restructure sat.py: clean up and more general interface

sat.py

@@ -1,121 +1,270 @@
 from pysmt.shortcuts import Symbol, Bool, Not, Implies, Iff, And, Or, AtMostOne, ExactlyOne, get_model, get_atoms, get_formula_size, get_unsat_core
 from pysmt.rewritings import conjunctive_partition
 import json
+from typing import List
 
-MAX_MOVES = 63
+from compress import DeckCard, Action, ActionType, link
-NUM_STRIKES = 3
-COLORS = 'rygbp'
-NUM_CARDS = 50
 
-deck_str = 'p5 p3 b4 r5 y4 y4 y5 r4 b2 y2 y3 g5 g2 g3 g4 p4 r3 b2 b3 b3 p4 b1 p2 b1 b1 p2 p1 p1 g1 r4 g1 r1 r3 r1 g1 r1 p1 b4 p3 g2 g3 g4 b5 y1 y1 y1 r2 r2 y2 y3'
+STANDARD_HAND_SIZE = {2: 5, 3: 5, 4: 4, 5: 4, 6: 3}
-
+NUM_STRIKES_TO_LOSE = 3
-# instance independent names of variables
-
-# clues[m][i] == "after move m we have at least i clues"
-clues = {-1: {i: Bool(i < 9) for i in range(0, 10)}, **{m: {0: Bool(True), 9: Bool(False), **{i: Symbol('m{}c{}'.format(m, i)) for i in range(1, 9)}} for m in range(MAX_MOVES)}}
-# strikes[m][i] == "after move m we have at least i strikes"
-strikes = {-1: {i: Bool(i == 0) for i in range(0,NUM_STRIKES+1)}, **{m: {0: Bool(True), NUM_STRIKES: Bool(False), **{s: Symbol('m{}s{}'.format(m,s)) for s in range(1,NUM_STRIKES)}} for m in range(MAX_MOVES)} }
-# extraturn[m] = "turn m is a move part of the extra round or a dummy turn"
-extraround = {-1: Bool(False), **{m: Bool(False) if m <= 29 else Symbol('m{}e'.format(m)) for m in range(0, MAX_MOVES)}}
-# dummyturn[m] = "turn m is a dummy nurn and not actually part of the game"
-dummyturn = {-1: Bool(False), **{m: Bool(False) if m <= 34 else Symbol('m{}dt'.format(m)) for m in range(0, MAX_MOVES)}}
-# strike[m] = "at move m we get a strike"
-strike = {-1: Bool(False), **{m: Symbol('m{}s+'.format(m)) for m in range(MAX_MOVES)}}
-# draw[m][i] == "at move m we play/discard deck[i]"
-discard = {m: {i: Symbol('m{}-{}'.format(m, i)) for i in range(NUM_CARDS)} for m in range(MAX_MOVES)}
-# progress[m][c, k] == "after move m we have played in color c until k"
-progress = {-1: {(c, k): Bool(k == 0) for c in COLORS for k in range(6)}, **{m: {**{(c, 0): Bool(True) for c in COLORS}, **{(c, k): Symbol('m{}:{}{}'.format(m, c, k)) for c in COLORS for k in range(1, 6)}} for m in range(MAX_MOVES)}}
-# discard_any[m] == "at move m we play/discard a card"
-discard_any = {m: Symbol('m{}d'.format(m)) for m in range(MAX_MOVES)}
-# draw_any[m] == "at move m we draw a card"
-draw_any = {m: Symbol('m{}D'.format(m)) for m in range(MAX_MOVES)}
-# play[m] == "at move m we play a card"
-play = {m: Symbol('m{}p'.format(m)) for m in range(MAX_MOVES)}
-# play5[m] == "at move m we play a 5"
-play5 = {m: Symbol('m{}p5'.format(m)) for m in range(MAX_MOVES)}
-# incr_clues[m] == "at move m we obtain a clue"
-incr_clues = {m: Symbol('m{}c+'.format(m)) for m in range(MAX_MOVES)}
-
-### this is dependent on the number of players
-# draw[m][i] == "at move m we draw deck[i]"
-
-hand_size = {2: 5, 3: 5, 4: 4, 5: 4, 6: 3}
-last_hand_card = {2: 9, 3: 14, 4: 15, 5: 19, 6: 17}
-max_moves = {2: -1, 3: 63, 4: 63, 5: 56, 6: 62}
-draw = {p: {-1: {i: Bool(i == last_hand_card[p]) for i in range(last_hand_card[p], NUM_CARDS)}, **{m: {last_hand_card[p]: Bool(False), **{i: Symbol('m{}+{}'.format(m, i)) for i in range(last_hand_card[p] + 1, NUM_CARDS)}} for m in range(max_moves[p])}} for p in range(2,7)}
 
