.3682

  var : v ref
  mean = [young = 0.7441,neutral = 0.1436,old = 0.1123]

  var : num young
  mean = 8.06

  var : num neutral
  mean = 1.216

  var : num old
  mean = 0.724


  first_hirer = neutral
  var : v
  mean = 1.4187

  var : v ref
  mean = [young = 0.7148,neutral = 0.1517,old = 0.1335]

  var : num young
  mean = 5.4855

  var : num neutral
  mean = 2.6585

  var : num old
  mean = 1.856


  first_hirer = old
  var : v
  mean = 1.4319

  var : v ref
  mean = [young = 0.7091,neutral = 0.1499,old = 0.141]

  var : num young
  mean = 4.9275

  var : num neutral
  mean = 1.58

  var : num old
  mean = 3.4925

*/
go2 =>
  [Young,Neutral,Old] = [1,2,3],                 
  Map = new_map([Young=young,Neutral=neutral,Old=old]),
  
  %             young   neural  old
  Transitions = [[9/10,  1/10,  0/10], % young (almost always hire younger people
                 [1/3 ,  1/3 ,  1/3 ], % neutral
                 [2/10, 2/10,  6/10]], % old (mostly hire older people)
  N = 10,
  member(FirstHirer,[Young,Neutral,Old]),
  println(first_hirer=Map.get(FirstHirer)),
  reset_store,
  run_model(10_000,$model2(Transitions,FirstHirer,N,Map),[mean]),
  nl,
  fail,
  nl.
go2 => true.

model2(Transitions,FirstHirer,N,Map) =>
  NumTransitions = Transitions.len,

  Init = one_hot(NumTransitions,FirstHirer),
  X = markov_chain(Transitions,Init,N),

  % Who was the last hired?
  V = X.last,
  VRef = Map.get(V),

  NumYoung = count_occurrences(1,X),
  NumNeutral = count_occurrences(2,X),
  NumOld = count_occurrences(3,X),
  
  add("v",V),
  add("v ref",VRef),
  add("num young",NumYoung),
  add("num neutral",NumNeutral),
  add("num old",NumOld).