/* 

  Swedish election 2018 - select majority subsets in Picat.

  Mandates from
  https://sv.wikipedia.org/wiki/Riksdagsvalet_i_Sverige_2018

  Party                    2014 2018  Diff
  ----------------------------------------
  Vänsterpartiet             21   28    -7
  Socialdemokraterna        113  100   -13
  Miljöpartiet               25   16    -9
  Centern                    22   31    +9
  Liberalerna                19   20    +1
  Moderaterna                84   70   -14
  Kristdemokraterna          16   22    +6
  Sverigedemokraterna        49   62   +13

  Objective: Select a subset of parties such that the total is >= 175. 

  We also include the constraints that some parties don't want 
  to accept a coalition including certain parties, i.e. v and sd.
  Note: in the original setting (in 2018) L stated that they 
        don't support a SD coalition. But much have changed in 2021:
        now L accept SD (and would not vote no to SD).

  Here are the 23 possible coalitions with >= 175 votes, with the no accept 
  constraints for v and sd (in go/0):

    num_coalitions = 23
    Votes: 182:  [s (100),l (20),sd (62)]
    Votes: 184:  [s (100),kd (22),sd (62)]
    Votes: 186:  [s (100),mp (16),m (70)]
    Votes: 189:  [s (100),mp (16),c (31),l (20),kd (22)]
    Votes: 190:  [s (100),l (20),m (70)]
    Votes: 192:  [s (100),m (70),kd (22)]
    Votes: 201:  [s (100),c (31),m (70)]
    Votes: 204:  [s (100),l (20),kd (22),sd (62)]
    Votes: 206:  [s (100),mp (16),l (20),m (70)]
    Votes: 208:  [s (100),mp (16),m (70),kd (22)]
    Votes: 212:  [s (100),l (20),m (70),kd (22)]
    Votes: 217:  [s (100),mp (16),c (31),m (70)]
    Votes: 221:  [s (100),c (31),l (20),m (70)]
    Votes: 223:  [s (100),c (31),m (70),kd (22)]
    Votes: 228:  [s (100),mp (16),l (20),m (70),kd (22)]
    Votes: 232:  [s (100),m (70),sd (62)]
    Votes: 237:  [s (100),mp (16),c (31),l (20),m (70)]
    Votes: 239:  [s (100),mp (16),c (31),m (70),kd (22)]
    Votes: 243:  [s (100),c (31),l (20),m (70),kd (22)]
    Votes: 252:  [s (100),l (20),m (70),sd (62)]
    Votes: 254:  [s (100),m (70),kd (22),sd (62)]
    Votes: 259:  [s (100),mp (16),c (31),l (20),m (70),kd (22)]
    Votes: 274:  [s (100),l (20),m (70),kd (22),sd (62)]

  The second scenario is the it's more realistic that S would vote
  against a coalition with SD so then we have these 16 coalitions:

     num_coalitions = 16
     With v/sd no vote constraints: Adding S is against SD.
     Votes: 186:  [s (100),mp (16),m (70)]
     Votes: 189:  [s (100),mp (16),c (31),l (20),kd (22)]
     Votes: 190:  [s (100),l (20),m (70)]
     Votes: 192:  [s (100),m (70),kd (22)]
     Votes: 201:  [s (100),c (31),m (70)]
     Votes: 206:  [s (100),mp (16),l (20),m (70)]
     Votes: 208:  [s (100),mp (16),m (70),kd (22)]
     Votes: 212:  [s (100),l (20),m (70),kd (22)]
     Votes: 217:  [s (100),mp (16),c (31),m (70)]
     Votes: 221:  [s (100),c (31),l (20),m (70)]
     Votes: 223:  [s (100),c (31),m (70),kd (22)]
     Votes: 228:  [s (100),mp (16),l (20),m (70),kd (22)]
     Votes: 237:  [s (100),mp (16),c (31),l (20),m (70)]
     Votes: 239:  [s (100),mp (16),c (31),m (70),kd (22)]
     Votes: 243:  [s (100),c (31),l (20),m (70),kd (22)]
     Votes: 259:  [s (100),mp (16),c (31),l (20),m (70),kd (22)]


  One can note that in all both these scenarious, s must not vote against
  the coalition.


  The third scenariou is with no constraints at all, with give 128 possible 
  (and probably some impossible) coalitions (go3/0).

