[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; } };