89. 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 - 001 - 111 - 310 - 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.
思路：算法设计与分析基础的4.3生成组合对象的算法
BRGC(n)
//递归生成n位的二进制反射格雷码
//输入：一个正整数n
//输出：所有长度为n的格雷码位串列表
if n=1,表L包含位串0和位串1
else 调用BRGC(n-1)生成长度为n-1的位串列表L1
把表L1倒序后复制给 表L2
把0加到表L1中的每个位串前面
把1加到表L2中的每个位串前面
把表L2添加到表L1后面得到表L
return L

class Solution {public:    vector<string> BRGC(int n){        if(n == 0) return {"0"};        if(n == 1) return {"0", "1"};        else {            vector<string> L1 = BRGC(n - 1);            vector<string> L2(L1);            vector<string> L;            reverse(L2.begin(), L2.end());            for(int i = 0; i < L1.size(); ++i)                L1[i].insert(L1[i].begin(), '0');            for(int i = 0; i < L2.size(); ++i)                L2[i].insert(L2[i].begin(), '1');            L1.insert(L1.end(), L2.begin(), L2.end());            L.insert(L.end(), L1.begin(), L1.end());            return L;        }    }    vector<int> grayCode(int n) {        vector<int> ans;        vector<string> L;        L = BRGC(n);        for(int i = 0; i < L.size(); ++i){            int res = 0;            int factor = 1;            for(int j = n - 1; j >= 0; --j){                if(L[i][j] == '1'){                    res += factor * (L[i][j] - '0');                }                factor <<= 1;            }            ans.push_back(res);        }        return ans;    }};