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# Time: O(logn)

# Space: O(1)

# 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

# Iterative solution.

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