from __future__ import print_function
# 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))
