gray-code (格雷码)

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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;
    }
};

 

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