Integer Replacement 🦘

Question

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

1. If n is even, replace n with n / 2.
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.

Example 1:

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

Example 2:

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

Example 3:

Input: n = 4
Output: 2

Constraints:

• 1 <= n <= 231 - 1

Solution

Time complexity O(log n)

Space complexity O(1)

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