from typing import Callable

from .board import Board


def solve(
    state: Board,
    is_solved: Callable[[Board], bool],
    *,
    history: list[tuple[int, Board]] | None = None,
) -> list[tuple[int, Board]] | None:

    if history is None:
        # create starting state
        history = [(-1, state)]

    if is_solved(state):
        return history

    for button in state.buttons:
        # try to click all buttons
        next = state.click(button)

        if next is not None:
            # click successful
            binary_history = (
                state.binary_repr
                for _, state in history
            )

            if next.binary_repr not in binary_history:
                # "next" is a new state
                solution = solve(
                    next, is_solved,
                    history=[*history, (button, next)]
                )

                if solution is not None:
                    return solution