/* 

  Parking cars in Picat.

  From https://www.reddit.com/r/Probability/comments/1f4dd3j/parking_cars/
  """
  Parking Cars

  I've been thinking through this probability question that has left me a little confused and 
  was wondering if there was anyone here who could help point me in the right direction. It goes 
  like this: 
  There are 10 spots in a parking lot arranged in a single row. Three cars are parked 
  randomly. What is the probability that none of these cars are in adjacent spots?
  """

  Note: num-adjacent here means number of adjacent pairs. This, for n parked cars,
  there are n-1 adjacent pairs.


  Cf my Gamble model gamble_parking_cars.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.

main => go.

/*

  num_to_park = 1
  var : num adjacent
  Probabilities:
  0: 1.0000000000000000
  mean = 0.0

  var : p
  Probabilities:
  true: 1.0000000000000000
  mean = [true = 1.0]


  num_to_park = 2
  var : num adjacent
  Probabilities:
  0: 0.8010000000000000
  1: 0.1990000000000000
  mean = 0.199

  var : p
  Probabilities:
  true: 0.8010000000000000
  false: 0.1990000000000000
  mean = [true = 0.801,false = 0.199]


  num_to_park = 3
  var : num adjacent
  Probabilities:
  0: 0.4667000000000000
  1: 0.4656000000000000
  2: 0.0677000000000000
  mean = 0.601

  var : p
  Probabilities:
  false: 0.5333000000000000
  true: 0.4667000000000000
  mean = [false = 0.5333,true = 0.4667]


  num_to_park = 4
  var : num adjacent
  Probabilities:
  1: 0.5029000000000000
  2: 0.2953000000000000
  0: 0.1695000000000000
  3: 0.0323000000000000
  mean = 1.1904

  var : p
  Probabilities:
  false: 0.8305000000000000
  true: 0.1695000000000000
  mean = [false = 0.8305,true = 0.1695]


  num_to_park = 5
  var : num adjacent
  Probabilities:
  2: 0.4848000000000000
  1: 0.2409000000000000
  3: 0.2308000000000000
  0: 0.0232000000000000
  4: 0.0203000000000000
  mean = 1.9841

  var : p
  Probabilities:
  false: 0.9768000000000000
  true: 0.0232000000000000
  mean = [false = 0.9768,true = 0.0232]


  num_to_park = 6
  var : num adjacent
  Probabilities:
  3: 0.4707000000000000
  4: 0.2429000000000000
  2: 0.2370000000000000
  5: 0.0267000000000000
  1: 0.0227000000000000
  mean = 3.0139

  var : p
  Probabilities:
  false: 1.0000000000000000
  mean = [false = 1.0]


  num_to_park = 7
  var : num adjacent
  Probabilities:
  4: 0.4977000000000000
  5: 0.2970000000000000
  3: 0.1743000000000000
  6: 0.0310000000000000
  mean = 4.1847

  var : p
  Probabilities:
  false: 1.0000000000000000
  mean = [false = 1.0]


  num_to_park = 8
  var : num adjacent
  Probabilities:
  5: 0.4664000000000000
  6: 0.4637000000000000
  7: 0.0699000000000000
  mean = 5.6035

  var : p
  Probabilities:
  false: 1.0000000000000000
  mean = [false = 1.0]


  num_to_park = 9
  var : num adjacent
  Probabilities:
  7: 0.7986000000000000
  8: 0.2014000000000000
  mean = 7.2014

  var : p
  Probabilities:
  false: 1.0000000000000000
  mean = [false = 1.0]


  num_to_park = 10
  var : num adjacent
  Probabilities:
  9: 1.0000000000000000
  mean = 9.0

  var : p
  Probabilities:
  false: 1.0000000000000000
  mean = [false = 1.0]

*/
go ?=>
  member(NumToPark,1..10),
  println(num_to_park=NumToPark),
  reset_store,
  run_model(10_000,$model(NumToPark),[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,
  fail,
  nl.
go => true.
  
  
model(NumToPark) =>

  NumCars = 10,

  Cars = draw_without_replacement(NumToPark,1..NumCars),
  CarsSorted = Cars.sort,

  NumAdjacent = [ cond(CarsSorted[I]-CarsSorted[I-1]==1,1,0) : I in 2..NumToPark].sum,
  P = check(NumAdjacent == 0),
  add("p",P),
  add("num adjacent",NumAdjacent).