Leetcode: Gray Code

URL

https://leetcode.com/problems/gray-code/#/description

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.

解题思路

解题之前我们先找找规律：

n=2时：0001-------1110n=3时：000001011010-------110111101100

我们可以发现当位数为n时，其前一半的情况正好等于n-1的所有情况（在数值上相等，表示的时候用0占位），其后一半的规律是开头都是1，后面的n-1位正好和前面一半的出现顺序相反。找到这样的规律之后代码实现就不难了。

代码

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