Implemented minimum steps to one using tabulation. (#3911)

* Implemented minimum steps to one using tabulation.

* Update minimum_steps_to_one.py

Made the parameter "n" more descriptive.  Changed it to number

* `n` to `number`

Co-authored-by: John Law <[email protected]>

Author: echoaj

Diff for: dynamic_programming/minimum_steps_to_one.py

@@ -0,0 +1,65 @@
+"""
+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()