From ba8313b4bbde925da701545355cfc66a894f295a Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Maximilian=20Ke=C3=9Fler?= Date: Mon, 13 Mar 2023 17:21:07 +0100 Subject: [PATCH] restructure sat.py: clean up and more general interface --- sat.py | 387 +++++++++++++++++++++++++++++++++++++++------------------ 1 file changed, 267 insertions(+), 120 deletions(-) diff --git a/sat.py b/sat.py index eec2253..065f75d 100644 --- a/sat.py +++ b/sat.py @@ -1,121 +1,270 @@ from pysmt.shortcuts import Symbol, Bool, Not, Implies, Iff, And, Or, AtMostOne, ExactlyOne, get_model, get_atoms, get_formula_size, get_unsat_core from pysmt.rewritings import conjunctive_partition import json +from typing import List -MAX_MOVES = 63 -NUM_STRIKES = 3 -COLORS = 'rygbp' -NUM_CARDS = 50 +from compress import DeckCard, Action, ActionType, link -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' - -# instance independent names of variables - -# clues[m][i] == "after move m we have at least i clues" -clues = {-1: {i: Bool(i < 9) for i in range(0, 10)}, **{m: {0: Bool(True), 9: Bool(False), **{i: Symbol('m{}c{}'.format(m, i)) for i in range(1, 9)}} for m in range(MAX_MOVES)}} -# strikes[m][i] == "after move m we have at least i strikes" -strikes = {-1: {i: Bool(i == 0) for i in range(0,NUM_STRIKES+1)}, **{m: {0: Bool(True), NUM_STRIKES: Bool(False), **{s: Symbol('m{}s{}'.format(m,s)) for s in range(1,NUM_STRIKES)}} for m in range(MAX_MOVES)} } -# extraturn[m] = "turn m is a move part of the extra round or a dummy turn" -extraround = {-1: Bool(False), **{m: Bool(False) if m <= 29 else Symbol('m{}e'.format(m)) for m in range(0, MAX_MOVES)}} -# dummyturn[m] = "turn m is a dummy nurn and not actually part of the game" -dummyturn = {-1: Bool(False), **{m: Bool(False) if m <= 34 else Symbol('m{}dt'.format(m)) for m in range(0, MAX_MOVES)}} -# strike[m] = "at move m we get a strike" -strike = {-1: Bool(False), **{m: Symbol('m{}s+'.format(m)) for m in range(MAX_MOVES)}} -# draw[m][i] == "at move m we play/discard deck[i]" -discard = {m: {i: Symbol('m{}-{}'.format(m, i)) for i in range(NUM_CARDS)} for m in range(MAX_MOVES)} -# progress[m][c, k] == "after move m we have played in color c until k" -progress = {-1: {(c, k): Bool(k == 0) for c in COLORS for k in range(6)}, **{m: {**{(c, 0): Bool(True) for c in COLORS}, **{(c, k): Symbol('m{}:{}{}'.format(m, c, k)) for c in COLORS for k in range(1, 6)}} for m in range(MAX_MOVES)}} -# discard_any[m] == "at move m we play/discard a card" -discard_any = {m: Symbol('m{}d'.format(m)) for m in range(MAX_MOVES)} -# draw_any[m] == "at move m we draw a card" -draw_any = {m: Symbol('m{}D'.format(m)) for m in range(MAX_MOVES)} -# play[m] == "at move m we play a card" -play = {m: Symbol('m{}p'.format(m)) for m in range(MAX_MOVES)} -# play5[m] == "at move m we play a 5" -play5 = {m: Symbol('m{}p5'.format(m)) for m in range(MAX_MOVES)} -# incr_clues[m] == "at move m we obtain a clue" -incr_clues = {m: Symbol('m{}c+'.format(m)) for m in range(MAX_MOVES)} - -### this is dependent on the number of players -# draw[m][i] == "at move m we draw deck[i]" - -hand_size = {2: 5, 3: 5, 4: 4, 5: 4, 6: 3} -last_hand_card = {2: 9, 3: 14, 4: 15, 5: 19, 6: 17} -max_moves = {2: -1, 3: 63, 4: 63, 5: 