/* 

  SEND+MORE=MONEY LP style in Picat.

  Ported from the Prolog code in
  http://www.inf.ed.ac.uk/teaching/courses/lp/slides/lp9.pdf 
  slide 5

  1) Without any extra constraints: about 1100 solutions with a lot of undistict solutions.
  2) With constraints M > 0: got about 167 solutions 3.9s,
  3) With all_are_different/1 constraint: 1 unique solution in 3.8s

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

*/

main => go.


go ?=>
  solve_money([S,E,N,D], [M,O,R,E], [M,O,N,E,Y]),
  println([[S,E,N,D], [M,O,R,E], [M,O,N,E,Y]]),
  fail, % ensure unique solution
  nl.

go => true.


solve_money([S,E,N,D], [M,O,R,E], [M,O,N,E,Y]) =>
   add([0,S,E,N,D], [0,M,O,R,E], [M,O,N,E,Y]),
   % hakank: added these two constraints
   M > 0,
   all_are_different([S,E,N,D,M,O,R,Y]).

% hakank: simple all_different/0 LP style.
% (don't want to use "all_different" here.
all_are_different([]) ?=> true.
all_are_different([H|T]) => 
  not membchk(H,T),
  all_are_different(T).


add(A, B, C) => 
  add(A, B, C, 0).

% add([], [], [], 0) ?=> true.
add(A, B, C, D) ?=> 
  A = [],
  B = [],
  C = [],
  D = 0.

add([A|As], [B|Bs], [C|Cs], Carry) =>
  between(0, 9, A),
  between(0, 9, B),
  add(As, Bs, Cs, NextCarry),
  C is (A + B + NextCarry) mod 10,
  Carry is (A + B + NextCarry) // 10.