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.

Example 1:

Input: 2
Output: [0,1,3,2]
Explanation:
00 - 0
01 - 1
11 - 3
10 - 2

For a given n
 
, a gray code sequence may not be uniquely defined.
For example, [0,2,3,1] is also a valid gray code sequence.

00 - 0
10 - 2
11 - 3
01 - 1

Example 2:

Input: 0
Output: [0]
Explanation: We define the gray code sequence to begin with 0.
             A gray code sequence of n has size = 2n, which for n = 0 the size is 20 = 1.
             Therefore, for n
 
 = 0 the gray code sequence is [0].

遠古關於格雷碼的記憶是貌似有一個數位DP，要麼是多校，要麼是有一年弱校聯萌

說到列舉，自己倒是能寫出來，但是規律沒看出來是，後面的是前一個vector翻轉加上當前位是1

class Solution {
public:
    vector<int> grayCode(int n) {
        vector<int>ans;
        if(n==0){
            ans.push_back(0);
            return ans;
        }
        ans.push_back(0);
        ans.push_back(1);
        for(int k=2;k<=n;k++){
            int sz=ans.size();
            for(int i=sz-1;i>=0;i--){
                ans.push_back((1<<(k-1))|ans[i]);
            }
        }
        return ans;
    }
};