/*

  Divisible by 1 to 9 in Picat

  http://mindyourdecisions.com/blog/2016/04/10/find-the-10-digit-number-where-n-digits-are-divisible-by-n-sunday-puzzle/
  """
  "
  Find a 10 digit number that uses each of the digits 0 to 9 exactly once and 
  where the number formed by the first n digits of the number is divisible by n.
  "
  You should read the digits of the number from left to right. For example, in the 
  number abcd, you need the number a to be divisible by 1, the number ab to be 
  divisible by 2, the number abc to be divisible by 3, and the entire number abcd 
  to be divisible by 4.
  """


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

*/

import cp.

main => go.

go =>
   foreach(Base in 2..14)
       nl,
       println(base=Base),
       (
       problem(Base, X, T) ->
          println(x=X),
          println(t=T),nl
        ;
          println("No solution"),
          true
       )
   end,
   nl.


% Finds all solutions
go2 =>
   foreach(Base in 2..14)
      nl,
      println(base=Base),
      L = findall([X, T], $problem(Base, X, T)),
      foreach([X2, T2] in L)
         println(x=X2),
         println(t=T2),
         nl
      end
    end.



go(N) ?=>
   problem(N, X, T),
   println(x=X),
   println(t=T),
   fail.

go(_) => true.

problem(Base, X, T) =>

   M = Base**(Base)-1, % largest value
   N = Base,   % the digits are in 1..N , 
                   % N is also the length of X 
   X = new_list(N),
   X :: 0..N-1,
   all_different(X),

   T = new_list(N),
   T :: 1..M,

   foreach(I in 1..N)
      XI = [X[J] : J in  1..I],
      to_num(XI, Base, T[I]),
      T[I] mod I #= 0
   end,
   Vars = T ++ X,
   solve([ff,split],Vars).


to_num(List, Base, Num) =>
   Len = length(List),
   Num #= sum([List[I]*Base**(Len-I) : I in 1..Len]).