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# Time: O(2^n)

# Space: O(1)

# The gray code is a binary numeral system where two successive values differ in only one bit.

#

# Given a non-negative integer n representing the total number of bits in the code,

# print the sequence of gray code. A gray code sequence must begin with 0.

#

# For example, given n = 2, return [0,1,3,2]. Its gray code sequence is:

#

# 00 - 0

# 01 - 1

# 11 - 3

# 10 - 2

# Note:

# For a given n, a gray code sequence is not uniquely defined.

#

# For example, [0,2,3,1] is also a valid gray code sequence according

# to the above definition.

#

# For now, the judge is able to judge based on one instance of gray code

# sequence. Sorry about that.

class Solution(object):

def grayCode(self, n):

"""

:type n: int

:rtype: List[int]

"""

result = [0]

for i in xrange(n):

for n in reversed(result):

result.append(1 << i | n)

return result

# Proof of closed form formula could be found here:

# http://math.stackexchange.com/questions/425894/proof-of-closed-form-formula-to-convert-a-binary-number-to-its-gray-code

class Solution2(object):

def grayCode(self, n):

"""

:type n: int

:rtype: List[int]

"""

return [i >> 1 ^ i for i in xrange(1 << n)]

if __name__ == "__main__":

print Solution().grayCode(0)

print Solution().grayCode(2)