--         File: send_more_money.sql
--      Version: 1.2
-- Last Changed: 2016-12-30
--           by: Damir;  https://www.damirsystems.com
--      Project: Send More Money Puzzle
--           DB: PostgreSQL



-- Return True if there are no duplicates in the input array.
--
CREATE OR REPLACE FUNCTION all_different(arr Integer[])
RETURNS Boolean
AS $BODY$

DECLARE
  crd  Integer ;
  cnt  Integer ;
  rslt Boolean ;

BEGIN

    crd := cardinality(arr);

    select count(distinct a) into cnt from unnest(arr) as a;

    -- expose edge cases [], [x]
    CASE
      WHEN crd = 0   THEN rslt := FALSE; -- []  empty array
      WHEN crd = 1   THEN rslt := TRUE;  -- [x] one element only
      WHEN cnt = crd THEN rslt := TRUE ; 
      ELSE                rslt := FALSE;
    END CASE ;

    RETURN rslt;
END;
$BODY$
LANGUAGE plpgsql;



-- The final query packaged into a view.
--
CREATE OR REPLACE VIEW Send_MM AS

with
Digit as ( -- {0, 1, ... 9}
   select generate_series(0,9)::Integer as z
),
Srch as ( -- Cartesian product and constraints
   select St.z as S
        , Et.z as E
        , Nt.z as N
        , Dt.z as D
        , Mt.z as M
        , Ot.z as O
        , Rt.z as R
        , Yt.z as Y
   from       Digit as St
   cross join Digit as Et
   cross join Digit as Nt
   cross join Digit as Dt
   cross join Digit as Mt
   cross join Digit as Ot
   cross join Digit as Rt
   cross join Digit as Yt

   where Mt.z = 1
     and St.z >= 8
     and (Dt.z + Et.z) % 10 = Yt.z

     and Dt.z * 1 + Nt.z * 10 + Et.z * 100 + St.z * 1000
       + Et.z * 1 + Rt.z * 10 + Ot.z * 100 + Mt.z * 1000
       = Yt.z * 1 + Et.z * 10 + Nt.z * 100 + Ot.z * 1000 + Mt.z * 10000
)
-- check for all different
select S,E,N,D,M,O,R,Y
from Srch
where all_different(ARRAY[S,E,N,D,M,O,R,Y])
;