/*

  Dots and Boxes Number of lines

  Calculate the formula of the number of lines for the dots and boxes problem (just for fun :-)).  
  For R rows and C columns, I manually calculated this as 
    (C-1)*(R*2-1)+(C-1)
  Is there a neater formula?

  [program = C * 2 * R * 1 - (R + (1 + 1 - (1 * 1 - 2) * (C - 2))),res = 4,count = 92]
  [program = (R + R) * 1 * C - (R + C),res = 4,count = 70]
  [program = C * 2 * R * 1 - (R + C),res = 4,count = 55]
  [program = (R + R) * 1 * C - (R + (1 + 1 - (1 * 1 - 2) * (C - 2))),res = 4,count = 50]
  [program = (2 * R - 1) * C - (1 - 1) - R,res = 4,count = 44]
  [program = (R + R) * 1 * C - (C + R) * 1,res = 4,count = 37]
  [program = (R + R) * 1 * C - (C + R),res = 4,count = 27]
  [program = C * 2 * R * 1 - (C + R),res = 4,count = 17]
  [program = R * (C * 2) - (R + C),res = 4,count = 16]
  [program = 2 - 2 + (R - (2 - 2) + R) * C - (C + R),res = 4,count = 12]
  [program = C * R - C - 2 + (R * C + 2 - R),res = 4,count = 11]
  [program = (2 * R - 1) * C - (1 - 1) - (2 + (R - 2)),res = 4,count = 6]
  [program = (2 * R - 1) * C - (1 - 1) - (R + 1 - 1),res = 4,count = 3]
  [program = 2 - 2 + (R - (2 - 2) + R) * C - (R + (1 + 1 - (1 * 1 - 2) * (C - 2))),res = 4,count = 1]

  resultMap = [4 = 14]


  Mathematica:
  In[1]:= (((R * (C + C)) - C) - R)
  Out[1]= -C - R + 2 C R

  In[1]:= C * 2 * R * 1 - (R + (1 + 1 - (1 * 1 - 2) * (C - 2)))
  Out[1]= -C - R + 2 C R


*/

data(dots_and_boxes,Data,Vars,Unknown,Ops,Constants,MaxSize,Params) :-
  Data = [[[3,2],7],
          [[3,4],17],
          [[4,3],17],
          [[3,3],12],
          [[5,5],40]
        ],
  Unknown = [2,2],
  Vars = ['R','C'],
  Ops = [+,-,*], 
  Constants = 1..2,
  MaxSize = 21,
  Params = new_map([num_gens=100]).