YouTube Explanation: https:www.youtube.comwatch?vf2xi3c1S95M Given an integer n, return the minimum steps from n to 1 AVAILABLE STEPS:  Decrement by 1  if n is divisible by 2, divide by 2  if n is divisible by 3, divide by 3 Example 1: n  10 10  9  3  1 Result: 3 steps Example 2: n  15 15  5  4  2  1 Result: 4 steps Example 3: n  6 6  2  1 Result: 2 step Minimum steps to 1 implemented using tabulation.  minstepstoone10 3  minstepstoone15 4  minstepstoone6 2 :param number: :return int: starting position check if out of bounds check if out of bounds
from __future__ import annotations

__author__ = "Alexander Joslin"


def min_steps_to_one(number: int) -> int:
    """
    Minimum steps to 1 implemented using tabulation.
    >>> min_steps_to_one(10)
    3
    >>> min_steps_to_one(15)
    4
    >>> min_steps_to_one(6)
    2

    :param number:
    :return int:
    """

    if number <= 0:
        msg = f"n must be greater than 0. Got n = {number}"
        raise ValueError(msg)

    table = [number + 1] * (number + 1)

    # starting position
    table[1] = 0
    for i in range(1, number):
        table[i + 1] = min(table[i + 1], table[i] + 1)
        # check if out of bounds
        if i * 2 <= number:
            table[i * 2] = min(table[i * 2], table[i] + 1)
        # check if out of bounds
        if i * 3 <= number:
            table[i * 3] = min(table[i * 3], table[i] + 1)
    return table[number]


if __name__ == "__main__":
    import doctest

    doctest.testmod()