 
-def solve(deck_str, num_players=5):
+# literals to model game as sat instance to check for feasibility
-    deck = [(s[0], int(s[1])) for s in deck_str.split(' ')]
+# variants 'throw it in a hole not handled', 'clue starved' and 'up or down' currently not handled
-    hand_size = globals()['hand_size'][num_players]
+class Literals():
-    last_hand_card = globals()['last_hand_card'][num_players]
+    # num_suits is total number of suits, i.e. also counts the dark suits
-    max_moves = globals()['max_moves'][num_players]
+    # default distribution among all suits is assumed
-    draw = globals()['draw'][num_players]
+    def __init__(self, num_players, num_suits, num_dark_suits=0):
+        assert ( 2 <= num_players <= 6 )
+
+        ## some game parameters
+        self.num_players = num_players
+        self.num_suits = num_suits
+        self.num_dark_suits = num_dark_suits
+
+        self.hand_size = STANDARD_HAND_SIZE[num_players]
+        self.num_strikes = NUM_STRIKES_TO_LOSE
+        self.deck_size = 10 * num_suits - 5 * num_dark_suits
+        self.distributed_cards = self.num_players * self.hand_size
+        self.draw_pile_size = self.deck_size - self.distributed_cards
+
+        ## maximum number of moves in any game that can achieve max score
+        # each suit gives 15 moves, as we can play and discard 5 cards each and give 5 clues. dark suits only give 5 moves, since no discards are added
+        # number of cards that remain in players hands after end of game. they cost 2 turns each, since we cannot discard them and also have one clue less
+        # 8 clues at beginning, one further clue for each suit but one (the clue of the last 5 is never useful since it is gained in the extra-round)
+        # subtract a further move for a second 5-clue that can't be used in 5 or 6-player games, since the extraround starts too soon
+        self.max_moves = 15 * num_suits - 10 * num_dark_suits    \
+                        - 2 * num_players * (self.hand_size - 1) \
+                        + 8 + (num_suits - 1)                    \
+                        + (-1 if num_players >= 5 else 0)
+
+        ###
+        # note that we generate 'literals' always one out of boundary and set them to explicit truth values. This makes sat formulation easier but has no actual overhead in solving it
+        # move are numbered starting with 0
+
+        # clues[m][i] == "after move m we have at least i clues"
+        self.clues = {
+                -1: { i: Bool(i < 9) for i in range(0, 10) }  # we have 8 clues after turn -1
+                , **{
+                        m: {
+                            0: Bool(True),                                                # always at least 0 clues
+                            **{ i: Symbol('m{}c{}'.format(m, i)) for i in range(1, 9) },
+                            9: Bool(False)                                                # never 9 or more clues. This will implicitly forbid discarding at 8 clues later
+                           }
+                        for m in range(self.max_moves)
+                    }
+                }
+
+        # strikes[m][i] == "after move m we have at least i strikes"
+        self.strikes = {
+                    -1: {i: Bool(i == 0) for i in range(0, self.num_strikes + 1)}    # no strikes when we start
+                  , **{
+                          m: {
+                              0: Bool(True),
+                              **{ s: Symbol('m{}s{}'.format(m,s)) for s in range(1, self.num_strikes) },
+                              self.num_strikes: Bool(False)                              # never so many clues that we lose. Implicitly forbids striking out
+                             }
+                          for m in range(self.max_moves)
+                      }
+                  }
+
+        # extraturn[m] = "turn m is a move part of the extra round or a dummy turn"
+        self.extraround = {
+                     -1: Bool(False)
+                     , **{
+                             m: Bool(False) if m < self.draw_pile_size else Symbol('m{}e'.format(m))   # it takes at least as many turns as cards in the draw pile to start the extra round
+                             for m in range(0, self.max_moves)
+                         }
+                     }
+
+        # dummyturn[m] = "turn m is a dummy nurn and not actually part of the game"
+        self.dummyturn = {
+                    -1: Bool(False)
+                    , **{
+                            m: Bool(False) if m < self.draw_pile_size + self.num_players else Symbol('m{}dt'.format(m))
+                            for m in range(0, self.max_moves)
+                        }
+                    }
+
+        # draw[m][i] == "at move m we play/discard deck[i]"
+        self.discard = {
+                    m: {i: Symbol('m{}-{}'.format(m, i)) for i in range(self.deck_size)}
+                    for m in range(self.max_moves)
+                  }
+
+        # draw[m][i] == "at move m we draw deck card i"
+        self.draw = {
+                -1: { i: Bool(i == self.distributed_cards - 1) for i in range(self.distributed_cards - 1, self.deck_size) }
+                , **{
+                        m: {
+                            self.distributed_cards - 1: Bool(False),
+                            **{i: Symbol('m{}+{}'.format(m, i)) for i in range(self.distributed_cards, self.deck_size)}
+                            }
+                        for m in range(self.max_moves)
+                    }
+               }
+
+        # strike[m] = "at move m we get a strike"
+        self.strike = {
+                 -1: Bool(False)
+                 , **{
+                        m: Symbol('m{}s+'.format(m))
+                        for m in range(self.max_moves)
+                     }
+                 }
+
+        # progress[m][card = (suitIndex, rank)] == "after move m we have played in suitIndex up to rank"
+        self.progress = {
+                     -1: {(s, r): Bool(r == 0) for s in range(0, self.num_suits) for r in range(0, 6)} # at start, have only played rank zero
+                   , **{
+                           m: {
+                               **{(s, 0): Bool(True) for s in range(0, self.num_suits)},
+                               **{(s, r): Symbol('m{}:{}{}'.format(m, s, r)) for s in range(0, self.num_suits) for r in range(1, 6)}
+                              }
+                           for m in range(self.max_moves)
+                       }
+                   }
+
+        ## Utility variables
+
+        # discard_any[m] == "at move m we play/discard a card"
+        self.discard_any = { m: Symbol('m{}d'.format(m)) for m in range(self.max_moves) }
+
+        # draw_any[m] == "at move m we draw a card"
+        self.draw_any = {m: Symbol('m{}D'.format(m)) for m in range(self.max_moves)}
+
+        # play[m] == "at move m we play a card"
+        self.play = {m: Symbol('m{}p'.format(m)) for m in range(self.max_moves)}
+
+        # play5[m] == "at move m we play a 5"
+        self.play5 = {m: Symbol('m{}p5'.format(m)) for m in range(self.max_moves)}
+
+        # incr_clues[m] == "at move m we obtain a clue"
+        self.incr_clues = {m: Symbol('m{}c+'.format(m)) for m in range(self.max_moves)}
+
+
+
+def solve(deck: List[DeckCard], num_players=5):
+
+    num_suits = max(map(lambda card: card.suitIndex, deck)) + 1
+    num_dark_suits = (len(deck) - 10 * num_suits) // (-5)
+
+    ls = Literals(num_players, num_suits, num_dark_suits)
 
