325 lines
15 KiB
Python
325 lines
15 KiB
Python
from pysmt.shortcuts import Symbol, Bool, Not, Implies, Iff, And, Or, AtMostOne, ExactlyOne, get_model, get_atoms, get_formula_size, get_unsat_core
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from pysmt.rewritings import conjunctive_partition
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import json
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from typing import List
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from concurrent.futures import ProcessPoolExecutor
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from compress import DeckCard, Action, ActionType, link
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from greedy_solver import GameState
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COLORS = 'rygbp'
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STANDARD_HAND_SIZE = {2: 5, 3: 5, 4: 4, 5: 4, 6: 3}
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NUM_STRIKES_TO_LOSE = 3
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# literals to model game as sat instance to check for feasibility
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# variants 'throw it in a hole not handled', 'clue starved' and 'up or down' currently not handled
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class Literals():
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# num_suits is total number of suits, i.e. also counts the dark suits
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# default distribution among all suits is assumed
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def __init__(self, num_players, num_suits, num_dark_suits=0):
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assert ( 2 <= num_players <= 6 )
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## some game parameters
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self.num_players = num_players
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self.num_suits = num_suits
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self.num_dark_suits = num_dark_suits
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self.hand_size = STANDARD_HAND_SIZE[num_players]
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self.num_strikes = NUM_STRIKES_TO_LOSE
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self.deck_size = 10 * num_suits - 5 * num_dark_suits
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self.distributed_cards = self.num_players * self.hand_size
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self.draw_pile_size = self.deck_size - self.distributed_cards
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## maximum number of moves in any game that can achieve max score
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# 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
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# 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
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# 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)
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# 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
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self.max_moves = 15 * num_suits - 10 * num_dark_suits \
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- 2 * num_players * (self.hand_size - 1) \
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+ 8 + (num_suits - 1) \
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+ (-1 if num_players >= 5 else 0)
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###
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# 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
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# move are numbered starting with 0
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# clues[m][i] == "after move m we have at least i clues"
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self.clues = {
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-1: { i: Bool(i < 9) for i in range(0, 10) } # we have 8 clues after turn -1
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, **{
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m: {
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0: Bool(True), # always at least 0 clues
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**{ i: Symbol('m{}c{}'.format(m, i)) for i in range(1, 9) },
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9: Bool(False) # never 9 or more clues. This will implicitly forbid discarding at 8 clues later
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}
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for m in range(self.max_moves)
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}
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}
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# strikes[m][i] == "after move m we have at least i strikes"
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self.strikes = {
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-1: {i: Bool(i == 0) for i in range(0, self.num_strikes + 1)} # no strikes when we start
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, **{
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m: {
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0: Bool(True),
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**{ s: Symbol('m{}s{}'.format(m,s)) for s in range(1, self.num_strikes) },
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self.num_strikes: Bool(False) # never so many clues that we lose. Implicitly forbids striking out
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}
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for m in range(self.max_moves)
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}
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}
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# extraturn[m] = "turn m is a move part of the extra round or a dummy turn"
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self.extraround = {
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-1: Bool(False)
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, **{
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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
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for m in range(0, self.max_moves)
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}
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}
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# dummyturn[m] = "turn m is a dummy nurn and not actually part of the game"
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self.dummyturn = {
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-1: Bool(False)
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, **{
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m: Bool(False) if m < self.draw_pile_size + self.num_players else Symbol('m{}dt'.format(m))
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for m in range(0, self.max_moves)
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}
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}
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# draw[m][i] == "at move m we play/discard deck[i]"
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self.discard = {
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m: {i: Symbol('m{}-{}'.format(m, i)) for i in range(self.deck_size)}
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for m in range(self.max_moves)
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}
