/* 

  Matchup PuzzlOR problem in Picat.

  http://puzzlor.com/2006-08_Matchup.html
  """
  Matchup

  As the owner of a new dating website, you’re working on the logic on how to best match 
  men and women together.  Providing people with good dating candidates is important to 
  keep them interested in using the website and for relationship success. So far, your first 
  clients are 10 women and 10 men.

  The table below shows the personality characteristics for each person.  The goal is to 
  match pairs (one man to one woman) so that the most number of characteristics match.  
  For each characteristic that matches, you earn one point.  For example, 
  matching Man 1 and Woman 1, would be worth two points (because the Living 
  Preference and Social characteristics match).
  
  Person    Politics    Hobby    Living Preference    Social
  ----------------------------------------------------------
  Man 1      Liberal    Running    Rural    Introverted
  Man 2      Liberal    Chess    Rural    Outgoing
  Man 3      Conservative    Running    Urban    Introverted
  Man 4      Liberal    Running    Rural    Introverted
  Man 5      Conservative    Running    Rural    Introverted
  Man 6      Conservative    Chess    Rural    Introverted
  Man 7      Conservative    Chess    Urban    Introverted
  Man 8      Liberal    Chess    Urban    Introverted
  Man 9      Liberal    Running    Urban    Introverted
  Man 10     Liberal    Running    Urban    Outgoing
  Woman 1    Conservative    Chess    Rural    Introverted
  Woman 2    Liberal    Running    Rural    Introverted
  Woman 3    Conservative    Chess    Rural    Outgoing
  Woman 4    Conservative    Running    Urban    Outgoing
  Woman 5    Conservative    Chess    Urban    Outgoing
  Woman 6    Liberal    Running    Urban    Introverted
  Woman 7    Conservative    Chess    Urban    Outgoing
  Woman 8    Conservative    Running    Urban    Outgoing
  Woman 9    Liberal    Chess    Urban    Introverted
  Woman 10   Liberal    Running    Rural    Introverted

  Question:  What is the maximum number of points you can achieve?
  
  Send your answer to puzzlor@gmail.com by October 15th, 2016.  
  The winner, chosen randomly from correct answers, will receive 
  a $25 Amazon Gift Card.  Past questions and answers can 
  be found at puzzlor.com.
  """


  There are 48 optimal solutions with a score of 33. 
  Here is one solution:

    z = 33
    x = [12,17,14,20,13,11,15,19,16,18]
    y = [4,2,3,4,2,4,3,4,4,3]
    Man  1 is matched with Woman  2 with score 4
    Man  2 is matched with Woman  7 with score 2
    Man  3 is matched with Woman  4 with score 3
    Man  4 is matched with Woman 10 with score 4
    Man  5 is matched with Woman  3 with score 2
    Man  6 is matched with Woman  1 with score 4
    Man  7 is matched with Woman  5 with score 3
    Man  8 is matched with Woman  9 with score 4
    Man  9 is matched with Woman  6 with score 4
    Man 10 is matched with Woman  8 with score 3


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

*/

import cp.

main => go.


go =>
  
  Liberal      = 1,
  Conservative = 2,
  Running      = 3,
  Chess        = 4,
  Rural        = 5,
  Urban        = 6,
  Introverted  = 7,
  Outgoing     = 8,

  Attributes = 
   [
     [Liberal,     Running,Rural,Introverted], % Man 1
     [Liberal,     Chess,  Rural,Outgoing],
     [Conservative,Running,Urban,Introverted],
     [Liberal,     Running,Rural,Introverted],
     [Conservative,Running,Rural,Introverted],
     [Conservative,Chess,  Rural,Introverted],
     [Conservative,Chess,  Urban,Introverted],
     [Liberal,     Chess,  Urban,Introverted],
     [Liberal,     Running,Urban,Introverted],
     [Liberal,     Running,Urban,Outgoing],    % Man 10

     [Conservative,Chess,  Rural,Introverted], % Woman 1
     [Liberal,     Running,Rural,Introverted],
     [Conservative,Chess,  Rural,Outgoing],
     [Conservative,Running,Urban,Outgoing],
     [Conservative,Chess,  Urban,Outgoing],
     [Liberal,     Running,Urban,Introverted],
     [Conservative,Chess,  Urban,Outgoing],
     [Conservative,Running,Urban,Outgoing],
     [Liberal,     Chess,  Urban,Introverted],
     [Liberal,     Running,Rural,Introverted] % Woman 10
   ],

  N = Attributes.len,
  P = N div 2,
  M = Attributes[1].len,

  % decision variables
  X = new_list(P),
  X :: P+1..P+10,

  Y = new_list(P),
  Y :: 0..M,

  Z #= sum(Y),

  % constraints
  all_different(X),

  foreach(I in 1..P)
    Y[I] #= sum([ Attributes[I,K] #= AJK : K in 1..M, matrix_element(Attributes,X[I],K,AJK)])
  end,

  % Z #= 33, % checking the number of optimal solutions

  Vars = X.vars() ++ Y,
  solve($[ff,split,max(Z)], Vars),
  % solve($[ff,split], Vars),

  println(z=Z),
  println(x=X),
  println(y=Y),

  foreach(I in 1..P)
    printf("Man %2d is matched with Woman %2d with score %d\n", I,X[I]-10, Y[I])
  end,

  % fail,

  nl.