     valid_move = lambda m: And(
-        Implies(dummyturn[m], Not(discard_any[m])),
+        # in dummy turns, nothing can be discarded
+        Implies(ls.dummyturn[m], Not(ls.discard_any[m])),
+
         # definition of discard_any
-        Iff(discard_any[m], Or(discard[m][i] for i in range(NUM_CARDS))),
+        Iff(ls.discard_any[m], Or(ls.discard[m][i] for i in range(ls.deck_size))),
+
         # definition of draw_any
-        Iff(draw_any[m], Or(draw[m][i] for i in range(last_hand_card + 1, NUM_CARDS))),
+        Iff(ls.draw_any[m], Or(ls.draw[m][i] for i in range(ls.distributed_cards, ls.deck_size))),
-        # draw implies discard (and converse true before last 5 moves)
+
-        Implies(draw_any[m], discard_any[m]),
+        # ls.draw implies ls.discard (and converse true before the ls.extraround)
-        Implies(discard_any[m], Or(extraround[m], draw_any[m])),
+        Implies(ls.draw_any[m], ls.discard_any[m]),
-        # play requires discard
+        Implies(ls.discard_any[m], Or(ls.extraround[m], ls.draw_any[m])),
-        Implies(play[m], discard_any[m]),
+
-        # definition of play5
+        # ls.play requires ls.discard
-        Iff(play5[m], And(play[m], Or(discard[m][i] for i in range(NUM_CARDS) if deck[i][1] == 5))),
+        Implies(ls.play[m], ls.discard_any[m]),
-        # definition of incr_clues
+
-        Iff(incr_clues[m], And(discard_any[m], Implies(play[m], And(play5[m], Not(clues[m-1][8]))))),
+        # definition of ls.play5
-        #Iff(incr_clues[m], And(discard_any[m], Implies(play[m], play5[m]))),
+        Iff(ls.play5[m], And(ls.play[m], Or(ls.discard[m][i] for i in range(ls.deck_size) if deck[i].rank == 5))),
-        # change of clues
+
-        *[Iff(clues[m][i], Or(clues[m-1][i+1], And(clues[m-1][i], Or(discard_any[m], dummyturn[m])), And(clues[m-1][i-1], incr_clues[m]))) for i in range(1, 9)],
+        # definition of ls.incr_clues
-        ## more than 8 clues not allowed, discarding produces a strike
+        Iff(ls.incr_clues[m], And(ls.discard_any[m], Implies(ls.play[m], And(ls.play5[m], Not(ls.clues[m-1][8]))))),
-        Iff(strike[m], And(discard_any[m], Not(play[m]), clues[m-1][8])),
+
+        # change of ls.clues
+        *[Iff(ls.clues[m][i], Or(ls.clues[m-1][i+1], And(ls.clues[m-1][i], Or(ls.discard_any[m], ls.dummyturn[m])), And(ls.clues[m-1][i-1], ls.incr_clues[m]))) for i in range(1, 9)],
+
+        ## more than 8 clues not allowed, ls.discarding produces a strike
+        # Note that this means that we will never strike while not at 8 clues.
+        # It's easy to see that if there is any solution to the instance, then there is also one where we only strike at 8 clues
+        # (or not at all) -> Just strike later if neccessary
+        # So, we decrease the solution space with this formulation, but do not change whether it's empty or not
+        Iff(ls.strike[m], And(ls.discard_any[m], Not(ls.play[m]), ls.clues[m-1][8])),
+
         # change of strikes
-        *[Iff(strikes[m][i], Or(strikes[m-1][i], And(strikes[m-1][i-1], strike[m]))) for i in range(1, NUM_STRIKES+1)],
+        *[Iff(ls.strikes[m][i], Or(ls.strikes[m-1][i], And(ls.strikes[m-1][i-1], ls.strike[m]))) for i in range(1, ls.num_strikes + 1)],
+
         # less than 0 clues not allowed
-        Implies(Not(discard_any[m]), Or(clues[m-1][1], dummyturn[m])),
+        Implies(Not(ls.discard_any[m]), Or(ls.clues[m-1][1], ls.dummyturn[m])),
-        # we can only draw card i if the last drawn card was i-1
+
-        *[Implies(draw[m][i], Or(And(draw[m0][i-1], *[Not(draw_any[m1]) for m1 in range(m0+1, m)]) for m0 in range(max(-1, m-9), m))) for i in range(last_hand_card + 1, NUM_CARDS)],
+        # we can only draw card i if the last ls.drawn card was i-1
