gray-code （格雷码）

Posted 2020-10-14 Tao-Coder

题目描述

The gray code（格雷码） 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.

 

什么是格雷码？

　　格雷码是一种循环二进制单位距离码，主要特点是两个相邻数的代码只有一位二进制数不同的编码，格雷码的处理主要是位操作 Bit Operation

解题思路：

• 二进制码->格雷码（编码）：从最右边一位起，依次将每一位与左边一位异或（XOR），作为对应格雷码该位的值，最左边一位不变（相当于左边是0）；

• 格雷码->二进制码（解码）：

　　从左边第二位起，将每位与左边一位解码后的值异或，作为该位解码后的值。

AC代码：

class Solution {
public:
    vector<int> grayCode(int n) {
        vector<int> res;
        for(int i=0;i<pow(2,n);i++){
            res.push_back((i>>1)^i);
        }
        return res;
    }
};