/* 

  Symmetry breaking in Picat.

  From 
  http://symnet.dcs.st-and.ac.uk/summerschool/Symnet2004Gent1.ppt,
  page 22


  With symmetry breaking this model has 6471432500 solutions
  (go2/0 too 11min3.31s).

  This program was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import cp.

main => go.

go =>
  model(L),
  print_sol(L),
  fail,

  nl.

go2 =>
  Count = count_all(model(_L)),
  println(count=Count),
  nl.

print_sol([A,B,C,D,E,F,G]) =>
  printf("%2d^3 + %2d^3 + %2d^3 + %2d^3 == %2d^3 + %2d^3 + %2d^3\n",A,B,C,D,E,F,G).

model(L) =>
  L = [A,B,C,D,E,F,G],
  L :: 1..50,
  
  A*A*A + B*B*B + C*C*C + D*D*D #= E*E*E + F*F*F + G*G*G /\

  % symmetries in left side
  A #<= B,
  B #<= C,
  C #<= D,

  % symmetries in right side
  E #<= F,
  F #<= G,
 
  % and between the sides
  A #<= E,

  solve($[ff,split],L).