Python/dynamic_programming/minimum_steps_to_one.py
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Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>
2023-10-10 00:34:36 -04:00

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Python

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