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 MAX_MOVES = 56 NUM_STRIKES = 3 NUM_PLAYERS = 5 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' # 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)} } # extraround[m][i] == "after move m, the extraround has started and at least i turns of it have taken place" # extraround = {28: {i: Bool(False) for i in range(0, NUM_PLAYERS)}, **{m: {NUM_PLAYERS+1: Bool(False), **{e: Symbol('m{}e{}'.format(m,t) for e in range(0, NUM_PLAYERS+1)}} 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: 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: 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 draw deck[i]" draw = {-1: {i: Bool(i == 19) for i in range(19, 50)}, **{m: {19: Bool(False), **{i: Symbol('m{}+{}'.format(m, i)) for i in range(20, 50)}} 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(50)} 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)} def solve(deck_str): deck = [(s[0], int(s[1])) for s in deck_str.split(' ')] valid_move = lambda m: And( Implies(dummyturn[m], Not(discard_any[m])), # definition of discard_any Iff(discard_any[m], Or(discard[m][i] for i in range(50))), # definition of draw_any Iff(draw_any[m], Or(draw[m][i] for i in range(20, 50))), # 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(50) 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])), # 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)], # 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(20, 50)], #*[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)], # we can only draw at most one card (NOTE: redundant, FIXME: avoid quadratic formula) AtMostOne(draw[m][i] for i in range(20, 50)), #*[Not(And(draw[m][i], draw[m][j])) for i in range(20, 50) for j in range(20, i)], # we can only discard a card if we drew it earlier... *[Implies(discard[m][i], Or(draw[m0][i] for m0 in range(m-5, -1, -5))) for i in range(20, 50)], # ...or if it was part of the initial hand *[Not(discard[m][i]) for i in range(20) if i//4 != m%5], # 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-5, -1, -5))) for i in range(50)], # we can only discard at most one card (FIXME: avoid quadratic formula) AtMostOne(discard[m][i] for i in range(50)), #*[Not(And(discard[m][i], discard[m][j])) for i in range(50) for j in range(i)], # 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(50)], # 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(50) if deck[i] == (c, k))))) for c in COLORS for k in range(1, 6)], # extra round bool Iff(extraround[m], Or(extraround[m-1], draw[m-1][49])), # dummy turn bool *[Iff(dummyturn[m], Or(dummyturn[m-1], draw[m-6][49])) for i in range(0,1) if m >= 5] ) 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)] ) constraints = And(*[valid_move(m) for m in range(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) return True, solution else: print('unsatisfiable') return False, None #conj = list(conjunctive_partition(constraints)) #print('statements: {}'.format(len(conj))) #ucore = get_unsat_core(conj) #print('unsat core size: {}'.format(len(ucore))) #for f in ucore: # print(f.serialize()) def print_model(model, deck): for m in range(MAX_MOVES): print('=== move {} ==='.format(m)) print('clues: ' + ''.join(str(i) for i in range(1, 9) if model.get_py_value(clues[m][i]))) print('strikes: ' + ''.join(str(i) for i in range(1, NUM_STRIKES) if model.get_py_value(strikes[m][i]))) print('draw: ' + ', '.join('{} [{}{}]'.format(i, deck[i][0], deck[i][1]) for i in range(20, 50) if model.get_py_value(draw[m][i]))) print('discard: ' + ', '.join('{} [{}{}]'.format(i, deck[i][0], deck[i][1]) for i in range(50) if model.get_py_value(discard[m][i]))) for c in COLORS: print('progress {}: '.format(c) + ''.join(str(k) for k in range(1, 6) if model.get_py_value(progress[m][c, k]))) flags = ['discard_any', 'draw_any', 'play', 'play5', 'incr_clues', 'strike', 'extraround', 'dummyturn'] print(', '.join(f for f in flags if model.get_py_value(globals()[f][m]))) def toJSON(model, deck): deck_json = [{"suitIndex": COLORS.index(s), "rank": r} for (s,r) in deck] players = ["Alice", "Bob", "Cathy", "Donald", "Emily"] hands = [deck[4*p:4*(p+1)] for p in range(0,5)] actions = [] for m in range(MAX_MOVES): if model.get_py_value(dummyturn[m]): break if model.get_py_value(discard_any[m]): discarded = next(i for i in range(0,50) if model.get_py_value(discard[m][i])) icard = hands[m % 5].index(deck[discarded]) for i in range(icard, 3): hands[m % 5][i] = hands[m % 5][i + 1] if model.get_py_value(draw_any[m]): hands[m % 5][3] = next(deck[i] for i in range(20, 50) 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 }) else: actions.append({ "type": 1, "target": discarded }) else: actions.append({ "type": 3, "target": (m + 1) % 5, "value": hands[(m+1) % 5][0][1] }) actions.append({ "type": 4, "value": 1 }) game = { "deck": deck_json, "players": players, "actions": actions, "first_player": 0, "options": { "variant": "No Variant", } } return json.dumps(game) solvable, sol = solve(deck_str) if solvable: print(sol)