算法系列——Gray Code

题目描述

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 - 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.

解题思路

仔细观察格雷码

当n=1时

10

当n=2时

00011110

当n=3时

000001011010110111101100

可以发现，n的格雷码，就是n-1的格雷码，再加上它们的逆序前面多一个1。

程序实现

public class Solution {    public List<Integer> grayCode(int n) {        List<Integer> res=new ArrayList<Integer>();        if(n<0)            return res;        res.add(0);        int highValue;        for(int i=0;i<n;i++){            highValue=1<<i;            for(int j=res.size()-1;j>=0;j--)                res.add(res.get(j)+highValue);        }        return res;    }}