/* 

  Drunk Ant in Picat.

  https://brainstellar.com/puzzles/probability/202
  """
  An ant is standing on one corner of a cube & can only walk on the 
  edges. The ant is drunk and from any corner, it moves randomly by 
  choosing any edge! What is the expected number of edges the ant travels, 
  to reach the opposite corner?

  Answer: 10
  """


  Cf my Gamble model gamble_drunk_ant.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.

/*

  0-based 

      4--------5
    / |      / |
   0--------1  |
   |  |     |  |
   |  |     |  |
   |  6-----|--7
   | /      | /
   2--------3


   Edges: 0 -> 1 2 4   
          1 -> 0 3 5
          2 -> 0 3 6
          3 -> 1 2 7
          4 -> 0 5 6
          5 -> 1 4 7
          6 -> 2 4 7
          7 -> 3 5 6

  Converting to 1-based in the model.

  var : a
  Probabilities (truncated):
  [1,5,6,8]: 0.0412000000000000
  [1,3,4,8]: 0.0367000000000000
  [1,2,6,8]: 0.0364000000000000
  [1,5,7,8]: 0.0355000000000000
  .........
  [1,2,1,2,1,2,1,2,1,5,1,2,1,2,4,3,4,8]: 0.0001000000000000
  [1,2,1,2,1,2,1,2,1,3,1,2,6,5,7,8]: 0.0001000000000000
  [1,2,1,2,1,2,1,2,1,2,6,2,4,8]: 0.0001000000000000
  [1,2,1,2,1,2,1,2,1,2,4,3,1,5,6,8]: 0.0001000000000000
  Mean (truncated)
  mean = [[1,5,6,8] = 0.0412,[1,3,4,8] = 0.0367,[1,2,6,8] = 0.0364,[1,5,7,8] = 0.0355,[1,3,7,8] = 0.0346,[1,2,4,8] = 0.0346,[1,2,1,5,7,8] = 0.0055,[1,2,6,5,7,8] = 0.0051,[1,2,4,3,4,8] = 0.0051,[1,3,7,3,7,8] = 0.005,[1,5,7,3,4,8] = 0.0049,[1,2,1,3,7,8] = 0.0049,[1,2,1,2,6,8] = 0.0048,[1,3,4,2,4,8] = 0.0047,[1,2,1,2,4,8] = 0.0047,[1,5,6,2,4,8] = 0.0046,[1,5,1,5,6,8] = 0.0044,[1,5,1,3,7,8] = 0.0044,[1,2,6,2,6,8] = 0.0044,[1,2,6,2,4,8] = 0.0044]

  var : len
  Probabilities (truncated):
  3: 0.2190000000000000
  5: 0.1689000000000000
  7: 0.1379000000000000
  9: 0.1040000000000000
  .........
  65: 0.0001000000000000
  63: 0.0001000000000000
  59: 0.0001000000000000
  57: 0.0001000000000000
  mean = 10.051


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

add1(N) = N + 1.

% Convert from (Gamble's) 0-based 
edges() = [[1,2,4],
           [0,3,5],
           [0,3,6],
           [1,2,7],
           [0,5,6],
           [1,4,7],
           [2,4,7],
           [3,5,6]].flatten.map(add1).chunks_of(3).

model() =>
  Start = 1,
  End = 8,
  Edges = edges(),
  OK = false,
  A = [Start],
  while (OK == false)
    Pos = A.last,
    if Pos == End then
      OK := A
    else
      A := A ++ [uniform_draw(Edges[Pos])]
    end
  end,

  Len = A.len - 1, % Don't count the start node
  add("a",A),
  add("len",Len).