/*
  Simple linear congruential random number generator with the
  following parameters
     X(n+1) = (a*X(n) + b) mod m
  where
     a = 11
     b = 23
     mod = 127
     X(1) = 1

  The first entries: 1 34 16 72 53 98 85 69 20 116 29 88
  It has a cycle of 125.

  Can we restore the parameters?

  Well, it's very easy when using the specific constants: [1,11,23,127]
  maxCount = 3
  code = (((A * 11) + 23) mod 127) = [[[1],34],[[34],16],[[16],72],[[72],53]] = [[53] = 98]

  but it's too hard when using e.g. 0..10 or 1..127

  With tabling get_op/5 it yields an "out_of_memory" error after 11 minutes during 
  maxCount = 3. (My Picat run is restricted to 32Gb RAM on a 64Gb RAM machine.)

  Now testing Constaints 0..127 without tabling: Nope. Stopped after 19 hours
  without any solution.

*/
data(linear_congruential_generator,Data,Vars,Unknown,Ops,Constants,MaxC) :-
  make_seq([1,34,16,72,53,98,85,69,20,116,29,88],1,Data,Unknown,Vars),
  % make_seq([1,34,16,72,53],1,Data,Unknown,Vars),  
  println(data=Data),
  % Ops = new_map([infix=["+","-","*","/","mod"]]),
  Ops = new_map([infix=["+","*","mod"]]), % We know that it's an LCG.
  Constants = [1,11,23,127], % OK, but cheating :-)
  % Constants = 0..10, % Too hard
  % Constants = 0..127, % Too hard
  MaxC = 5.