/*

  Number of moves for a leap frog puzzle.

  See leap_frog_puzzle.pi

  For N = 1..15 (go2/0) this program gives these counts (lengths):
    counts=[3,8,15,24,35,48,63,80,99,120,143,168,195,224,255]

  It's http://oeis.org/A005563
  """
  A005563   n*(n+2) (or, (n+1)^2-1)
  ....
  
  This is also the number of moves that it takes n frogs to swap places with n 
  toads on a strip of 2n+1 squares (or positions, or lilypads) where a move is 
  a single slide or jump,
  """

  * Point sequence
    [program = A * (2 + A),res = 120,count = 14]
    [program = A * (A + 2),res = 120,count = 10]
    [program = (2 + A) * A,res = 120,count = 9]
    [program = 1 * (2 + A) * A,res = 120,count = 9]
    [program = 1 * A * (A + 2),res = 120,count = 9]
    [program = A * 1 * (1 + 1 + A),res = 120,count = 7]
    [program = 1 * ((A + 2) * A),res = 120,count = 7]
    [program = (1 + (A + 1)) * A,res = 120,count = 5]
    [program = A * (2 + A) * 1,res = 120,count = 5]
    [program = A * (1 * A + 2),res = 120,count = 5]
    [program = A * A + (A + A),res = 120,count = 4]
    [program = A + (1 + A) * A,res = 120,count = 4]
    [program = (2 + A) * 1 * A,res = 120,count = 4]
    [program = (A + 2) * A * 1,res = 120,count = 3]
    [program = A * (A + 2) * 1,res = 120,count = 3]
    [program = A * 1 * (1 * (2 + A)),res = 120,count = 3]
    [program = A + (A + A * A),res = 120,count = 2]
    [program = (2 + A * 1) * A,res = 120,count = 2]
    [program = (A + 2) * A * (1 + (A - A)),res = 120,count = 2]
    [program = 1 * A * (1 * (2 + A)),res = 120,count = 2]
    [program = A * (2 * 1 + A),res = 120,count = 2]
    [program = 2 - 2 - (A - A) + A * (A + 2),res = 120,count = 1]
    [program = A + (A - A) + 1 * A * (1 + A),res = 120,count = 1]
    [program = A + A * A + A,res = 120,count = 1]
    [program = (2 - 1) * A + 1 * A * (1 + A),res = 120,count = 1]
    [program = (1 - 1) * 2 + (A + 2) * A,res = 120,count = 1]
    [program = (A + 2) * A + (A - A),res = 120,count = 1]
    [program = (A + 2) * A + (A - A) * 1,res = 120,count = 1]
    [program = (A + 1) * A + A,res = 120,count = 1]
    [program = 1 * A * 2 + A * A,res = 120,count = 1]
    [program = A * (A - 2) + 2 * (A + A),res = 120,count = 1]
    [program = A * A + A * (1 * 2),res = 120,count = 1]
    [program = 2 * (A * 1) + A * A,res = 120,count = 1]
    [program = A + (A * A + A),res = 120,count = 1]
    [program = A + A * (A + 1),res = 120,count = 1]
    [program = (A - (A - A)) * (2 * 1 + A),res = 120,count = 1]
    [program = (A - (A - A)) * (1 * A + 2),res = 120,count = 1]
    [program = (1 + A + (2 - 1)) * A,res = 120,count = 1]
    [program = (2 * 1 + A) * A,res = 120,count = 1]
    [program = (1 * A + 2) * A,res = 120,count = 1]
    [program = (A + 2) * A,res = 120,count = 1]
    [program = (2 + A) * 1 * (A - (A - A)),res = 120,count = 1]
    [program = A * (A + 1 + 1),res = 120,count = 1]

    resultMap = [120 = 43]


  * Recursive sequence, order 2
    [program = 2 + 2 * B - A,res = 120,count = 9]
    [program = B - A + (1 + B) + 1,res = 120,count = 9]
    [program = 2 * 1 + (B + B - A),res = 120,count = 8]
    [program = 1 + B + B + (1 - A * 1),res = 120,count = 7]
    [program = 2 - A + (B + B),res = 120,count = 4]
    [program = B - A + (1 + B) + (2 - 1),res = 120,count = 4]
    [program = 2 * (1 + B) - A,res = 120,count = 2]
    [program = 1 + (B - A + (1 + B)),res = 120,count = 1]

    resultMap = [120 = 8]
*/

data(leap_frog_puzzle,Data,Vars,Unknown,Ops,Constants,MaxSize,Params) :-
  Seq = [3,8,15,24,35,48,63,80,99], % ,120,143,168,195,224,255],
  (
    % println("point_seq:"),
    % make_point_seq(Seq,Data,Unknown,Vars)
   % ;
    println("seq:"),
    make_seq(Seq,2,Data,Unknown,Vars)
  ), 
  Ops = [+,-,*],
  Constants = 1..2,
  MaxSize = 5,
  Params = new_map().