/* 

  Matchmaker problem (PuzzlOR) in Picat.

  http://puzzlor.editme.com/Matchmaker:
  """
  The Matchmaker was an honored profession in past cultures, serving the valuable 
  purpose of pairing off men and women in hopes of a long and successful relationship.  
  The Matchmaker would carefully consider the characteristics of each partner to 
  determine which pairs would be compatible. 

  Figure 1 shows six men and six women each with varying hair color and eye color.  
  A man or woman will only accept a partner that has at least one of these traits in 
  common.  For example, Man A and Woman 5 would make a matching pair because they 
  have at least one trait in common (same hair color).  However Man A and Woman 1 would 
  not make a matching pair because they do not have any traits in common.
  
  Question:  What pairings of men and women allow for everyone to have a partner with 
  at least one trait in common?  (There are several correct answers.)
  """

  Women   Hair color  Eye color
  1       Yellow      Brown       
  2       Red         Green
  3       Black       Blue
  4       Black       Brown
  5       Red         Brown
  6       Black       Brown

  Men   Hair color  Eye color
  A       Red         Green
  B       Yellow      Blue
  C       Yellow      Brown  
  D       Red         Green
  E       Black       Green
  F       Yellow      Blue


  There are 8 optimal solutions with Total = 7 common traits. Here is one of them:

  total = 7
  x = [2,1,6,3,4,5]
  numMatches = [1,2,1,1,1,1]
  [women,1,match,man,B,common = [hair = [Yellow,Yellow],eyes = [Brown,Blue]],numMatches = 1]
  [women,2,match,man,A,common = [hair = [Red,Red],eyes = [Green,Green]],numMatches = 2]
  [women,3,match,man,F,common = [hair = [Black,Yellow],eyes = [Blue,Blue]],numMatches = 1]
  [women,4,match,man,C,common = [hair = [Black,Yellow],eyes = [Brown,Brown]],numMatches = 1]
  [women,5,match,man,D,common = [hair = [Red,Red],eyes = [Brown,Green]],numMatches = 1]
  [women,6,match,man,E,common = [hair = [Black,Black],eyes = [Brown,Green]],numMatches = 1]

  Here are all 8 solutions:

[women,1,match,man,B]
[women,2,match,man,A]
[women,3,match,man,F]
[women,4,match,man,C]
[women,5,match,man,D]
[women,6,match,man,E]

[women,1,match,man,B]
[women,2,match,man,A]
[women,3,match,man,F]
[women,4,match,man,E]
[women,5,match,man,D]
[women,6,match,man,C]

[women,1,match,man,B]
[women,2,match,man,D]
[women,3,match,man,F]
[women,4,match,man,C]
[women,5,match,man,A]
[women,6,match,man,E]

[women,1,match,man,B]
[women,2,match,man,D]
[women,3,match,man,F]
[women,4,match,man,E]
[women,5,match,man,A]
[women,6,match,man,C]

[women,1,match,man,F]
[women,2,match,man,A]
[women,3,match,man,B]
[women,4,match,man,C]
[women,5,match,man,D]
[women,6,match,man,E]

[women,1,match,man,F]
[women,2,match,man,A]
[women,3,match,man,B]
[women,4,match,man,E]
[women,5,match,man,D]
[women,6,match,man,C]

[women,1,match,man,F]
[women,2,match,man,D]
[women,3,match,man,B]
[women,4,match,man,C]
[women,5,match,man,A]
[women,6,match,man,E]

[women,1,match,man,F]
[women,2,match,man,D]
[women,3,match,man,B]
[women,4,match,man,E]
[women,5,match,man,A]
[women,6,match,man,C]


  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 ?=>
  N = 6,

  Colors = [Yellow,Brown,Red,Green,Black,Blue],
  Colors = 1..Colors.len,
  ColorStr = ["Yellow", "Brown", "Red", "Green", "Black", "Blue"],

  Women = {
       % Hair       Eyes
       {Yellow,      Brown}, % 1
       {Red,         Green}, % 2
       {Black,       Blue},  % 3
       {Black,       Brown}, % 4
       {Red,         Brown}, % 5
       {Black,       Brown}  % 6
     },

  Men = {
       % Hair       Eyes
       {Red,         Green},  % A
       {Yellow,      Blue},   % B
       {Yellow,      Brown},  % C
       {Red,         Green},  % D
       {Black,       Green},  % E
       {Yellow,      Blue}    % F
     },
  MenS = ["A","B","C","D","E","F"],


  % Here we try to match the women 1..6 with some of the men A..F
  X = new_list(N),
  X :: 1..N,

  % total matchings (to maximize)
  Total :: 0..2*N,
  
  % for presentation
  NumMatches = new_list(N),
  NumMatches :: 1..2, 

  all_different(X),
  foreach(I in 1..N) 
    % count the matches
    matrix_element(Men,X[I],1,MenXI1),
    matrix_element(Men,X[I],2,MenXI2),
    NumMatches[I] #= (Women[I,1] #= MenXI1) + (Women[I,2] #= MenXI2)    
  end,

  Total #= sum(NumMatches),
  % Total #= 7,

  Vars = X ++ NumMatches,
  solve($[max(Total)],Vars),
  % solve($[],Vars),  

  println(total=Total),
  println(x=X),
  println(numMatches=NumMatches),
  foreach(I in 1..N)
    Common = [hair=[ColorStr[Women[I,1]],ColorStr[Men[X[I],1]]],eyes=[ColorStr[Women[I,2]],ColorStr[Men[X[I],2]]]],
    println([women,I,match,man,MenS[X[I]],common=Common,numMatches=NumMatches[I]])
    % println([women,I,match,man,MenS[X[I]]])    
  end,
  nl,
  
  fail,
  nl.

go => true.