integer-replacement.py

# 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