Maximilian Keßler
a93601c997
We now only use relative imports for files in the same directory Also, only modules are imported, never classes/functions etc Furthermore, main methods in package files have been removed, since they do not belong there
373 lines
16 KiB
Python
373 lines
16 KiB
Python
import copy
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from typing import Optional, Tuple
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from pysmt.shortcuts import Symbol, Bool, Not, Implies, Iff, And, Or, AtMostOne, get_model, Equals, GE, NotEquals, Int
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from pysmt.typing import INT
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from hanabi import logger
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from hanabi import constants
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from hanabi import hanab_game
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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, instance: hanab_game.HanabiInstance):
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# clues[m][i] == "after move m we have i clues", in clue starved, this counts half clues
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self.clues = {
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-1: Int(16 if instance.clue_starved else 8) # we have 8 clues after turn
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, **{
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m: Symbol('m{}clues'.format(m), INT)
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for m in range(instance.max_winning_moves)
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}
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}
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self.pace = {
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-1: Int(instance.initial_pace)
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, **{
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m: Symbol('m{}pace'.format(m), INT)
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for m in range(instance.max_winning_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, instance.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{}strikes{}'.format(m, s)) for s in range(1, instance.num_strikes)},
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instance.num_strikes: Bool(False)
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# never so many clues that we lose. Implicitly forbids striking out
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}
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for m in range(instance.max_winning_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 < instance.draw_pile_size else Symbol('m{}extra'.format(m))
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# 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, instance.max_winning_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 < instance.draw_pile_size + instance.num_players else Symbol('m{}dummy'.format(m))
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for m in range(0, instance.max_winning_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{}discard{}'.format(m, i)) for i in range(instance.deck_size)}
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for m in range(instance.max_winning_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 == instance.num_dealt_cards - 1) for i in
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range(instance.num_dealt_cards - 1, instance.deck_size)}
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, **{
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m: {
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instance.num_dealt_cards - 1: Bool(False),
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**{i: Symbol('m{}draw{}'.format(m, i)) for i in range(instance.num_dealt_cards, instance.deck_size)}
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}
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for m in range(instance.max_winning_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{}newstrike'.format(m))
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for m in range(instance.max_winning_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, instance.num_suits) for r in range(0, 6)}
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# 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, instance.num_suits)},
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**{(s, r): Symbol('m{}progress{}{}'.format(m, s, r)) for s in range(0, instance.num_suits) for r in
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range(1, 6)}
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}
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for m in range(instance.max_winning_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{}discard_any'.format(m)) for m in range(instance.max_winning_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{}draw_any'.format(m)) for m in range(instance.max_winning_moves)}
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# play[m] == "at move m we play a card"
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self.play = {m: Symbol('m{}play'.format(m)) for m in range(instance.max_winning_moves)}
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# play5[m] == "at move m we play a 5"
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self.play5 = {m: Symbol('m{}play5'.format(m)) for m in range(instance.max_winning_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(instance.max_winning_moves)}
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def solve_sat(starting_state: hanab_game.GameState | hanab_game.HanabiInstance, min_pace: Optional[int] = 0) -> Tuple[
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bool, Optional[hanab_game.GameState]]:
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if isinstance(starting_state, hanab_game.HanabiInstance):
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instance = starting_state
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game_state = hanab_game.GameState(instance)
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elif isinstance(starting_state, hanab_game.GameState):
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instance = starting_state.instance
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game_state = starting_state
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else:
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raise ValueError("Bad argument type")
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ls = Literals(instance)
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##### setup of initial game state
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# properties used later to model valid moves
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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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if isinstance(starting_state, hanab_game.GameState):
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# have to set additional variables
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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] = Int(game_state.clues)
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# set initial pace
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ls.pace[first_turn - 1] = Int(game_state.pace)
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# set initial strikes
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for i in range(0, instance.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(instance.num_players * instance.hand_size, instance.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, instance.max_winning_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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# definition of discard_any
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Iff(ls.discard_any[m], Or(ls.discard[m][i] for i in range(instance.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(game_state.progress, instance.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],
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And(ls.play[m], Or(ls.discard[m][i] for i in range(instance.deck_size) if instance.deck[i].rank == 5))),
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# definition of ls.incr_clues
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Iff(ls.incr_clues[m],
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And(ls.discard_any[m], NotEquals(ls.clues[m - 1], Int(16 if instance.clue_starved else 8)),
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Implies(ls.play[m], ls.play5[m]))),
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# change of ls.clues
