initial version from matthias
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101
sat.py
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101
sat.py
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from pysmt.shortcuts import Symbol, Bool, Not, Implies, Iff, And, Or, AtMostOne, ExactlyOne, get_model, get_atoms, get_formula_size, get_unsat_core
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from pysmt.rewritings import conjunctive_partition
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colors = 'pbryg'
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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'
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deck = [(s[0], int(s[1])) for s in deck_str.split(' ')]
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MOVES = 52
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# clues[m][i] == "after move m we have at least i clues"
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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)}}
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# draw[m][i] == "at move m we draw deck[i]"
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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)}}
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# draw[m][i] == "at move m we play/discard deck[i]"
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discard = {m: {i: Symbol('m{}-{}'.format(m, i)) for i in range(50)} for m in range(MOVES)}
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# progress[m][c, k] == "after move m we have played in color c until k"
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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)}}
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# discard_any[m] == "at move m we play/discard a card"
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discard_any = {m: Symbol('m{}d'.format(m)) for m in range(MOVES)}
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# draw_any[m] == "at move m we draw a card"
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draw_any = {m: Symbol('m{}D'.format(m)) for m in range(MOVES)}
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# play[m] == "at move m we play a card"
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play = {m: Symbol('m{}p'.format(m)) for m in range(MOVES)}
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# play5[m] == "at move m we play a 5"
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play5 = {m: Symbol('m{}p5'.format(m)) for m in range(MOVES)}
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# incr_clues[m] == "at move m we obtain a clue"
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incr_clues = {m: Symbol('m{}c+'.format(m)) for m in range(MOVES)}
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def print_model(model):
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for m in range(MOVES):
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print('=== move {} ==='.format(m))
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print('clues: ' + ''.join(str(i) for i in range(1, 9) if model.get_py_value(clues[m][i])))
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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])))
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print('discard: ' + ', '.join('{} [{}{}]'.format(i, deck[i][0], deck[i][1]) for i in range(50) if model.get_py_value(discard[m][i])))
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for c in colors:
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print('progress {}: '.format(c) + ''.join(str(k) for k in range(1, 6) if model.get_py_value(progress[m][c, k])))
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flags = ['discard_any', 'draw_any', 'play', 'play5', 'incr_clues']
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print(', '.join(f for f in flags if model.get_py_value(globals()[f][m])))
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valid_move = lambda m: And(
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# definition of discard_any
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Iff(discard_any[m], Or(discard[m][i] for i in range(50))),
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# definition of draw_any
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Iff(draw_any[m], Or(draw[m][i] for i in range(20, 50))),
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# draw implies discard (and converse true before last 5 moves)
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(Iff if m < MOVES-5 else Implies)(draw_any[m], discard_any[m]),
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# play requires discard
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Implies(play[m], discard_any[m]),
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# definition of play5
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Iff(play5[m], And(play[m], Or(discard[m][i] for i in range(50) if deck[i][1] == 5))),
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# definition of incr_clues
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Iff(incr_clues[m], And(discard_any[m], Implies(play[m], And(play5[m], Not(clues[m-1][8]))))),
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#Iff(incr_clues[m], And(discard_any[m], Implies(play[m], play5[m]))),
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# change of clues
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*[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)],
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## more than 8 clues not allowed (TODO: not really. 2x we can deliberately play unplayable card to discard it)
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#Implies(incr_clues[m], Not(clues[m-1][8])),
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# less than 0 clues not allowed
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Implies(Not(discard_any[m]), clues[m-1][1]),
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# we can only draw card i if the last drawn card was i-1
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*[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)],
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#*[Implies(draw[m][i], Not(draw[m0][i])) for m0 in range(m) for i in range(20, 50)],
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#*[Implies(draw[m][i], Or(draw[m0][i-1] for m0 in range(max(-1, m-9), m))) for i in range(20, 50)],
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# we can only draw at most one card (NOTE: redundant, FIXME: avoid quadratic formula)
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AtMostOne(draw[m][i] for i in range(20, 50)),
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#*[Not(And(draw[m][i], draw[m][j])) for i in range(20, 50) for j in range(20, i)],
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# we can only discard a card if we drew it earlier...
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*[Implies(discard[m][i], Or(draw[m0][i] for m0 in range(m-5, -1, -5))) for i in range(20, 50)],
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# ...or if it was part of the initial hand
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*[Not(discard[m][i]) for i in range(20) if i//4 != m%5],
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# we can only discard a card if we did not discard it yet
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*[Implies(discard[m][i], And(Not(discard[m0][i]) for m0 in range(m-5, -1, -5))) for i in range(50)],
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# we can only discard at most one card (FIXME: avoid quadratic formula)
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AtMostOne(discard[m][i] for i in range(50)),
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#*[Not(And(discard[m][i], discard[m][j])) for i in range(50) for j in range(i)],
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# we can only play a card if it matches the progress
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*[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)],
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# change of progress
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*[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)]
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)
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win = And(
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# maximum progress at each color
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*[progress[MOVES-1][c, 5] for c in colors],
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# played every color/value combination (NOTE: redundant)
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*[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)]
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)
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constraints = And(*[valid_move(m) for m in range(MOVES)], draw[MOVES-6][49], win)
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print('{} 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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print_model(model)
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else:
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print('unsatisfiable')
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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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