adjust sat solver to handle mid-game states
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165
sat.py
165
sat.py
@ -4,8 +4,8 @@ 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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from compress import DeckCard, Action, ActionType, link, decompress_deck
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from greedy_solver import GameState, GreedyStrategy
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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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@ -51,7 +51,7 @@ class Literals():
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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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**{ i: Symbol('m{}clues{}'.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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@ -64,7 +64,7 @@ class Literals():
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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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**{ s: Symbol('m{}strikes{}'.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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@ -75,7 +75,7 @@ class Literals():
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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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m: Bool(False) if m < self.draw_pile_size else Symbol('m{}extra'.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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@ -84,14 +84,14 @@ class Literals():
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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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m: Bool(False) if m < self.draw_pile_size + self.num_players else Symbol('m{}dummy'.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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m: {i: Symbol('m{}discard{}'.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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@ -101,7 +101,7 @@ class Literals():
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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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**{i: Symbol('m{}draw{}'.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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@ -111,7 +111,7 @@ class Literals():
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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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m: Symbol('m{}newstrike'.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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@ -122,7 +122,7 @@ class Literals():
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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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**{(s, r): Symbol('m{}progress{}{}'.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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@ -131,29 +131,66 @@ class Literals():
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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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self.discard_any = { m: Symbol('m{}discard_any'.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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self.draw_any = {m: Symbol('m{}draw_any'.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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self.play = {m: Symbol('m{}play'.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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self.play5 = {m: Symbol('m{}play5'.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(game_state: GameState):
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ls = Literals(game_state.num_players, game_state.num_suits, game_state.num_dark_suits)
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def solve(deck: List[DeckCard], num_players=5):
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##### setup of initial game state
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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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# properties used later to model valid moves
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num_dark_suits = game_state.num_dark_suits
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num_suits = game_state.num_suits
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deck = game_state.deck
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next_draw = game_state.progress
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ls = Literals(num_players, num_suits, num_dark_suits)
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starting_hands = [[card.deck_index for card in hand] for hand in game_state.hands]
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first_turn = len(game_state.actions)
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# set initial clues
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for i in range(0,10):
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ls.clues[first_turn - 1][i] = Bool(i <= game_state.clues)
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# set initial strikes
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for i in range(0, game_state.num_strikes + 1):
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ls.strikes[first_turn - 1][i] = Bool(i <= game_state.strikes)
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# check if extraround has started (usually not)
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ls.extraround[first_turn - 1] = Bool(game_state.remaining_extra_turns < game_state.num_players)
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ls.dummyturn[first_turn -1] = Bool(False)
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# set recent draws: important to model progress
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# we just pretend that the last card drawn was in fact drawn last turn,
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# regardless of when it was actually drawn
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for neg_turn in range(1, min(9, first_turn + 2)):
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for i in range(game_state.num_players * game_state.hand_size, game_state.deck_size):
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ls.draw[first_turn - neg_turn][i] = Bool(neg_turn == 1 and i == game_state.progress - 1)
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# forbid re-drawing of the last card drawn
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for m in range(first_turn, ls.max_moves):
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ls.draw[m][game_state.progress - 1] = Bool(False)
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# model initial progress
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for s in range(0, game_state.num_suits):
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for r in range(0, 6):
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ls.progress[first_turn - 1][s, r] = Bool(r <= game_state.stacks[s])
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### Now, model all valid moves
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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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@ -162,7 +199,7 @@ def solve(deck: List[DeckCard], num_players=5):
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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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Iff(ls.draw_any[m], Or(ls.draw[m][i] for i in range(next_draw, 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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@ -194,19 +231,19 @@ def solve(deck: List[DeckCard], num_players=5):
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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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*[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(first_turn - 1, m-9), m))) for i in range(next_draw, 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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AtMostOne(ls.draw[m][i] for i in range(next_draw, 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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*[Implies(ls.discard[m][i], Or(ls.draw[m0][i] for m0 in range(m-ls.num_players, first_turn - 1, -ls.num_players))) for i in range(next_draw, 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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*[Not(ls.discard[m][i]) for i in range(0, next_draw) if i not in starting_hands[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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*[Implies(ls.discard[m][i], And(Not(ls.discard[m0][i]) for m0 in range(m-ls.num_players, first_turn - 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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@ -252,73 +289,93 @@ def solve(deck: List[DeckCard], num_players=5):
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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 m in range(first_turn, 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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if game_state.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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if r > game_state.stacks[s]
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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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constraints = And(*[valid_move(m) for m in range(first_turn, 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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# print_model(model, game_state, ls)
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solution = toJSON(model, game_state, 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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return False, None
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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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def print_model(model, cur_game_state, ls: Literals):
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deck = cur_game_state.deck
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for m in range(ls.max_moves):
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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(ls.clues[m][i])))
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print('strikes: ' + ''.join(str(i) for i in range(1, 3) if model.get_py_value(ls.strikes[m][i])))
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print('draw: ' + ', '.join('{}: {}'.format(i, deck[i]) for i in range(cur_game_state.progress, 50) if model.get_py_value(ls.draw[m][i])))
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print('discard: ' + ', '.join('{}: {}'.format(i, deck[i]) for i in range(50) if model.get_py_value(ls.discard[m][i])))
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for s in range(0, ls.num_suits):
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print('progress {}: '.format(COLORS[s]) + ''.join(str(r) for r in range(1, 6) if model.get_py_value(ls.progress[m][s, r])))
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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(getattr(ls, f)[m])))
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def toJSON(model, cur_game_state: GameState, ls: Literals) -> dict:
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for m in range(len(cur_game_state.actions), 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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cur_game_state.play(card_idx)
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else:
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gs.discard(card_idx)
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cur_game_state.discard(card_idx)
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else:
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gs.clue()
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cur_game_state.clue()
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return gs.to_json()
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return cur_game_state.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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puzzle = True
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if puzzle:
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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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num_p = 5
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else:
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deck_str = "15gfvqluvuwaqnmrkpkaignlaxpjbmsprksfcddeybfixchuhtwo"
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deck = decompress_deck(deck_str)
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num_p = 4
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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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gs = GameState(num_p, deck)
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if puzzle:
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gs.play(2)
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pass
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else:
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strat = GreedyStrategy(gs)
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for _ in range(18):
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strat.make_move()
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print(link(gs.to_json()))
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solvable, sol = solve(gs)
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if solvable:
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print(sol)
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print(link(sol))
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else:
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print('unsolvable')
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if __name__ == "__main__":
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run_deck()
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