import copy
from typing import Optional, Tuple

from pysmt.shortcuts import Symbol, Bool, Not, Implies, Iff, And, Or, AtMostOne, get_model, Equals, GE, NotEquals, Int
from pysmt.typing import INT

from hanabi import logger
from hanabi import constants
from hanabi import hanab_game


# 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, instance: hanab_game.HanabiInstance):
        # clues[m][i] == "after move m we have i clues", in clue starved, this counts half clues
        self.clues = {
            -1: Int(16 if instance.clue_starved else 8)  # we have 8 clues after turn
            , **{
                m: Symbol('m{}clues'.format(m), INT)
                for m in range(instance.max_winning_moves)
            }
        }

        self.pace = {
            -1: Int(instance.initial_pace)
            , **{
                m: Symbol('m{}pace'.format(m), INT)
                for m in range(instance.max_winning_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, instance.num_strikes + 1)}  # no strikes when we start
            , **{
                m: {
                    0: Bool(True),
                    **{s: Symbol('m{}strikes{}'.format(m, s)) for s in range(1, instance.num_strikes)},
                    instance.num_strikes: Bool(False)
                    # never so many clues that we lose. Implicitly forbids striking out
                }
                for m in range(instance.max_winning_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 < instance.draw_pile_size else Symbol('m{}extra'.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, instance.max_winning_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 < instance.draw_pile_size + instance.num_players else Symbol('m{}dummy'.format(m))
                for m in range(0, instance.max_winning_moves)
            }
        }

        # draw[m][i] == "at move m we play/discard deck[i]"
        self.discard = {
            m: {i: Symbol('m{}discard{}'.format(m, i)) for i in range(instance.deck_size)}
            for m in range(instance.max_winning_moves)
        }

        # draw[m][i] == "at move m we draw deck card i"
        self.draw = {
            -1: {i: Bool(i == instance.num_dealt_cards - 1) for i in
                 range(instance.num_dealt_cards - 1, instance.deck_size)}
            , **{
                m: {
                    instance.num_dealt_cards - 1: Bool(False),
                    **{i: Symbol('m{}draw{}'.format(m, i)) for i in range(instance.num_dealt_cards, instance.deck_size)}
                }
                for m in range(instance.max_winning_moves)
            }
        }

        # strike[m] = "at move m we get a strike"
        self.strike = {
            -1: Bool(False)
            , **{
                m: Symbol('m{}newstrike'.format(m))
                for m in range(instance.max_winning_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, instance.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, instance.num_suits)},
                    **{(s, r): Symbol('m{}progress{}{}'.format(m, s, r)) for s in range(0, instance.num_suits) for r in
                       range(1, 6)}
                }
                for m in range(instance.max_winning_moves)
            }
        }

        ## Utility variables

        # discard_any[m] == "at move m we play/discard a card"
        self.discard_any = {m: Symbol('m{}discard_any'.format(m)) for m in range(instance.max_winning_moves)}

        # draw_any[m] == "at move m we draw a card"
        self.draw_any = {m: Symbol('m{}draw_any'.format(m)) for m in range(instance.max_winning_moves)}

        # play[m] == "at move m we play a card"
        self.play = {m: Symbol('m{}play'.format(m)) for m in range(instance.max_winning_moves)}

        # play5[m] == "at move m we play a 5"
        self.play5 = {m: Symbol('m{}play5'.format(m)) for m in range(instance.max_winning_moves)}

        # incr_clues[m] == "at move m we obtain a clue"
        self.incr_clues = {m: Symbol('m{}c+'.format(m)) for m in range(instance.max_winning_moves)}


def solve_sat(starting_state: hanab_game.GameState | hanab_game.HanabiInstance, min_pace: Optional[int] = 0) -> Tuple[
    bool, Optional[hanab_game.GameState]]:
    if isinstance(starting_state, hanab_game.HanabiInstance):
        instance = starting_state
        game_state = hanab_game.GameState(instance)
    elif isinstance(starting_state, hanab_game.GameState):
        instance = starting_state.instance
        game_state = starting_state
    else:
        raise ValueError("Bad argument type")

    ls = Literals(instance)

    ##### setup of initial game state

    # properties used later to model valid moves

    starting_hands = [[card.deck_index for card in hand] for hand in game_state.hands]
    first_turn = len(game_state.actions)

    if isinstance(starting_state, hanab_game.GameState):
        # have to set additional variables

