[LeetCode] 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 - 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.

思路：

　　二进制码→格雷码（编码）：
　　此方法从对应的n位二进制码字中直接得到n位格雷码码字，步骤如下：

对n位二进制的码字，从右到左，以0到n-1编号

如果二进制码字的第i位和i+1位相同，则对应的格雷码的第i位为0，否则为1（当i+1=n时，二进制码字的第n位被认为是0，即第n-1位不变）

[b]　　公式表示：[/b]

　　

（G：格雷码，B：二进制码）

class Solution {
public:
vector<int> grayCode(int n) {
vector<int> res;
const int size = 1 << n;
for (int i = 0; i < size; ++i) {
res.push_back((i>>1) ^ i);
}

return res;

}
};