/*

  General store problem in Picat.
 
  From
  http://www.comp.nus.edu.sg/~henz/projects/puzzles/digits/index.html

  """
  The General Store  from "Mathematical Puzzles of Sam Loyd", number 30

  The owner of a general store, who is something of a puzzlist, has put
  up this sign to see if any of his mathematical friends can translate
  it properly. Each different letter stands for a different digit. The
  words above the horizontal line represent numbers that add to the
  total of "ALL WOOL". The problem is to change all the letters to the
  correct digits.

         C H E S S
   +       C A S H
   +   B O W W O W
   +     C H O P S
   +   A L S O P S
   + P A L E A L E
   +       C O O L
   +       B A S S
   +       H O P S
   +       A L E S
   +       H O E S
   +   A P P L E S
   +       C O W S 
   +   C H E E S E
   +   C H S O A P
   +     S H E E P
   _______________
     A L L W O O L
   """

  Here are three different models, inspired by the Oz solutions from
  the page above.


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

*/

import cp.


main => go.

go =>
   writef("Model 1: "),
   L1 = findall([c=C, h=H, e=E, s=S, a=A, b=B, o=O, w=W, p=P, l=L], $store1([C, H, E, S, A, B, O, W, P, L])),
   writeln([sort(T) : T in L1]),

   writef("Model 2: "),
   L2 = findall([c=C, h=H, e=E, s=S, a=A, b=B, o=O, w=W, p=P, l=L], $store2([C, H, E, S, A, B, O, W, P, L])),
   writeln([sort(T) : T in L2]),

   writef("Model 3: "),
   L3 = findall([a=A, b=B, c=C, e=E, h=H, l=L, o=O, p=P, s=S, w=W], $store3([A, B, C, E, H, L, O, P, S, W])),
   writeln([sort(T) : T in L3]).


store1(LD) =>

   LD = [C, H, E, S, A, B, O, W, P, L],
   LD :: 0..9,
 
   all_different(LD),
   
   10000*C + 1000*H + 100*E + 10*S + S
   + 1000*C + 100*A + 10*S + H
   + 100000*B + 10000*O + 1000*W + 100*W + 10*O + W
   + 10000*C + 1000*H + 100*O + 10*P + S
   + 100000*A + 10000*L + 1000*S + 100*O + 10*P + S
   + 1000000*P + 100000*A + 10000*L + 1000*E + 100*A + 10*L + E
   + 1000*C + 100*O + 10*O + L
   + 1000*B + 100*A + 10*S + S
   + 1000*H + 100*O + 10*P + S
   + 1000*A + 100*L + 10*E + S
   + 1000*H + 100*O + 10*E + S
   + 100000*A + 10000*P + 1000*P + 100*L + 10*E + S
   + 1000*C + 100*O + 10*W + S
   + 100000*C + 10000*H + 1000*E + 100*E + 10*S + E
   + 100000*C + 10000*H + 1000*S + 100*O + 10*A + P
   + 10000*S + 1000*H + 100*E + 10*E + P
   
   #= 1000000*A + 100000*L + 10000*L + 1000*W + 100*O + 10*O + L,

   solve(LD).
   


store2(LD) =>
   LD=[C, H, E, S, A, B, O, W, P, L],
   LD :: 0..9,

   all_different(LD),

   Carries= [C11, C12, C21, C22, C31, C32, C41, C42, C51, C52, C61, C62],
   Carries :: 0..9,

   S+H+W+S+S+E+L+S+S+S+S+S+S+E+P+P       #= L+ 10*C11+ 100*C12,
   S+S+O+P+P+L+O+S+P+E+E+E+W+S+A+E+ C11       #= O+ 10*C21+ 100*C22,
   E+A+W+O+O+A+O+A+O+L+O+L+O+E+O+E+ C21 + C12 #= O+ 10*C31+ 100*C32,
   H+C+W+H+S+E+C+B+H+A+H+P+C+E+S+H+ C31 + C22 #= W+ 10*C41+ 100*C42,
   C+  O+C+L+L+     P+  H+H+S+ C41 + C32 #= L+ 10*C51+ 100*C52,
   B+ A+A+     A+  C+C  + C51 + C42 #= L+ 10*C61+ 100*C62,
   P          + C61 + C52 #= A,

   solve(LD),
   solve(Carries).



store3(LD) =>

   CarriesLow = [C11, C21, C31, C41, C51, C61],
   CarriesHigh =[C12, C22, C32, C42, C52],
   LD = [A, B, C, E, H, L, O, P, S, W],
   LD :: 0..9,

   all_different(LD),

   CarriesLow :: 0..9,
   CarriesHigh :: 0..1,
   
   10000*C + 1000*H + 100*E + 10*S + S
   + 1000*C + 100*A + 10*S + H
   + 100000*B + 10000*O + 1000*W + 100*W + 10*O + W
   + 10000*C + 1000*H + 100*O + 10*P + S
   + 100000*A + 10000*L + 1000*S + 100*O + 10*P + S
   + 1000000*P + 100000*A + 10000*L + 1000*E + 100*A + 10*L + E
   + 1000*C + 100*O + 10*O + L
   + 1000*B + 100*A + 10*S + S
   + 1000*H + 100*O + 10*P + S
   + 1000*A + 100*L + 10*E + S
   + 1000*H + 100*O + 10*E + S
   + 100000*A + 10000*P + 1000*P + 100*L + 10*E + S
   + 1000*C + 100*O + 10*W + S
   + 100000*C + 10000*H + 1000*E + 100*E + 10*S + E
   + 100000*C + 10000*H + 1000*S + 100*O + 10*A + P
   + 10000*S + 1000*H + 100*E + 10*E + P   
   #= 1000000*A + 100000*L + 10000*L + 1000*W + 100*O + 10*O + L,
   
   S+H+W+S+S+E+L+S+S+S+S+S+S+E+P+P       #= L+ 10*C11+ 100*C12,
   S+S+O+P+P+L+O+S+P+E+E+E+W+S+A+E+ C11       #= O+ 10*C21+ 100*C22,
   E+A+W+O+O+A+O+A+O+L+O+L+O+E+O+E+ C21+ C12  #= O+ 10*C31+ 100*C32,
   H+C+W+H+S+E+C+B+H+A+H+P+C+E+S+H+ C31+ C22  #= W+ 10*C41+ 100*C42,
   C+  O+C+L+L+     P+  H+H+S+ C41+ C32  #= L+ 10*C51+ 100*C52,
   B+  A+A+     A+  C+C      + C51+ C42  #= L+ 10*C61,
   P               + C61+ C52  #= A,


   solve(LD ++ CarriesLow ++ CarriesHigh).