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.

解法一:观察格雷码规律得到的挫挫的算法.

class Solution {public:    vector<int> grayCode(int n) {        // Start typing your C/C++ solution below        // DO NOT write int main() function        vector<int> ret(1,0);        if(n == 0) return ret;                for(int i = 0; i < n;i++)        {            int size = ret.size();            for(int j = size-1; j>=0;j--)            {                ret.push_back(pow(2,i) + ret[j]);            }        }        return ret;    }};

32 milli secs.

解法二：事实上，格雷码有生成公式，按照公式来写是很简单的。

（G：格雷码，B：二进制码）

class Solution {public:    vector<int> grayCode(int n) {        // Start typing your C/C++ solution below        // DO NOT write int main() function        vector<int> ret;        int size = 1 << n;        for(int i = 0; i < size;i++)        {            ret.push_back(i^(i>>1));        }        return ret;    }};

28 milli secs.