integer-replacement.py

# V0 

# V1 
# https://blog.csdn.net/fuxuemingzhu/article/details/79495908
# IDEA : RECURSION  
class Solution(object):
    def integerReplacement(self, n):
        """
        :type n: int
        :rtype: int
        """
        if n == 1: return 0
        if n % 2 == 0:
            return 1 + self.integerReplacement(n / 2)
        else:
            return 1 + min(self.integerReplacement(n + 1), self.integerReplacement(n - 1))

# V1' 
# https://blog.csdn.net/fuxuemingzhu/article/details/79495908
class Solution(object):
    def integerReplacement(self, n):
        """
        :type n: int
        :rtype: int
        """
        count = 0
        while n > 1:
            count += 1
            if n & 1: # odd 
                if n & 2 and n != 3: # tail = 11 
                    n += 1
                else: # tail = 01 
                    n -= 1
            else: # even 
                n >>= 1
        return count

# V2 
# Time:  O(logn)
# Space: O(1)
class Solution(object):
    def integerReplacement(self, n):
        """
        :type n: int
        :rtype: int
        """
        result = 0
        while n != 1:
            b = n & 3
            if n == 3:
                n -= 1
            elif b == 3:
                n += 1
            elif b == 1:
                n -= 1
            else:
                n /= 2
            result += 1

        return result


# Time:  O(logn)
# Space: O(logn)
# Recursive solution.
class Solution2(object):
    def integerReplacement(self, n):
        """
        :type n: int
        :rtype: int
        """
        if n < 4:
            return [0, 0, 1, 2][n]
        if n % 4 in (0, 2):
            return self.integerReplacement(n / 2) + 1
        elif n % 4 == 1:
            return self.integerReplacement((n - 1) / 4) + 3
        else:
            return self.integerReplacement((n + 1) / 4) + 3