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.

思路：格雷码问题。

　　   二进制转格雷码：二进制最高位作为格雷码最高位。格雷码其他各位是相应的二进制位其较高临位的异或。

　　　即，gray_code(t) = binary_code(t) //t是最高位

　　　　　gray_code(i) = binary_code(i) ^binary_code(i + 1)  // 0<= i < t;

 1 class Solution { 2 public: 3     vector<int> grayCode(int n) { 4         vector<int> res; 5         const int size = 1 << n; 6         for (int i = 0; i < size; ++i) { 7             res.push_back((i>>1) ^ i); 8         } 9         10         return res;11         12     }13 };

拓展：

1. 格雷码转二进制：二进制最高位是为格雷码的最高位。二进制次高位是二进制高位与格雷码次高位异或，其他各位与次高位求法相同

　　　　　　binary_code(t) = gray_code(t) //t是最高位

　　　　　　binary_code(i) = gray_code(i) ^ binary_code(i ＋1) // 0 <=i < t

　　2. 整数n的格雷码为: n^(n/2)

[LeetCode] Gray Code