leetcode: Gray Code

问题描述：

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.

原问题链接：https://leetcode.com/problems/gray-code/

 

问题分析

　　这个问题如果结合gray code的定义来看，它其实有一个规律。就是如果我们要定义的gray code是n位的，那么最终出来的所有编码有2 ** n个。所以一种思路就是给定一个数字n，从0到 2 ** n遍历，然后求每个数字的gray code转换，将转换后的代码放入列表中就可以了。

　　而对于每个数字的gray code编码其实就是一个如下的运算：

　　i ^ (i  >> 1)。

　　所以可以很容易得到如下的代码：

 

public class Solution {
    public List<Integer> grayCode(int n) {
        List<Integer> list = new LinkedList<>();
        for(int i = 0; i < (1 << n); i++) {
            list.add(i ^ (i >> 1));
        }
        return list;
    }
}

 

参考材料

https://en.wikipedia.org/wiki/Gray_code