Python/dynamic_programming/minimum_steps_to_one.py

"""
YouTube Explanation: https://www.youtube.com/watch?v=f2xi3c1S95M

Given an integer n, return the minimum steps 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
"""

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

    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()