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.

二进制码->格雷码（编码）：从最右边一位起，依次将每一位与左边一位异或（XOR），作为对应格雷码该位的值，最左边一位不变（相当于左边是0）；
格雷码->二进制码（解码）：从左边第二位起，将每位与左边一位解码后的值异或，作为该位解码后的值（最左边一位依然不变）。

Gray Code 0 = 0, 下一项是toggle最右边的bit(LSB), 再下一项是toggle最右边值为 “1” bit的左边一个bit，然后重复。直到最右边值为 “1” 的bit在最左边了，结束。

C++代码实现：

#include<iostream>
#include<vector>
#include<cmath>
using namespace std;

class Solution {
public:
    vector<int> grayCode(int n) {
        vector<int> ret;
        int i;
        for(i=0;i<pow(2,n);i++)
        {
            ret.push_back((i>>1)^i);
        }
        return ret;
    }
};

int main()
{
    Solution s;
    vector<int> result=s.grayCode(4);
    for(auto v:result)
        cout<<v<<" ";
    cout<<endl;
}

运行结果：