397. Integer Replacement

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

If n is even, replace n with n/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

Idea:

1. Even: >>1 can be used to divided by 2
2. Odd: choose results returned by min(n+1, n-1)
3. After all, recursion is a good idea to do this problem

Solution:

class Solution(object):
    def integerReplacement(self, n):
        """
        :type n: int
        :rtype: int
        """
        if n == 1:
            return 0
        return self.integerReplacement(n >> 1)+1 if not n % 2 else min(self.integerReplacement(n + 1), self.integerReplacement(n + 1)) + 1

Note:

Even though it looks a bit ugly since it's mixed with bit operation and regular operation, but it's quite straightforward.