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* 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 <johnlaw.po@gmail.com>
66 lines
1.3 KiB
Python
66 lines
1.3 KiB
Python
"""
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YouTube Explanation: https://www.youtube.com/watch?v=f2xi3c1S95M
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Given an integer n, return the minimum steps to 1
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AVAILABLE STEPS:
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* Decrement by 1
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* if n is divisible by 2, divide by 2
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* if n is divisible by 3, divide by 3
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Example 1: n = 10
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10 -> 9 -> 3 -> 1
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Result: 3 steps
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Example 2: n = 15
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15 -> 5 -> 4 -> 2 -> 1
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Result: 4 steps
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Example 3: n = 6
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6 -> 2 -> 1
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Result: 2 step
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"""
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from __future__ import annotations
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__author__ = "Alexander Joslin"
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def min_steps_to_one(number: int) -> int:
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"""
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Minimum steps to 1 implemented using tabulation.
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>>> min_steps_to_one(10)
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3
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>>> min_steps_to_one(15)
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4
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>>> min_steps_to_one(6)
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2
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:param number:
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:return int:
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"""
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if number <= 0:
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raise ValueError(f"n must be greater than 0. Got n = {number}")
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table = [number + 1] * (number + 1)
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# starting position
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table[1] = 0
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for i in range(1, number):
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table[i + 1] = min(table[i + 1], table[i] + 1)
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# check if out of bounds
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if i * 2 <= number:
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table[i * 2] = min(table[i * 2], table[i] + 1)
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# check if out of bounds
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if i * 3 <= number:
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table[i * 3] = min(table[i * 3], table[i] + 1)
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return table[number]
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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