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 - 001 - 111 - 310 - 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.

n = 2: [0,1,3,2]
 n=3: [0,1,3,2,6,7,5,4]
 we found that the first four numbers in case n=3 are the same as the the numbers in case n=4.  Besides, [6,7,5,4] = [2+4,3+4,1+4,0+4]. 

Have you been asked this question in an interview? 
非递归写法（当然也可以用递归写）：

public class Solution {    public List<Integer> grayCode(int n) {        List<Integer> res = new ArrayList<Integer>();        res.add(0);        for (int i = 0; i < n; i++){            int l = res.size();            for (int j = l - 1; j >= 0; j--) {                res.add(res.get(j)|1<<i );            }        }        return res;    }}

数学解法：

public class Solution {    public List<Integer> grayCode(int n) {        List<Integer> result = new ArrayList<Integer>();        int m=1<<n;        for(int i=0; i<m ; i++) {            result.add(i^(i>>1));        }        return result;     }}