-        #*[Implies(draw[m][i], Not(draw[m0][i])) for m0 in range(m) for i in range(20, 50)],
+        *[Implies(ls.draw[m][i], Or(And(ls.draw[m0][i-1], *[Not(ls.draw_any[m1]) for m1 in range(m0+1, m)]) for m0 in range(max(-1, m-9), m))) for i in range(ls.distributed_cards, ls.deck_size)],
-        #*[Implies(draw[m][i], Or(draw[m0][i-1] for m0 in range(max(-1, m-9), m))) for i in range(20, 50)],
+
         # we can only draw at most one card (NOTE: redundant, FIXME: avoid quadratic formula)
-        AtMostOne(draw[m][i] for i in range(last_hand_card + 1, NUM_CARDS)),
+        AtMostOne(ls.draw[m][i] for i in range(ls.distributed_cards, ls.deck_size)),
-        #*[Not(And(draw[m][i], draw[m][j])) for i in range(20, 50) for j in range(20, i)],
+
         # we can only discard a card if we drew it earlier...
-        *[Implies(discard[m][i], Or(draw[m0][i] for m0 in range(m-num_players, -1, -num_players))) for i in range(last_hand_card + 1, NUM_CARDS)],
+        *[Implies(ls.discard[m][i], Or(ls.draw[m0][i] for m0 in range(m-ls.num_players, -1, -ls.num_players))) for i in range(ls.distributed_cards, ls.deck_size)],
+
         # ...or if it was part of the initial hand
-        *[Not(discard[m][i]) for i in range(last_hand_card + 1) if i//hand_size != m % num_players],
+        *[Not(ls.discard[m][i]) for i in range(0, ls.distributed_cards) if i // ls.hand_size != m % ls.num_players],
+
         # we can only discard a card if we did not discard it yet
-        *[Implies(discard[m][i], And(Not(discard[m0][i]) for m0 in range(m-num_players, -1, -num_players))) for i in range(NUM_CARDS)],
+        *[Implies(ls.discard[m][i], And(Not(ls.discard[m0][i]) for m0 in range(m-ls.num_players, -1, -ls.num_players))) for i in range(ls.deck_size)],
+
         # we can only discard at most one card (FIXME: avoid quadratic formula)
-        AtMostOne(discard[m][i] for i in range(NUM_CARDS)),
+        AtMostOne(ls.discard[m][i] for i in range(ls.deck_size)),
-        #*[Not(And(discard[m][i], discard[m][j])) for i in range(NUM_CARDS) for j in range(i)],
+
         # we can only play a card if it matches the progress
-        *[Implies(And(discard[m][i], play[m]), And(Not(progress[m-1][deck[i]]), progress[m-1][deck[i][0], deck[i][1]-1])) for i in range(NUM_CARDS)],
+        *[Implies(
+                    And(ls.discard[m][i], ls.play[m]),
+                    And(
+                        Not(ls.progress[m-1][deck[i].suitIndex, deck[i].rank]),
+                        ls.progress[m-1][deck[i].suitIndex, deck[i].rank-1 ]
+                       )
+                  )
+          for i in range(ls.deck_size)
+          ],
+
         # change of progress
-        *[Iff(progress[m][c, k], Or(progress[m-1][c, k], And(play[m], Or(discard[m][i] for i in range(NUM_CARDS) if deck[i] == (c, k))))) for c in COLORS for k in range(1, 6)],
+        *[
+            Iff(
+                ls.progress[m][s, r],
+                Or(
+                    ls.progress[m-1][s, r],
+                    And(ls.play[m], Or(ls.discard[m][i]
+                        for i in range(0, ls.deck_size)
+                        if deck[i] == DeckCard(s, r) ))
+                  )
+                )
+            for s in range(0, ls.num_suits)
+            for r in range(1, 6)
+         ],
+
         # extra round bool
-        Iff(extraround[m], Or(extraround[m-1], draw[m-1][NUM_CARDS-1])),
+        Iff(ls.extraround[m], Or(ls.extraround[m-1], ls.draw[m-1][ls.deck_size-1])),
+
         # dummy turn bool
-        *[Iff(dummyturn[m], Or(dummyturn[m-1], draw[m-1 - num_players][NUM_CARDS-1])) for i in range(0,1) if m >= num_players]
+        *[Iff(ls.dummyturn[m], Or(ls.dummyturn[m-1], ls.draw[m-1 - ls.num_players][ls.deck_size-1])) for i in range(0,1) if m >= ls.num_players]
     )
 
