【DP】格雷码

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 - 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.

确实没有找到规律....思路参考的题解。

递推公式：n每增加一位，其格雷码为上一次的格雷码顺次添加0再逆向添加1，如：

00 01 11 10———>000 001 011 010 110 111 101 100....

T T真的强...

ps 吐槽一下判题系统，n=0返回0为的格雷码，0位不应该是空吗...竟然还需要返回个0

import java.util.ArrayList;public class Solution {    public ArrayList<Integer> grayCode(int n) {        ArrayList<Integer> res = new ArrayList<Integer> ();        if(n == 0){            res.add(0);            return res;        }        res.add(0);res.add(1);        if(n == 1)            return res;                int base = 1;        while(base != n){                        for(int i = res.size() - 1; i >= 0; --i){                int temp = res.get(i);                temp = temp | (1<<base);                res.add(temp);            }            base++;        }        return res;    }}