        # set initial clues
        for i in range(0, 10):
            ls.clues[first_turn - 1] = Int(game_state.clues)

        # set initial pace
        ls.pace[first_turn - 1] = Int(game_state.pace)

        # set initial strikes
        for i in range(0, instance.num_strikes + 1):
            ls.strikes[first_turn - 1][i] = Bool(i <= game_state.strikes)

        # check if extraround has started (usually not)
        ls.extraround[first_turn - 1] = Bool(game_state.remaining_extra_turns < game_state.num_players)
        ls.dummyturn[first_turn - 1] = Bool(False)

        # set recent draws: important to model progress
        # we just pretend that the last card drawn was in fact drawn last turn,
        # regardless of when it was actually drawn
        for neg_turn in range(1, min(9, first_turn + 2)):
            for i in range(instance.num_players * instance.hand_size, instance.deck_size):
                ls.draw[first_turn - neg_turn][i] = Bool(neg_turn == 1 and i == game_state.progress - 1)
        # forbid re-drawing of the last card drawn
        for m in range(first_turn, instance.max_winning_moves):
            ls.draw[m][game_state.progress - 1] = Bool(False)

        # model initial progress
        for s in range(0, game_state.num_suits):
            for r in range(0, 6):
                ls.progress[first_turn - 1][s, r] = Bool(r <= game_state.stacks[s])

    ### Now, model all valid moves

    valid_move = lambda m: And(
        # in dummy turns, nothing can be discarded
        Implies(ls.dummyturn[m], Not(ls.discard_any[m])),

        # definition of discard_any
        Iff(ls.discard_any[m], Or(ls.discard[m][i] for i in range(instance.deck_size))),

        # definition of draw_any
        Iff(ls.draw_any[m], Or(ls.draw[m][i] for i in range(game_state.progress, instance.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(instance.deck_size) if instance.deck[i].rank == 5))),

        # definition of ls.incr_clues
        Iff(ls.incr_clues[m],
            And(ls.discard_any[m], NotEquals(ls.clues[m - 1], Int(16 if instance.clue_starved else 8)),
                Implies(ls.play[m], ls.play5[m]))),

        # change of ls.clues
        Implies(And(Not(ls.discard_any[m]), Not(ls.dummyturn[m])),
                Equals(ls.clues[m], ls.clues[m - 1] - (2 if instance.clue_starved else 1))),
        Implies(ls.incr_clues[m], Equals(ls.clues[m], ls.clues[m - 1] + 1)),
        Implies(And(Or(ls.discard_any[m], ls.dummyturn[m]), Not(ls.incr_clues[m])),
                Equals(ls.clues[m], ls.clues[m - 1])),

        # change of pace
        Implies(And(ls.discard_any[m], Or(ls.strike[m], Not(ls.play[m]))), Equals(ls.pace[m], ls.pace[m - 1] - 1)),
        Implies(Or(Not(ls.discard_any[m]), And(Not(ls.strike[m]), ls.play[m])), Equals(ls.pace[m], ls.pace[m - 1])),

        # pace is nonnegative
        GE(ls.pace[m], Int(min_pace)),

        ## 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]), Equals(ls.clues[m - 1], Int(16 if instance.clue_starved else 8)))),

        # change of strikes
        *[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, instance.num_strikes + 1)],

        # less than 0 clues not allowed
        Implies(Not(ls.discard_any[m]), Or(GE(ls.clues[m - 1], Int(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(first_turn - 1, m - 9), m))) for i in range(game_state.progress, instance.deck_size)],

        # we can only draw at most one card (NOTE: redundant, FIXME: avoid quadratic formula)
        AtMostOne(ls.draw[m][i] for i in range(game_state.progress, instance.deck_size)),

        # we can only discard a card if we drew it earlier...
        *[Implies(ls.discard[m][i],
                  Or(ls.draw[m0][i] for m0 in range(m - instance.num_players, first_turn - 1, -instance.num_players)))
          for i in range(game_state.progress, instance.deck_size)],

        # ...or if it was part of the initial hand
        *[Not(ls.discard[m][i]) for i in range(0, game_state.progress) if
          i not in starting_hands[m % instance.num_players]],

        # we can only discard a card if we did not discard it yet
        *[Implies(ls.discard[m][i], And(
            Not(ls.discard[m0][i]) for m0 in range(m - instance.num_players, first_turn - 1, -instance.num_players)))
          for i in range(instance.deck_size)],

        # we can only discard at most one card (FIXME: avoid quadratic formula)
        AtMostOne(ls.discard[m][i] for i in range(instance.deck_size)),

