/*
   From Muhammad Zain Sarwar: 
   "Finding the Missing Numbers in the Sequence?"
   https://medium.com/puzzle-sphere/finding-the-missing-numbers-in-the-sequence-a9e607a2d844
   """
   5,10,12,24,26,52,54,?,?   
   """


   The answer is 108,110 according to these operations:

   5*2=10
   10+2=12
   12*2=24
   24+2=26
   26*2=52
   52+2=54

   54*2=108
   108+2=110

   This was much easier to solve manually than writing a program for. :-)
   
   The problem here is the representation of the problem since it's not
   the same operation for each step (which is the standard approach), but two.
   
   * Let's start with the simple representation of a "point sequence", i.e.
     the dependent variable only rely on the indices.

     data = [[[1],5],[[2],10],[[3],12],[[4],24],[[5],26],[[6],52],[[7],54]]
     This does not work.

  * Let's now try with a recursive sequence: 

    data = [[[5],10],[[10],12],[[12],24],[[24],26],[[26],52],[[52],54]]

   This is better: It actually give the next value 54 -> 108.

   [program = if_then_else((A + 10) mod 7,2 * A,A + 2),res = 108,count = 757]

   The if_then_else/3 function is interpreted as if Cond > 0 then Expr1 else Expr

   Test:
    A = 54

    if_then_else ((A + 10) mod 7) > 0 then 
        2 * A
    else 
        A + 2 
    end

    if ((54 + 10) mod 7) > 0 then 2*54 else 54 + 2 end  -> 108. Correct

    Now we test the second, with A = 108
    
    if ((108 + 10) mod 7) > 0 then 2*108 else 109 + 2 end  -> 216. Incorrect!

    It fails since it cannot distinguish between the odd'th or even'th expressions.


  * Another representation introduces indices:
       Index, This -> Next and with mod/2 and cond/3
    Data = [ [[1,5],10],
             [[2,10],12],
             [[3,12],24],
             [[4,24],26],
             [[5,26],52],
             [[6,52],54]

  Expected program:
    * cond(I mod 2==1,A*2,A+2)

    * if I mod 2 == 1 then A*2 else A+2 end

  Here are some for if_then_else/3:

  [program = if_then_else(I mod 2,A * if_then_else(A,if_then_else(8,2 - I,I),2),5 mod 3 + A mod (4 * A)),res = 108,count = 630]
  [program = if_then_else(I mod 2,2 * A,5 mod 3 + A mod (4 * A)),res = 108,count = 560]
  [program = if_then_else(I mod 2,2 * A,A + 2),res = 108,count = 479]
  [program = if_then_else(I mod 2,A + A,5 mod 3 + A mod (4 * A)),res = 108,count = 462]
  [program = if_then_else(I mod 2,A * if_then_else(A,if_then_else(8,2 - I,I),2),A + 2),res = 108,count = 427]
  [program = if_then_else(I mod 2,if_then_else(5 + A,if_then_else(A + 5 * A,7,A),A) + A,5 mod 3 + A mod (4 * A)),res = 108,count = 371]
  [program = if_then_else(I mod 2,A + A,A + 2),res = 108,count = 333]
  [program = if_then_else(I mod 2,if_then_else(5 + A,if_then_else(A + 5 * A,7,A),A) + A,A + 2),res = 108,count = 285]
  [program = if_then_else(I mod 2,A * if_then_else(A,if_then_else(8,2 - I,I),2),2 + A),res = 108,count = 266]
  [program = if_then_else(I mod 2,2 * A,2 + A),res = 108,count = 221]
  [program = if_then_else(I mod 2,A * 2,A + 2),res = 108,count = 210]
  [program = if_then_else(I mod 2,A * 2,2 + A),res = 108,count = 192]
  [program = if_then_else(I mod 2,A * 2,5 mod 3 + A mod (4 * A)),res = 108,count = 182]
  [program = if_then_else(I mod 2,A + A,2 + A),res = 108,count = 84]
  [program = if_then_else(I mod 2,if_then_else(5 + A,if_then_else(A + 5 * A,7,A),A) + A,2 + A),res = 108,count = 2]
  [program = if_then_else(if_then_else(I mod I,9 * 7,if_then_else(9,5,I) mod 2),A * if_then_else(A,if_then_else(8,2 - I,I),2),A + 2),res = 108,count = 1]
  [program = if_then_else(if_then_else(I mod I,9 * 7,if_then_else(9,5,I) mod 2),A * if_then_else(A,if_then_else(8,2 - I,I),2),2 + A),res = 108,count = 1]

  Let's check with this program: 
   if_then_else(I mod 2,A + A,A + 2)

  a) I = 7, A = 54
     if_then_else( (7 mod 2) > 0 then 54+54 else 54+2)    -> 108. Correct
  b) I = 8, A = 108
     if_then_else( (8 mod 2) > 0 then 108+108 else 108+2) -> 110. Correct
  

*/
data(missing_numer,Data,Vars,Unknown,Ops,Constants,MaxSize,Params) :-
  % make_point_seq([5,10,12,24,26,52,54],Data,Unknown,Vars), % nope
  % make_seq([5,10,12,24,26,52,54],1,Data,Unknown,Vars), % first ok, second not ok
  Data = [ [[1,5],10],
           [[2,10],12],
           [[3,12],24],
           [[4,24],26],
           [[5,26],52],
           [[6,52],54]
           % , [[7,54],108] % checking
           ],
  Vars = ['I','A'],
  Unknown = [7,54], % should be 108
  % Unknown = [8,108], % checking: should be 110
  
  Ops = [+,*,-,mod,if_then_else,==],
  % Ops = [+,*,-,mod,cond,==],  
  Constants = 1..10,
  MaxSize = 11,
  Params = new_map([init_size=1000,
                    num_gens=1000
                   ]).