LeetCode-Integer Replacement

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:

public class Solution {
    public int integerReplacement(int n) {
        if (n<1) return -1;
        
        int steps = 0;
        while (n!=1){
            if (n%2==0){
                n /= 2;
            } else {
                // We have: steps(2x) <= steps(2x-1) && steps(2x) <= steps(2x+1),i.e.,
                // for odd number, we go to (n-1) if (n-1)/2 is an even number. 
                // IMPORTANT: the only exception is n=3, for which we should choose n-1,because (n-1)/2 is 1 directly.
                // NOTE: We need take care of n==Integer.MAX_VALUE, in which we cannot perform n+1.
                if (n==Integer.MAX_VALUE){
                    n = n/2+1;
                    steps++;
                } else if (((n-1)/2)%2==0 || (n-1)/2==1){
                    n = n-1;
                } else {
                    n = n+1;
                }
            }
            steps++;
        }
        return steps;
    }
}