# Gray Code
# 
# 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.
# 
# debug = True
# debug = False


# from CommonClasses import * # hxl: comment out this line for submission


class Solution:
    
    # @return a list of integers
    def grayCode(self, n):
        
        # hxl: see the reflex method here: http://en.wikipedia.org/wiki/Gray_code
        
        if n == 0:
            return [0]
        
        r = [0, 1]
        
        for i in range(1, n):
            curLen = len(r)
            j = curLen - 1
            while j >= 0:
                r.append(r[j] + (1 << i))
                j -= 1
        
        return r
