lexicographical_numbers.py

from collections.abc import Iterator


def lexical_order(max_number: int) -> Iterator[str]:
    """
    Generate numbers in lexical order from 1 to max_number.

    >>> " ".join(lexical_order(13))
    '1 10 11 12 13 2 3 4 5 6 7 8 9'
    >>> list(lexical_order(1))
    ['1']
    >>> " ".join(lexical_order(20))
    '1 10 11 12 13 14 15 16 17 18 19 2 20 3 4 5 6 7 8 9'
    >>> " ".join(lexical_order(25))
    '1 10 11 12 13 14 15 16 17 18 19 2 20 21 22 23 24 25 3 4 5 6 7 8 9'
    >>> list(lexical_order(12))
    ['1', '10', '11', '12', '2', '3', '4', '5', '6', '7', '8', '9']
    """

    stack = [1]

    while stack:
        num = stack.pop()
        if num > max_number:
            continue

        yield (str(num))
        if (num % 10) != 9:
            stack.append(num + 1)

        stack.append(num * 10)


if __name__ == "__main__":
    from doctest import testmod

    testmod()
    print(f"Numbers from 1 to 25 in lexical order: {list(lexical_order(26))}")