Gray Code(格雷码)

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.

格雷码的定义：百度百科

　　　　　　二进制      格雷码

0               000            000

1               001            001

2               010            011

3               011            010

4               100            110

5               101            100

6               110            101

7              111             100

方法即：把二进制码从右往左的，把第一位和下一位做异或运算，最左边一位保持不动。

那么把110右移为011，再和自身异或

110^011=101 这种错位的异或，刚好实现了需求

格雷码解码的时候反过来即可，从左边第二位开始与下一位异或。

代码：

class Solution {
public:
    vector<int> grayCode(int n) {
        vector<int> res;
        res.push_back(0);
        for(int i=1;i<(1<<n);++i){
            res.push_back((i>>1)^i);
        }
        return res;
    }
};