old_contents: # 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 Solution(object):
      def grayCode2(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)
  
new_contents: # 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)
  
subject: Update gray-code.py