56, 6: 62} -draw = {p: {-1: {i: Bool(i == last_hand_card[p]) for i in range(last_hand_card[p], NUM_CARDS)}, **{m: {last_hand_card[p]: Bool(False), **{i: Symbol('m{}+{}'.format(m, i)) for i in range(last_hand_card[p] + 1, NUM_CARDS)}} for m in range(max_moves[p])}} for p in range(2,7)} +STANDARD_HAND_SIZE = {2: 5, 3: 5, 4: 4, 5: 4, 6: 3} +NUM_STRIKES_TO_LOSE = 3 -def solve(deck_str, num_players=5): - deck = [(s[0], int(s[1])) for s in deck_str.split(' ')] - hand_size = globals()['hand_size'][num_players] - last_hand_card = globals()['last_hand_card'][num_players] - max_moves = globals()['max_moves'][num_players] - draw = globals()['draw'][num_players] +# 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( - Implies(dummyturn[m], Not(discard_any[m])), + # in dummy turns, nothing can be discarded + Implies(ls.dummyturn[m], Not(ls.discard_any[m])), + # definition of discard_any - Iff(discard_any[m], Or(discard[m][i] for i in range(NUM_CARDS))), + Iff(ls.discard_any[m], Or(ls.discard[m][i] for i in range(ls.deck_size))), + # definition of draw_any - Iff(draw_any[m], Or(draw[m][i] for i in range(last_hand_card + 1, NUM_CARDS))), - # draw implies discard (and converse true before last 5 moves) - Implies(draw_any[m], discard_any[m]), - Implies(discard_any[m], Or(extraround[m], draw_any[m])), - # play requires discard - Implies(play[m], discard_any[m]), - # definition of play5 - Iff(play5[m], And(play[m], Or(discard[m][i] for i in range(NUM_CARDS) if deck[i][1] == 5))), - # definition of incr_clues - Iff(incr_clues[m], And(discard_any[m], Implies(play[m], And(play5[m], Not(clues[m-1][8]))))), - #Iff(incr_clues[m], And(discard_any[m], Implies(play[m], play5[m]))), - # change of clues - *[Iff(clues[m][i], Or(clues[m-1][i+1], And(clues[m-1][i], Or(discard_any[m], dummyturn[m])), And(clues[m-1][i-1], incr_clues[m]))) for i in range(1, 9)], - ## more than 8 clues not allowed, discarding produces a strike - Iff(strike[m], And(discard_any[m], Not(play[m]), clues[m-1][8])), + 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(strikes[m][i], Or(strikes[m-1][i], And(strikes[m-1][i-1], strike[m]))) for i in range(1, NUM_STRIKES+1)], + *[Iff(ls.strikes[m][i], Or(ls.strikes[m-1][i], And(ls.strikes[m-1][i-1], ls.strike[m]))) for i in range(1, ls.num_strikes + 1)], + # less than 0 clues not allowed - Implies(Not(discard_any[m]), Or(clues[m-1][1], dummyturn[m])), - # we can only draw card i if the last drawn card was i-1 - *[Implies(draw[m][i], Or(And(draw[m0][i-1], *[Not(draw_any[m1]) for m1 in range(m0+1, m)]) for m0 in range(max(-1, m-9), m))) for i in range(last_hand_card + 1, NUM_CARDS)], - #*[Implies(draw[m][i], Not(draw[m0][i])) for m0 in range(m) for i in range(20, 50)], - #*[Implies(draw[m][i], Or(draw[m0][i-1] for m0 in range(max(-1, m-9), m))) for i in range(20, 50)], + 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(draw[m][i] for i in range(last_hand_card + 1, NUM_CARDS)), - #*[Not(And(draw[m][i], draw[m][j])) for i in range(20, 50) for j in range(20, i)], + 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(discard[m][i], Or(draw[m0][i] for m0 in range(m-num_players, -1, -num_players))) for i in range(last_hand_card + 1, NUM_CARDS)], + *[Implies(ls.discard[m][i], Or(ls.draw[m0][i] for