Gray Code

Description:
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.
分析：
格雷码有数学公式，整数 n 的格雷码是 n ⊕ (n/2)。
最简单的方法，利用数学公式，对从 0 ∼ 2^n− 1 的所有整数，转化为格雷码。

#include <iostream>#include <vector>using namespace std;class SolutionMath{public:    vector<int> grayCode(int n)    {        vector<int> result;        size_t n_size = 1<<n;    //2^n;        for (size_t i=0; i < n_size ; ++i)        {            result.push_back(binaryTogray(i));        }        return result;    }private:    unsigned int binaryTogray(unsigned int n)    {        return  n ^ (n>>1);    }};int main(){    vector<int> result;    int n=2;    SolutionMath solution_1;    result = solution_1.grayCode(n);    for (auto it= result.begin(); it != result.end(); ++it)    {        cout<<*it<<" ";    }    cout<<endl;    return 0;}