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 - 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.

求n位格雷码集合。

n+1位格雷码集合 = n格雷码集合 + （2^n + n位格雷码逆序）集合。如：

n = 2，{00， 01， 11， 10}， n = 3时，格雷码 = {000， 001， 011， 010， 110， 111， 101， 100}，后个格雷码是n=2时的格雷码逆序{10， 11， 01， 00}分别在第三个比特位加上1，相当于整体加上2^n-1(当前n=3)。具体定义见百度格雷码。

程序如下：

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