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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 - 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.

格雷码的定义:百度百科

      二进制      格雷码

0               000            000

1               001            001

2               010            011

3               011            010

4               100            110

5               101            100

6               110            101

7              111             100

方法即:把二进制码从右往左的,把第一位和下一位做异或运算,最左边一位保持不动。

那么把110右移为011,再和自身异或

110^011=101 这种错位的异或,刚好实现了需求

格雷码解码的时候反过来即可,从左边第二位开始与下一位异或。

代码:

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

 

 

Gray Code(格雷码)