m0 in range(m-ls.num_players, -1, -ls.num_players))) for i in range(ls.distributed_cards, ls.deck_size)], + # ...or if it was part of the initial hand - *[Not(discard[m][i]) for i in range(last_hand_card + 1) if i//hand_size != m % num_players], + *[Not(ls.discard[m][i]) for i in range(0, ls.distributed_cards) if i // ls.hand_size != m % ls.num_players], + # we can only discard a card if we did not discard it yet - *[Implies(discard[m][i], And(Not(discard[m0][i]) for m0 in range(m-num_players, -1, -num_players))) for i in range(NUM_CARDS)], + *[Implies(ls.discard[m][i], And(Not(ls.discard[m0][i]) for m0 in range(m-ls.num_players, -1, -ls.num_players))) for i in range(ls.deck_size)], + # we can only discard at most one card (FIXME: avoid quadratic formula) - AtMostOne(discard[m][i] for i in range(NUM_CARDS)), - #*[Not(And(discard[m][i], discard[m][j])) for i in range(NUM_CARDS) for j in range(i)], + 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(discard[m][i], play[m]), And(Not(progress[m-1][deck[i]]), progress[m-1][deck[i][0], deck[i][1]-1])) for i in range(NUM_CARDS)], + *[Implies( + And(ls.discard[m][i], ls.play[m]), + And( + Not(ls.progress[m-1][deck[i].suitIndex, deck[i].rank]), + ls.progress[m-1][deck[i].suitIndex, deck[i].rank-1 ] + ) + ) + for i in range(ls.deck_size) + ], + # change of progress - *[Iff(progress[m][c, k], Or(progress[m-1][c, k], And(play[m], Or(discard[m][i] for i in range(NUM_CARDS) if deck[i] == (c, k))))) for c in COLORS for k in range(1, 6)], + *[ + Iff( + ls.progress[m][s, r], + Or( + ls.progress[m-1][s, r], + And(ls.play[m], Or(ls.discard[m][i] + for i in range(0, ls.deck_size) + if deck[i] == DeckCard(s, r) )) + ) + ) + for s in range(0, ls.num_suits) + for r in range(1, 6) + ], + # extra round bool - Iff(extraround[m], Or(extraround[m-1], draw[m-1][NUM_CARDS-1])), + Iff(ls.extraround[m], Or(ls.extraround[m-1], ls.draw[m-1][ls.deck_size-1])), + # dummy turn bool - *[Iff(dummyturn[m], Or(dummyturn[m-1], draw[m-1 - num_players][NUM_CARDS-1])) for i in range(0,1) if m >= num_players] + *[Iff(ls.dummyturn[m], Or(ls.dummyturn[m-1], ls.draw[m-1 - ls.num_players][ls.deck_size-1])) for i in range(0,1) if m >= ls.num_players] ) win = And( # maximum progress at each color - *[progress[max_moves-1][c, 5] for c in COLORS], - # played every color/value combination (NOTE: redundant) - *[Or(And(discard[m][i], play[m]) for m in range(max_moves) for i in range(50) if deck[i] == (c, k)) for c in COLORS for k in range(1, 6)] + *[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(max_moves)], win) + constraints = And(*[valid_move(m) for m in range(ls.max_moves)], win) # print('Solving instance with {} variables, {} nodes'.format(len(get_atoms(constraints)), get_formula_size(constraints))) model = get_model(constraints) if model: # print_model(model, deck) - solution = toJSON(model, deck, num_players) + solution = toJSON(model, deck, ls) return True, solution else: print('unsatisfiable') @@ -140,44 +289,35 @@ def print_model(model, deck, num_players): flags = ['discard_any', 'draw_any', 'play', 'play5', 'incr_clues', 'strike', 'extraround', 'dummyturn'] print(', '.join(f for f in flags if model.get_py_value(globals()[f][m]))) -def