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.

题解:查了资料才发现，原来可以从二进制码转成gray码。比如说二进制码1101，要转成gray码，过程如下：

（1）左边第一位保留：1

（2）第二位与第一位异或得到第二位：1^1 = 0

（3）第三位与第二位异或得到第三位：0^1 = 1

（4）第四位与第三位异或得到第四位：1^0 = 1

所以最后得到的gray码是1011

有一个简单的公式，二进制码x对应的gray码为(x>>1)^x，上情况就是（1101>>1)^1101=1011,原理就是上述描述的过程，把x右移一位，然后错位相异或。至于第一位，如果原来是1，那么右移后得到的0和这个1相异或得到的还是1；如果原来是0，那么右移后得到的0与这个0相异或得到的还是0.

代码如下：

 1 class Solution {
 2 public:
 3     vector<int> grayCode(int n) {
 4         int total_number = 1 << n;
 5         vector<int> answer;
 6         
 7         for(int i = 0;i < total_number;i++){
 8             answer.push_back((i>>1)^i);
 9         }
10         return answer;
11     }
12 };