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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:
# 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)

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