        # we can only play a card if it matches the progress
        *[Implies(
            And(ls.discard[m][i], ls.play[m]),
            And(
                Not(ls.progress[m - 1][instance.deck[i].suitIndex, instance.deck[i].rank]),
                ls.progress[m - 1][instance.deck[i].suitIndex, instance.deck[i].rank - 1]
            )
        )
            for i in range(instance.deck_size)
        ],

        # change of progress
        *[
            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, instance.deck_size)
                                       if instance.deck[i] == hanab_game.DeckCard(s, r)))
                )
            )
            for s in range(0, instance.num_suits)
            for r in range(1, 6)
        ],

        # extra round bool
        Iff(ls.extraround[m], Or(ls.extraround[m - 1], ls.draw[m - 1][instance.deck_size - 1])),

        # dummy turn bool
        *[Iff(ls.dummyturn[m], Or(ls.dummyturn[m - 1], ls.draw[m - 1 - instance.num_players][instance.deck_size - 1]))
          for i in range(0, 1) if m >= instance.num_players]
    )

    win = And(
        # maximum progress at each color
        *[ls.progress[instance.max_winning_moves - 1][s, 5] for s in range(0, instance.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(first_turn, instance.max_winning_moves)
                for i in range(instance.deck_size)
                if game_state.deck[i] == hanab_game.DeckCard(s, r)
            )
            for s in range(0, instance.num_suits)
            for r in range(1, 6)
            if r > game_state.stacks[s]
        ]
    )

    constraints = And(*[valid_move(m) for m in range(first_turn, instance.max_winning_moves)], win)
    #    print('Solving instance with {} variables, {} nodes'.format(len(get_atoms(constraints)), get_formula_size(constraints)))

    model = get_model(constraints)
    if model:
        log_model(model, game_state, ls)
        solution = evaluate_model(model, copy.deepcopy(game_state), ls)
        return True, solution
    else:
        # 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())
        return False, None


def log_model(model, cur_game_state, ls: Literals):
    deck = cur_game_state.deck
    first_turn = len(cur_game_state.actions)
    if first_turn > 0:
        logger.debug('[print_model] Note: Omitting first {} turns, since they were fixed already.'.format(first_turn))
    for m in range(first_turn, cur_game_state.instance.max_winning_moves):
        logger.debug('=== move {} ==='.format(m))
        logger.debug('clues: {}'.format(model.get_py_value(ls.clues[m])))
        logger.debug('strikes: ' + ''.join(str(i) for i in range(1, 3) if model.get_py_value(ls.strikes[m][i])))
        logger.debug('draw: ' + ', '.join(
            '{}: {}'.format(i, deck[i]) for i in range(cur_game_state.progress, cur_game_state.instance.deck_size) if
            model.get_py_value(ls.draw[m][i])))
        logger.debug('discard: ' + ', '.join(
            '{}: {}'.format(i, deck[i]) for i in range(cur_game_state.instance.deck_size) if
            model.get_py_value(ls.discard[m][i])))
        logger.debug('pace: {}'.format(model.get_py_value(ls.pace[m])))
        for s in range(0, cur_game_state.instance.num_suits):
            logger.debug('progress {}: '.format(constants.COLOR_INITIALS[s]) + ''.join(
                str(r) for r in range(1, 6) if model.get_py_value(ls.progress[m][s, r])))
        flags = ['discard_any', 'draw_any', 'play', 'play5', 'incr_clues', 'strike', 'extraround', 'dummyturn']
        logger.debug(', '.join(f for f in flags if model.get_py_value(getattr(ls, f)[m])))


# given the initial game state and the model found by the SAT solver,
# evaluates the model to produce a full game history
def evaluate_model(model, cur_game_state: hanab_game.GameState, ls: Literals) -> hanab_game.GameState:
    for m in range(len(cur_game_state.actions), cur_game_state.instance.max_winning_moves):
        if model.get_py_value(ls.dummyturn[m]) or cur_game_state.is_over():
            break
        if model.get_py_value(ls.discard_any[m]):
            card_idx = next(
                i for i in range(0, cur_game_state.instance.deck_size) if model.get_py_value(ls.discard[m][i]))
            if model.get_py_value(ls.play[m]) or model.get_py_value(ls.strike[m]):
                cur_game_state.play(card_idx)
            else:
                cur_game_state.discard(card_idx)
        else:
            cur_game_state.clue()

    return cur_game_state