    Without v/sd no vote constraints
    num_coalitions = 128
    Votes: 175:  [v (28),s (100),mp (16),c (31)]
    Votes: 176:  [v (28),mp (16),m (70),sd (62)]
    Votes: 178:  [s (100),mp (16),sd (62)]
    Votes: 179:  [mp (16),c (31),m (70),sd (62)]
   	         [v (28),mp (16),c (31),l (20),kd (22),sd (62)]
	         [v (28),s (100),c (31),l (20)]
    Votes: 180:  [v (28),l (20),m (70),sd (62)]
    Votes: 181:  [v (28),s (100),c (31),kd (22)]
    Votes: 182:  [s (100),l (20),sd (62)]
	         [v (28),m (70),kd (22),sd (62)]
    Votes: 183:  [c (31),l (20),m (70),sd (62)]
    Votes: 184:  [s (100),kd (22),sd (62)]
    Votes: 185:  [c (31),m (70),kd (22),sd (62)]
    Votes: 186:  [s (100),mp (16),m (70)]
	         [v (28),s (100),mp (16),l (20),kd (22)]
    Votes: 187:  [v (28),mp (16),c (31),l (20),m (70),kd (22)]
    Votes: 189:  [s (100),mp (16),c (31),l (20),kd (22)]
    Votes: 190:  [mp (16),l (20),m (70),kd (22),sd (62)]
                 [s (100),l (20),m (70)]
                 [v (28),s (100),sd (62)]
    Votes: 191:  [v (28),c (31),m (70),sd (62)]
    Votes: 192:  [s (100),m (70),kd (22)]
    Votes: 193:  [s (100),c (31),sd (62)]
    Votes: 195:  [v (28),s (100),mp (16),c (31),l (20)]
    Votes: 196:  [v (28),mp (16),l (20),m (70),sd (62)]
    Votes: 197:  [v (28),s (100),mp (16),c (31),kd (22)]
    Votes: 198:  [s (100),mp (16),l (20),sd (62)]
                 [v (28),mp (16),m (70),kd (22),sd (62)]
                 [v (28),s (100),m (70)]
    Votes: 199:  [mp (16),c (31),l (20),m (70),sd (62)]
    Votes: 200:  [s (100),mp (16),kd (22),sd (62)]
    Votes: 201:  [mp (16),c (31),m (70),kd (22),sd (62)]
                 [s (100),c (31),m (70)]
                 [v (28),s (100),c (31),l (20),kd (22)]
    Votes: 202:  [v (28),l (20),m (70),kd (22),sd (62)]
    Votes: 204:  [s (100),l (20),kd (22),sd (62)]
    Votes: 205:  [c (31),l (20),m (70),kd (22),sd (62)]
    Votes: 206:  [s (100),mp (16),l (20),m (70)]
                 [v (28),s (100),mp (16),sd (62)]
    Votes: 207:  [v (28),mp (16),c (31),m (70),sd (62)]
    Votes: 208:  [s (100),mp (16),m (70),kd (22)]
    Votes: 209:  [s (100),mp (16),c (31),sd (62)]
    Votes: 210:  [v (28),s (100),l (20),sd (62)]
    Votes: 211:  [v (28),c (31),l (20),m (70),sd (62)]
    Votes: 212:  [s (100),l (20),m (70),kd (22)]
                 [v (28),s (100),kd (22),sd (62)]
    Votes: 213:  [s (100),c (31),l (20),sd (62)]
                 [v (28),c (31),m (70),kd (22),sd (62)]
    Votes: 214:  [v (28),s (100),mp (16),m (70)]
    Votes: 215:  [s (100),c (31),kd (22),sd (62)]
    Votes: 217:  [s (100),mp (16),c (31),m (70)]
                 [v (28),s (100),mp (16),c (31),l (20),kd (22)]
    Votes: 218:  [v (28),mp (16),l (20),m (70),kd (22),sd (62)]
                 [v (28),s (100),l (20),m (70)]
    Votes: 220:  [s (100),mp (16),l (20),kd (22),sd (62)]
                 [v (28),s (100),m (70),kd (22)]
    Votes: 221:  [mp (16),c (31),l (20),m (70),kd (22),sd (62)]
                 [s (100),c (31),l (20),m (70)]
                 [v (28),s (100),c (31),sd (62)]
    Votes: 223:  [s (100),c (31),m (70),kd (22)]
    Votes: 226:  [v (28),s (100),mp (16),l (20),sd (62)]
    Votes: 227:  [v (28),mp (16),c (31),l (20),m (70),sd (62)]
    Votes: 228:  [s (100),mp (16),l (20),m (70),kd (22)]
                 [v (28),s (100),mp (16),kd (22),sd (62)]
    Votes: 229:  [s (100),mp (16),c (31),l (20),sd (62)]
                 [v (28),mp (16),c (31),m (70),kd (22),sd (62)]
                 [v (28),s (100),c (31),m (70)]
    Votes: 231:  [s (100),mp (16),c (31),kd (22),sd (62)]
    Votes: 232:  [s (100),m (70),sd (62)]
