89. 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.

假设知道n=2的格雷码：00 01 11 10

n=3时，前面4个格雷码就是n=2的格雷码：000 001 011 010 

只需从后往前加4(二进制100)就可以了。000  001 011 010  -->   110 111 101 100

class Solution {
public:
    vector<int> grayCode(int n) {
        vector<int> res;
        res.push_back(0);
        for(int i=0;i<n;++i){
            int res_size = res.size();
            for(int j=res_size-1;j>=0;--j){
                res.push_back(res[j] | (1<<i));
            }
        }
        return res;
    }
};