From 369fc03158d715b0b29b99f4c684e225c2d0971b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Maximilian=20Ke=C3=9Fler?= Date: Tue, 28 Feb 2023 14:19:01 +0100 Subject: [PATCH] initial version from matthias --- sat.py | 101 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 101 insertions(+) create mode 100644 sat.py diff --git a/sat.py b/sat.py new file mode 100644 index 0000000..469281c --- /dev/null +++ b/sat.py @@ -0,0 +1,101 @@ +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 + +colors = 'pbryg' +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(' ')] +MOVES = 52 + +# 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(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(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(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(MOVES)}} +# discard_any[m] == "at move m we play/discard a card" +discard_any = {m: Symbol('m{}d'.format(m)) for m in range(MOVES)} +# draw_any[m] == "at move m we draw a card" +draw_any = {m: Symbol('m{}D'.format(m)) for m in range(MOVES)} +# play[m] == "at move m we play a card" +play = {m: Symbol('m{}p'.format(m)) for m in range(MOVES)} +# play5[m] == "at move m we play a 5" +play5 = {m: Symbol('m{}p5'.format(m)) for m in range(MOVES)} +# incr_clues[m] == "at move m we obtain a clue" +incr_clues = {m: Symbol('m{}c+'.format(m)) for m in range(MOVES)} + +def print_model(model): + for m in range(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('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'] + print(', '.join(f for f in flags if model.get_py_value(globals()[f][m]))) + +valid_move = lambda m: And( + # 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) + (Iff if m < MOVES-5 else Implies)(draw_any[m], discard_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], discard_any[m]), And(clues[m-1][i-1], incr_clues[m]))) for i in range(1, 9)], + ## more than 8 clues not allowed (TODO: not really. 2x we can deliberately play unplayable card to discard it) + #Implies(incr_clues[m], Not(clues[m-1][8])), + # less than 0 clues not allowed + Implies(Not(discard_any[m]), clues[m-1][1]), + # 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)] +) + +win = And( + # maximum progress at each color + *[progress[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(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(MOVES)], draw[MOVES-6][49], win) +print('{} variables, {} nodes'.format(len(get_atoms(constraints)), get_formula_size(constraints))) + +model = get_model(constraints) +if model: + print_model(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())