leetcode Gray Code题解

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.

Example 1:

Input: 2 Output: [0,1,3,2] Explanation: 00 - 0 01 - 1 11 - 3 10 - 2 For a given n, a gray code sequence may not be uniquely defined. For example, [0,2,3,1] is also a valid gray code sequence. 00 - 0 10 - 2 11 - 3 01 - 1

Example 2:

Input: 0 Output: [0] Explanation: We define the gray code sequence to begin with 0.   A gray code sequence of n has size = 2n, which for n = 0 the size is 20 = 1.   Therefore, for n = 0 the gray code sequence is [0].

中文理解：

给定一个整数，返回结果有2^n个数据，同时相邻两个元素是通过改变一个二进制位得到的，给出有效的序列。

解题思路：

首先返回结果第一个元素总是0，然后取0，与1不同左移0到n-1位进行异或，如果某一个结果不在返回list中，则将这个加入list，然后继续取list中最后一个元素重复上述过程，最终得到结果。

代码（java）：

class Solution { public List<Integer> grayCode(int n) { List<Integer> list=new ArrayList(); list.add(0); if(n==0)return list; int xor=1; int lastElement=list.get(list.size()-1); for(int i=1;i<Math.pow(2,n);i++){ for(int j=0;j<n;j++){ xor=1; lastElement=list.get(list.size()-1); lastElement=lastElement^(xor<<j); if(!list.contains(lastElement)){ list.add(lastElement); break; } } } return list; } }