// Source : https://oj.leetcode.com/problems/gray-code/
// Author : Hao Chen
// Date   : 2014-06-20

/********************************************************************************** 
* 
* 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.
*               
**********************************************************************************/

#include 
#include 
#include 
#include 
using namespace std;


vector grayCode(int n) {
    vector v;
    //n = 1