From aae9dec3515112b641942a3ce9bfe9e6723005ca Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Maximilian=20Ke=C3=9Fler?= Date: Tue, 28 Feb 2023 22:30:27 +0100 Subject: [PATCH] refactor file: use methods dependent on deck type --- sat.py | 172 ++++++++++++++++++++++++++++++--------------------------- 1 file changed, 91 insertions(+), 81 deletions(-) diff --git a/sat.py b/sat.py index 44542a5..05a0f9b 100644 --- a/sat.py +++ b/sat.py @@ -1,13 +1,15 @@ 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 = 60 + +MAX_MOVES = 56 NUM_STRIKES = 3 NUM_PLAYERS = 5 +COLORS = 'rygbp' -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 = [(s[0], int(s[1])) for s in deck_str.split(' ')] + +# 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)}} @@ -26,7 +28,7 @@ draw = {-1: {i: Bool(i == 19) for i in range(19, 50)}, **{m: {19: Bool(False), * # 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)}} +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" @@ -38,20 +40,99 @@ 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 print_model(model): + +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('{} variables, {} nodes'.format(len(get_atoms(constraints)), get_formula_size(constraints))) + + model = get_model(constraints) + if model: +# print_model(model, deck) + print(toJSON(model, deck)) + return True + else: + print('unsatisfiable') + return False + #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: + 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_json = [{"suitIndex": colors.index(s), "rank": r} for (s,r) in deck] +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 = [] @@ -94,77 +175,6 @@ def toJSON(model): "variant": "No Variant", } } - print(json.dumps(game)) + return json.dumps(game) -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('{} variables, {} nodes'.format(len(get_atoms(constraints)), get_formula_size(constraints))) - -model = get_model(constraints) -if model: - print_model(model) - toJSON(model) -else: - print('unsatisfiable') - #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()) +solve(deck_str)