class Tape:
    def __init__(self, input_str: str):
        self.tape = list(input_str)
        self.head = 0

    def read(self):
        if self.head < 0:
            self.tape = ["•"] * (-self.head) + self.tape
            self.head = 0
        elif self.head >= len(self.tape):
            self.tape += ["•"] * (self.head - len(self.tape) + 1)
        return self.tape[self.head]

    def write(self, symbol):
        self.tape[self.head] = symbol

    def move(self, direction):
        if direction == "g":
            self.head -= 1
        elif direction == "d":
            self.head += 1

    def __str__(self):
        tape_str = "".join(self.tape)
        pointer = " " * self.head + "^"
        return f"{tape_str}\n{pointer}"


class TuringMachine:
    def __init__(self, transitions, initial_state, final_state):
        self.transitions = transitions
        self.state = initial_state
        self.final_state = final_state

    def run(self, input_str):
        tape = Tape(input_str)
        steps = 0
        while self.state != self.final_state:
            current_symbol = tape.read()
            if (
                self.state not in self.transitions
                or current_symbol not in self.transitions[self.state]
            ):
                print("No transition rule found. Halting.")
                break
            write_symbol, direction, next_state = self.transitions[self.state][
                current_symbol
            ]
            tape.write(write_symbol)
            tape.move(direction)
            self.state = next_state
            steps += 1
            print(f"Étape {steps} - État: {self.state}")
            print(tape)
        print("Machine arrêtée.")


transitions = {
    "init": {"1": ("1", "d", "init"), "0": ("0", "d", "init"), "•": ("1", "g", "end")}
}
tm = TuringMachine(transitions, initial_state="init", final_state="end")
tm.run("1011")