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

本题可以直接用递归的方法求解，并可以通过OJ.

 def integerReplacement(self, n):
         """
         :type n: int
         :rtype: int
         """
         if n == 1:
             return 0

         if n % 2 == 0:
             return self.integerReplacement(n/2) + 1
         else:
             return min(self.integerReplacement(n-1), self.integerReplacement(n+1)) + 1

不用递归的话，对于偶数的n，处理方式是确定的 n /= 2。关键在于对于奇数的n，处理方式应该是n-1还是n+1。经过观察，如果n + 1是4的倍数(除了3， see L14)。那么应该取加1。比如 n = 7, 15, ...

     def integerReplacement(self, n):
         """
         :type n: int
         :rtype: int
         """
         if n == 1:
             return 0

         count = 0
         while n > 1:
             if n % 2 == 0:
                 n /= 2
                 count += 1
             elif (n+1) % 4 == 0 and n != 3:
                 n += 1
                 count += 1
             else:
                 n -= 1
                 count += 1

         return count