397. Integer Replacement

• Difficulty: Medium

• Topics: Math, Bit Manipulation

• Similar Questions:

Problem:

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?

</p>

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 </pre> </p>

Solutions:

class Solution {
public:
    int integerReplacement(int N) {
        int count = 0;
        long n = N; // to prevent overflow
        while (n > 3) {
            if (n % 2 == 0) {
                n = (n >> 1);
            } else {
                if ((n & 0x2) == 0) {
                    n -= 1;
                } else {
                    n += 1;
                }
            }
            ++count;
        }

        if (n == 3) return count + 2; // special check
        if (n == 2) return count + 1; // special check
        return count;
    }
};