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# draw[m][i] == "at move m we draw deck card i"
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self.draw = {
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-1: { i: Bool(i == self.distributed_cards - 1) for i in range(self.distributed_cards - 1, self.deck_size) }
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, **{
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m: {
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self.distributed_cards - 1: Bool(False),
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**{i: Symbol('m{}+{}'.format(m, i)) for i in range(self.distributed_cards, self.deck_size)}
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}
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for m in range(self.max_moves)
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}
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}
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# strike[m] = "at move m we get a strike"
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self.strike = {
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-1: Bool(False)
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, **{
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m: Symbol('m{}s+'.format(m))
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for m in range(self.max_moves)
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}
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}
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# progress[m][card = (suitIndex, rank)] == "after move m we have played in suitIndex up to rank"
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self.progress = {
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-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
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, **{
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m: {
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**{(s, 0): Bool(True) for s in range(0, self.num_suits)},
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**{(s, r): Symbol('m{}:{}{}'.format(m, s, r)) for s in range(0, self.num_suits) for r in range(1, 6)}
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}
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for m in range(self.max_moves)
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}
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}
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## Utility variables
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# discard_any[m] == "at move m we play/discard a card"
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self.discard_any = { m: Symbol('m{}d'.format(m)) for m in range(self.max_moves) }
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# draw_any[m] == "at move m we draw a card"
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self.draw_any = {m: Symbol('m{}D'.format(m)) for m in range(self.max_moves)}
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# play[m] == "at move m we play a card"
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self.play = {m: Symbol('m{}p'.format(m)) for m in range(self.max_moves)}
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# play5[m] == "at move m we play a 5"
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self.play5 = {m: Symbol('m{}p5'.format(m)) for m in range(self.max_moves)}
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# incr_clues[m] == "at move m we obtain a clue"
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self.incr_clues = {m: Symbol('m{}c+'.format(m)) for m in range(self.max_moves)}
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def solve(deck: List[DeckCard], num_players=5):
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num_suits = max(map(lambda card: card.suitIndex, deck)) + 1
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num_dark_suits = (len(deck) - 10 * num_suits) // (-5)
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ls = Literals(num_players, num_suits, num_dark_suits)
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valid_move = lambda m: And(
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# in dummy turns, nothing can be discarded
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Implies(ls.dummyturn[m], Not(ls.discard_any[m])),
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# definition of discard_any
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Iff(ls.discard_any[m], Or(ls.discard[m][i] for i in range(ls.deck_size))),
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# definition of draw_any
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Iff(ls.draw_any[m], Or(ls.draw[m][i] for i in range(ls.distributed_cards, ls.deck_size))),
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# ls.draw implies ls.discard (and converse true before the ls.extraround)
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Implies(ls.draw_any[m], ls.discard_any[m]),
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Implies(ls.discard_any[m], Or(ls.extraround[m], ls.draw_any[m])),
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# ls.play requires ls.discard
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Implies(ls.play[m], ls.discard_any[m]),
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# definition of ls.play5
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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))),
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# definition of ls.incr_clues
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Iff(ls.incr_clues[m], And(ls.discard_any[m], Implies(ls.play[m], And(ls.play5[m], Not(ls.clues[m-1][8]))))),
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# change of ls.clues
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*[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)],
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## more than 8 clues not allowed, ls.discarding produces a strike
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# Note that this means that we will never strike while not at 8 clues.
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# 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
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# (or not at all) -> Just strike later if neccessary
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# So, we decrease the solution space with this formulation, but do not change whether it's empty or not
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Iff(ls.strike[m], And(ls.discard_any[m], Not(ls.play[m]), ls.clues[m-1][8])),
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# change of strikes
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*[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)],
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# less than 0 clues not allowed
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Implies(Not(ls.discard_any[m]), Or(ls.clues[m-1][1], ls.dummyturn[m])),
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# we can only draw card i if the last ls.drawn card was i-1
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*[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)],
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# we can only draw at most one card (NOTE: redundant, FIXME: avoid quadratic formula)
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AtMostOne(ls.draw[m][i] for i in range(ls.distributed_cards, ls.deck_size)),
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# we can only discard a card if we drew it earlier...
