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 from concurrent.futures import ProcessPoolExecutor from compress import DeckCard, Action, ActionType, link from greedy_solver import GameState COLORS = 'rygbp' STANDARD_HAND_SIZE = {2: 5, 3: 5, 4: 4, 5: 4, 6: 3} NUM_STRIKES_TO_LOSE = 3 # literals to model game as sat instance to check for feasibility # variants 'throw it in a hole not handled', 'clue starved' and 'up or down' currently not handled class Literals(): # num_suits is total number of suits, i.e. also counts the dark suits # default distribution among all suits is assumed 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( # in dummy turns, nothing can be discarded Implies(ls.dummyturn[m], Not(ls.discard_any[m])), # definition of discard_any Iff(ls.discard_any[m], Or(ls.discard[m][i] for i in range(ls.deck_size))), # definition of draw_any Iff(ls.draw_any[m], Or(ls.draw[m][i] for i in range(ls.distributed_cards, ls.deck_size))), # ls.draw implies ls.discard (and converse true before the ls.extraround) Implies(ls.draw_any[m], ls.discard_any[m]), Implies(ls.discard_any[m], Or(ls.extraround[m], ls.draw_any[m])), # ls.play requires ls.discard Implies(ls.play[m], ls.discard_any[m]), # definition of ls.play5 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))), # definition of ls.incr_clues Iff(ls.incr_clues[m], And(ls.discard_any[m], Implies(ls.play[m], And(ls.play5[m], Not(ls.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(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(ls.discard_any[m]), Or(ls.clues[m-1][1], ls.dummyturn[m])), # we can only draw card i if the last ls.drawn card was i-1 *[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)], # we can only draw at most one card (NOTE: redundant, FIXME: avoid quadratic formula) AtMostOne(ls.draw[m][i] for i in range(ls.distributed_cards, ls.deck_size)), # we can only discard a card if we drew it earlier... *[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(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(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(ls.discard[m][i] for i in range(ls.deck_size)), # we can only play a card if it matches the progress *[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( 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(ls.extraround[m], Or(ls.extraround[m-1], ls.draw[m-1][ls.deck_size-1])), # dummy turn bool *[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 *[ls.progress[ls.max_moves-1][s, 5] for s in range(0, ls.num_suits)], # 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(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, ls) return True, solution else: return False, None #conj = list(conjunctive_partition(constraints)) #print('statements: {}'.format(len(conj))) #ucore = get_unsat_core(conj) #print('unsat core size: {}'.format(len(ucore))) #for f in ucore: # print(f.serialize()) def print_model(model, deck, num_players): draw = globals()['draw'][num_players] for m in range(max_moves[num_players]): print('=== move {} ==='.format(m)) print('clues: ' + ''.join(str(i) for i in range(1, 9) if model.get_py_value(clues[m][i]))) print('strikes: ' + ''.join(str(i) for i in range(1, NUM_STRIKES) if model.get_py_value(strikes[m][i]))) print('draw: ' + ', '.join('{} [{}{}]'.format(i, deck[i][0], deck[i][1]) for i in range(20, 50) if model.get_py_value(draw[m][i]))) print('discard: ' + ', '.join('{} [{}{}]'.format(i, deck[i][0], deck[i][1]) for i in range(50) if model.get_py_value(discard[m][i]))) for c in COLORS: print('progress {}: '.format(c) + ''.join(str(k) for k in range(1, 6) if model.get_py_value(progress[m][c, k]))) 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: List[DeckCard], ls: Literals) -> dict: gs = GameState(ls.num_players, deck) for m in range(ls.max_moves): if model.get_py_value(ls.dummyturn[m]): break if model.get_py_value(ls.discard_any[m]): card_idx = next(i for i in range(0, ls.deck_size) if model.get_py_value(ls.discard[m][i])) if model.get_py_value(ls.play[m]) or model.get_py_value(ls.strike[m]): gs.play(card_idx) else: gs.discard(card_idx) else: gs.clue() return gs.to_json() def run_deck(): 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)) if __name__ == "__main__": run_deck()