{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}

{-
%   File   : olympic.pl
%   Author : Neng-Fa ZHOU
%   Date   : 1993
%   Purpose: solve a puzzle taken from Olympic Arithmetic Contest
/***********************************************************************
   Given ten variables with the following configuration:

               X7   X8   X9   X10

                  X4   X5   X6

                     X2   X3             

                        X1

  We already know that X1 is equal to 3 and want to assign each variable
  with a different integer from {1,2,...,10} such that for any three
  variables 
                      Xi   Xj

                         Xk
  the following constraint is satisfied:

                    |Xi-Xj| = Xk
***********************************************************************/
-}


import Control.CP.FD.Example

main = example_sat_main_void model

model :: ExampleModel ()
model _ = exists $ \col -> do
  [x1,x2,x3,x4,x5,x6,x7,x8,x9,x10] <- colList col 10
  col `allin` (cte 1, cte 10) 
  allDiff col
  x1 @= 3
  minus x2 x3 x1
  minus x4 x5 x2
  minus x5 x6 x3
  minus x7 x8 x4
  minus x8 x9 x5
  minus x9 x10 x6
  return col

minus x1 x2 x3 = (abs (x1-x2)) @= x3