                 [v (28),s (100),l (20),kd (22),sd (62)]
    Votes: 233:  [v (28),c (31),l (20),m (70),kd (22),sd (62)]
    Votes: 234:  [v (28),s (100),mp (16),l (20),m (70)]
    Votes: 235:  [s (100),c (31),l (20),kd (22),sd (62)]
    Votes: 236:  [v (28),s (100),mp (16),m (70),kd (22)]
    Votes: 237:  [s (100),mp (16),c (31),l (20),m (70)]
                 [v (28),s (100),mp (16),c (31),sd (62)]
    Votes: 239:  [s (100),mp (16),c (31),m (70),kd (22)]
    Votes: 240:  [v (28),s (100),l (20),m (70),kd (22)]
    Votes: 241:  [v (28),s (100),c (31),l (20),sd (62)]
    Votes: 243:  [s (100),c (31),l (20),m (70),kd (22)]
                 [v (28),s (100),c (31),kd (22),sd (62)]
    Votes: 245:  [v (28),s (100),mp (16),c (31),m (70)]
    Votes: 248:  [s (100),mp (16),m (70),sd (62)]
                 [v (28),s (100),mp (16),l (20),kd (22),sd (62)]
    Votes: 249:  [v (28),mp (16),c (31),l (20),m (70),kd (22),sd (62)]
                 [v (28),s (100),c (31),l (20),m (70)]
    Votes: 251:  [s (100),mp (16),c (31),l (20),kd (22),sd (62)]
                 [v (28),s (100),c (31),m (70),kd (22)]
    Votes: 252:  [s (100),l (20),m (70),sd (62)]
    Votes: 254:  [s (100),m (70),kd (22),sd (62)]
    Votes: 256:  [v (28),s (100),mp (16),l (20),m (70),kd (22)]
    Votes: 257:  [v (28),s (100),mp (16),c (31),l (20),sd (62)]
    Votes: 259:  [s (100),mp (16),c (31),l (20),m (70),kd (22)]
                 [v (28),s (100),mp (16),c (31),kd (22),sd (62)]
    Votes: 260:  [v (28),s (100),m (70),sd (62)]
    Votes: 263:  [s (100),c (31),m (70),sd (62)]
                 [v (28),s (100),c (31),l (20),kd (22),sd (62)]
    Votes: 265:  [v (28),s (100),mp (16),c (31),l (20),m (70)]
    Votes: 267:  [v (28),s (100),mp (16),c (31),m (70),kd (22)]
    Votes: 268:  [s (100),mp (16),l (20),m (70),sd (62)]
    Votes: 270:  [s (100),mp (16),m (70),kd (22),sd (62)]
    Votes: 271:  [v (28),s (100),c (31),l (20),m (70),kd (22)]
    Votes: 274:  [s (100),l (20),m (70),kd (22),sd (62)]
    Votes: 276:  [v (28),s (100),mp (16),m (70),sd (62)]
    Votes: 279:  [s (100),mp (16),c (31),m (70),sd (62)]
                 [v (28),s (100),mp (16),c (31),l (20),kd (22),sd (62)]
    Votes: 280:  [v (28),s (100),l (20),m (70),sd (62)]
    Votes: 282:  [v (28),s (100),m (70),kd (22),sd (62)]
    Votes: 283:  [s (100),c (31),l (20),m (70),sd (62)]
    Votes: 285:  [s (100),c (31),m (70),kd (22),sd (62)]
    Votes: 287:  [v (28),s (100),mp (16),c (31),l (20),m (70),kd (22)]
    Votes: 290:  [s (100),mp (16),l (20),m (70),kd (22),sd (62)]
    Votes: 291:  [v (28),s (100),c (31),m (70),sd (62)]
    Votes: 296:  [v (28),s (100),mp (16),l (20),m (70),sd (62)]
    Votes: 298:  [v (28),s (100),mp (16),m (70),kd (22),sd (62)]
    Votes: 299:  [s (100),mp (16),c (31),l (20),m (70),sd (62)]
    Votes: 301:  [s (100),mp (16),c (31),m (70),kd (22),sd (62)]
    Votes: 302:  [v (28),s (100),l (20),m (70),kd (22),sd (62)]
    Votes: 305:  [s (100),c (31),l (20),m (70),kd (22),sd (62)]
    Votes: 307:  [v (28),s (100),mp (16),c (31),m (70),sd (62)]
    Votes: 311:  [v (28),s (100),c (31),l (20),m (70),sd (62)]
    Votes: 313:  [v (28),s (100),c (31),m (70),kd (22),sd (62)]
    Votes: 318:  [v (28),s (100),mp (16),l (20),m (70),kd (22),sd (62)]
    Votes: 321:  [s (100),mp (16),c (31),l (20),m (70),kd (22),sd (62)]
    Votes: 327:  [v (28),s (100),mp (16),c (31),l (20),m (70),sd (62)]
    Votes: 329:  [v (28),s (100),mp (16),c (31),m (70),kd (22),sd (62)]
    Votes: 333:  [v (28),s (100),c (31),l (20),m (70),kd (22),sd (62)]
    Votes: 349:  [v (28),s (100),mp (16),c (31),l (20),m (70),kd (22),sd (62)]


