leetcode 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 - 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.

输出格雷码，从全0开始，每次相邻格雷码只能有一个bit位不同。

有用DFS做的，有用数学推导做的，方法挺多，学格雷码公式过去好久，记不太清了。

我这个方法是用了格雷码的对称性，即上半区和下半区关于中线对称，上半区第一位是0，下半区第一位是1.

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