/*

  Devil's word in Picat.

  Translate each character in a word to ASCII value and then try
  to sum its values (either positive or negative) to a total.
  
  E.g. "hakankjellerstrand" and total 666 gives 359 solutions.
  Here is the first:
  +104 +97 +107 +97 +110 +107 +106 -101 +108 +108 -101 +114 +115 +116 -114 -97 -110 -100
 
  Also, see http://www.hakank.org/data_snooping/666.html

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

*/
import cp.

main => go.

go =>
   Name = [h,a,k,a,n, k,j,e,l,l,e,r,s,t,r,a,n,d],
   convert_list(Name, Res),
   printf("%s", Name), 
   nl,
   Total #= 666,
   writeln(total=Total),
   devils_word(Res, SignedRes,Total),
   solve([ff],SignedRes),
      
   writeln([Total, SignedRes]),
   nl.


%
% Let's see how many solutions there are.
%
go2 =>

   Name = [h,a,k,a,n, k,j,e,l,l,e,r,s,t,r,a,n,d],
   convert_list(Name, Res),
   printf("%s", Name),
   nl,
   Total #= 666,
   L = findall(SignedRes, $(devils_word(Res, SignedRes,Total),
                           solve([ff],SignedRes))
                           ), 
   printf("There are %d solutions.\n", L.length),
   nl.

% Let us go crazy and set Total free as well
go3 =>

   Name = [h,a,k,a,n],
   % Name = [k,j,e,l,l,e,r,s,t,r,a,n,d],
   convert_list(Name, Res),
   printf("%s", Name),
   nl,
   Total :: 1..sum([abs(R) : R in Res]),
   L = findall([Total,SignedRes], $(devils_word(Res, SignedRes,Total),
                           solve([ff],SignedRes))), 
   foreach([Total2,W] in L) writeln([total=Total2,w=W]) end,
   printf("There are %d solutions.\n", L.length),
   nl.


scalar_product(A, X, Product) => 
   Product #= sum([S : I in 1..A.length, S #= A[I]*X[I]]).


%
% Signs is the list of [-1,1] for which
%   List[i]*Signs[i] = Total
%
% SignedRes is the resulting list of 
%   SignedRes[i] = List[i]*Signs[i]
%
devils_word(List, SignedRes, Total) =>
   println($devils_word(List, SignedRes, Total)),
   Len = length(List),
   Signs = new_list(Len),
   writeln(here),
   Signs :: [-1,1],
   writeln(here2),
   scalar_product(List,Signs,Total),
   % create the resulting list of ASCII codes with +/- signs
   SignedRes = [ SR : {S,R} in zip(Signs,List), SR #= S*R].


% 
% convert a list of atoms to ASCII code
%
convert_list(List, Res) =>
   Res = [I : El in List, I = ord(El)].