[leetcode]89. Gray Code

题目链接：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.

 解题思路：

手动地列出n=3时候的情况，会发现。n=3的结果如下:

000
001
011
010  ↑
--------
110  ↓
111
101
100

可看成是上下对称的2部分。上半部分是n=2时候的结果再在最高位加"0"的结果。下半部分是n=2时候的结果逆序之后再在最高位加"1"的结果。

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