# 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)