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.

以3位格雷码为例。
0 0 0
0 0 1
0 1 1
0 1 0
1 1 0
1 1 1
1 0 1
1 0 0
可以看到第n位的格雷码由两部分构成，一部分是n-1位格雷码，再加上 1<<(n-1)和n-1位格雷码的逆序的和

class Solution {
public:
    vector<int> grayCode(int n) {
        if(n==0)
        {
            vector<int>ret;
            ret.push_back(0);
            return ret;
        }
        else
        {
            vector<int>tmp=grayCode(n-1);
            vector<int>ret;
            for(int i=0;i<tmp.size();++i)
            {
                ret.push_back(tmp[i]);
            }
            for(int i=tmp.size()-1;i>=0;--i)
            {
                ret.push_back((1<<(n-1))+tmp[i]);
            }
            return ret;
        }
    }
};

LeetCode Gray Code