/* 

  State name puzzle (Rosetta Code) in Picat.

  From http://rosettacode.org/wiki/State_name_puzzle
  """
  Background

  This task is inspired by Mark Nelson's DDJ Column "Wordplay" and one of the weekly 
  puzzle challenges from Will Shortz on NPR Weekend Edition [1] and originally 
  attributed to David Edelheit.

  The challenge was to take the names of two U.S. States, mix them all together, then 
  rearrange the letters to form the names of two different U.S. States (so that all four 
  state names differ from one another). What states are these?

  The problem was reissued on the Unicon Discussion Web which includes several solutions 
  with analysis. Several techniques may be helpful and you may wish to refer to Gödel 
  numbering, equivalence relations, and equivalence classes. The basic merits of these 
  were discussed in the Unicon Discussion Web.

  A second challenge in the form of a set of fictitious new states was also presented.

  Task:
  Write a program to solve the challenge using both the original list of states and 
  the fictitious list.

  Caveats:

   - case and spacing isn't significant - just letters (harmonize case)
   - don't expect the names to be in any order - such as being sorted
   - don't rely on names to be unique (eliminate duplicates - meaning if Iowa 
     appears twice you can only use it once) 

  Comma separated list of state names used in the original puzzle:

    "Alabama", "Alaska", "Arizona", "Arkansas",
    "California", "Colorado", "Connecticut",
    "Delaware",    
    "Florida", "Georgia", "Hawaii",
    "Idaho", "Illinois", "Indiana", "Iowa",
    "Kansas", "Kentucky", "Louisiana",
    "Maine", "Maryland", "Massachusetts", "Michigan",
    "Minnesota", "Mississippi", "Missouri", "Montana",
    "Nebraska", "Nevada", "New Hampshire", "New Jersey",
    "New Mexico", "New York", "North Carolina", "North Dakota",
    "Ohio", "Oklahoma", "Oregon",
    "Pennsylvania", "Rhode Island",
    "South Carolina", "South Dakota", "Tennessee", "Texas",
    "Utah", "Vermont", "Virginia",
    "Washington", "West Virginia", "Wisconsin", "Wyoming"

  Comma separated list of additional fictitious state names to be added 
  to the original (Includes a duplicate):

  "New Kory", "Wen Kory", "York New", "Kory New", "New Kory"

  """

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

*/


main => time(go).


go => 
    States = [
    "Alabama", "Alaska", "Arizona", "Arkansas",
    "California", "Colorado", "Connecticut",
    "Delaware",    
    "Florida", "Georgia", "Hawaii",
    "Idaho", "Illinois", "Indiana", "Iowa",
    "Kansas", "Kentucky", "Louisiana",
    "Maine", "Maryland", "Massachusetts", "Michigan",
    "Minnesota", "Mississippi", "Missouri", "Montana",
    "Nebraska", "Nevada", "New Hampshire", "New Jersey",
    "New Mexico", "New York", 
    "North Carolina", "North Dakota",
    "Ohio", "Oklahoma", "Oregon",
    "Pennsylvania", "Rhode Island",
    "South Carolina", "South Dakota", 
    "Tennessee", "Texas",
    "Utah", "Vermont", "Virginia",
    "Washington", "West Virginia", "Wisconsin", "Wyoming"
    % ,"New Kory", "Wen Kory", "York New", "Kory New", "New Kory"
    ],

    % ┌──────────────┬──────────────┐
    % │North Carolina│South Dakota  │
    % ├──────────────┼──────────────┤
    % │North Dakota  │South Carolina│
    % └──────────────┴──────────────┘
    Sorted = new_map([(S=S.to_lowercase().sort()) : S in States]),
    Map = new_map(),
    foreach((S1State=S1Sort) in Sorted, (S2State=S2Sort) in Sorted, S1State @< S2State)
        M = (S1Sort ++ S2Sort).sort(),
        Map.put(M,Map.get(M,[]) ++ [[S1State,S2State]])
    end,
    foreach((MM=SS) in Map) 
       if SS.length > 1 then
          println(ss=SS),
          % foreach(S in SS) 
          %    % println([mm=MM, ss=SS])  
          %    println(S)  
          % end
       end
    end,

    % foreach(S1 in Sorted, S2 in Sorted, 
    %         S3 in Sorted, S4 in Sorted, 
    %         compare_terms(S1[1],S2[1]) < 0,
    %         compare_terms(S3[1],S4[1]) < 0,
    %         compare_terms(S1[1],S3[1]) < 0,
    %         (S1[2] ++ S2[2]).sort() == (S3[2] ++ S4[2]).sort(),
    %         alldifferent([S1[1],S2[1],S3[1],S4[1]])
    %         )
    %         printf("%w|%w <-> %w|%w\n", S1[1],S2[1],S3[1],S4[1])
    % end,
    nl.

alldifferent(L) => 
   foreach(I in 1..L.length, J in 1..I-1) L[I] != L[J] end.


alldifferent2([L1,L2|Rest]) => 
   L1 != L2,
   alldifferent([L2|Rest]).