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Implies(And(Not(ls.discard_any[m]), Not(ls.dummyturn[m])),
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Equals(ls.clues[m], ls.clues[m - 1] - (2 if instance.clue_starved else 1))),
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Implies(ls.incr_clues[m], Equals(ls.clues[m], ls.clues[m - 1] + 1)),
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Implies(And(Or(ls.discard_any[m], ls.dummyturn[m]), Not(ls.incr_clues[m])),
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Equals(ls.clues[m], ls.clues[m - 1])),
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# change of pace
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Implies(And(ls.discard_any[m], Or(ls.strike[m], Not(ls.play[m]))), Equals(ls.pace[m], ls.pace[m - 1] - 1)),
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Implies(Or(Not(ls.discard_any[m]), And(Not(ls.strike[m]), ls.play[m])), Equals(ls.pace[m], ls.pace[m - 1])),
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# pace is nonnegative
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GE(ls.pace[m], Int(min_pace)),
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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],
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And(ls.discard_any[m], Not(ls.play[m]), Equals(ls.clues[m - 1], Int(16 if instance.clue_starved else 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
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range(1, instance.num_strikes + 1)],
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# less than 0 clues not allowed
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Implies(Not(ls.discard_any[m]), Or(GE(ls.clues[m - 1], Int(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(
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And(ls.draw[m0][i - 1], *[Not(ls.draw_any[m1]) for m1 in range(m0 + 1, m)]) for m0 in
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range(max(first_turn - 1, m - 9), m))) for i in range(game_state.progress, instance.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(game_state.progress, instance.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],
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Or(ls.draw[m0][i] for m0 in range(m - instance.num_players, first_turn - 1, -instance.num_players)))
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for i in range(game_state.progress, instance.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, game_state.progress) if
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i not in starting_hands[m % instance.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(
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Not(ls.discard[m0][i]) for m0 in range(m - instance.num_players, first_turn - 1, -instance.num_players)))
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for i in range(instance.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(instance.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][instance.deck[i].suitIndex, instance.deck[i].rank]),
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ls.progress[m - 1][instance.deck[i].suitIndex, instance.deck[i].rank - 1]
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)
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)
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for i in range(instance.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, instance.deck_size)
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if instance.deck[i] == hanab_game.DeckCard(s, r)))
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)
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)
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for s in range(0, instance.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][instance.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 - instance.num_players][instance.deck_size - 1]))
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for i in range(0, 1) if m >= instance.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[instance.max_winning_moves - 1][s, 5] for s in range(0, instance.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(first_turn, instance.max_winning_moves)
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for i in range(instance.deck_size)
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if game_state.deck[i] == hanab_game.DeckCard(s, r)
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)
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for s in range(0, instance.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(first_turn, instance.max_winning_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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log_model(model, game_state, ls)
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solution = evaluate_model(model, copy.deepcopy(game_state), ls)
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return True, solution
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else:
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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 log_model(model, cur_game_state, ls: Literals):
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deck = cur_game_state.deck
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first_turn = len(cur_game_state.actions)
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if first_turn > 0:
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logger.debug('[print_model] Note: Omitting first {} turns, since they were fixed already.'.format(first_turn))
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for m in range(first_turn, cur_game_state.instance.max_winning_moves):
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logger.debug('=== move {} ==='.format(m))
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logger.debug('clues: {}'.format(model.get_py_value(ls.clues[m])))
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logger.debug('strikes: ' + ''.join(str(i) for i in range(1, 3) if model.get_py_value(ls.strikes[m][i])))
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logger.debug('draw: ' + ', '.join(
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'{}: {}'.format(i, deck[i]) for i in range(cur_game_state.progress, cur_game_state.instance.deck_size) if
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model.get_py_value(ls.draw[m][i])))
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logger.debug('discard: ' + ', '.join(
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'{}: {}'.format(i, deck[i]) for i in range(cur_game_state.instance.deck_size) if
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model.get_py_value(ls.discard[m][i])))
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logger.debug('pace: {}'.format(model.get_py_value(ls.pace[m])))
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for s in range(0, cur_game_state.instance.num_suits):
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logger.debug('progress {}: '.format(constants.COLOR_INITIALS[s]) + ''.join(
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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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logger.debug(', '.join(f for f in flags if model.get_py_value(getattr(ls, f)[m])))
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# given the initial game state and the model found by the SAT solver,
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# evaluates the model to produce a full game history
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def evaluate_model(model, cur_game_state: hanab_game.GameState, ls: Literals) -> hanab_game.GameState:
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for m in range(len(cur_game_state.actions), cur_game_state.instance.max_winning_moves):
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if model.get_py_value(ls.dummyturn[m]) or cur_game_state.is_over():
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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(
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i for i in range(0, cur_game_state.instance.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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cur_game_state.play(card_idx)
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else:
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cur_game_state.discard(card_idx)
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else:
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cur_game_state.clue()
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return cur_game_state
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