toJSON(model, deck, num_players): - deck_json = [{"suitIndex": COLORS.index(s), "rank": r} for (s,r) in deck] - players = ["Alice", "Bob", "Cathy", "Donald", "Emily"][:num_players] - hands = [deck[hand_size[num_players]*p:hand_size[num_players]*(p+1)] for p in range(0,num_players)] - draw = globals()['draw'][num_players] +def toJSON(model, deck: List[DeckCard], ls: Literals) -> dict: + players = ["Alice", "Bob", "Cathy", "Donald", "Emily"][:ls.num_players] + # we keep track of the hands to output some dummy clues + hands = [deck[ls.hand_size * p : ls.hand_size *(p+1)] for p in range(0, ls.num_players)] actions = [] - for m in range(max_moves[num_players]): - if model.get_py_value(dummyturn[m]): + for m in range(ls.max_moves): + if model.get_py_value(ls.dummyturn[m]): break - if model.get_py_value(discard_any[m]): - discarded = next(i for i in range(0,NUM_CARDS) if model.get_py_value(discard[m][i])) - icard = hands[m % num_players].index(deck[discarded]) - for i in range(icard, hand_size[num_players] - 1): - hands[m % num_players][i] = hands[m % num_players][i + 1] - if model.get_py_value(draw_any[m]): - hands[m % num_players][hand_size[num_players] - 1] = next(deck[i] for i in range(last_hand_card[num_players] + 1, NUM_CARDS) if model.get_py_value(draw[m][i])) - if model.get_py_value(play[m]) or model.get_py_value(strike[m]): - actions.append({ - "type": 0, - "target": discarded - }) + if model.get_py_value(ls.discard_any[m]): + discarded = next(i for i in range(0,ls.deck_size) if model.get_py_value(ls.discard[m][i])) + icard = hands[m % ls.num_players].index(deck[discarded]) + for i in range(icard, ls.hand_size - 1): + hands[m % ls.num_players][i] = hands[m % ls.num_players][i + 1] + if model.get_py_value(ls.draw_any[m]): + hands[m % ls.num_players][ls.hand_size - 1] = next(deck[i] for i in range(ls.distributed_cards, ls.deck_size) if model.get_py_value(ls.draw[m][i])) + if model.get_py_value(ls.play[m]) or model.get_py_value(ls.strike[m]): + actions.append( Action( ActionType.Play, target=discarded) ) else: - actions.append({ - "type": 1, - "target": discarded - }) + actions.append( Action( ActionType.Discard, target=discarded) ) else: - actions.append({ - "type": 3, - "target": (m + 1) % num_players, - "value": hands[(m+1) % num_players][0][1] - }) - actions.append({ - "type": 4, - "value": 1 - }) + actions.append( Action( + ActionType.RankClue, + target=(m+1) % ls.num_players, # clue next player + value=hands[(m+1) % ls.num_players][0].rank # clue rank of rightmost card + ) + ) + actions.append( Action (ActionType.EndGame, target=0, value=1)) game = { - "deck": deck_json, + "deck": deck, "players": players, "actions": actions, "first_player": 0, @@ -185,9 +325,16 @@ def toJSON(model, deck, num_players): "variant": "No Variant", } } - return json.dumps(game) + return game if __name__ == "__main__": - solvable, sol = solve(deck_str) + COLORS = 'rygbp' + deck_str = 'p5 p3 b4 r5 y4 y4 y5 r4 b2 y2 y3 g5 g2 g3 g4 p4 r3 b2 b3 b3 p4 b1 p2 b1 b1 p2 p1 p1 g1 r4 g1 r1 r3 r1 g1 r1 p1 b4 p3 g2 g3 g4 b5 y1 y1 y1 r2 r2 y2 y3' + + deck = [DeckCard(COLORS.index(c[0]), int(c[1])) for c in deck_str.split(" ")] + print(deck) + + solvable, sol = solve(deck, num_players=5) if solvable: print(sol) + print(link(sol))