/* 

  Probability of index of the smallest value in a list in Picat.

  What is the probability of the index of the smallest value in a list.  
  There are two cases, dependending how we handle ties:
  * if a tie: pick the smallest index with the smallest value
  * if a tie: pick any of the indices for the smallest value

  Cf my Gamble model gamble_index_of_smallest_value.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.

/*
  * The first approach (pick the first value has a bias towards the first indices.

    var : amin
    Probabilities:
    1: 0.3119000000000000
    2: 0.2367000000000000
    3: 0.1907000000000000
    4: 0.1439000000000000
    5: 0.1168000000000000
    mean = 2.517

    var : amax
    Probabilities:
    1: 0.3045000000000000
    2: 0.2393000000000000
    3: 0.1891000000000000
    4: 0.1464000000000000
    5: 0.1207000000000000
    mean = 2.5395
  
  * By randomly picking indices with ties for the smallest value theres no bias

    var : amin2
    Probabilities:
    5: 0.2074000000000000
    1: 0.2002000000000000
    3: 0.1990000000000000
    2: 0.1978000000000000
    4: 0.1956000000000000
    mean = 3.0122

    var : amax2
    Probabilities:
    5: 0.2074000000000000
    3: 0.2055000000000000
    2: 0.1976000000000000
    4: 0.1954000000000000
    1: 0.1941000000000000
    mean = 3.0244

  This difference is - of course - only relevant when there are duplicate 
  values in the list.


*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean % ,
                           % show_percentiles,show_histogram,
                           % show_hpd_intervals,hpd_intervals=[0.94],
                           % min_accepted_samples=1000,show_accepted_samples=true
                          ]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
model() =>
  N = 5,
  Q = random_integer_n(N,N),

  % Ties are handled by picking the first
  AMin = argmin(Q).first,
  AMax = argmax(Q).first,

  % Ties are handled by picking any of the indices for the smallest value
  AMin2 = argmin_random_ties(Q),
  AMax2 = argmax_random_ties(Q),

  add("amin",AMin),
  add("amax",AMax),  
  add("amin2",AMin2),
  add("amax2",AMax2).