     win = And(
         # maximum progress at each color
-        *[progress[max_moves-1][c, 5] for c in COLORS],
+        *[ls.progress[ls.max_moves-1][s, 5] for s in range(0, ls.num_suits)],
-        # played every color/value combination (NOTE: redundant)
+
-        *[Or(And(discard[m][i], play[m]) for m in range(max_moves) for i in range(50) if deck[i] == (c, k)) for c in COLORS for k in range(1, 6)]
+        # played every color/value combination (NOTE: redundant, but makes solving faster)
+        *[
+            Or(
+               And(ls.discard[m][i], ls.play[m])
+               for m in range(ls.max_moves)
+               for i in range(ls.deck_size)
+               if deck[i] == DeckCard(s, r)
+              )
+          for s in range(0, ls.num_suits)
+          for r in range(1, 6)
+          ]
     )
 
-    constraints = And(*[valid_move(m) for m in range(max_moves)], win)
+    constraints = And(*[valid_move(m) for m in range(ls.max_moves)], win)
 #    print('Solving instance with {} variables, {} nodes'.format(len(get_atoms(constraints)), get_formula_size(constraints)))
 
     model = get_model(constraints)
     if model:
 #        print_model(model, deck)
-        solution = toJSON(model, deck, num_players)
+        solution = toJSON(model, deck, ls)
         return True, solution
     else:
         print('unsatisfiable')
@@ -140,44 +289,35 @@ def print_model(model, deck, num_players):
         flags = ['discard_any', 'draw_any', 'play', 'play5', 'incr_clues', 'strike', 'extraround', 'dummyturn']
         print(', '.join(f for f in flags if model.get_py_value(globals()[f][m])))
 
