Question

Given a positive integer n and you can do operations as follow:

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

What is the minimum number of replacements needed for n to become 1?

Example 1:

Input:
8

Output:
3

Explanation:
8 -> 4 -> 2 -> 1

Example 2:

Input:
7

Output:
4

Explanation:
7 -> 8 -> 4 -> 2 -> 1
or
7 -> 6 -> 3 -> 2 -> 1

Solution

Be careful about n + 1 because it can overflow.

class Solution {
    public int integerReplacement(int n) {
        if(n == 1) return 0;
        else {
            if((n & 1) == 0) return 1 + integerReplacement(n >> 1);
            else return 2 + Math.min(integerReplacement((n >> 1) + 1), integerReplacement(n >> 1));
        }
    }
}