/*
  See nartoo_meon_planning*.pi for the planning problem. 

  In https://groups.google.com/g/picat-lang/c/_yUOuRq-cis/m/qGOV9u84AQAJ
  Nartoo Meon asked about a planning problem.

  Here I check for the closed formula for the number of steps given 
   (number of black, number of white)

  Here the output from a single run:

  [program = A * 1 + (//(9,9) + A) * B,res = 15,count = 92]
  [program = A + (//(9,9) + A) * B,res = 15,count = 90]
  [program = A * B + (B + A),res = 15,count = 89]
  [program = (//(9,9) + A) * B + A,res = 15,count = 88]
  [program = B * A + (B + A),res = 15,count = 55]
  [program = (//(9,9) + A) * B + (B - A + (A - B + A)),res = 15,count = 44]
  [program = (//(9,9) + A) * B + (//(//(B,B),3 + (5 - 3)) * B + A),res = 15,count = 39]
  [program = B * A + (A + B),res = 15,count = 35]
  [program = A * B + (A + B),res = 15,count = 34]
  [program = B - A + (A - B + A) + (//(9,9) + A) * B,res = 15,count = 30]
  [program = B + A + A * B,res = 15,count = 26]
  [program = (//(9,9) + A) * B + A * 1,res = 15,count = 16]
  [program = //(//(B,B),3 + (5 - 3)) * B + A + (//(9,9) + A) * B,res = 15,count = 15]
  [program = (//(9,9) + A) * B + (A - //(1,10)),res = 15,count = 12]
  [program = A - //(1,10) + (//(9,9) + A) * B,res = 15,count = 9]
  [program = B + A + B * A,res = 15,count = 4]
  [program = (//(9,9) + A) * B - (//(5,//(4 * B,3) + 8) - A),res = 15,count = 1]
  [program = (//(9,9) + A) * B - (B - (B + A)),res = 15,count = 1]
  [program = B + A + B * 1 * A,res = 15,count = 1]
  [program = A + B + B * A,res = 15,count = 1]
  [program = A + B + A * B,res = 15,count = 1]
  [program = (//(9,9) + A) * B + //(A,1),res = 15,count = 1]

  So it's simply A*B + A + B.

  Checking:

  Picat> foreach(B in 1..10, W in 1..10) println([B,W,(B*W+B+W)]) end
[1,1,3]
[1,2,5]
[1,3,7]
[1,4,9]
[1,5,11]
[1,6,13]
[1,7,15]
[1,8,17]
[1,9,19]
[1,10,21]
[2,1,5]
[2,2,8]
[2,3,11]
[2,4,14]
[2,5,17]
[2,6,20]
[2,7,23]
[2,8,26]
[2,9,29]
[2,10,32]
[3,1,7]
[3,2,11]
[3,3,15]
[3,4,19]
[3,5,23]
[3,6,27]
[3,7,31]
[3,8,35]
[3,9,39]
[3,10,43]
[4,1,9]
[4,2,14]
[4,3,19]
[4,4,24]
[4,5,29]
[4,6,34]
[4,7,39]
[4,8,44]
[4,9,49]
[4,10,54]
[5,1,11]
[5,2,17]
[5,3,23]
[5,4,29]
[5,5,35]
[5,6,41]
[5,7,47]
[5,8,53]
[5,9,59]
[5,10,65]
[6,1,13]
[6,2,20]
[6,3,27]
[6,4,34]
[6,5,41]
[6,6,48]
[6,7,55]
[6,8,62]
[6,9,69]
[6,10,76]
[7,1,15]
[7,2,23]
[7,3,31]
[7,4,39]
[7,5,47]
[7,6,55]
[7,7,63]
[7,8,71]
[7,9,79]
[7,10,87]
[8,1,17]
[8,2,26]
[8,3,35]
[8,4,44]
[8,5,53]
[8,6,62]
[8,7,71]
[8,8,80]
[8,9,89]
[8,10,98]
[9,1,19]
[9,2,29]
[9,3,39]
[9,4,49]
[9,5,59]
[9,6,69]
[9,7,79]
[9,8,89]
[9,9,99]
[9,10,109]
[10,1,21]
[10,2,32]
[10,3,43]
[10,4,54]
[10,5,65]
[10,6,76]
[10,7,87]
[10,8,98]
[10,9,109]
[10,10,120]

  Use this with http://hakank.org/picat/symbolic_regression.pi

  $ picat symbolic_regression.pi symbolic_regression_nartoo_meon_planning.pi

*/ 
data(facebook_puzzle,Data,Vars,Unknown,Ops,Constants,MaxSize,Params) :-

  Data = [[[1,1],3],
          [[1,2],5],
          [[1,3],7],
          [[1,4],9],
          [[1,5],11],
          [[1,6],13],
          [[2,1],5],
          [[2,2],8],
          [[2,3],11],
          [[2,4],14],
          [[2,5],17],
          [[2,6],20],
          [[3,1],7],
          [[3,2],11],
          [[3,3],15],
          [[3,4],19],
          [[3,5],23],
          [[3,6],27],
          [[4,1],9],
          [[4,2],14],
          [[4,3],19],
          [[4,4],24],
          [[4,5],29],
          [[4,6],34],
          [[5,1],11],
          [[5,2],17],
          [[5,3],23],
          [[5,4],29],
          [[5,5],35],
          [[5,6],41],
          [[6,1],13],
          [[6,2],20],
          [[6,3],27],
          [[6,4],34],
          [[6,5],41],
          [[6,6],48]],


  Vars = ['A','B'],
  Unknown = [10,10],
  Ops = [+,*,//,-],
  Constants = 1..10,
  MaxSize = 15,  
  Params = new_map([init_size=1000,
                    num_gens=100
                   ]).