State = tuple[int, list[str | int]]  # Tuple of player (whose turn it is),
# and the buckets (as str)
# or the number in a bucket
Action = str | int  # Bucket choice (as str) or choice of number


class Game:
    def initial_state(self) -> State:
        return 0, ["A", "B", "C"]

    def to_move(self, state: State) -> int:
        player, _ = state
        return player

    def actions(self, state: State) -> list[Action]:
        _, actions = state
        return actions

    def result(self, state: State, action: Action) -> State:
        if action == "A":
            return (self.to_move(state) + 1) % 2, [-50, 50]
        elif action == "B":
            return (self.to_move(state) + 1) % 2, [3, 1]
        elif action == "C":
            return (self.to_move(state) + 1) % 2, [-5, 15]
        assert type(action) is int
        return (self.to_move(state) + 1) % 2, [action]

    def is_terminal(self, state: State) -> bool:
        _, actions = state
        return len(actions) == 1

    def utility(self, state: State, player: int) -> float:
        assert self.is_terminal(state)
        _, actions = state
        assert type(actions[0]) is int
        return actions[0] if player == self.to_move(state) else -actions[0]

    def print(self, state):
        print(f"The state is {state} and ", end="")
        if self.is_terminal(state):
            print(f"P1's utility is {self.utility(state, 0)}")
        else:
            print(f"it is P{self.to_move(state)+1}'s turn")