  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.

%
% With the v/sd no-vote constraints
%
go ?=> 
  coalitions(v_sd_1),
  print_map(get_global_map()),
  nl.
go => true.

go2 ?=> 
  coalitions(v_sd_2),
  print_map(get_global_map()),
  nl.
go2 => true.


%
% Without any v/sd no-vote constraints
%
go3 ?=>
  coalitions(false),
  print_map(get_global_map()),
  nl.

go3 => true.

%
% Print the coalition map
%
print_map(Map) =>
  println(num_coalitions=sum([Len : M in Map, Len = second(M.to_list()).len])),
  foreach(Votes=Coalitions in Map.to_list.sort)
     printf("Votes: %d:  ",Votes),
     Count = 0,
     foreach(C in Coalitions)
       Count := Count + 1,
       if Count > 1 then
          print("\t     ")
       end,
       println(C)
     end
  end,
  nl.

%
% Get all possible coalitions.
% if V_SD_Constraints == true then include
% the no vote constraints regarding v and sd.
%
coalitions(V_SD_Constraints) ?=>
  Map = get_global_map(),
  election(2018,Mandat),
  println(total=sum(Mandat)),  
  N = Mandat.len,

  [V,S,MP,C,L,M,KD,SD] = [I : I in 1..N],

  Parties = [v,s,mp,c,l,m,kd,sd],
  
  % decision variables
  X = new_list(N),
  X :: 0..1,
  
  Z #= sum([Mandat[I]*X[I] : I in 1..N]),  
  Z #>= 175,

  if V_SD_Constraints != false then
     println("With v/sd no vote constraints part 1"),
     % what happens if v is in the coalition?
     %    L vote no
     %    C vote no
     %    M vote no
     %    KD vote no
     %    SD vote no
     (X[V] #= 1 #=> (X[L] #= 0 #/\ X[C] #= 0 #/\ X[M] #= 0 #/\ X[KD] #= 0 #/\ X[SD] #= 0)),

     % what happens if sd is in the coalition?
     %   C vote no
     %   V note no
     %   MP vote no
     % 
     (X[SD] #= 1 #=> (X[C] #= 0 #/\ X[V] #= 0 #/\ X[MP] #= 0)),

     if V_SD_Constraints == v_sd_2 then
        % Second scenario: S would also vote no to SD
        println("With v/sd no vote constraints: Adding S is against SD."),
        (X[SD] #= 1 #=> X[S] #= 0)
     end
  else
     println("Without v/sd no vote constraints")
  end,

  solve($[],X ++ [Z]),

  Res = [Parties[I].to_string() ++ " (" ++ Mandat[I].to_string() ++ ")" : I in 1..N, X[I] == 1],
  Map.put(Z,Map.get(Z,[]) ++ [Res]),
  fail,
  nl.

coalitions(_) => true.


election(2018, Mandat) =>
 Mandat = [ 28,100, 16, 31, 20, 70, 22, 62].

election(2014, Mandat) =>
 Mandat = [21,113,25,22,19,84,16,49].