Integer Replacement Python Solution with Tests

Tested Python solution for LeetCode 397 with 22 pytest cases. Generate a practice environment with lcpy.

LeetCode 397, Medium. Topics: Dynamic Programming, Greedy, Bit Manipulation, Memoization. View on LeetCode.

Generate this problem as a practice environment: tested reference solution, 22 parametrized pytest cases, and a playground notebook:

lcpy gen -n 397   # by problem number
lcpy gen -s integer_replacement   # by problem name

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Problem

Given a positive integer n, you can apply one of the following operations:

• If n is even, replace n with n / 2.
• If n is odd, replace n with either n + 1 or n - 1.

Return the minimum number of operations needed for n to become 1.

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Examples

Input: n = 8
Output: 3
Explanation: 8 -> 4 -> 2 -> 1

Input: n = 7
Output: 4
Explanation: 7 -> 8 -> 4 -> 2 -> 1
or 7 -> 6 -> 3 -> 2 -> 1

Input: n = 4
Output: 2

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Constraints

• 1 <= n <= 2^31 - 1

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Solution

Reference implementation from solution.py on GitHub, full suite in test_solution.py:

class Solution:
    # Time: O(log n)
    # Space: O(log n)
    def integer_replacement(self, n: int) -> int:
        ops = 0
        while n != 1:
            if n % 2 == 0:
                n //= 2
            elif n == 3 or n % 4 == 1:
                n -= 1
            else:
                n += 1
            ops += 1
        return ops

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Complexity

Time	Space
O(log n)	O(log n)

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