-def toJSON(model, deck, num_players):
+def toJSON(model, deck: List[DeckCard], ls: Literals) -> dict:
-    deck_json = [{"suitIndex": COLORS.index(s), "rank": r} for (s,r) in deck]
+    players = ["Alice", "Bob", "Cathy", "Donald", "Emily"][:ls.num_players]
-    players = ["Alice", "Bob", "Cathy", "Donald", "Emily"][:num_players]
+    # we keep track of the hands to output some dummy clues
-    hands = [deck[hand_size[num_players]*p:hand_size[num_players]*(p+1)] for p in range(0,num_players)]
+    hands = [deck[ls.hand_size * p : ls.hand_size *(p+1)] for p in range(0, ls.num_players)]
-    draw = globals()['draw'][num_players]
     actions = []
-    for m in range(max_moves[num_players]):
+    for m in range(ls.max_moves):
-        if model.get_py_value(dummyturn[m]):
+        if model.get_py_value(ls.dummyturn[m]):
             break
-        if model.get_py_value(discard_any[m]):
+        if model.get_py_value(ls.discard_any[m]):
-            discarded = next(i for i in range(0,NUM_CARDS) if model.get_py_value(discard[m][i]))
+            discarded = next(i for i in range(0,ls.deck_size) if model.get_py_value(ls.discard[m][i]))
-            icard = hands[m % num_players].index(deck[discarded])
+            icard = hands[m % ls.num_players].index(deck[discarded])
-            for i in range(icard, hand_size[num_players] - 1):
+            for i in range(icard, ls.hand_size - 1):
-                hands[m % num_players][i] = hands[m % num_players][i + 1]
+                hands[m % ls.num_players][i] = hands[m % ls.num_players][i + 1]
-            if model.get_py_value(draw_any[m]):
+            if model.get_py_value(ls.draw_any[m]):
-                hands[m % num_players][hand_size[num_players] - 1] = next(deck[i] for i in range(last_hand_card[num_players] + 1, NUM_CARDS) if model.get_py_value(draw[m][i]))
+                hands[m % ls.num_players][ls.hand_size - 1] = next(deck[i] for i in range(ls.distributed_cards, ls.deck_size) if model.get_py_value(ls.draw[m][i]))
-            if model.get_py_value(play[m]) or model.get_py_value(strike[m]):
+            if model.get_py_value(ls.play[m]) or model.get_py_value(ls.strike[m]):
-                actions.append({
+                actions.append( Action( ActionType.Play, target=discarded) )
-                    "type": 0,
-                    "target": discarded
-                    })
             else:
-                actions.append({
+                actions.append( Action( ActionType.Discard, target=discarded) )
-                    "type": 1,
-                    "target": discarded
-                    })
         else:
-            actions.append({
+            actions.append( Action(
-                "type": 3,
+                ActionType.RankClue,
-                "target": (m + 1) % num_players,
+                target=(m+1) % ls.num_players,                 # clue next player
-                "value": hands[(m+1) % num_players][0][1]
+                value=hands[(m+1) % ls.num_players][0].rank    # clue rank of rightmost card
-                })
+                )
-    actions.append({
+                           )
-        "type": 4,
+    actions.append( Action (ActionType.EndGame, target=0, value=1))
-        "value": 1
-        })
     game = {
-            "deck": deck_json,
+            "deck": deck,
             "players": players,
             "actions": actions,
             "first_player": 0,
@@ -185,9 +325,16 @@ def toJSON(model, deck, num_players):
                 "variant": "No Variant",
                 }
             }
-    return json.dumps(game)
+    return game
 
 if __name__ == "__main__":
-    solvable, sol = solve(deck_str)
+    COLORS = 'rygbp'
+    deck_str = 'p5 p3 b4 r5 y4 y4 y5 r4 b2 y2 y3 g5 g2 g3 g4 p4 r3 b2 b3 b3 p4 b1 p2 b1 b1 p2 p1 p1 g1 r4 g1 r1 r3 r1 g1 r1 p1 b4 p3 g2 g3 g4 b5 y1 y1 y1 r2 r2 y2 y3'
+
+    deck = [DeckCard(COLORS.index(c[0]), int(c[1])) for c in deck_str.split(" ")]
+    print(deck)
+
+    solvable, sol = solve(deck, num_players=5)
     if solvable:
         print(sol)
+        print(link(sol))