Gray Code 格雷码

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.

解决这道题目关键在于了解格雷码的编码规则，什么是格雷码，可以参考之前的一篇有关 格雷码的介绍，这里不再赘述。实现代码如下：

public class Solution {
    public List<Integer> grayCode(int n) {
        List<Integer> list = new ArrayList<Integer>();
        list.add(0);
        for(int i = 1; i <=n; i++) {
            for(int j = list.size() - 1; j >=0; j--) {
                list.add(list.get(j) + (int)Math.pow(2, i - 1));
            }
        }
        return list;
    }
}