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*[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)],
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# ...or if it was part of the initial hand
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*[Not(ls.discard[m][i]) for i in range(0, ls.distributed_cards) if i // ls.hand_size != m % ls.num_players],
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# we can only discard a card if we did not discard it yet
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*[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)],
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# we can only discard at most one card (FIXME: avoid quadratic formula)
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AtMostOne(ls.discard[m][i] for i in range(ls.deck_size)),
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# we can only play a card if it matches the progress
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*[Implies(
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And(ls.discard[m][i], ls.play[m]),
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And(
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Not(ls.progress[m-1][deck[i].suitIndex, deck[i].rank]),
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ls.progress[m-1][deck[i].suitIndex, deck[i].rank-1 ]
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)
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)
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for i in range(ls.deck_size)
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],
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# change of progress
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*[
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Iff(
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ls.progress[m][s, r],
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Or(
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ls.progress[m-1][s, r],
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And(ls.play[m], Or(ls.discard[m][i]
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for i in range(0, ls.deck_size)
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if deck[i] == DeckCard(s, r) ))
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)
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)
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for s in range(0, ls.num_suits)
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for r in range(1, 6)
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],
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# extra round bool
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Iff(ls.extraround[m], Or(ls.extraround[m-1], ls.draw[m-1][ls.deck_size-1])),
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# dummy turn bool
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*[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]
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)
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win = And(
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# maximum progress at each color
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*[ls.progress[ls.max_moves-1][s, 5] for s in range(0, ls.num_suits)],
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# played every color/value combination (NOTE: redundant, but makes solving faster)
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*[
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Or(
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And(ls.discard[m][i], ls.play[m])
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for m in range(ls.max_moves)
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for i in range(ls.deck_size)
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if deck[i] == DeckCard(s, r)
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)
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for s in range(0, ls.num_suits)
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for r in range(1, 6)
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]
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)
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constraints = And(*[valid_move(m) for m in range(ls.max_moves)], win)
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# print('Solving instance with {} variables, {} nodes'.format(len(get_atoms(constraints)), get_formula_size(constraints)))
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model = get_model(constraints)
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if model:
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# print_model(model, deck)
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solution = toJSON(model, deck, ls)
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return True, solution
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else:
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return False, None
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#conj = list(conjunctive_partition(constraints))
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#print('statements: {}'.format(len(conj)))
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#ucore = get_unsat_core(conj)
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#print('unsat core size: {}'.format(len(ucore)))
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#for f in ucore:
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# print(f.serialize())
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def print_model(model, deck, num_players):
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draw = globals()['draw'][num_players]
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for m in range(max_moves[num_players]):
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print('=== move {} ==='.format(m))
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print('clues: ' + ''.join(str(i) for i in range(1, 9) if model.get_py_value(clues[m][i])))
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print('strikes: ' + ''.join(str(i) for i in range(1, NUM_STRIKES) if model.get_py_value(strikes[m][i])))
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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])))
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print('discard: ' + ', '.join('{} [{}{}]'.format(i, deck[i][0], deck[i][1]) for i in range(50) if model.get_py_value(discard[m][i])))
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for c in COLORS:
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print('progress {}: '.format(c) + ''.join(str(k) for k in range(1, 6) if model.get_py_value(progress[m][c, k])))
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flags = ['discard_any', 'draw_any', 'play', 'play5', 'incr_clues', 'strike', 'extraround', 'dummyturn']
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print(', '.join(f for f in flags if model.get_py_value(globals()[f][m])))
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def toJSON(model, deck: List[DeckCard], ls: Literals) -> dict:
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gs = GameState(ls.num_players, deck)
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for m in range(ls.max_moves):
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if model.get_py_value(ls.dummyturn[m]):
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break
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if model.get_py_value(ls.discard_any[m]):
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card_idx = next(i for i in range(0, ls.deck_size) if model.get_py_value(ls.discard[m][i]))
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if model.get_py_value(ls.play[m]) or model.get_py_value(ls.strike[m]):
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gs.play(card_idx)
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else:
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gs.discard(card_idx)
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else:
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gs.clue()
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return gs.to_json()
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def run_deck():
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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'
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deck = [DeckCard(COLORS.index(c[0]), int(c[1])) for c in deck_str.split(" ")]
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print(deck)
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solvable, sol = solve(deck, num_players=5)
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if solvable:
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print(sol)
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print(link(sol))
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if __name__ == "__main__":
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run_deck()
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