LeetCode89. Gray Code

题目：

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

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.

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思路：

嗯，腾讯的笔试题好像也出过。
题目是在一组数的编码中，若任意不相邻的代码只有一位二进制数不同，则称这种编码为格雷码(Gray Code),请编写一个函数，使用递归的方法生成N位的格雷码。给定一个整数n，请返回n位的格雷码，顺序从0开始。
以3为例
0 0 0
0 0 1
0 1 1
0 1 0 ↑
1 1 0 ↓
1 1 1
1 0 1
1 0 0
从中我们可以发现规律，从分界处上下两部分不看第一位，是对称的。
而上面那部分是n-1的格雷码。下半部分是上半部分结果逆序再在最高位加1的结果。

代码：

class Solution {
public:
    vector<int> grayCode(int n) {
       if(n==0){
           vector<int> res;
           res.push_back(0);
           return res;
       }
       vector<int> preRes=grayCode(n-1);
       vector<int> res(preRes);
       int cur;
       for(int i=preRes.size()-1;i>=0;i--){
           cur=preRes[i]+pow(2,n-1);
           res.push_back(cur);
       }
       return res;
    }
};