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： 00 01 ------- 11 10 n=3时： 000 001 011 010 ------- 110 111 101 100

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))); } } }