Gray Code

标签：sequence   system   example   number   return   

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.

生成规则：

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：

1. 对n位二进制的码字，从右到左，以0到n-1编号

2. 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）

即，高位不变，低位依次和近邻的高位异或的到相应graycode

可以用n^(n>>1)  这里n必须是逻辑右移，即高位补0，可以通过unsigend int 表示

同时注意，n位bits 总共有2^n个graycode

vector<int> grayCode(int n) {

         vector<int> res;

         size_t size=1<<n;

        for(unsigned int i=0;i<size;++i)

            res.push_back(i^(i>>1));

        return res;

    }

Gray Code

标签：sequence   system   example   number   return   

原文地址：http://searchcoding.blog.51cto.com/1335412/1695702